%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : FLD030-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:04:58 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 34 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 141 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 185 ( 87 ~; 82 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 77 ( 69 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(d_type,type,
d: $i ).
tff(multiply_type,type,
multiply: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(defined_type,type,
defined: $i > $o ).
tff(1,plain,
( ~ equalish(multiply(d,b),multiply(a,b))
<=> ~ equalish(multiply(d,b),multiply(a,b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ equalish(multiply(d,b),multiply(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply_not_equal_to_multiply_5) ).
tff(3,plain,
~ equalish(multiply(d,b),multiply(a,b)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( defined(b)
<=> defined(b) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_is_defined) ).
tff(6,plain,
defined(b),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z) )
<=> ( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ) )),
( ( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z))
| ~ equalish(X,Y) ) )),
rewrite(( ( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z))
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) )),
( ( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] :
( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [Z: $i,Y: $i,X: $i] :
( equalish(multiply(X,Z),multiply(Y,Z))
| ~ defined(Z)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',compatibility_of_equality_and_multiplication) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(b)
| ~ equalish(d,a)
| equalish(multiply(d,b),multiply(a,b)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(b)
| ~ equalish(d,a)
| equalish(multiply(d,b),multiply(a,b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(b)
| ~ equalish(d,a)
| equalish(multiply(d,b),multiply(a,b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(Z)
| ~ equalish(X,Y)
| equalish(multiply(X,Z),multiply(Y,Z)) )
| ~ defined(b)
| ~ equalish(d,a)
| equalish(multiply(d,b),multiply(a,b)) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
~ equalish(d,a),
inference(unit_resolution,[status(thm)],[19,16,6,3]) ).
tff(21,plain,
( equalish(a,d)
<=> equalish(a,d) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
equalish(a,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_d_4) ).
tff(23,plain,
equalish(a,d),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
^ [Y: $i,X: $i] :
refl(( ( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ( equalish(X,Y)
| ~ equalish(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
<=> ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/FLD001-0.ax',symmetry_of_equality) ).
tff(28,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) ),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(d,a)
| ~ equalish(a,d) )
<=> ( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(d,a)
| ~ equalish(a,d) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(d,a)
| ~ equalish(a,d) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Y: $i,X: $i] :
( equalish(X,Y)
| ~ equalish(Y,X) )
| equalish(d,a)
| ~ equalish(a,d) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,23,20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : FLD030-1 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.14/0.35 % Computer : n013.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 : Thu Jun 19 13:33:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39 % SZS output start Proof
% See solution above
% 0.21/0.40 % E exiting
%------------------------------------------------------------------------------