%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET606+3 : 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 : n019.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 03:32:20 PM UTC 2025
% Result : Theorem 97.48s 12.61s
% Output : CNFRefutation 97.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 5 unt; 0 def)
% Number of atoms : 78 ( 11 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 79 ( 34 ~; 39 |; 2 &)
% ( 3 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 3 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_difference_into_intersection,plain,
! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_difference_into_intersection) ).
fof(prove_difference_into_intersection_negated,plain,
~ ! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
inference(negate_conjecture,[status(cth)],[prove_difference_into_intersection]) ).
cnf(22,plain,
difference(sK4,intersection(sK4,sK5)) != difference(sK4,sK5),
inference(cnf,[status(esa)],[prove_difference_into_intersection_negated]) ).
cnf(l0,plain,
difference(sK4,intersection(sK4,sK5)) != difference(sK4,sK5),
inference(instantiation,[status(thm)],[22]) ).
fof(member_equal,plain,
! [B,C] :
( ! [D] :
( member(D,B)
<=> member(D,C) )
=> B = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_equal) ).
cnf(1,plain,
( ~ member(sK1(X0,X1),X0)
| ~ member(sK1(X0,X1),X1)
| X0 = X1 ),
inference(cnf,[status(esa)],[member_equal]) ).
cnf(l1,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,intersection(sK4,sK5)))
| ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5))
| difference(sK4,intersection(sK4,sK5)) = difference(sK4,sK5) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(0,plain,
( X0 = X1
| member(sK1(X0,X1),X0)
| member(sK1(X0,X1),X1) ),
inference(cnf,[status(esa)],[member_equal]) ).
cnf(l3,plain,
( difference(sK4,intersection(sK4,sK5)) = difference(sK4,sK5)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,intersection(sK4,sK5)))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[0]) ).
fof(difference_defn,plain,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',difference_defn) ).
cnf(7,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l5,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,intersection(sK4,sK5)))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK4)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(difference(sK4,intersection(sK4,sK5)),sK4)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(6,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l24,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK4)
| ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(difference(sK4,intersection(sK4,sK5)),sK4)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(5,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l25,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,intersection(sK4,sK5)))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK4) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l2,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK4)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),intersection(sK4,sK5))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[7]) ).
fof(intersection_defn,plain,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',intersection_defn) ).
cnf(4,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l16,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK4)
| ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK5)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),intersection(sK4,sK5)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l70,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),intersection(sK4,sK5))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(intersection(sK4,sK5),difference(sK4,sK5))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l19,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK4)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK5)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l68,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK4)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(difference(sK4,sK5),sK4)) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(l69,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(difference(sK4,sK5),sK4))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l113,plain,
( difference(sK4,intersection(sK4,sK5)) = difference(sK4,sK5)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,intersection(sK4,sK5)))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l18,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),intersection(sK4,sK5))
| ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,intersection(sK4,sK5))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l92,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5))
| ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(intersection(sK4,sK5),difference(sK4,sK5))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l95,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK5)
| ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l102,plain,
( difference(sK4,intersection(sK4,sK5)) = difference(sK4,sK5)
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,intersection(sK4,sK5)))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l90,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),difference(sK4,sK5))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK4) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(3,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l97,plain,
( ~ member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),intersection(sK4,sK5))
| member(sK1(difference(sK4,intersection(sK4,sK5)),difference(sK4,sK5)),sK5) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l5,l24,l25,l2,l16,l70,l19,l68,l69,l113,l18,l92,l95,l102,l90,l97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET606+3 : TPTP v9.0.0. Released v2.2.0.
% 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n019.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 22:06:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % 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: 5
% 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: 3
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.19/0.38 % launching worker at depth: 11
% 6.06/1.12 % launching worker at depth: 12
% 97.48/12.61 % SZS status Theorem for theBenchmark
% 97.48/12.61 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------