TSTP Solution File: CAT009-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Tue Sep 6 17:29:42 EDT 2022
% Result : Unsatisfiable 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 73
% Syntax : Number of formulae : 167 ( 50 unt; 7 typ; 0 def)
% Number of atoms : 775 ( 57 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1102 ( 517 ~; 507 |; 0 &)
% ( 78 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 30 ( 30 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 5 >; 4 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 407 ( 378 !; 0 ?; 407 :)
% Comments :
%------------------------------------------------------------------------------
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(domain_type,type,
domain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(defined_type,type,
defined: ( $i * $i ) > $o ).
tff(identity_map_type,type,
identity_map: $i > $o ).
tff(1,plain,
^ [X: $i] :
refl(
( defined(X,domain(X))
<=> defined(X,domain(X)) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : defined(X,domain(X))
<=> ! [X: $i] : defined(X,domain(X)) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : defined(X,domain(X))
<=> ! [X: $i] : defined(X,domain(X)) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : defined(X,domain(X)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',mapping_from_x_to_its_domain) ).
tff(5,plain,
! [X: $i] : defined(X,domain(X)),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : defined(X,domain(X)),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : defined(X,domain(X)),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : defined(X,domain(X))
| defined(compose(b,a),domain(compose(b,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
defined(compose(b,a),domain(compose(b,a))),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
<=> ( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).
tff(14,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(compose(b,a),domain(compose(b,a)))
| product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a)))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(compose(b,a),domain(compose(b,a)))
| product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a)))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(compose(b,a),domain(compose(b,a)))
| product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(compose(b,a),domain(compose(b,a)))
| product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a)))) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a)))),
inference(unit_resolution,[status(thm)],[19,16,9]) ).
tff(21,plain,
^ [X: $i] :
refl(
( product(X,domain(X),X)
<=> product(X,domain(X),X) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [X: $i] : product(X,domain(X),X)
<=> ! [X: $i] : product(X,domain(X),X) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,plain,
( ! [X: $i] : product(X,domain(X),X)
<=> ! [X: $i] : product(X,domain(X),X) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
! [X: $i] : product(X,domain(X),X),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',product_on_domain) ).
tff(25,plain,
! [X: $i] : product(X,domain(X),X),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [X: $i] : product(X,domain(X),X),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [X: $i] : product(X,domain(X),X),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ~ ! [X: $i] : product(X,domain(X),X)
| product(compose(b,a),domain(compose(b,a)),compose(b,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
product(compose(b,a),domain(compose(b,a)),compose(b,a)),
inference(unit_resolution,[status(thm)],[28,27]) ).
tff(30,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
refl(
( ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [W: $i,Z: $i,Y: $i,X: $i] :
rewrite(
( ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
<=> ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',composition_is_well_defined) ).
tff(36,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(compose(b,a),domain(compose(b,a)),compose(b,a))
| ~ product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a))))
| ( compose(b,a) = compose(compose(b,a),domain(compose(b,a))) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(compose(b,a),domain(compose(b,a)),compose(b,a))
| ~ product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a))))
| ( compose(b,a) = compose(compose(b,a),domain(compose(b,a))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(compose(b,a),domain(compose(b,a)),compose(b,a))
| ~ product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a))))
| ( compose(b,a) = compose(compose(b,a),domain(compose(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(42,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(compose(b,a),domain(compose(b,a)),compose(b,a))
| ~ product(compose(b,a),domain(compose(b,a)),compose(compose(b,a),domain(compose(b,a))))
| ( compose(b,a) = compose(compose(b,a),domain(compose(b,a))) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
compose(b,a) = compose(compose(b,a),domain(compose(b,a))),
inference(unit_resolution,[status(thm)],[42,39,29,20]) ).
tff(44,plain,
compose(compose(b,a),domain(compose(b,a))) = compose(b,a),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
<=> defined(compose(b,a),domain(compose(b,a))) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( defined(compose(b,a),domain(compose(b,a)))
<=> defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a))) ),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a))),
inference(modus_ponens,[status(thm)],[9,46]) ).
tff(48,plain,
( ~ ! [X: $i] : defined(X,domain(X))
| defined(a,domain(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
defined(a,domain(a)),
inference(unit_resolution,[status(thm)],[48,7]) ).
tff(50,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(a,domain(a))
| product(a,domain(a),compose(a,domain(a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(a,domain(a))
| product(a,domain(a),compose(a,domain(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(a,domain(a))
| product(a,domain(a),compose(a,domain(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(52,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(a,domain(a))
| product(a,domain(a),compose(a,domain(a))) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
product(a,domain(a),compose(a,domain(a))),
inference(unit_resolution,[status(thm)],[52,16,49]) ).
tff(54,plain,
( ~ ! [X: $i] : product(X,domain(X),X)
| product(a,domain(a),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(55,plain,
product(a,domain(a),a),
inference(unit_resolution,[status(thm)],[54,27]) ).
tff(56,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(a,domain(a),a)
| ~ product(a,domain(a),compose(a,domain(a)))
| ( a = compose(a,domain(a)) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(a,domain(a),a)
| ~ product(a,domain(a),compose(a,domain(a)))
| ( a = compose(a,domain(a)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(a,domain(a),a)
| ~ product(a,domain(a),compose(a,domain(a)))
| ( a = compose(a,domain(a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(58,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(a,domain(a),a)
| ~ product(a,domain(a),compose(a,domain(a)))
| ( a = compose(a,domain(a)) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
a = compose(a,domain(a)),
inference(unit_resolution,[status(thm)],[58,39,55,53]) ).
tff(60,plain,
compose(a,domain(a)) = a,
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
( product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a))))
<=> product(b,a,compose(b,a)) ),
inference(monotonicity,[status(thm)],[60,44]) ).
tff(62,plain,
( product(b,a,compose(b,a))
<=> product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a)))) ),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
( defined(b,a)
<=> defined(b,a) ),
inference(rewrite,[status(thm)],]) ).
tff(64,axiom,
defined(b,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ba_defined) ).
tff(65,plain,
defined(b,a),
inference(modus_ponens,[status(thm)],[64,63]) ).
tff(66,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,a)
| product(b,a,compose(b,a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,a)
| product(b,a,compose(b,a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,a)
| product(b,a,compose(b,a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,a)
| product(b,a,compose(b,a)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
product(b,a,compose(b,a)),
inference(unit_resolution,[status(thm)],[68,16,65]) ).
tff(70,plain,
product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a)))),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
^ [Xy: $i,Z: $i,Y: $i,X: $i] :
refl(
( ( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
<=> ( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ) )),
inference(bind,[status(th)],]) ).
tff(72,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ) ),
inference(quant_intro,[status(thm)],[71]) ).
tff(73,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ) ),
inference(rewrite,[status(thm)],]) ).
tff(74,plain,
^ [Xy: $i,Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ product(X,Y,Xy)
| ~ defined(Xy,Z) )
<=> ( ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ) )),
( ( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) )
<=> ( ~ defined(Xy,Z)
| ~ product(X,Y,Xy)
| defined(Y,Z) ) )),
rewrite(
( ( ~ defined(Xy,Z)
| ~ product(X,Y,Xy)
| defined(Y,Z) )
<=> ( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ) )),
( ( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) )
<=> ( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,axiom,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Xy)
| ~ defined(Xy,Z)
| defined(Y,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',associative_property2) ).
tff(77,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[76,75]) ).
tff(78,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[77,73]) ).
tff(79,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(skolemize,[status(sab)],[78]) ).
tff(80,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[79,72]) ).
tff(81,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a))))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| defined(compose(a,domain(a)),domain(compose(b,a))) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a))))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| defined(compose(a,domain(a)),domain(compose(b,a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( defined(compose(a,domain(a)),domain(compose(b,a)))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a)))) )
<=> ( ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a))))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| defined(compose(a,domain(a)),domain(compose(b,a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(compose(a,domain(a)),domain(compose(b,a)))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a)))) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a))))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| defined(compose(a,domain(a)),domain(compose(b,a))) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(compose(a,domain(a)),domain(compose(b,a)))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a)))) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a))))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| defined(compose(a,domain(a)),domain(compose(b,a))) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(compose(a,domain(a)),domain(compose(b,a)))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a)))) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ product(b,compose(a,domain(a)),compose(compose(b,a),domain(compose(b,a))))
| ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| defined(compose(a,domain(a)),domain(compose(b,a))) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ defined(compose(compose(b,a),domain(compose(b,a))),domain(compose(b,a)))
| defined(compose(a,domain(a)),domain(compose(b,a))) ),
inference(unit_resolution,[status(thm)],[86,80,70]) ).
tff(88,plain,
defined(compose(a,domain(a)),domain(compose(b,a))),
inference(unit_resolution,[status(thm)],[87,47]) ).
tff(89,plain,
^ [X: $i] :
refl(
( identity_map(domain(X))
<=> identity_map(domain(X)) )),
inference(bind,[status(th)],]) ).
tff(90,plain,
( ! [X: $i] : identity_map(domain(X))
<=> ! [X: $i] : identity_map(domain(X)) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [X: $i] : identity_map(domain(X))
<=> ! [X: $i] : identity_map(domain(X)) ),
inference(rewrite,[status(thm)],]) ).
tff(92,axiom,
! [X: $i] : identity_map(domain(X)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
tff(93,plain,
! [X: $i] : identity_map(domain(X)),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
! [X: $i] : identity_map(domain(X)),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [X: $i] : identity_map(domain(X)),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
( ~ ! [X: $i] : identity_map(domain(X))
| identity_map(domain(compose(b,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
identity_map(domain(compose(b,a))),
inference(unit_resolution,[status(thm)],[96,95]) ).
tff(98,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(99,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) ),
inference(quant_intro,[status(thm)],[98]) ).
tff(100,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ defined(X,Y)
| ~ identity_map(Y) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y) ) )),
( ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) )),
rewrite(
( ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) )),
( ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(102,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ) ),
inference(quant_intro,[status(thm)],[101]) ).
tff(103,axiom,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity2) ).
tff(104,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
inference(modus_ponens,[status(thm)],[104,100]) ).
tff(106,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
inference(skolemize,[status(sab)],[105]) ).
tff(107,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) ),
inference(modus_ponens,[status(thm)],[106,99]) ).
tff(108,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(compose(b,a)))
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(compose(b,a)))
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(109,plain,
( ( ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| ~ identity_map(domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) )
<=> ( ~ identity_map(domain(compose(b,a)))
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| ~ identity_map(domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(compose(b,a)))
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) ) ),
inference(monotonicity,[status(thm)],[109]) ).
tff(111,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| ~ identity_map(domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(compose(b,a)))
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) ) ),
inference(transitivity,[status(thm)],[110,108]) ).
tff(112,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| ~ identity_map(domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(compose(b,a)))
| ~ defined(compose(a,domain(a)),domain(compose(b,a)))
| product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))),
inference(unit_resolution,[status(thm)],[113,107,97,88]) ).
tff(115,plain,
( defined(compose(a,domain(a)),domain(a))
<=> defined(a,domain(a)) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(116,plain,
( defined(a,domain(a))
<=> defined(compose(a,domain(a)),domain(a)) ),
inference(symmetry,[status(thm)],[115]) ).
tff(117,plain,
defined(compose(a,domain(a)),domain(a)),
inference(modus_ponens,[status(thm)],[49,116]) ).
tff(118,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a)))
| defined(domain(compose(b,a)),domain(a)) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a)))
| defined(domain(compose(b,a)),domain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ( defined(domain(compose(b,a)),domain(a))
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) )
<=> ( ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a)))
| defined(domain(compose(b,a)),domain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(domain(compose(b,a)),domain(a))
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a)))
| defined(domain(compose(b,a)),domain(a)) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(domain(compose(b,a)),domain(a))
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a)))
| defined(domain(compose(b,a)),domain(a)) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(domain(compose(b,a)),domain(a))
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| ~ defined(compose(a,domain(a)),domain(a))
| ~ product(compose(a,domain(a)),domain(compose(b,a)),compose(a,domain(a)))
| defined(domain(compose(b,a)),domain(a)) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
defined(domain(compose(b,a)),domain(a)),
inference(unit_resolution,[status(thm)],[123,80,117,114]) ).
tff(125,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
<=> ( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) )),
inference(bind,[status(th)],]) ).
tff(126,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) ),
inference(quant_intro,[status(thm)],[125]) ).
tff(127,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(128,plain,
^ [Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ defined(X,Y)
| ~ identity_map(X) )
<=> ( ~ defined(X,Y)
| ~ identity_map(X) ) )),
( ( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) )
<=> ( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ) )),
rewrite(
( ( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) )
<=> ( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) )),
( ( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) )
<=> ( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) )),
inference(bind,[status(th)],]) ).
tff(129,plain,
( ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) )
<=> ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,axiom,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(X)
| product(X,Y,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',identity1) ).
tff(131,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ identity_map(domain(compose(b,a)))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ defined(domain(compose(b,a)),domain(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ identity_map(domain(compose(b,a)))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ defined(domain(compose(b,a)),domain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ( ~ defined(domain(compose(b,a)),domain(a))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ identity_map(domain(compose(b,a))) )
<=> ( ~ identity_map(domain(compose(b,a)))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ defined(domain(compose(b,a)),domain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(137,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(domain(compose(b,a)),domain(a))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ identity_map(domain(compose(b,a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ identity_map(domain(compose(b,a)))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ defined(domain(compose(b,a)),domain(a)) ) ),
inference(monotonicity,[status(thm)],[136]) ).
tff(138,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(domain(compose(b,a)),domain(a))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ identity_map(domain(compose(b,a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ identity_map(domain(compose(b,a)))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ defined(domain(compose(b,a)),domain(a)) ) ),
inference(transitivity,[status(thm)],[137,135]) ).
tff(139,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ defined(domain(compose(b,a)),domain(a))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ identity_map(domain(compose(b,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(140,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,Y)
| ~ identity_map(X) )
| ~ identity_map(domain(compose(b,a)))
| product(domain(compose(b,a)),domain(a),domain(a))
| ~ defined(domain(compose(b,a)),domain(a)) ),
inference(modus_ponens,[status(thm)],[139,138]) ).
tff(141,plain,
product(domain(compose(b,a)),domain(a),domain(a)),
inference(unit_resolution,[status(thm)],[140,134,97,124]) ).
tff(142,plain,
( ~ ! [X: $i] : identity_map(domain(X))
| identity_map(domain(a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(143,plain,
identity_map(domain(a)),
inference(unit_resolution,[status(thm)],[142,95]) ).
tff(144,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ defined(domain(compose(b,a)),domain(a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ defined(domain(compose(b,a)),domain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(145,plain,
( ( ~ defined(domain(compose(b,a)),domain(a))
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a))) )
<=> ( ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ defined(domain(compose(b,a)),domain(a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(146,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(domain(compose(b,a)),domain(a))
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ defined(domain(compose(b,a)),domain(a)) ) ),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(domain(compose(b,a)),domain(a))
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ defined(domain(compose(b,a)),domain(a)) ) ),
inference(transitivity,[status(thm)],[146,144]) ).
tff(148,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ defined(domain(compose(b,a)),domain(a))
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(149,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ identity_map(Y)
| product(X,Y,X) )
| ~ identity_map(domain(a))
| product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ defined(domain(compose(b,a)),domain(a)) ),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
product(domain(compose(b,a)),domain(a),domain(compose(b,a))),
inference(unit_resolution,[status(thm)],[149,107,143,124]) ).
tff(151,plain,
( ( domain(compose(b,a)) != domain(a) )
<=> ( domain(compose(b,a)) != domain(a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,axiom,
domain(compose(b,a)) != domain(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).
tff(153,plain,
domain(compose(b,a)) != domain(a),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( domain(compose(b,a)) = domain(a) )
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a))) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( domain(compose(b,a)) = domain(a) )
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(155,plain,
( ( ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ( domain(compose(b,a)) = domain(a) ) )
<=> ( ( domain(compose(b,a)) = domain(a) )
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ( domain(compose(b,a)) = domain(a) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( domain(compose(b,a)) = domain(a) )
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ) ),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ( domain(compose(b,a)) = domain(a) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( domain(compose(b,a)) = domain(a) )
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ) ),
inference(transitivity,[status(thm)],[156,154]) ).
tff(158,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a)))
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ( domain(compose(b,a)) = domain(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(159,plain,
( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ( domain(compose(b,a)) = domain(a) )
| ~ product(domain(compose(b,a)),domain(a),domain(a))
| ~ product(domain(compose(b,a)),domain(a),domain(compose(b,a))) ),
inference(modus_ponens,[status(thm)],[158,157]) ).
tff(160,plain,
$false,
inference(unit_resolution,[status(thm)],[159,39,153,150,141]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : CAT009-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue Aug 30 06:13:35 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.56 % SZS status Unsatisfiable
% 0.20/0.56 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------