%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SET296-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 05:25:35 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 12 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 16 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 5 ~; 1 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 10 ( 9 !; 0 ?; 10 :)
% Comments :
%------------------------------------------------------------------------------
tff(range_of_type,type,
range_of: $i > $i ).
tff(x_type,type,
x: $i ).
tff(domain_of_type,type,
domain_of: $i > $i ).
tff(inverse_type,type,
inverse: $i > $i ).
tff(1,plain,
( ( domain_of(inverse(x)) != range_of(x) )
<=> ( domain_of(inverse(x)) != range_of(x) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
domain_of(inverse(x)) != range_of(x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_inverse_1) ).
tff(3,plain,
domain_of(inverse(x)) != range_of(x),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Z: $i] :
refl(( ( domain_of(inverse(Z)) = range_of(Z) )
<=> ( domain_of(inverse(Z)) = range_of(Z) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) )
<=> ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) )
<=> ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',range_of) ).
tff(8,plain,
! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ~ ! [Z: $i] : ( domain_of(inverse(Z)) = range_of(Z) )
| ( domain_of(inverse(x)) = range_of(x) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(12,plain,
$false,
inference(unit_resolution,[status(thm)],[11,10,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET296-6 : TPTP v9.0.0. Bugfixed v2.1.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n004.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 04:44:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40 % SZS output start Proof
% See solution above
% 0.20/0.41 % E exiting
%------------------------------------------------------------------------------