TSTP Solution File: PUZ130+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : PUZ130+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 : Sun Sep 18 14:11:31 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 57
% Syntax : Number of formulae : 117 ( 33 unt; 11 typ; 0 def)
% Number of atoms : 598 ( 64 equ)
% Maximal formula atoms : 16 ( 5 avg)
% Number of connectives : 763 ( 311 ~; 280 |; 36 &)
% ( 116 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 40 ( 40 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 8 >; 3 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 142 ( 126 !; 0 ?; 142 :)
% Comments :
%------------------------------------------------------------------------------
tff(hates_type,type,
hates: ( $i * $i ) > $o ).
tff(owner_of_type,type,
owner_of: $i > $i ).
tff(odie_type,type,
odie: $i ).
tff(garfield_type,type,
garfield: $i ).
tff(jon_type,type,
jon: $i ).
tff(owner_type,type,
owner: ( $i * $i ) > $o ).
tff(pet_type,type,
pet: $i > $o ).
tff(dog_type,type,
dog: $i > $o ).
tff(human_type,type,
human: $i > $o ).
tff(cat_type,type,
cat: $i > $o ).
tff(chased_type,type,
chased: ( $i * $i ) > $o ).
tff(1,plain,
^ [A: $i] :
refl(
( ( pet(A)
| ~ dog(A) )
<=> ( pet(A)
| ~ dog(A) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [A: $i] :
( pet(A)
| ~ dog(A) )
<=> ! [A: $i] :
( pet(A)
| ~ dog(A) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] :
( pet(A)
| ~ dog(A) )
<=> ! [A: $i] :
( pet(A)
| ~ dog(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
^ [A: $i] :
rewrite(
( ( dog(A)
=> pet(A) )
<=> ( pet(A)
| ~ dog(A) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [A: $i] :
( dog(A)
=> pet(A) )
<=> ! [A: $i] :
( pet(A)
| ~ dog(A) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [A: $i] :
( dog(A)
=> pet(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dog_pet_type) ).
tff(7,plain,
! [A: $i] :
( pet(A)
| ~ dog(A) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
! [A: $i] :
( pet(A)
| ~ dog(A) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
! [A: $i] :
( pet(A)
| ~ dog(A) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [A: $i] :
( pet(A)
| ~ dog(A) ),
inference(modus_ponens,[status(thm)],[9,2]) ).
tff(11,plain,
( dog(odie)
<=> dog(odie) ),
inference(rewrite,[status(thm)],]) ).
tff(12,axiom,
dog(odie),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odie_type) ).
tff(13,plain,
dog(odie),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
( ( ~ ! [A: $i] :
( pet(A)
| ~ dog(A) )
| pet(odie)
| ~ dog(odie) )
<=> ( ~ ! [A: $i] :
( pet(A)
| ~ dog(A) )
| pet(odie)
| ~ dog(odie) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ~ ! [A: $i] :
( pet(A)
| ~ dog(A) )
| pet(odie)
| ~ dog(odie) ),
inference(quant_inst,[status(thm)],]) ).
tff(16,plain,
( ~ ! [A: $i] :
( pet(A)
| ~ dog(A) )
| pet(odie)
| ~ dog(odie) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
pet(odie),
inference(unit_resolution,[status(thm)],[16,13,10]) ).
tff(18,plain,
^ [X: $i,Y: $i] :
refl(
( ( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
<=> ( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
<=> ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
^ [X: $i,Y: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( human(X)
& pet(Y) )
<=> ~ ( ~ human(X)
| ~ pet(Y) ) )),
( ~ ( human(X)
& pet(Y) )
<=> ~ ~ ( ~ human(X)
| ~ pet(Y) ) )),
rewrite(
( ~ ~ ( ~ human(X)
| ~ pet(Y) )
<=> ( ~ human(X)
| ~ pet(Y) ) )),
( ~ ( human(X)
& pet(Y) )
<=> ( ~ human(X)
| ~ pet(Y) ) )),
( ( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) )
<=> ( ~ human(X)
| ~ pet(Y)
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) ) )),
rewrite(
( ( ~ human(X)
| ~ pet(Y)
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) )
<=> ( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) ) )),
( ( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) )
<=> ( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [X: $i,Y: $i] :
( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) )
<=> ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [X: $i,Y: $i] :
( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) )
<=> ! [X: $i,Y: $i] :
( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( ( human(X)
& pet(Y) )
=> ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) )
<=> ( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [X: $i,Y: $i] :
( ( human(X)
& pet(Y) )
=> ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) )
<=> ! [X: $i,Y: $i] :
( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,axiom,
! [X: $i,Y: $i] :
( ( human(X)
& pet(Y) )
=> ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',owner_def) ).
tff(26,plain,
! [X: $i,Y: $i] :
( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [X: $i,Y: $i] :
( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) ),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
! [X: $i,Y: $i] :
( ~ ( human(X)
& pet(Y) )
| ( owner(X,Y)
<=> ( X = owner_of(Y) ) ) ),
inference(skolemize,[status(sab)],[27]) ).
tff(29,plain,
! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) ),
inference(modus_ponens,[status(thm)],[28,21]) ).
tff(30,plain,
! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) ),
inference(modus_ponens,[status(thm)],[29,19]) ).
tff(31,plain,
( human(jon)
<=> human(jon) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
human(jon),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',jon_type) ).
tff(33,plain,
human(jon),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ( owner(jon,odie)
<=> ( jon = owner_of(odie) ) )
| ~ pet(odie)
| ~ human(jon) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ( owner(jon,odie)
<=> ( jon = owner_of(odie) ) )
| ~ pet(odie)
| ~ human(jon) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ( owner(jon,odie)
<=> ( jon = owner_of(odie) ) )
| ~ pet(odie)
| ~ human(jon) ),
inference(quant_inst,[status(thm)],]) ).
tff(36,plain,
( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ( owner(jon,odie)
<=> ( jon = owner_of(odie) ) )
| ~ pet(odie)
| ~ human(jon) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
( owner(jon,odie)
<=> ( jon = owner_of(odie) ) ),
inference(unit_resolution,[status(thm)],[36,33,30,17]) ).
tff(38,plain,
( owner(jon,odie)
<=> owner(jon,odie) ),
inference(rewrite,[status(thm)],]) ).
tff(39,axiom,
owner(jon,odie),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',jon_o_owner_axiom) ).
tff(40,plain,
owner(jon,odie),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
( ~ ( owner(jon,odie)
<=> ( jon = owner_of(odie) ) )
| ~ owner(jon,odie)
| ( jon = owner_of(odie) ) ),
inference(tautology,[status(thm)],]) ).
tff(42,plain,
( ~ ( owner(jon,odie)
<=> ( jon = owner_of(odie) ) )
| ( jon = owner_of(odie) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
jon = owner_of(odie),
inference(unit_resolution,[status(thm)],[42,37]) ).
tff(44,plain,
owner_of(odie) = jon,
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
^ [A: $i] :
refl(
( ( pet(A)
| ~ cat(A) )
<=> ( pet(A)
| ~ cat(A) ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [A: $i] :
( pet(A)
| ~ cat(A) )
<=> ! [A: $i] :
( pet(A)
| ~ cat(A) ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [A: $i] :
( pet(A)
| ~ cat(A) )
<=> ! [A: $i] :
( pet(A)
| ~ cat(A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,plain,
^ [A: $i] :
rewrite(
( ( cat(A)
=> pet(A) )
<=> ( pet(A)
| ~ cat(A) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [A: $i] :
( cat(A)
=> pet(A) )
<=> ! [A: $i] :
( pet(A)
| ~ cat(A) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,axiom,
! [A: $i] :
( cat(A)
=> pet(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cat_pet_type) ).
tff(51,plain,
! [A: $i] :
( pet(A)
| ~ cat(A) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
! [A: $i] :
( pet(A)
| ~ cat(A) ),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
! [A: $i] :
( pet(A)
| ~ cat(A) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [A: $i] :
( pet(A)
| ~ cat(A) ),
inference(modus_ponens,[status(thm)],[53,46]) ).
tff(55,plain,
( cat(garfield)
<=> cat(garfield) ),
inference(rewrite,[status(thm)],]) ).
tff(56,axiom,
cat(garfield),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',garfield_type) ).
tff(57,plain,
cat(garfield),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
( ( ~ ! [A: $i] :
( pet(A)
| ~ cat(A) )
| pet(garfield)
| ~ cat(garfield) )
<=> ( ~ ! [A: $i] :
( pet(A)
| ~ cat(A) )
| pet(garfield)
| ~ cat(garfield) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ! [A: $i] :
( pet(A)
| ~ cat(A) )
| pet(garfield)
| ~ cat(garfield) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
( ~ ! [A: $i] :
( pet(A)
| ~ cat(A) )
| pet(garfield)
| ~ cat(garfield) ),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
pet(garfield),
inference(unit_resolution,[status(thm)],[60,57,54]) ).
tff(62,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ~ human(jon)
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ~ human(jon)
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield) ) ),
inference(rewrite,[status(thm)],]) ).
tff(63,plain,
( ( ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield)
| ~ human(jon) )
<=> ( ~ human(jon)
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield) ) ),
inference(rewrite,[status(thm)],]) ).
tff(64,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield)
| ~ human(jon) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ~ human(jon)
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield) ) ),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
( ( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield)
| ~ human(jon) )
<=> ( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ~ human(jon)
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield) ) ),
inference(transitivity,[status(thm)],[64,62]) ).
tff(66,plain,
( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield)
| ~ human(jon) ),
inference(quant_inst,[status(thm)],]) ).
tff(67,plain,
( ~ ! [X: $i,Y: $i] :
( ( owner(X,Y)
<=> ( X = owner_of(Y) ) )
| ~ pet(Y)
| ~ human(X) )
| ~ human(jon)
| ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ pet(garfield) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) ),
inference(unit_resolution,[status(thm)],[67,33,30,61]) ).
tff(69,plain,
( owner(jon,garfield)
<=> owner(jon,garfield) ),
inference(rewrite,[status(thm)],]) ).
tff(70,axiom,
owner(jon,garfield),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',jon_g_owner_axiom) ).
tff(71,plain,
owner(jon,garfield),
inference(modus_ponens,[status(thm)],[70,69]) ).
tff(72,plain,
( ~ ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ~ owner(jon,garfield)
| ( jon = owner_of(garfield) ) ),
inference(tautology,[status(thm)],]) ).
tff(73,plain,
( ~ ( owner(jon,garfield)
<=> ( jon = owner_of(garfield) ) )
| ( jon = owner_of(garfield) ) ),
inference(unit_resolution,[status(thm)],[72,71]) ).
tff(74,plain,
jon = owner_of(garfield),
inference(unit_resolution,[status(thm)],[73,68]) ).
tff(75,plain,
owner_of(garfield) = jon,
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
( hates(owner_of(garfield),owner_of(odie))
<=> hates(jon,jon) ),
inference(monotonicity,[status(thm)],[75,44]) ).
tff(77,plain,
( hates(jon,jon)
<=> hates(owner_of(garfield),owner_of(odie)) ),
inference(symmetry,[status(thm)],[76]) ).
tff(78,plain,
( ~ hates(jon,jon)
<=> ~ hates(owner_of(garfield),owner_of(odie)) ),
inference(monotonicity,[status(thm)],[77]) ).
tff(79,plain,
( ~ hates(jon,jon)
<=> ~ hates(jon,jon) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
~ hates(jon,jon),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',jon_conjecture) ).
tff(81,plain,
~ hates(jon,jon),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
~ hates(owner_of(garfield),owner_of(odie)),
inference(modus_ponens,[status(thm)],[81,78]) ).
tff(83,plain,
( chased(odie,garfield)
<=> chased(odie,garfield) ),
inference(rewrite,[status(thm)],]) ).
tff(84,axiom,
chased(odie,garfield),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',odie_chase_axiom) ).
tff(85,plain,
chased(odie,garfield),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
^ [X: $i,Y: $i] :
refl(
( ( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
<=> ( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) ) )),
inference(bind,[status(th)],]) ).
tff(87,plain,
( ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
<=> ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) ) ),
inference(quant_intro,[status(thm)],[86]) ).
tff(88,plain,
^ [X: $i,Y: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( cat(X)
& dog(Y) )
<=> ~ ( ~ cat(X)
| ~ dog(Y) ) )),
( ~ ( cat(X)
& dog(Y) )
<=> ~ ~ ( ~ cat(X)
| ~ dog(Y) ) )),
rewrite(
( ~ ~ ( ~ cat(X)
| ~ dog(Y) )
<=> ( ~ cat(X)
| ~ dog(Y) ) )),
( ~ ( cat(X)
& dog(Y) )
<=> ( ~ cat(X)
| ~ dog(Y) ) )),
( ( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) )
<=> ( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ cat(X)
| ~ dog(Y) ) )),
rewrite(
( ( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ cat(X)
| ~ dog(Y) )
<=> ( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) ) )),
( ( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) )
<=> ( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) )
<=> ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,plain,
( ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) )
<=> ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(91,plain,
^ [X: $i,Y: $i] :
trans(
monotonicity(
rewrite(
( ( chased(Y,X)
=> hates(owner_of(X),owner_of(Y)) )
<=> ( ~ chased(Y,X)
| hates(owner_of(X),owner_of(Y)) ) )),
( ( ( cat(X)
& dog(Y) )
=> ( chased(Y,X)
=> hates(owner_of(X),owner_of(Y)) ) )
<=> ( ( cat(X)
& dog(Y) )
=> ( ~ chased(Y,X)
| hates(owner_of(X),owner_of(Y)) ) ) )),
rewrite(
( ( ( cat(X)
& dog(Y) )
=> ( ~ chased(Y,X)
| hates(owner_of(X),owner_of(Y)) ) )
<=> ( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) ) )),
( ( ( cat(X)
& dog(Y) )
=> ( chased(Y,X)
=> hates(owner_of(X),owner_of(Y)) ) )
<=> ( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [X: $i,Y: $i] :
( ( cat(X)
& dog(Y) )
=> ( chased(Y,X)
=> hates(owner_of(X),owner_of(Y)) ) )
<=> ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,axiom,
! [X: $i,Y: $i] :
( ( cat(X)
& dog(Y) )
=> ( chased(Y,X)
=> hates(owner_of(X),owner_of(Y)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cat_chase_axiom) ).
tff(94,plain,
! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) ),
inference(modus_ponens,[status(thm)],[93,92]) ).
tff(95,plain,
! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) ),
inference(modus_ponens,[status(thm)],[94,90]) ).
tff(96,plain,
! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ chased(Y,X)
| ~ ( cat(X)
& dog(Y) ) ),
inference(skolemize,[status(sab)],[95]) ).
tff(97,plain,
! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) ),
inference(modus_ponens,[status(thm)],[96,89]) ).
tff(98,plain,
! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) ),
inference(modus_ponens,[status(thm)],[97,87]) ).
tff(99,plain,
( ( ~ ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
| ~ dog(odie)
| ~ cat(garfield)
| hates(owner_of(garfield),owner_of(odie))
| ~ chased(odie,garfield) )
<=> ( ~ ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
| ~ dog(odie)
| ~ cat(garfield)
| hates(owner_of(garfield),owner_of(odie))
| ~ chased(odie,garfield) ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,plain,
( ( hates(owner_of(garfield),owner_of(odie))
| ~ dog(odie)
| ~ chased(odie,garfield)
| ~ cat(garfield) )
<=> ( ~ dog(odie)
| ~ cat(garfield)
| hates(owner_of(garfield),owner_of(odie))
| ~ chased(odie,garfield) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ( ~ ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
| hates(owner_of(garfield),owner_of(odie))
| ~ dog(odie)
| ~ chased(odie,garfield)
| ~ cat(garfield) )
<=> ( ~ ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
| ~ dog(odie)
| ~ cat(garfield)
| hates(owner_of(garfield),owner_of(odie))
| ~ chased(odie,garfield) ) ),
inference(monotonicity,[status(thm)],[100]) ).
tff(102,plain,
( ( ~ ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
| hates(owner_of(garfield),owner_of(odie))
| ~ dog(odie)
| ~ chased(odie,garfield)
| ~ cat(garfield) )
<=> ( ~ ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
| ~ dog(odie)
| ~ cat(garfield)
| hates(owner_of(garfield),owner_of(odie))
| ~ chased(odie,garfield) ) ),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
( ~ ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
| hates(owner_of(garfield),owner_of(odie))
| ~ dog(odie)
| ~ chased(odie,garfield)
| ~ cat(garfield) ),
inference(quant_inst,[status(thm)],]) ).
tff(104,plain,
( ~ ! [X: $i,Y: $i] :
( hates(owner_of(X),owner_of(Y))
| ~ dog(Y)
| ~ chased(Y,X)
| ~ cat(X) )
| ~ dog(odie)
| ~ cat(garfield)
| hates(owner_of(garfield),owner_of(odie))
| ~ chased(odie,garfield) ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
hates(owner_of(garfield),owner_of(odie)),
inference(unit_resolution,[status(thm)],[104,57,13,98,85]) ).
tff(106,plain,
$false,
inference(unit_resolution,[status(thm)],[105,82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : PUZ130+1 : TPTP v8.1.0. Released v4.1.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n017.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 : Fri Sep 2 18:27:23 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.
% 0.13/0.40 % SZS status Theorem
% 0.13/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------