%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET608+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 : n020.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 03:32:21 PM UTC 2025
% Result : Theorem 88.59s 11.49s
% Output : CNFRefutation 88.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 9 unt; 0 def)
% Number of atoms : 136 ( 20 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 135 ( 58 ~; 70 |; 2 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 8 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_union_intersection_difference,plain,
! [B,C] : union(intersection(B,C),difference(B,C)) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_union_intersection_difference) ).
fof(prove_union_intersection_difference_negated,plain,
~ ! [B,C] : union(intersection(B,C),difference(B,C)) = B,
inference(negate_conjecture,[status(cth)],[prove_union_intersection_difference]) ).
cnf(24,plain,
union(intersection(sK3,sK4),difference(sK3,sK4)) != sK3,
inference(cnf,[status(esa)],[prove_union_intersection_difference_negated]) ).
cnf(l0,plain,
union(intersection(sK3,sK4),difference(sK3,sK4)) != sK3,
inference(instantiation,[status(thm)],[24]) ).
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(21,plain,
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l1,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3)
| union(intersection(sK3,sK4),difference(sK3,sK4)) = sK3
| sP0(sK3,union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[21]) ).
cnf(22,plain,
( ~ member(sK2(X0,X1),X0)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l377,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4)))
| ~ sP0(sK3,union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(18,plain,
( ~ member(X0,X1)
| X1 != X2
| member(X0,X2) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l2,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(sK3,union(sK3,sK3)))
| union(sK3,union(sK3,sK3)) != sK3
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l224,plain,
( ~ member(sK2(union(sK3,union(sK3,sK3)),sK3),sK3)
| union(sK3,union(sK3,sK3)) = sK3
| sP0(sK3,union(sK3,union(sK3,sK3))) ),
inference(instantiation,[status(thm)],[21]) ).
cnf(l228,plain,
( ~ member(sK2(union(sK3,union(sK3,sK3)),sK3),union(sK3,union(sK3,sK3)))
| ~ sP0(sK3,union(sK3,union(sK3,sK3))) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(19,plain,
( ~ member(X0,X1)
| X2 != X1
| member(X0,X2) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l229,plain,
( ~ member(sK2(union(sK3,union(sK3,sK3)),sK3),union(union(sK3,sK3),sK3))
| union(sK3,union(sK3,sK3)) != union(union(sK3,sK3),sK3)
| member(sK2(union(sK3,union(sK3,sK3)),sK3),union(sK3,union(sK3,sK3))) ),
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(4,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l4,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(X1_4,union(sK3,union(sK3,sK3))))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(sK3,union(sK3,sK3))) ),
inference(instantiation,[status(thm)],[4]) ).
fof(union_defn,plain,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',union_defn) ).
cnf(0,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l7,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(X1_4,union(sK3,union(sK3,sK3))),union(intersection(sK3,sK4),difference(sK3,sK4))))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(X1_4,union(sK3,union(sK3,sK3))))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(23,plain,
( member(sK2(X0,X1),X1)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l227,plain,
( member(sK2(union(sK3,union(sK3,sK3)),sK3),sK3)
| ~ sP0(sK3,union(sK3,union(sK3,sK3))) ),
inference(instantiation,[status(thm)],[23]) ).
fof(commutativity_of_union,plain,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
cnf(12,plain,
union(X0,X1) = union(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_union]) ).
cnf(l522,plain,
union(union(sK3,sK3),sK3) = union(sK3,union(sK3,sK3)),
inference(instantiation,[status(thm)],[12]) ).
cnf(2,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l231,plain,
( ~ member(sK2(union(sK3,union(sK3,sK3)),sK3),sK3)
| member(sK2(union(sK3,union(sK3,sK3)),sK3),union(union(sK3,sK3),sK3)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l232,plain,
( member(sK2(union(sK3,union(sK3,sK3)),sK3),sK3)
| ~ sP0(sK3,union(sK3,union(sK3,sK3))) ),
inference(instantiation,[status(thm)],[23]) ).
cnf(20,plain,
( member(sK2(X0,X1),X0)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l236,plain,
( member(sK2(union(sK3,union(sK3,sK3)),sK3),union(sK3,union(sK3,sK3)))
| union(sK3,union(sK3,sK3)) = sK3
| sP0(sK3,union(sK3,union(sK3,sK3))) ),
inference(instantiation,[status(thm)],[20]) ).
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(8,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l8,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4)))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(X1_4,union(sK3,union(sK3,sK3))),union(intersection(sK3,sK4),difference(sK3,sK4))))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),difference(union(intersection(sK3,sK4),difference(sK3,sK4)),union(intersection(X1_4,union(sK3,union(sK3,sK3))),union(intersection(sK3,sK4),difference(sK3,sK4))))) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l12,plain,
( member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4)))
| union(intersection(sK3,sK4),difference(sK3,sK4)) = sK3
| sP0(sK3,union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[20]) ).
cnf(l307,plain,
( ~ member(sK2(union(sK3,union(sK3,sK3)),sK3),union(sK3,union(sK3,sK3)))
| member(sK2(union(sK3,union(sK3,sK3)),sK3),sK3)
| member(sK2(union(sK3,union(sK3,sK3)),sK3),union(sK3,sK3)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l39,plain,
( member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3)
| ~ sP0(sK3,union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[23]) ).
cnf(l329,plain,
( ~ member(sK2(union(sK3,union(sK3,sK3)),sK3),union(sK3,sK3))
| member(sK2(union(sK3,union(sK3,sK3)),sK3),sK3)
| member(sK2(union(sK3,union(sK3,sK3)),sK3),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l378,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(difference(sK3,sK4),intersection(sK3,sK4)))
| union(difference(sK3,sK4),intersection(sK3,sK4)) != union(intersection(sK3,sK4),difference(sK3,sK4))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[18]) ).
cnf(l599,plain,
union(difference(sK3,sK4),intersection(sK3,sK4)) = union(intersection(sK3,sK4),difference(sK3,sK4)),
inference(instantiation,[status(thm)],[12]) ).
cnf(5,plain,
( ~ member(X0,X1)
| ~ member(X0,X2)
| member(X0,intersection(X1,X2)) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l218,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4)))
| ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),difference(sK3,sK4))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(union(intersection(sK3,sK4),difference(sK3,sK4)),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l437,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(sK3,sK4))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(difference(sK3,sK4),intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l438,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(sK3,intersection(sK3,sK4)))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3)
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(6,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l9,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),difference(union(intersection(sK3,sK4),difference(sK3,sK4)),union(intersection(X1_4,union(sK3,union(sK3,sK3))),union(intersection(sK3,sK4),difference(sK3,sK4)))))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(1,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l443,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3)
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(sK3,intersection(sK3,sK4))) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l18,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4)))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(X1_4,union(sK3,union(sK3,sK3))),union(intersection(sK3,sK4),difference(sK3,sK4)))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l595,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3)
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK4)
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l618,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3)
| ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK4)
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(sK3,sK4)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l623,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),difference(sK3,sK4))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l446,plain,
( member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3)
| ~ sP0(sK3,union(intersection(sK3,sK4),difference(sK3,sK4))) ),
inference(instantiation,[status(thm)],[23]) ).
cnf(l297,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(union(intersection(sK3,sK4),difference(sK3,sK4)),difference(sK3,sK4)))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l302,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),union(intersection(sK3,sK4),difference(sK3,sK4)))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(sK3,sK4))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),difference(sK3,sK4)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l298,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),difference(sK3,sK4))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(3,plain,
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[intersection_defn]) ).
cnf(l303,plain,
( ~ member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),intersection(sK3,sK4))
| member(sK2(union(intersection(sK3,sK4),difference(sK3,sK4)),sK3),sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l377,l2,l224,l228,l229,l4,l7,l227,l522,l231,l232,l236,l8,l12,l307,l39,l329,l378,l599,l218,l437,l438,l9,l443,l18,l595,l618,l623,l446,l297,l302,l298,l303]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET608+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n020.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 22:06:49 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.19/0.35 % launching worker at depth: 11
% 0.19/0.46 % launching worker at depth: 12
% 88.59/11.49 % SZS status Theorem for theBenchmark
% 88.59/11.49 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------