%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET046-5 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:24:58 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 52 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 255 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 367 ( 168 ~; 172 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 4 ( 4 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; 1 con; 0-1 aty)
% Number of variables : 92 ( 86 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
tff(element_type,type,
element: ( $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
tff(f_type,type,
f: $i > $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
<=> ( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
<=> ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
<=> ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ~ element(X,a)
| ~ element(X,Y)
| ~ element(Y,X) )
<=> ( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( ~ element(X,a)
| ~ element(X,Y)
| ~ element(Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [Y: $i,X: $i] :
( ~ element(X,a)
| ~ element(X,Y)
| ~ element(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
tff(7,plain,
! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( ~ element(a,a)
| ~ element(a,a)
| ~ element(a,a) )
<=> ~ element(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,a)
| ~ element(a,a)
| ~ element(a,a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,a) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,a)
| ~ element(a,a)
| ~ element(a,a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,a) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,a)
| ~ element(a,a)
| ~ element(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
~ element(a,a),
inference(unit_resolution,[status(thm)],[16,10]) ).
tff(18,plain,
^ [X: $i] :
refl(( ( element(f(X),X)
| element(X,a) )
<=> ( element(f(X),X)
| element(X,a) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
( element(f(X),X)
| element(X,a) )
<=> ! [X: $i] :
( element(f(X),X)
| element(X,a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [X: $i] :
( element(f(X),X)
| element(X,a) )
<=> ! [X: $i] :
( element(f(X),X)
| element(X,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [X: $i] :
( element(f(X),X)
| element(X,a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
tff(22,plain,
! [X: $i] :
( element(f(X),X)
| element(X,a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [X: $i] :
( element(f(X),X)
| element(X,a) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( element(f(X),X)
| element(X,a) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( element(f(X),X)
| element(X,a) )
| element(a,a)
| element(f(a),a) )
<=> ( ~ ! [X: $i] :
( element(f(X),X)
| element(X,a) )
| element(a,a)
| element(f(a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( element(f(a),a)
| element(a,a) )
<=> ( element(a,a)
| element(f(a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(27,plain,
( ( ~ ! [X: $i] :
( element(f(X),X)
| element(X,a) )
| element(f(a),a)
| element(a,a) )
<=> ( ~ ! [X: $i] :
( element(f(X),X)
| element(X,a) )
| element(a,a)
| element(f(a),a) ) ),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
( ( ~ ! [X: $i] :
( element(f(X),X)
| element(X,a) )
| element(f(a),a)
| element(a,a) )
<=> ( ~ ! [X: $i] :
( element(f(X),X)
| element(X,a) )
| element(a,a)
| element(f(a),a) ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
( ~ ! [X: $i] :
( element(f(X),X)
| element(X,a) )
| element(f(a),a)
| element(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [X: $i] :
( element(f(X),X)
| element(X,a) )
| element(a,a)
| element(f(a),a) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
element(f(a),a),
inference(unit_resolution,[status(thm)],[30,24,17]) ).
tff(32,plain,
^ [X: $i] :
refl(( ( element(X,f(X))
| element(X,a) )
<=> ( element(X,f(X))
| element(X,a) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [X: $i] :
( element(X,f(X))
| element(X,a) )
<=> ! [X: $i] :
( element(X,f(X))
| element(X,a) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
( ! [X: $i] :
( element(X,f(X))
| element(X,a) )
<=> ! [X: $i] :
( element(X,f(X))
| element(X,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(35,axiom,
! [X: $i] :
( element(X,f(X))
| element(X,a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
tff(36,plain,
! [X: $i] :
( element(X,f(X))
| element(X,a) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i] :
( element(X,f(X))
| element(X,a) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [X: $i] :
( element(X,f(X))
| element(X,a) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
( ( ~ ! [X: $i] :
( element(X,f(X))
| element(X,a) )
| element(a,a)
| element(a,f(a)) )
<=> ( ~ ! [X: $i] :
( element(X,f(X))
| element(X,a) )
| element(a,a)
| element(a,f(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( element(a,f(a))
| element(a,a) )
<=> ( element(a,a)
| element(a,f(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [X: $i] :
( element(X,f(X))
| element(X,a) )
| element(a,f(a))
| element(a,a) )
<=> ( ~ ! [X: $i] :
( element(X,f(X))
| element(X,a) )
| element(a,a)
| element(a,f(a)) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [X: $i] :
( element(X,f(X))
| element(X,a) )
| element(a,f(a))
| element(a,a) )
<=> ( ~ ! [X: $i] :
( element(X,f(X))
| element(X,a) )
| element(a,a)
| element(a,f(a)) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [X: $i] :
( element(X,f(X))
| element(X,a) )
| element(a,f(a))
| element(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [X: $i] :
( element(X,f(X))
| element(X,a) )
| element(a,a)
| element(a,f(a)) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
element(a,f(a)),
inference(unit_resolution,[status(thm)],[44,38,17]) ).
tff(46,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,f(a))
| ~ element(f(a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,f(a))
| ~ element(f(a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ( ~ element(a,f(a))
| ~ element(f(a),a)
| ~ element(f(a),a) )
<=> ( ~ element(a,f(a))
| ~ element(f(a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,f(a))
| ~ element(f(a),a)
| ~ element(f(a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,f(a))
| ~ element(f(a),a) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,f(a))
| ~ element(f(a),a)
| ~ element(f(a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,f(a))
| ~ element(f(a),a) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,f(a))
| ~ element(f(a),a)
| ~ element(f(a),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] :
( ~ element(Y,X)
| ~ element(X,Y)
| ~ element(X,a) )
| ~ element(a,f(a))
| ~ element(f(a),a) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
$false,
inference(unit_resolution,[status(thm)],[51,10,45,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET046-5 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 04:09:18 EDT 2025
% 0.12/0.34 % 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
%------------------------------------------------------------------------------