%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET809+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 : Fri Jul 25 03:32:42 PM UTC 2025
% Result : Theorem 90.91s 11.80s
% Output : CNFRefutation 90.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 5 unt; 0 def)
% Number of atoms : 74 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 78 ( 31 ~; 24 |; 11 &)
% ( 5 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 36 ( 1 sgn 19 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thV2,plain,
! [A] :
( member(A,on)
=> ~ member(A,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thV2) ).
fof(thV2_negated,plain,
~ ! [A] :
( member(A,on)
=> ~ member(A,A) ),
inference(negate_conjecture,[status(cth)],[thV2]) ).
cnf(64,plain,
member(sK16,on),
inference(cnf,[status(esa)],[thV2_negated]) ).
cnf(l0,plain,
member(sK16,on),
inference(instantiation,[status(thm)],[64]) ).
fof(difference,plain,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
file('Axioms/SET006+0.ax',difference) ).
cnf(17,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference]) ).
cnf(l1,plain,
( ~ member(sK16,on)
| member(sK16,sK16)
| member(sK16,difference(on,sK16)) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l15,plain,
( ~ member(sK16,difference(on,sK16))
| member(sK16,sK16)
| member(sK16,difference(difference(on,sK16),sK16)) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(16,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf,[status(esa)],[difference]) ).
cnf(l22,plain,
( ~ member(sK16,sK16)
| ~ member(sK16,difference(difference(on,sK16),sK16)) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(l48,plain,
( ~ member(sK16,sK16)
| ~ member(sK16,difference(on,sK16)) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(65,plain,
member(sK16,sK16),
inference(cnf,[status(esa)],[thV2_negated]) ).
cnf(l27,plain,
member(sK16,sK16),
inference(instantiation,[status(thm)],[65]) ).
fof(strict_order,plain,
! [R,E] :
( strict_order(R,E)
<=> ( ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ~ ( apply(R,X,Y)
& apply(R,Y,X) ) )
& ! [X,Y,Z] :
( ( member(X,E)
& member(Y,E)
& member(Z,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,Z) )
=> apply(R,X,Z) ) ) ) ),
file('Axioms/SET006+4.ax',strict_order) ).
cnf(46,plain,
( ~ member(X0,X1)
| ~ member(X2,X1)
| ~ strict_order(X3,X1)
| ~ apply(X3,X0,X2)
| ~ apply(X3,X2,X0) ),
inference(cnf,[status(esa)],[strict_order]) ).
cnf(l2,plain,
( ~ member(sK16,sK16)
| ~ member(sK16,sK16)
| ~ strict_order(member_predicate,sK16)
| ~ apply(member_predicate,sK16,sK16)
| ~ apply(member_predicate,sK16,sK16) ),
inference(instantiation,[status(thm)],[46]) ).
fof(strict_well_order,plain,
! [R,E] :
( strict_well_order(R,E)
<=> ( strict_order(R,E)
& ! [A] :
( ( subset(A,E)
& ? [X] : member(X,A) )
=> ? [Y] : least(Y,R,A) ) ) ),
file('Axioms/SET006+4.ax',strict_well_order) ).
cnf(34,plain,
( ~ strict_well_order(X0,X1)
| strict_order(X0,X1) ),
inference(cnf,[status(esa)],[strict_well_order]) ).
cnf(l51,plain,
( ~ strict_well_order(member_predicate,sK16)
| strict_order(member_predicate,sK16) ),
inference(instantiation,[status(thm)],[34]) ).
fof(rel_member,plain,
! [X,Y] :
( apply(member_predicate,X,Y)
<=> member(X,Y) ),
file('Axioms/SET006+4.ax',rel_member) ).
cnf(45,plain,
( ~ member(X0,X1)
| apply(member_predicate,X0,X1) ),
inference(cnf,[status(esa)],[rel_member]) ).
cnf(l90,plain,
( ~ member(sK16,sK16)
| apply(member_predicate,sK16,sK16) ),
inference(instantiation,[status(thm)],[45]) ).
cnf(l93,plain,
( ~ member(sK16,sK16)
| apply(member_predicate,sK16,sK16) ),
inference(instantiation,[status(thm)],[45]) ).
fof(ordinal_number,plain,
! [A] :
( member(A,on)
<=> ( set(A)
& strict_well_order(member_predicate,A)
& ! [X] :
( member(X,A)
=> subset(X,A) ) ) ),
file('Axioms/SET006+4.ax',ordinal_number) ).
cnf(30,plain,
( ~ member(X0,on)
| strict_well_order(member_predicate,X0) ),
inference(cnf,[status(esa)],[ordinal_number]) ).
cnf(l53,plain,
( ~ member(sK16,on)
| strict_well_order(member_predicate,sK16) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l15,l22,l48,l27,l2,l51,l90,l93,l53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET809+4 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 22:44:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 9
% 0.19/0.36 % launching worker at depth: 10
% 1.89/0.56 % launching worker at depth: 11
% 90.91/11.80 % SZS status Theorem for theBenchmark
% 90.91/11.80 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------