%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT014-2 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:00:23 AM UTC 2025
% Result : Unsatisfiable 0.19s 0.37s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 25 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 36 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 6 ~; 2 |; 0 &)
% ( 7 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 2 ( 2 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 : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 20 ( 18 !; 0 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
tff(codomain_type,type,
codomain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( domain(codomain(X)) = codomain(X) )
<=> ( domain(codomain(X)) = codomain(X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( domain(codomain(X)) = codomain(X) )
<=> ! [X: $i] : ( domain(codomain(X)) = codomain(X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( domain(codomain(X)) = codomain(X) )
<=> ! [X: $i] : ( domain(codomain(X)) = codomain(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( domain(codomain(X)) = codomain(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT002-0.ax',domain_of_codomain_is_codomain) ).
tff(5,plain,
! [X: $i] : ( domain(codomain(X)) = codomain(X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( domain(codomain(X)) = codomain(X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( domain(codomain(X)) = codomain(X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( domain(codomain(X)) = codomain(X) )
| ( domain(codomain(a)) = codomain(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
domain(codomain(a)) = codomain(a),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [X: $i] :
refl(( ( codomain(domain(X)) = domain(X) )
<=> ( codomain(domain(X)) = domain(X) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [X: $i] : ( codomain(domain(X)) = domain(X) )
<=> ! [X: $i] : ( codomain(domain(X)) = domain(X) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [X: $i] : ( codomain(domain(X)) = domain(X) )
<=> ! [X: $i] : ( codomain(domain(X)) = domain(X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT002-0.ax',codomain_of_domain_is_domain) ).
tff(14,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [X: $i] : ( codomain(domain(X)) = domain(X) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [X: $i] : ( codomain(domain(X)) = domain(X) )
| ( codomain(domain(codomain(a))) = domain(codomain(a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
codomain(domain(codomain(a))) = domain(codomain(a)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
codomain(domain(codomain(a))) = codomain(codomain(a)),
inference(monotonicity,[status(thm)],[9]) ).
tff(20,plain,
codomain(codomain(a)) = codomain(domain(codomain(a))),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
codomain(codomain(a)) = codomain(a),
inference(transitivity,[status(thm)],[20,18,9]) ).
tff(22,plain,
( ( codomain(codomain(a)) != codomain(a) )
<=> ( codomain(codomain(a)) != codomain(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
codomain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_is_idempotent) ).
tff(24,plain,
codomain(codomain(a)) != codomain(a),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
$false,
inference(unit_resolution,[status(thm)],[24,21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : CAT014-2 : TPTP v9.0.0. Released v1.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n001.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 : Thu Jun 19 11:57:03 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.37 % SZS status Unsatisfiable
% 0.19/0.37 % SZS output start Proof
% See solution above
% 0.19/0.37 % E exiting
%------------------------------------------------------------------------------