%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET776+4 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n024.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 03:32:39 PM UTC 2025
% Result : Theorem 7.35s 1.28s
% Output : CNFRefutation 7.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 2
% Syntax : Number of formulae : 35 ( 25 unt; 0 def)
% Number of atoms : 99 ( 0 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 97 ( 33 ~; 30 |; 20 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 33 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIII12,plain,
! [E,P,R] :
( ( pre_order(P,E)
& ! [A,B] :
( ( member(A,E)
& member(B,E) )
=> ( apply(R,A,B)
<=> ( apply(P,A,B)
& apply(P,B,A) ) ) ) )
=> ! [X1,X2,Y1,Y2] :
( ( member(X1,E)
& member(X2,E)
& member(Y1,E)
& member(Y2,E) )
=> ( ( apply(R,X1,Y1)
& apply(R,X2,Y2)
& apply(P,X1,X2) )
=> apply(P,Y1,Y2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII12) ).
fof(thIII12_negated,plain,
~ ! [E,P,R] :
( ( pre_order(P,E)
& ! [A,B] :
( ( member(A,E)
& member(B,E) )
=> ( apply(R,A,B)
<=> ( apply(P,A,B)
& apply(P,B,A) ) ) ) )
=> ! [X1,X2,Y1,Y2] :
( ( member(X1,E)
& member(X2,E)
& member(Y1,E)
& member(Y2,E) )
=> ( ( apply(R,X1,Y1)
& apply(R,X2,Y2)
& apply(P,X1,X2) )
=> apply(P,Y1,Y2) ) ) ),
inference(negate_conjecture,[status(cth)],[thIII12]) ).
cnf(73,plain,
pre_order(sK24,sK23),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l0,plain,
pre_order(sK24,sK23),
inference(instantiation,[status(thm)],[73]) ).
fof(pre_order,plain,
! [R,E] :
( pre_order(R,E)
<=> ( ! [X] :
( member(X,E)
=> apply(R,X,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+2.ax',pre_order) ).
cnf(64,plain,
( ~ member(X0,X1)
| ~ member(X2,X1)
| ~ member(X3,X1)
| ~ pre_order(X4,X1)
| ~ apply(X4,X0,X2)
| ~ apply(X4,X2,X3)
| apply(X4,X0,X3) ),
inference(cnf,[status(esa)],[pre_order]) ).
cnf(l1,plain,
( ~ member(sK28,sK23)
| ~ member(sK26,sK23)
| ~ member(sK27,sK23)
| ~ pre_order(sK24,sK23)
| ~ apply(sK24,sK28,sK26)
| ~ apply(sK24,sK26,sK27)
| apply(sK24,sK28,sK27) ),
inference(instantiation,[status(thm)],[64]) ).
cnf(83,plain,
apply(sK24,sK26,sK27),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l11,plain,
apply(sK24,sK26,sK27),
inference(instantiation,[status(thm)],[83]) ).
cnf(78,plain,
member(sK27,sK23),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l3,plain,
member(sK27,sK23),
inference(instantiation,[status(thm)],[78]) ).
cnf(l34,plain,
( ~ member(sK28,sK23)
| ~ member(sK27,sK23)
| ~ member(sK29,sK23)
| ~ pre_order(sK24,sK23)
| ~ apply(sK24,sK28,sK27)
| ~ apply(sK24,sK27,sK29)
| apply(sK24,sK28,sK29) ),
inference(instantiation,[status(thm)],[64]) ).
cnf(84,plain,
~ apply(sK24,sK28,sK29),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l138,plain,
~ apply(sK24,sK28,sK29),
inference(instantiation,[status(thm)],[84]) ).
cnf(74,plain,
( ~ member(X0,sK23)
| ~ member(X1,sK23)
| ~ apply(sK25,X0,X1)
| apply(sK24,X0,X1) ),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l134,plain,
( ~ member(sK27,sK23)
| ~ member(sK29,sK23)
| ~ apply(sK25,sK27,sK29)
| apply(sK24,sK27,sK29) ),
inference(instantiation,[status(thm)],[74]) ).
cnf(80,plain,
member(sK29,sK23),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l45,plain,
member(sK29,sK23),
inference(instantiation,[status(thm)],[80]) ).
cnf(79,plain,
member(sK28,sK23),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l56,plain,
member(sK28,sK23),
inference(instantiation,[status(thm)],[79]) ).
cnf(l2,plain,
member(sK28,sK23),
inference(instantiation,[status(thm)],[79]) ).
cnf(82,plain,
apply(sK25,sK27,sK29),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l139,plain,
apply(sK25,sK27,sK29),
inference(instantiation,[status(thm)],[82]) ).
cnf(l135,plain,
member(sK29,sK23),
inference(instantiation,[status(thm)],[80]) ).
cnf(77,plain,
member(sK26,sK23),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l5,plain,
member(sK26,sK23),
inference(instantiation,[status(thm)],[77]) ).
cnf(l50,plain,
member(sK27,sK23),
inference(instantiation,[status(thm)],[78]) ).
cnf(75,plain,
( ~ member(X0,sK23)
| ~ member(X1,sK23)
| ~ apply(sK25,X0,X1)
| apply(sK24,X1,X0) ),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l4,plain,
( ~ member(sK26,sK23)
| ~ member(sK28,sK23)
| ~ apply(sK25,sK26,sK28)
| apply(sK24,sK28,sK26) ),
inference(instantiation,[status(thm)],[75]) ).
cnf(l137,plain,
member(sK27,sK23),
inference(instantiation,[status(thm)],[78]) ).
cnf(81,plain,
apply(sK25,sK26,sK28),
inference(cnf,[status(esa)],[thIII12_negated]) ).
cnf(l53,plain,
apply(sK25,sK26,sK28),
inference(instantiation,[status(thm)],[81]) ).
cnf(l55,plain,
member(sK26,sK23),
inference(instantiation,[status(thm)],[77]) ).
cnf(l6,plain,
member(sK28,sK23),
inference(instantiation,[status(thm)],[79]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l11,l3,l34,l138,l134,l45,l56,l2,l139,l135,l5,l50,l4,l137,l53,l55,l6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SET776+4 : TPTP v9.0.0. Released v2.2.0.
% 0.04/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n024.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 22:38:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 5
% 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: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.19/0.53 % launching worker at depth: 10
% 7.35/1.28 % SZS status Theorem for theBenchmark
% 7.35/1.28 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------