%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET011+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n021.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 03:31:04 PM UTC 2025
% Result : Theorem 252.93s 32.07s
% Output : CNFRefutation 252.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 13 unt; 0 def)
% Number of atoms : 96 ( 16 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 93 ( 43 ~; 42 |; 3 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 4 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_difference_difference_intersection,plain,
! [B,C] : difference(B,difference(B,C)) = intersection(B,C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_difference_difference_intersection) ).
fof(prove_difference_difference_intersection_negated,plain,
~ ! [B,C] : difference(B,difference(B,C)) = intersection(B,C),
inference(negate_conjecture,[status(cth)],[prove_difference_difference_intersection]) ).
cnf(20,plain,
difference(sK3,difference(sK3,sK4)) != intersection(sK3,sK4),
inference(cnf,[status(esa)],[prove_difference_difference_intersection_negated]) ).
cnf(l0,plain,
difference(sK3,difference(sK3,sK4)) != intersection(sK3,sK4),
inference(instantiation,[status(thm)],[20]) ).
fof(equal_member_defn,plain,
! [B,C] :
( B = C
<=> ! [D] :
( member(D,B)
<=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_member_defn) ).
cnf(16,plain,
( member(sK2(X0,X1),X0)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l1,plain,
( member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,difference(sK3,sK4)))
| difference(sK3,difference(sK3,sK4)) = intersection(sK3,sK4)
| sP0(intersection(sK3,sK4),difference(sK3,difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(19,plain,
( member(sK2(X0,X1),X1)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l3,plain,
( member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),intersection(sK3,sK4))
| ~ sP0(intersection(sK3,sK4),difference(sK3,difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[19]) ).
fof(intersection_defn,plain,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',intersection_defn) ).
cnf(2,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l2,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3))
| ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,difference(sK3,sK4)))
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),intersection(difference(difference(sK3,difference(sK3,sK4)),sK3),difference(sK3,difference(sK3,sK4)))) ),
inference(instantiation,[status(thm)],[2]) ).
fof(equal_defn,plain,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_defn) ).
cnf(8,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf,[status(esa)],[equal_defn]) ).
cnf(l390,plain,
( ~ subset(intersection(difference(difference(sK3,difference(sK3,sK4)),sK3),difference(sK3,difference(sK3,sK4))),intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)))
| ~ subset(intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)),intersection(difference(difference(sK3,difference(sK3,sK4)),sK3),difference(sK3,difference(sK3,sK4))))
| intersection(difference(difference(sK3,difference(sK3,sK4)),sK3),difference(sK3,difference(sK3,sK4))) = intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)) ),
inference(instantiation,[status(thm)],[8]) ).
fof(difference_defn,plain,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( member(D,B)
& ~ member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',difference_defn) ).
cnf(5,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l126,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,difference(sK3,sK4)))
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK3)
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(1,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l462,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)))
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(0,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l5,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),intersection(sK3,sK4))
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
fof(commutativity_of_intersection,plain,
! [B,C] : intersection(B,C) = intersection(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_intersection) ).
cnf(9,plain,
intersection(X0,X1) = intersection(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_intersection]) ).
cnf(l402,plain,
intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)) = intersection(difference(difference(sK3,difference(sK3,sK4)),sK3),difference(sK3,difference(sK3,sK4))),
inference(instantiation,[status(thm)],[9]) ).
fof(reflexivity_of_subset,plain,
! [B] : subset(B,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_of_subset) ).
cnf(13,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_of_subset]) ).
cnf(l413,plain,
subset(intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)),intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3))),
inference(instantiation,[status(thm)],[13]) ).
cnf(4,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l464,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK3)
| ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(3,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l468,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,difference(sK3,sK4)))
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l397,plain,
subset(intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)),intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3))),
inference(instantiation,[status(thm)],[13]) ).
cnf(l393,plain,
intersection(difference(sK3,difference(sK3,sK4)),difference(difference(sK3,difference(sK3,sK4)),sK3)) = intersection(difference(difference(sK3,difference(sK3,sK4)),sK3),difference(sK3,difference(sK3,sK4))),
inference(instantiation,[status(thm)],[9]) ).
cnf(l11,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK3)
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,sK4))
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(18,plain,
( ~ member(sK2(X0,X1),X0)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l39,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,difference(sK3,sK4)))
| ~ sP0(intersection(sK3,sK4),difference(sK3,difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l14,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK4)
| ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l29,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),intersection(sK3,sK4))
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK4) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l130,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK3)
| ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK4)
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(17,plain,
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l158,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),intersection(sK3,sK4))
| difference(sK3,difference(sK3,sK4)) = intersection(sK3,sK4)
| sP0(intersection(sK3,sK4),difference(sK3,difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l131,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK3)
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),sK4)
| member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l227,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,difference(sK3,sK4)))
| ~ sP0(intersection(sK3,sK4),difference(sK3,difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l226,plain,
( ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,sK4))
| ~ member(sK2(difference(sK3,difference(sK3,sK4)),intersection(sK3,sK4)),difference(sK3,difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l3,l2,l390,l126,l462,l5,l402,l413,l464,l468,l397,l393,l11,l39,l14,l29,l130,l158,l131,l227,l226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET011+3 : TPTP v9.0.0. Released v2.2.0.
% 0.10/0.11 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Jul 21 19:12:34 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % launching worker at depth: 4
% 0.11/0.33 % launching worker at depth: 8
% 0.11/0.33 % launching worker at depth: 5
% 0.11/0.33 % launching worker at depth: 3
% 0.11/0.33 % launching worker at depth: 6
% 0.11/0.33 % launching worker at depth: 2
% 0.11/0.33 % launching worker at depth: 7
% 0.11/0.33 % launching worker at depth: 1
% 0.11/0.33 % launching worker at depth: 9
% 0.11/0.33 % launching worker at depth: 10
% 0.11/0.34 % launching worker at depth: 11
% 0.18/0.42 % launching worker at depth: 12
% 33.26/4.49 % launching worker at depth: 13
% 252.93/32.07 % SZS status Theorem for theBenchmark
% 252.93/32.07 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------