TSTP Solution File: CAT018-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT018-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n008.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 17:29:49 EDT 2022
% Result : Unsatisfiable 0.12s 0.41s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 67
% Syntax : Number of formulae : 147 ( 46 unt; 8 typ; 0 def)
% Number of atoms : 761 ( 25 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 1104 ( 526 ~; 505 |; 0 &)
% ( 73 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 44 ( 44 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 : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 461 ( 414 !; 0 ?; 461 :)
% Comments :
%------------------------------------------------------------------------------
tff(defined_type,type,
defined: ( $i * $i ) > $o ).
tff(c_type,type,
c: $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(b_type,type,
b: $i ).
tff(product_type,type,
product: ( $i * $i * $i ) > $o ).
tff(a_type,type,
a: $i ).
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(b,domain(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
defined(b,domain(b)),
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(b,domain(b))
| product(b,domain(b),compose(b,domain(b))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,domain(b))
| product(b,domain(b),compose(b,domain(b))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,domain(b))
| product(b,domain(b),compose(b,domain(b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,domain(b))
| product(b,domain(b),compose(b,domain(b))) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
product(b,domain(b),compose(b,domain(b))),
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(b,domain(b),b) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
product(b,domain(b),b),
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(b,domain(b),b)
| ~ product(b,domain(b),compose(b,domain(b)))
| ( b = compose(b,domain(b)) ) )
<=> ( ~ ! [W: $i,Z: $i,Y: $i,X: $i] :
( ~ product(X,Y,Z)
| ~ product(X,Y,W)
| ( Z = W ) )
| ~ product(b,domain(b),b)
| ~ product(b,domain(b),compose(b,domain(b)))
| ( b = compose(b,domain(b)) ) ) ),
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(b,domain(b),b)
| ~ product(b,domain(b),compose(b,domain(b)))
| ( b = compose(b,domain(b)) ) ),
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(b,domain(b),b)
| ~ product(b,domain(b),compose(b,domain(b)))
| ( b = compose(b,domain(b)) ) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
b = compose(b,domain(b)),
inference(unit_resolution,[status(thm)],[42,39,29,20]) ).
tff(44,plain,
compose(b,domain(b)) = b,
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( defined(compose(b,domain(b)),c)
<=> defined(b,c) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( defined(b,c)
<=> defined(compose(b,domain(b)),c) ),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( defined(b,c)
<=> defined(b,c) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
defined(b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_bc_exists) ).
tff(49,plain,
defined(b,c),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
defined(compose(b,domain(b)),c),
inference(modus_ponens,[status(thm)],[49,46]) ).
tff(51,plain,
( product(compose(b,domain(b)),domain(b),compose(b,domain(b)))
<=> product(b,domain(b),b) ),
inference(monotonicity,[status(thm)],[44,44]) ).
tff(52,plain,
( product(b,domain(b),b)
<=> product(compose(b,domain(b)),domain(b),compose(b,domain(b))) ),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
product(compose(b,domain(b)),domain(b),compose(b,domain(b))),
inference(modus_ponens,[status(thm)],[29,52]) ).
tff(54,plain,
( defined(a,b)
<=> defined(a,b) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
defined(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assume_ab_exists) ).
tff(56,plain,
defined(a,b),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(a,b)
| product(a,b,compose(a,b)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(a,b)
| product(a,b,compose(a,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(a,b)
| product(a,b,compose(a,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(a,b)
| product(a,b,compose(a,b)) ),
inference(modus_ponens,[status(thm)],[58,57]) ).
tff(60,plain,
product(a,b,compose(a,b)),
inference(unit_resolution,[status(thm)],[59,16,56]) ).
tff(61,plain,
^ [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
refl(
( ( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
<=> ( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
^ [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
<=> ( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
( ( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz) )
<=> ( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz) ) )),
rewrite(
( ( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz) )
<=> ( ~ defined(X,Yz)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
( ( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz) )
<=> ( ~ defined(X,Yz)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
( ( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz)
| defined(Xy,Z) )
<=> ( ~ defined(X,Yz)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| defined(Xy,Z) ) )),
rewrite(
( ( ~ defined(X,Yz)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| defined(Xy,Z) )
<=> ( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
( ( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz)
| defined(Xy,Z) )
<=> ( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz)
| defined(Xy,Z) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,axiom,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| ~ defined(X,Yz)
| defined(Xy,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom4) ).
tff(67,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[67,63]) ).
tff(69,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[69,62]) ).
tff(71,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(a,b)
| ~ product(a,b,compose(a,b))
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(a,b)
| ~ product(a,b,compose(a,b))
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ defined(a,b)
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b)
| ~ product(a,b,compose(a,b)) )
<=> ( ~ defined(a,b)
| ~ product(a,b,compose(a,b))
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b) ) ),
inference(rewrite,[status(thm)],]) ).
tff(73,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(a,b)
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b)
| ~ product(a,b,compose(a,b)) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(a,b)
| ~ product(a,b,compose(a,b))
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(a,b)
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b)
| ~ product(a,b,compose(a,b)) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(a,b)
| ~ product(a,b,compose(a,b))
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(a,b)
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b)
| ~ product(a,b,compose(a,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(76,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ defined(X,Yz)
| defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| ~ defined(a,b)
| ~ product(a,b,compose(a,b))
| defined(compose(a,b),domain(b))
| ~ product(b,domain(b),b) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
defined(compose(a,b),domain(b)),
inference(unit_resolution,[status(thm)],[76,70,56,60,29]) ).
tff(78,plain,
^ [X: $i] :
refl(
( identity_map(domain(X))
<=> identity_map(domain(X)) )),
inference(bind,[status(th)],]) ).
tff(79,plain,
( ! [X: $i] : identity_map(domain(X))
<=> ! [X: $i] : identity_map(domain(X)) ),
inference(quant_intro,[status(thm)],[78]) ).
tff(80,plain,
( ! [X: $i] : identity_map(domain(X))
<=> ! [X: $i] : identity_map(domain(X)) ),
inference(rewrite,[status(thm)],]) ).
tff(81,axiom,
! [X: $i] : identity_map(domain(X)),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',domain_is_an_identity_map) ).
tff(82,plain,
! [X: $i] : identity_map(domain(X)),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
! [X: $i] : identity_map(domain(X)),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [X: $i] : identity_map(domain(X)),
inference(modus_ponens,[status(thm)],[83,79]) ).
tff(85,plain,
( ~ ! [X: $i] : identity_map(domain(X))
| identity_map(domain(b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
identity_map(domain(b)),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,c)
| product(b,c,compose(b,c)) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,c)
| product(b,c,compose(b,c)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,c)
| product(b,c,compose(b,c)) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [Y: $i,X: $i] :
( ~ defined(X,Y)
| product(X,Y,compose(X,Y)) )
| ~ defined(b,c)
| product(b,c,compose(b,c)) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
product(b,c,compose(b,c)),
inference(unit_resolution,[status(thm)],[89,16,49]) ).
tff(91,plain,
( ~ defined(a,compose(b,c))
<=> ~ defined(a,compose(b,c)) ),
inference(rewrite,[status(thm)],]) ).
tff(92,axiom,
~ defined(a,compose(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_bc_exists) ).
tff(93,plain,
~ defined(a,compose(b,c)),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
^ [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
refl(
( ( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
<=> ( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) ),
inference(rewrite,[status(thm)],]) ).
tff(97,plain,
^ [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
trans(
monotonicity(
rewrite(
( ( ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz)
| ~ defined(Xy,Z) )
<=> ( ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
( ( ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz)
| ~ defined(Xy,Z)
| defined(X,Yz) )
<=> ( ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| defined(X,Yz) ) )),
rewrite(
( ( ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy)
| defined(X,Yz) )
<=> ( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
( ( ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz)
| ~ defined(Xy,Z)
| defined(X,Yz) )
<=> ( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz)
| ~ defined(Xy,Z)
| defined(X,Yz) )
<=> ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( ~ product(X,Y,Xy)
| ~ product(Y,Z,Yz)
| ~ defined(Xy,Z)
| defined(X,Yz) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom1) ).
tff(100,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| defined(a,compose(b,c))
| ~ defined(compose(a,b),c)
| ~ product(b,c,compose(b,c))
| ~ product(a,b,compose(a,b)) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| defined(a,compose(b,c))
| ~ defined(compose(a,b),c)
| ~ product(b,c,compose(b,c))
| ~ product(a,b,compose(a,b)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(105,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| defined(a,compose(b,c))
| ~ defined(compose(a,b),c)
| ~ product(b,c,compose(b,c))
| ~ product(a,b,compose(a,b)) ),
inference(quant_inst,[status(thm)],]) ).
tff(106,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i,Yz: $i] :
( defined(X,Yz)
| ~ defined(Xy,Z)
| ~ product(Y,Z,Yz)
| ~ product(X,Y,Xy) )
| defined(a,compose(b,c))
| ~ defined(compose(a,b),c)
| ~ product(b,c,compose(b,c))
| ~ product(a,b,compose(a,b)) ),
inference(modus_ponens,[status(thm)],[105,104]) ).
tff(107,plain,
~ defined(compose(a,b),c),
inference(unit_resolution,[status(thm)],[106,103,93,60,90]) ).
tff(108,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(109,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)],[108]) ).
tff(110,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(111,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(112,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)],[111]) ).
tff(113,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| ~ defined(Y,Z)
| ~ identity_map(Y)
| defined(X,Z) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT001-0.ax',category_theory_axiom6) ).
tff(114,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ),
inference(modus_ponens,[status(thm)],[113,112]) ).
tff(115,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ),
inference(skolemize,[status(sab)],[115]) ).
tff(117,plain,
! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) ),
inference(modus_ponens,[status(thm)],[116,109]) ).
tff(118,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(compose(a,b),c)
| ~ defined(compose(a,b),domain(b))
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(compose(a,b),c)
| ~ defined(compose(a,b),domain(b))
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(119,plain,
( ( ~ defined(compose(a,b),domain(b))
| defined(compose(a,b),c)
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) )
<=> ( defined(compose(a,b),c)
| ~ defined(compose(a,b),domain(b))
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(120,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| ~ defined(compose(a,b),domain(b))
| defined(compose(a,b),c)
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(compose(a,b),c)
| ~ defined(compose(a,b),domain(b))
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) ) ),
inference(monotonicity,[status(thm)],[119]) ).
tff(121,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| ~ defined(compose(a,b),domain(b))
| defined(compose(a,b),c)
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(compose(a,b),c)
| ~ defined(compose(a,b),domain(b))
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) ) ),
inference(transitivity,[status(thm)],[120,118]) ).
tff(122,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| ~ defined(compose(a,b),domain(b))
| defined(compose(a,b),c)
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) ),
inference(quant_inst,[status(thm)],]) ).
tff(123,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( ~ defined(X,Y)
| defined(X,Z)
| ~ identity_map(Y)
| ~ defined(Y,Z) )
| defined(compose(a,b),c)
| ~ defined(compose(a,b),domain(b))
| ~ identity_map(domain(b))
| ~ defined(domain(b),c) ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
~ defined(domain(b),c),
inference(unit_resolution,[status(thm)],[123,117,107,86,77]) ).
tff(125,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(126,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)],[125]) ).
tff(127,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(128,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(129,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)],[128]) ).
tff(130,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(131,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[130,129]) ).
tff(132,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[131,127]) ).
tff(133,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(skolemize,[status(sab)],[132]) ).
tff(134,plain,
! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) ),
inference(modus_ponens,[status(thm)],[133,126]) ).
tff(135,plain,
( ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(domain(b),c)
| ~ defined(compose(b,domain(b)),c)
| ~ product(compose(b,domain(b)),domain(b),compose(b,domain(b))) )
<=> ( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(domain(b),c)
| ~ defined(compose(b,domain(b)),c)
| ~ product(compose(b,domain(b)),domain(b),compose(b,domain(b))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(136,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(domain(b),c)
| ~ defined(compose(b,domain(b)),c)
| ~ product(compose(b,domain(b)),domain(b),compose(b,domain(b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(137,plain,
( ~ ! [Xy: $i,Z: $i,Y: $i,X: $i] :
( defined(Y,Z)
| ~ defined(Xy,Z)
| ~ product(X,Y,Xy) )
| defined(domain(b),c)
| ~ defined(compose(b,domain(b)),c)
| ~ product(compose(b,domain(b)),domain(b),compose(b,domain(b))) ),
inference(modus_ponens,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ defined(compose(b,domain(b)),c)
| ~ product(compose(b,domain(b)),domain(b),compose(b,domain(b))) ),
inference(unit_resolution,[status(thm)],[137,134,124]) ).
tff(139,plain,
$false,
inference(unit_resolution,[status(thm)],[138,53,50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : CAT018-1 : TPTP v8.1.0. Released v1.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n008.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 : Tue Aug 30 06:32:10 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.41 % SZS status Unsatisfiable
% 0.12/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------