%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT010-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:00:21 AM UTC 2025
% Result : Unsatisfiable 0.20s 0.38s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 32
% Syntax : Number of formulae : 83 ( 30 unt; 0 typ; 0 def)
% Number of atoms : 216 ( 72 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 225 ( 99 ~; 92 |; 0 &)
% ( 34 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 7 ( 7 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 125 ( 113 !; 0 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
tff(there_exists_type,type,
there_exists: $i > $o ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(b_type,type,
b: $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/CAT004-0.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,
compose(compose(codomain(a),a),b) = compose(a,b),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
<=> ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',associativity_of_compose) ).
tff(15,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [Z: $i,Y: $i,X: $i] : ( compose(X,compose(Y,Z)) = compose(compose(X,Y),Z) )
| ( compose(codomain(a),compose(a,b)) = compose(compose(codomain(a),a),b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
compose(codomain(a),compose(a,b)) = compose(compose(codomain(a),a),b),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
compose(codomain(a),compose(a,b)) = compose(a,b),
inference(transitivity,[status(thm)],[19,10]) ).
tff(21,plain,
( there_exists(compose(codomain(a),compose(a,b)))
<=> there_exists(compose(a,b)) ),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
( there_exists(compose(a,b))
<=> there_exists(compose(codomain(a),compose(a,b))) ),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
( there_exists(compose(a,b))
<=> there_exists(compose(a,b)) ),
inference(rewrite,[status(thm)],[]) ).
tff(24,axiom,
there_exists(compose(a,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ab_exists) ).
tff(25,plain,
there_exists(compose(a,b)),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
there_exists(compose(codomain(a),compose(a,b))),
inference(modus_ponens,[status(thm)],[25,22]) ).
tff(27,plain,
( ( codomain(a) = codomain(compose(a,b)) )
<=> ( codomain(compose(a,b)) = codomain(a) ) ),
inference(commutativity,[status(thm)],[]) ).
tff(28,plain,
( there_exists(compose(codomain(a),a))
<=> there_exists(a) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(29,plain,
( there_exists(a)
<=> there_exists(compose(codomain(a),a)) ),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
^ [Y: $i,X: $i] :
refl(( ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,plain,
^ [Y: $i,X: $i] :
rewrite(( ( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) )
<=> ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) )),
inference(bind,[status(th)],[]) ).
tff(34,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).
tff(36,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,b)) )
<=> ( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,b)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,b)) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
there_exists(domain(a)),
inference(unit_resolution,[status(thm)],[42,39,25]) ).
tff(44,plain,
^ [X: $i] :
refl(( ( there_exists(X)
| ~ there_exists(domain(X)) )
<=> ( there_exists(X)
| ~ there_exists(domain(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,plain,
( ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
^ [X: $i] :
rewrite(( ( ~ there_exists(domain(X))
| there_exists(X) )
<=> ( there_exists(X)
| ~ there_exists(domain(X)) ) )),
inference(bind,[status(th)],[]) ).
tff(48,plain,
( ! [X: $i] :
( ~ there_exists(domain(X))
| there_exists(X) )
<=> ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ) ),
inference(quant_intro,[status(thm)],[47]) ).
tff(49,axiom,
! [X: $i] :
( ~ there_exists(domain(X))
| there_exists(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',domain_has_elements) ).
tff(50,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(skolemize,[status(sab)],[51]) ).
tff(53,plain,
! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
inference(modus_ponens,[status(thm)],[52,45]) ).
tff(54,plain,
( ( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
| there_exists(a)
| ~ there_exists(domain(a)) )
<=> ( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
| there_exists(a)
| ~ there_exists(domain(a)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
| there_exists(a)
| ~ there_exists(domain(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [X: $i] :
( there_exists(X)
| ~ there_exists(domain(X)) )
| there_exists(a)
| ~ there_exists(domain(a)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
there_exists(a),
inference(unit_resolution,[status(thm)],[56,53,43]) ).
tff(58,plain,
there_exists(compose(codomain(a),a)),
inference(modus_ponens,[status(thm)],[57,29]) ).
tff(59,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(60,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)],[59]) ).
tff(61,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(62,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition1) ).
tff(63,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,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(67,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(68,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)],[67,66]) ).
tff(69,plain,
( ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) ),
inference(unit_resolution,[status(thm)],[68,65]) ).
tff(70,plain,
domain(codomain(a)) = codomain(a),
inference(unit_resolution,[status(thm)],[69,58]) ).
tff(71,plain,
( ( domain(codomain(a)) = codomain(compose(a,b)) )
<=> ( codomain(a) = codomain(compose(a,b)) ) ),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
( ( domain(codomain(a)) = codomain(compose(a,b)) )
<=> ( codomain(compose(a,b)) = codomain(a) ) ),
inference(transitivity,[status(thm)],[71,27]) ).
tff(73,plain,
( ( codomain(compose(a,b)) = codomain(a) )
<=> ( domain(codomain(a)) = codomain(compose(a,b)) ) ),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
( ( codomain(compose(a,b)) != codomain(a) )
<=> ( domain(codomain(a)) != codomain(compose(a,b)) ) ),
inference(monotonicity,[status(thm)],[73]) ).
tff(75,plain,
( ( codomain(compose(a,b)) != codomain(a) )
<=> ( codomain(compose(a,b)) != codomain(a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(76,axiom,
codomain(compose(a,b)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).
tff(77,plain,
codomain(compose(a,b)) != codomain(a),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
domain(codomain(a)) != codomain(compose(a,b)),
inference(modus_ponens,[status(thm)],[77,74]) ).
tff(79,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),compose(a,b)))
| ( domain(codomain(a)) = codomain(compose(a,b)) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),compose(a,b)))
| ( domain(codomain(a)) = codomain(compose(a,b)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),compose(a,b)))
| ( domain(codomain(a)) = codomain(compose(a,b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(81,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),compose(a,b)))
| ( domain(codomain(a)) = codomain(compose(a,b)) ) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
( ~ there_exists(compose(codomain(a),compose(a,b)))
| ( domain(codomain(a)) = codomain(compose(a,b)) ) ),
inference(unit_resolution,[status(thm)],[81,65]) ).
tff(83,plain,
$false,
inference(unit_resolution,[status(thm)],[82,78,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CAT010-4 : TPTP v9.0.0. Released v1.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n007.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 11:53:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.38 % SZS status Unsatisfiable
% 0.20/0.38 % SZS output start Proof
% See solution above
% 0.20/0.39 % E exiting
%------------------------------------------------------------------------------