%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : CAT007-1 : 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 05:00:20 AM UTC 2025
% Result : Unsatisfiable 0.21s 0.38s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 23
% Syntax : Number of formulae : 58 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 223 ( 5 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 288 ( 134 ~; 127 |; 0 &)
% ( 27 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 11 ( 11 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 93 ( 84 !; 0 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
tff(defined_type,type,
defined: ( $i * $i ) > $o ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(identity_map_type,type,
identity_map: $i > $o ).
tff(1,plain,
( ( domain(a) = codomain(b) )
<=> ( domain(a) = codomain(b) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
domain(a) = codomain(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_a_equals_codomain_of_b) ).
tff(3,plain,
domain(a) = codomain(b),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
codomain(b) = domain(a),
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
( defined(a,codomain(b))
<=> defined(a,domain(a)) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( defined(a,domain(a))
<=> defined(a,codomain(b)) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
^ [X: $i] :
refl(( defined(X,domain(X))
<=> defined(X,domain(X)) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [X: $i] : defined(X,domain(X))
<=> ! [X: $i] : defined(X,domain(X)) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
( ! [X: $i] : defined(X,domain(X))
<=> ! [X: $i] : defined(X,domain(X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
! [X: $i] : defined(X,domain(X)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
tff(11,plain,
! [X: $i] : defined(X,domain(X)),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
! [X: $i] : defined(X,domain(X)),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [X: $i] : defined(X,domain(X)),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
( ~ ! [X: $i] : defined(X,domain(X))
| defined(a,domain(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(15,plain,
defined(a,domain(a)),
inference(unit_resolution,[status(thm)],[14,13]) ).
tff(16,plain,
defined(a,codomain(b)),
inference(modus_ponens,[status(thm)],[15,6]) ).
tff(17,plain,
( identity_map(codomain(b))
<=> identity_map(domain(a)) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(18,plain,
( identity_map(domain(a))
<=> identity_map(codomain(b)) ),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
^ [X: $i] :
refl(( identity_map(domain(X))
<=> identity_map(domain(X)) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X: $i] : identity_map(domain(X))
<=> ! [X: $i] : identity_map(domain(X)) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : identity_map(domain(X))
<=> ! [X: $i] : identity_map(domain(X)) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [X: $i] : identity_map(domain(X)),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
tff(23,plain,
! [X: $i] : identity_map(domain(X)),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : identity_map(domain(X)),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : identity_map(domain(X)),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : identity_map(domain(X))
| identity_map(domain(a)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
identity_map(domain(a)),
inference(unit_resolution,[status(thm)],[26,25]) ).
tff(28,plain,
identity_map(codomain(b)),
inference(modus_ponens,[status(thm)],[27,18]) ).
tff(29,plain,
^ [X: $i] :
refl(( defined(codomain(X),X)
<=> defined(codomain(X),X) )),
inference(bind,[status(th)],[]) ).
tff(30,plain,
( ! [X: $i] : defined(codomain(X),X)
<=> ! [X: $i] : defined(codomain(X),X) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [X: $i] : defined(codomain(X),X)
<=> ! [X: $i] : defined(codomain(X),X) ),
inference(rewrite,[status(thm)],[]) ).
tff(32,axiom,
! [X: $i] : defined(codomain(X),X),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',mapping_from_codomain_of_x_to_x) ).
tff(33,plain,
! [X: $i] : defined(codomain(X),X),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [X: $i] : defined(codomain(X),X),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [X: $i] : defined(codomain(X),X),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [X: $i] : defined(codomain(X),X)
| defined(codomain(b),b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
defined(codomain(b),b),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
( ~ defined(a,b)
<=> ~ defined(a,b) ),
inference(rewrite,[status(thm)],[]) ).
tff(39,axiom,
~ defined(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_ab_is_defined) ).
tff(40,plain,
~ defined(a,b),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(( ( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
<=> ( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(42,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ) ),
inference(quant_intro,[status(thm)],[41]) ).
tff(43,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(monotonicity(rewrite(( ( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| ~ defined(Y,Z) ) )),
( ( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y)
| defined(X,Z) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| ~ defined(Y,Z)
| defined(X,Z) ) )),
rewrite(( ( ~ defined(X,Y)
| ~ identity_map(Y)
| ~ defined(Y,Z)
| defined(X,Z) )
<=> ( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ) )),
( ( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y)
| defined(X,Z) )
<=> ( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ) )),
inference(bind,[status(th)],[]) ).
tff(45,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y)
| defined(X,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ) ),
inference(quant_intro,[status(thm)],[44]) ).
tff(46,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y)
| defined(X,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
tff(47,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ),
inference(skolemize,[status(sab)],[48]) ).
tff(50,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ),
inference(modus_ponens,[status(thm)],[49,42]) ).
tff(51,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(a,b)
| ~ defined(codomain(b),b)
| ~ defined(a,codomain(b))
| ~ identity_map(codomain(b)) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(a,b)
| ~ defined(codomain(b),b)
| ~ defined(a,codomain(b))
| ~ identity_map(codomain(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(52,plain,
( ( ~ defined(a,codomain(b))
| defined(a,b)
| ~ identity_map(codomain(b))
| ~ defined(codomain(b),b) )
<=> ( defined(a,b)
| ~ defined(codomain(b),b)
| ~ defined(a,codomain(b))
| ~ identity_map(codomain(b)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(53,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| ~ defined(a,codomain(b))
| defined(a,b)
| ~ identity_map(codomain(b))
| ~ defined(codomain(b),b) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(a,b)
| ~ defined(codomain(b),b)
| ~ defined(a,codomain(b))
| ~ identity_map(codomain(b)) ) ),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| ~ defined(a,codomain(b))
| defined(a,b)
| ~ identity_map(codomain(b))
| ~ defined(codomain(b),b) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(a,b)
| ~ defined(codomain(b),b)
| ~ defined(a,codomain(b))
| ~ identity_map(codomain(b)) ) ),
inference(transitivity,[status(thm)],[53,51]) ).
tff(55,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| ~ defined(a,codomain(b))
| defined(a,b)
| ~ identity_map(codomain(b))
| ~ defined(codomain(b),b) ),
inference(quant_inst,[status(thm)],[]) ).
tff(56,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(a,b)
| ~ defined(codomain(b),b)
| ~ defined(a,codomain(b))
| ~ identity_map(codomain(b)) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ~ defined(a,codomain(b))
| ~ identity_map(codomain(b)) ),
inference(unit_resolution,[status(thm)],[56,50,40,37]) ).
tff(58,plain,
$false,
inference(unit_resolution,[status(thm)],[57,28,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : CAT007-1 : TPTP v9.0.0. Released v1.0.0.
% 0.04/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Jun 19 11:53:19 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
%------------------------------------------------------------------------------