%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN073-1 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:38:09 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 10
% Syntax : Number of formulae : 22 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 55 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 53 ( 22 ~; 24 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 37 ( 34 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
tff(big_f_type,type,
big_f: ( $i * $i ) > $o ).
tff(f_type,type,
f: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [X: $i] :
refl(( ~ big_f(X,f(X))
<=> ~ big_f(X,f(X)) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ~ big_f(X,f(X))
<=> ! [X: $i] : ~ big_f(X,f(X)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ~ big_f(X,f(X))
<=> ! [X: $i] : ~ big_f(X,f(X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ~ big_f(X,f(X)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
tff(5,plain,
! [X: $i] : ~ big_f(X,f(X)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ~ big_f(X,f(X)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ~ big_f(X,f(X)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ~ big_f(X,f(X))
| ~ big_f(f(a),f(f(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
~ big_f(f(a),f(f(a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( ~ ! [X: $i] : ~ big_f(X,f(X))
| ~ big_f(a,f(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(11,plain,
~ big_f(a,f(a)),
inference(unit_resolution,[status(thm)],[10,7]) ).
tff(12,plain,
^ [Y: $i,X: $i] :
refl(( ( big_f(a,X)
| big_f(X,Y) )
<=> ( big_f(a,X)
| big_f(X,Y) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) )
<=> ! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) )
<=> ! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(15,axiom,
! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
tff(16,plain,
! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
( ( ~ ! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) )
| big_f(a,f(a))
| big_f(f(a),f(f(a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) )
| big_f(a,f(a))
| big_f(f(a),f(f(a))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,plain,
( ~ ! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) )
| big_f(a,f(a))
| big_f(f(a),f(f(a))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(21,plain,
( ~ ! [Y: $i,X: $i] :
( big_f(a,X)
| big_f(X,Y) )
| big_f(a,f(a))
| big_f(f(a),f(f(a))) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
$false,
inference(unit_resolution,[status(thm)],[21,18,11,9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SYN073-1 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n012.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 12:27:10 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
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------