%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN327-1 : TPTP v9.0.0. Released v1.2.0.
% 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 05:38:46 AM UTC 2025
% Result : Unsatisfiable 0.24s 0.42s
% Output : Proof 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 49 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 214 ( 0 equ)
% Maximal formula atoms : 11 ( 4 avg)
% Number of connectives : 314 ( 154 ~; 137 |; 0 &)
% ( 23 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 5 ( 5 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 : 59 ( 54 !; 0 ?; 59 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $o ).
tff(z_type,type,
z: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [Y: $i] :
refl(( ( f(a,Y)
| f(Y,a) )
<=> ( f(a,Y)
| f(Y,a) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
<=> ! [Y: $i] :
( f(a,Y)
| f(Y,a) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
<=> ! [Y: $i] :
( f(a,Y)
| f(Y,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [Y: $i] :
rewrite(( ( f(Y,a)
| f(a,Y) )
<=> ( f(a,Y)
| f(Y,a) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i] :
( f(Y,a)
| f(a,Y) )
<=> ! [Y: $i] :
( f(a,Y)
| f(Y,a) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [Y: $i] :
( f(Y,a)
| f(a,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause1) ).
tff(7,plain,
! [Y: $i] :
( f(a,Y)
| f(Y,a) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [Y: $i] :
( f(a,Y)
| f(Y,a) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [Y: $i] :
( f(a,Y)
| f(Y,a) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i] :
( f(a,Y)
| f(Y,a) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,a) )
<=> ( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( f(a,a)
| f(a,a) )
<=> f(a,a) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,a)
| f(a,a) )
<=> ( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,a) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,a)
| f(a,a) )
<=> ( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,a) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,a)
| f(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,a) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
f(a,a),
inference(unit_resolution,[status(thm)],[16,10]) ).
tff(18,plain,
^ [Y: $i] :
refl(( ( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
<=> ( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
<=> ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
<=> ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
^ [Y: $i] :
rewrite(( ( ~ f(a,Y)
| ~ f(Y,a)
| ~ f(z(Y),Y) )
<=> ( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ) )),
inference(bind,[status(th)],[]) ).
tff(22,plain,
( ! [Y: $i] :
( ~ f(a,Y)
| ~ f(Y,a)
| ~ f(z(Y),Y) )
<=> ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(Y,a)
| ~ f(z(Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause6) ).
tff(24,plain,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
| ~ f(a,a)
| ~ f(z(a),a) )
<=> ( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
| ~ f(a,a)
| ~ f(z(a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ( ~ f(a,a)
| ~ f(z(a),a)
| ~ f(a,a) )
<=> ( ~ f(a,a)
| ~ f(z(a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,plain,
( ( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
| ~ f(a,a)
| ~ f(z(a),a)
| ~ f(a,a) )
<=> ( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
| ~ f(a,a)
| ~ f(z(a),a) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
| ~ f(a,a)
| ~ f(z(a),a)
| ~ f(a,a) )
<=> ( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
| ~ f(a,a)
| ~ f(z(a),a) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
| ~ f(a,a)
| ~ f(z(a),a)
| ~ f(a,a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(z(Y),Y)
| ~ f(Y,a) )
| ~ f(a,a)
| ~ f(z(a),a) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ f(z(a),a),
inference(unit_resolution,[status(thm)],[33,27,17]) ).
tff(35,plain,
( ( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,z(a))
| f(z(a),a) )
<=> ( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,z(a))
| f(z(a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,z(a))
| f(z(a),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [Y: $i] :
( f(a,Y)
| f(Y,a) )
| f(a,z(a))
| f(z(a),a) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
f(a,z(a)),
inference(unit_resolution,[status(thm)],[37,10,34]) ).
tff(39,plain,
^ [Y: $i] :
refl(( ( ~ f(a,Y)
| ~ f(a,z(Y)) )
<=> ( ~ f(a,Y)
| ~ f(a,z(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(40,plain,
( ! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) )
<=> ! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) ) ),
inference(quant_intro,[status(thm)],[39]) ).
tff(41,plain,
( ! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) )
<=> ! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,axiom,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause5) ).
tff(43,plain,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) ),
inference(skolemize,[status(sab)],[43]) ).
tff(45,plain,
! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) ),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
( ( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) )
| ~ f(a,a)
| ~ f(a,z(a)) )
<=> ( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) )
| ~ f(a,a)
| ~ f(a,z(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) )
| ~ f(a,a)
| ~ f(a,z(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [Y: $i] :
( ~ f(a,Y)
| ~ f(a,z(Y)) )
| ~ f(a,a)
| ~ f(a,z(a)) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
$false,
inference(unit_resolution,[status(thm)],[48,45,17,38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14 % Problem : SYN327-1 : TPTP v9.0.0. Released v1.2.0.
% 0.09/0.14 % Command : run_E %s %d THM
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri Jun 20 12:30:53 EDT 2025
% 0.14/0.36 % CPUTime :
% 0.24/0.42 % SZS status Unsatisfiable
% 0.24/0.42 % SZS output start Proof
% See solution above
% 0.24/0.43 % E exiting
%------------------------------------------------------------------------------