%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT013-3 : 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 05:00:22 AM UTC 2025
% Result : Unsatisfiable 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 19
% Syntax : Number of formulae : 44 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 35 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 122 ( 55 ~; 50 |; 0 &)
% ( 17 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 53 ( 48 !; 0 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
tff(there_exists_type,type,
there_exists: $i > $o ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(1,plain,
^ [X: $i] :
refl(( ( compose(codomain(X),X) = X )
<=> ( compose(codomain(X),X) = X ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i] : ( compose(codomain(X),X) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT003-0.ax',compose_codomain) ).
tff(5,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( compose(codomain(X),X) = X )
| ( compose(codomain(a),a) = a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
compose(codomain(a),a) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( there_exists(compose(codomain(a),a))
<=> there_exists(a) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( there_exists(a)
<=> there_exists(compose(codomain(a),a)) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( there_exists(codomain(a))
<=> there_exists(codomain(a)) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
there_exists(codomain(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_codomain_exists) ).
tff(14,plain,
there_exists(codomain(a)),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
^ [X: $i] :
refl(( ( there_exists(X)
| ~ there_exists(codomain(X)) )
<=> ( there_exists(X)
| ~ there_exists(codomain(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
^ [X: $i] :
rewrite(( ( ~ there_exists(codomain(X))
| there_exists(X) )
<=> ( there_exists(X)
| ~ there_exists(codomain(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(19,plain,
( ! [X: $i] :
( ~ there_exists(codomain(X))
| there_exists(X) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,axiom,
! [X: $i] :
( ~ there_exists(codomain(X))
| there_exists(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT003-0.ax',codomain_has_elements) ).
tff(21,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
inference(modus_ponens,[status(thm)],[23,16]) ).
tff(25,plain,
( ( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
| there_exists(a)
| ~ there_exists(codomain(a)) )
<=> ( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
| there_exists(a)
| ~ there_exists(codomain(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
| there_exists(a)
| ~ there_exists(codomain(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(codomain(X)) )
| there_exists(a)
| ~ there_exists(codomain(a)) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
there_exists(a),
inference(unit_resolution,[status(thm)],[27,24,14]) ).
tff(29,plain,
there_exists(compose(codomain(a),a)),
inference(modus_ponens,[status(thm)],[28,11]) ).
tff(30,plain,
( ( domain(codomain(a)) != codomain(a) )
<=> ( domain(codomain(a)) != codomain(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(31,axiom,
domain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_codomain_is_codomain) ).
tff(32,plain,
domain(codomain(a)) != codomain(a),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
^ [Y: $i,X: $i] :
refl(( ( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition1) ).
tff(37,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[38,34]) ).
tff(40,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
~ there_exists(compose(codomain(a),a)),
inference(unit_resolution,[status(thm)],[42,39,32]) ).
tff(44,plain,
$false,
inference(unit_resolution,[status(thm)],[43,29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT013-3 : TPTP v9.0.0. Released v1.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n002.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 11:54:31 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.37 % SZS status Unsatisfiable
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------