%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN350-1 : TPTP v9.0.0. Released v1.2.0.
% 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 05:38:51 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 26
% Syntax : Number of formulae : 62 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 320 ( 0 equ)
% Maximal formula atoms : 11 ( 5 avg)
% Number of connectives : 423 ( 172 ~; 220 |; 0 &)
% ( 31 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 7 ( 7 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; 0-2 aty)
% Number of variables : 152 ( 138 !; 0 ?; 152 :)
% Comments :
%------------------------------------------------------------------------------
tff(f_type,type,
f: ( $i * $i ) > $o ).
tff(z_type,type,
z: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [Y: $i,X: $i] :
refl(( ( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
<=> ( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
<=> ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
<=> ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,plain,
^ [Y: $i,X: $i] :
rewrite(( ( f(a,z(X,Y))
| f(Y,z(X,Y))
| f(X,z(X,Y)) )
<=> ( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| f(X,z(X,Y)) )
<=> ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| f(X,z(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause3) ).
tff(7,plain,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
| f(a,z(a,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
| f(a,z(a,a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( ( f(a,z(a,a))
| f(a,z(a,a))
| f(a,z(a,a)) )
<=> f(a,z(a,a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
( ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
| f(a,z(a,a))
| f(a,z(a,a))
| f(a,z(a,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
| f(a,z(a,a)) ) ),
inference(monotonicity,[status(thm)],[12]) ).
tff(14,plain,
( ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
| f(a,z(a,a))
| f(a,z(a,a))
| f(a,z(a,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
| f(a,z(a,a)) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
| f(a,z(a,a))
| f(a,z(a,a))
| f(a,z(a,a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(16,plain,
( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(X,z(X,Y))
| f(Y,z(X,Y)) )
| f(a,z(a,a)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
f(a,z(a,a)),
inference(unit_resolution,[status(thm)],[16,10]) ).
tff(18,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ f(a,z(X,Y))
| f(z(X,Y),a) )
<=> ( ~ f(a,z(X,Y))
| f(z(X,Y),a) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) )
<=> ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) )
<=> ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,axiom,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause1) ).
tff(22,plain,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) ),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) ),
inference(modus_ponens,[status(thm)],[23,19]) ).
tff(25,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) )
| ~ f(a,z(a,a))
| f(z(a,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) )
| ~ f(a,z(a,a))
| f(z(a,a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) )
| ~ f(a,z(a,a))
| f(z(a,a),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| f(z(X,Y),a) )
| ~ f(a,z(a,a))
| f(z(a,a),a) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
f(z(a,a),a),
inference(unit_resolution,[status(thm)],[27,24,17]) ).
tff(29,plain,
^ [Y: $i,X: $i] :
refl(( ( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,plain,
^ [Y: $i,X: $i] :
rewrite(( ( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause5) ).
tff(35,plain,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
( ( f(a,z(z(a,a),a))
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) )
<=> ( f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
| f(a,z(z(a,a),a))
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
| f(a,z(z(a,a),a))
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
| f(a,z(z(a,a),a))
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [Y: $i,X: $i] :
( f(a,z(X,Y))
| f(Y,z(X,Y))
| ~ f(X,Y) )
| f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
f(a,z(z(a,a),a)),
inference(unit_resolution,[status(thm)],[44,38,28]) ).
tff(46,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(47,plain,
( ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(50,plain,
( ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
<=> ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ) ),
inference(quant_intro,[status(thm)],[49]) ).
tff(51,axiom,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause6) ).
tff(52,plain,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ),
inference(modus_ponens,[status(thm)],[52,48]) ).
tff(54,plain,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ),
inference(skolemize,[status(sab)],[53]) ).
tff(55,plain,
! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) ),
inference(modus_ponens,[status(thm)],[54,47]) ).
tff(56,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,plain,
( ( ~ f(a,z(z(a,a),a))
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) )
<=> ( ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(58,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
| ~ f(a,z(z(a,a),a))
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ) ),
inference(monotonicity,[status(thm)],[57]) ).
tff(59,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
| ~ f(a,z(z(a,a),a))
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ) ),
inference(transitivity,[status(thm)],[58,56]) ).
tff(60,plain,
( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
| ~ f(a,z(z(a,a),a))
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
( ~ ! [Y: $i,X: $i] :
( ~ f(a,z(X,Y))
| ~ f(Y,z(X,Y))
| ~ f(X,Y) )
| ~ f(a,z(z(a,a),a))
| ~ f(z(a,a),a) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
$false,
inference(unit_resolution,[status(thm)],[61,55,28,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SYN350-1 : TPTP v9.0.0. Released v1.2.0.
% 0.12/0.12 % 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 12:31:33 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39 % SZS output start Proof
% See solution above
% 0.12/0.40 % E exiting
%------------------------------------------------------------------------------