%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT007-3 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:00:20 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 26 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 164 ( 78 ~; 74 |; 0 &)
% ( 12 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 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 : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 38 !; 0 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
tff(there_exists_type,type,
there_exists: $i > $o ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(c1_type,type,
c1: $i ).
tff(c2_type,type,
c2: $i ).
tff(equalish_type,type,
equalish: ( $i * $i ) > $o ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(1,plain,
( ~ there_exists(compose(c2,c1))
<=> ~ there_exists(compose(c2,c1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ there_exists(compose(c2,c1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c1_c2_is_defined) ).
tff(3,plain,
~ there_exists(compose(c2,c1)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
( equalish(domain(c2),codomain(c1))
<=> equalish(domain(c2),codomain(c1)) ),
inference(rewrite,[status(thm)],[]) ).
tff(5,axiom,
equalish(domain(c2),codomain(c1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_c2_equals_codomain_of_c1) ).
tff(6,plain,
equalish(domain(c2),codomain(c1)),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
( there_exists(domain(c2))
<=> there_exists(domain(c2)) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,axiom,
there_exists(domain(c2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_c2_exists) ).
tff(9,plain,
there_exists(domain(c2)),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
<=> ( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ~ there_exists(domain(X))
| ~ equalish(domain(X),codomain(Y))
| there_exists(compose(X,Y)) )
<=> ( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(14,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| ~ equalish(domain(X),codomain(Y))
| there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| ~ equalish(domain(X),codomain(Y))
| there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition2) ).
tff(16,plain,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1))
| ~ there_exists(domain(c2)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1))
| ~ there_exists(domain(c2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(21,plain,
( ( ~ there_exists(domain(c2))
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1)) )
<=> ( there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1))
| ~ there_exists(domain(c2)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
| ~ there_exists(domain(c2))
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1))
| ~ there_exists(domain(c2)) ) ),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
| ~ there_exists(domain(c2))
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1))
| ~ there_exists(domain(c2)) ) ),
inference(transitivity,[status(thm)],[22,20]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
| ~ there_exists(domain(c2))
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(domain(X))
| there_exists(compose(X,Y))
| ~ equalish(domain(X),codomain(Y)) )
| there_exists(compose(c2,c1))
| ~ equalish(domain(c2),codomain(c1))
| ~ there_exists(domain(c2)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
$false,
inference(unit_resolution,[status(thm)],[25,19,9,6,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : CAT007-3 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 11:53:31 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.21/0.38 % SZS status Unsatisfiable
% 0.21/0.38 % SZS output start Proof
% See solution above
% 0.21/0.38 % E exiting
%------------------------------------------------------------------------------