%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET792+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 : 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 03:32:41 PM UTC 2025
% Result : Theorem 12.06s 1.85s
% Output : CNFRefutation 12.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 10 unt; 0 def)
% Number of atoms : 90 ( 6 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 93 ( 35 ~; 34 |; 12 &)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 42 ( 1 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV4,plain,
! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> min(M,R,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV4) ).
fof(thIV4_negated,plain,
~ ! [R,E,M] :
( ( order(R,E)
& least(M,R,E) )
=> min(M,R,E) ),
inference(negate_conjecture,[status(cth)],[thIV4]) ).
cnf(59,plain,
least(sK19,sK17,sK18),
inference(cnf,[status(esa)],[thIV4_negated]) ).
cnf(l0,plain,
least(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[59]) ).
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(l1,plain,
( ~ member(sK14(sK17,sK18,sK19),sK18)
| ~ least(sK19,sK17,sK18)
| apply(sK17,sK19,sK14(sK17,sK18,sK19)) ),
inference(instantiation,[status(thm)],[33]) ).
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(l4,plain,
( ~ order(sK17,sK18)
| ~ member(sK19,sK18)
| ~ member(sK14(sK17,sK18,sK19),sK18)
| ~ apply(sK17,sK19,sK14(sK17,sK18,sK19))
| ~ apply(sK17,sK14(sK17,sK18,sK19),sK19)
| sK19 = sK14(sK17,sK18,sK19) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(58,plain,
order(sK17,sK18),
inference(cnf,[status(esa)],[thIV4_negated]) ).
cnf(l5,plain,
order(sK17,sK18),
inference(instantiation,[status(thm)],[58]) ).
fof(min,plain,
! [R,E,M] :
( min(M,R,E)
<=> ( member(M,E)
& ! [X] :
( ( member(X,E)
& apply(R,X,M) )
=> M = X ) ) ),
file('Axioms/SET006+3.ax',min) ).
cnf(43,plain,
( ~ member(X0,X1)
| member(sK14(X2,X1,X0),X1)
| min(X0,X2,X1) ),
inference(cnf,[status(esa)],[min]) ).
cnf(l128,plain,
( ~ member(sK19,sK18)
| member(sK14(sK17,sK18,sK19),sK18)
| min(sK19,sK17,sK18) ),
inference(instantiation,[status(thm)],[43]) ).
cnf(44,plain,
( ~ member(X0,X1)
| apply(X2,sK14(X2,X1,X0),X0)
| min(X0,X2,X1) ),
inference(cnf,[status(esa)],[min]) ).
cnf(l31,plain,
( ~ member(sK19,sK18)
| apply(sK17,sK14(sK17,sK18,sK19),sK19)
| min(sK19,sK17,sK18) ),
inference(instantiation,[status(thm)],[44]) ).
cnf(32,plain,
( ~ least(X0,X1,X2)
| member(X0,X2) ),
inference(cnf,[status(esa)],[least]) ).
cnf(l129,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l13,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l240,plain,
( ~ member(sK19,sK18)
| member(sK14(sK17,sK18,sK19),sK18)
| min(sK19,sK17,sK18) ),
inference(instantiation,[status(thm)],[43]) ).
cnf(60,plain,
~ min(sK19,sK17,sK18),
inference(cnf,[status(esa)],[thIV4_negated]) ).
cnf(l193,plain,
~ min(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(l34,plain,
~ min(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(l252,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l32,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l244,plain,
~ min(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(45,plain,
( X0 != sK14(X1,X2,X0)
| ~ member(X0,X2)
| min(X0,X1,X2) ),
inference(cnf,[status(esa)],[min]) ).
cnf(l300,plain,
( sK19 != sK14(sK17,sK18,sK19)
| ~ member(sK19,sK18)
| min(sK19,sK17,sK18) ),
inference(instantiation,[status(thm)],[45]) ).
cnf(l303,plain,
( ~ least(sK19,sK17,sK18)
| member(sK19,sK18) ),
inference(instantiation,[status(thm)],[32]) ).
cnf(l301,plain,
~ min(sK19,sK17,sK18),
inference(instantiation,[status(thm)],[60]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l4,l5,l128,l31,l129,l13,l240,l193,l34,l252,l32,l244,l300,l303,l301]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET792+4 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n024.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Jul 21 22:43:04 EDT 2025
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.36 % launching worker at depth: 10
% 0.21/0.46 % launching worker at depth: 11
% 12.06/1.85 % SZS status Theorem for theBenchmark
% 12.06/1.85 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------