%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET790+4 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n023.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 03:32:40 PM UTC 2025
% Result : Theorem 3.94s 0.87s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 70 ( 7 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 67 ( 24 ~; 21 |; 10 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 31 ( 1 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV2,plain,
! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV2) ).
fof(thIV2_negated,plain,
~ ! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> ! [X] :
( least(X,R,E)
=> M = X ) ),
inference(negate_conjecture,[status(cth)],[thIV2]) ).
cnf(58,plain,
order(sK17,sK18),
inference(cnf,[status(esa)],[thIV2_negated]) ).
cnf(l0,plain,
order(sK17,sK18),
inference(instantiation,[status(thm)],[58]) ).
fof(order,plain,
! [R,E] :
( order(R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,X) )
& ! [X,Y] :
( ( member(X,E)
& member(Y,E) )
=> ( ( apply(R,X,Y)
& apply(R,Y,X) )
=> X = Y ) )
& ! [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+3.ax',order) ).
cnf(1,plain,
( ~ order(X0,X1)
| ~ member(X2,X1)
| ~ member(X3,X1)
| ~ apply(X0,X2,X3)
| ~ apply(X0,X3,X2)
| X2 = X3 ),
inference(cnf,[status(esa)],[order]) ).
cnf(l1,plain,
( ~ order(sK17,sK18)
| ~ member(sK20,sK18)
| ~ member(sK19,sK18)
| ~ apply(sK17,sK20,sK19)
| ~ apply(sK17,sK19,sK20)
| sK20 = sK19 ),
inference(instantiation,[status(thm)],[1]) ).
fof(least,plain,
! [R,E,M] :
( least(M,R,E)
<=> ( member(M,E)
& ! [X] :
( member(X,E)
=> apply(R,M,X) ) ) ),
file('Axioms/SET006+3.ax',least) ).
cnf(33,plain,
( ~ member(X0,X1)
| ~ least(X2,X3,X1)
| apply(X3,X2,X0) ),
inference(cnf,[status(esa)],[least]) ).
cnf(l71,plain,
( ~ member(sK19,sK18)
| ~ least(sK20,sK17,sK18)
| apply(sK17,sK20,sK19) ),
inference(instantiation,[status(thm)],[33]) ).
cnf(l120,plain,
( ~ member(sK20,sK18)
| ~ least(sK19,sK17,sK18)
| apply(sK17,sK19,sK20) ),
inference(instantiation,[status(thm)],[33]) ).
cnf(60,plain,
least(sK20,sK17,sK18),
inference(cnf,[status(esa)],[thIV2_negated]) ).
cnf(l82,plain,
least(sK20,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(32,plain,
( ~ least(X0,X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[least]) ).
cnf(l2,plain,
( ~ least(sK20,sK17,sK18)
| member(sK20,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l3,plain,
least(sK20,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(l122,plain,
( ~ least(sK20,sK17,sK18)
| member(sK20,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(59,plain,
least(sK19,sK17,sK18),
inference(cnf,[status(esa)],[thIV2_negated]) ).
cnf(l128,plain,
least(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[59]) ).
cnf(l145,plain,
least(sK20,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(l4,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l5,plain,
least(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[59]) ).
cnf(l140,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l150,plain,
least(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[59]) ).
cnf(61,plain,
sK19 != sK20,
inference(cnf,[status(esa)],[thIV2_negated]) ).
cnf(l123,plain,
sK19 != sK20,
inference(instantiation,[status(thm)],[61]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l71,l120,l82,l2,l3,l122,l128,l145,l4,l5,l140,l150,l123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : SET790+4 : TPTP v9.0.0. Released v3.2.0.
% 0.08/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n023.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 : Mon Jul 21 22:42:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.35 % launching worker at depth: 10
% 0.18/0.47 % launching worker at depth: 11
% 3.94/0.87 % SZS status Theorem for theBenchmark
% 3.94/0.87 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------