%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM019-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 15
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 169 ( 80 ~; 75 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 73 ( 66 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(aa_type,type,
aa: $i ).
tff(1,plain,
( ~ equalish(aa,a)
<=> ~ equalish(aa,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ equalish(aa,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_b_equals_a) ).
tff(3,plain,
~ equalish(aa,a),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( equalish(a,aa)
<=> equalish(a,aa) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
equalish(a,aa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_aa) ).
tff(6,plain,
equalish(a,aa),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
<=> ( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [Z: $i,Y: $i,X: $i] :
rewrite(( ( ~ equalish(X,Y)
| ~ equalish(X,Z)
| equalish(Y,Z) )
<=> ( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ equalish(X,Z)
| equalish(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| ~ equalish(X,Z)
| equalish(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
| equalish(aa,a)
| ~ equalish(a,aa)
| ~ equalish(a,a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
| equalish(aa,a)
| ~ equalish(a,aa)
| ~ equalish(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ( ~ equalish(a,aa)
| equalish(aa,a)
| ~ equalish(a,a) )
<=> ( equalish(aa,a)
| ~ equalish(a,aa)
| ~ equalish(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
| ~ equalish(a,aa)
| equalish(aa,a)
| ~ equalish(a,a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
| equalish(aa,a)
| ~ equalish(a,aa)
| ~ equalish(a,a) ) ),
inference(monotonicity,[status(thm)],[18]) ).
tff(20,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
| ~ equalish(a,aa)
| equalish(aa,a)
| ~ equalish(a,a) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
| equalish(aa,a)
| ~ equalish(a,aa)
| ~ equalish(a,a) ) ),
inference(transitivity,[status(thm)],[19,17]) ).
tff(21,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
| ~ equalish(a,aa)
| equalish(aa,a)
| ~ equalish(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(22,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ equalish(X,Y)
| equalish(Y,Z)
| ~ equalish(X,Z) )
| equalish(aa,a)
| ~ equalish(a,aa)
| ~ equalish(a,a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
~ equalish(a,a),
inference(unit_resolution,[status(thm)],[22,16,6,3]) ).
tff(24,plain,
^ [X: $i] :
refl(( equalish(X,X)
<=> equalish(X,X) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [X: $i] : equalish(X,X)
<=> ! [X: $i] : equalish(X,X) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [X: $i] : equalish(X,X)
<=> ! [X: $i] : equalish(X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,axiom,
! [X: $i] : equalish(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
tff(28,plain,
! [X: $i] : equalish(X,X),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [X: $i] : equalish(X,X),
inference(skolemize,[status(sab)],[28]) ).
tff(30,plain,
! [X: $i] : equalish(X,X),
inference(modus_ponens,[status(thm)],[29,25]) ).
tff(31,plain,
( ~ ! [X: $i] : equalish(X,X)
| equalish(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
$false,
inference(unit_resolution,[status(thm)],[31,30,23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM019-1 : TPTP v9.0.0. Bugfixed v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Fri Jun 20 00:03:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------