%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET607+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 : 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 03:32:21 PM UTC 2025
% Result : Theorem 29.12s 3.99s
% Output : CNFRefutation 29.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 128 ( 17 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 123 ( 52 ~; 64 |; 1 &)
% ( 5 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 7 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th79,plain,
! [B,C] : union(B,difference(C,B)) = union(B,C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th79) ).
fof(prove_th79_negated,plain,
~ ! [B,C] : union(B,difference(C,B)) = union(B,C),
inference(negate_conjecture,[status(cth)],[prove_th79]) ).
cnf(20,plain,
union(sK3,difference(sK4,sK3)) != union(sK3,sK4),
inference(cnf,[status(esa)],[prove_th79_negated]) ).
cnf(l0,plain,
union(sK3,difference(sK4,sK3)) != union(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/sandbox2/benchmark/theBenchmark.p',equal_member_defn) ).
cnf(17,plain,
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l302,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| union(sK3,sK4) = union(difference(sK4,sK3),sK3)
| sP0(union(difference(sK4,sK3),sK3),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(18,plain,
( ~ member(sK2(X0,X1),X0)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l303,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,sK4))
| ~ sP0(union(difference(sK4,sK3),sK3),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[18]) ).
fof(subset_defn,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset_defn) ).
cnf(10,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l331,plain,
( ~ subset(sK4,union(sK3,sK4))
| ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK4)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(12,plain,
( ~ member(sK1(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l492,plain,
( ~ member(sK1(sK4,union(sK3,sK4)),union(sK3,sK4))
| subset(sK4,union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(15,plain,
( ~ member(X0,X1)
| X2 != X1
| member(X0,X2) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l493,plain,
( ~ member(sK1(sK4,union(sK3,sK4)),union(sK4,sK3))
| union(sK3,sK4) != union(sK4,sK3)
| member(sK1(sK4,union(sK3,sK4)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[15]) ).
fof(union_defn,plain,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_defn) ).
cnf(1,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l499,plain,
( ~ member(sK1(sK4,union(sK3,sK4)),sK4)
| member(sK1(sK4,union(sK3,sK4)),union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(11,plain,
( subset(X0,X1)
| member(sK1(X0,X1),X0) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l500,plain,
( subset(sK4,union(sK3,sK4))
| member(sK1(sK4,union(sK3,sK4)),sK4) ),
inference(instantiation,[status(thm)],[11]) ).
fof(commutativity_of_union,plain,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
cnf(9,plain,
union(X0,X1) = union(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_union]) ).
cnf(l2,plain,
union(sK3,difference(sK4,sK3)) = union(difference(sK4,sK3),sK3),
inference(instantiation,[status(thm)],[9]) ).
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(5,plain,
( ~ member(X0,X1)
| member(X0,X2)
| member(X0,difference(X1,X2)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l367,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(union(sK3,difference(sK4,sK3)),X2_459))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK4)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(union(union(sK3,difference(sK4,sK3)),X2_459),sK4)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l416,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,difference(sK4,sK3)))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(union(sK3,difference(sK4,sK3)),X2_459))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(union(sK3,difference(sK4,sK3)),union(union(sK3,difference(sK4,sK3)),X2_459))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(0,plain,
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l310,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3)))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3)) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l317,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3)),union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3))))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3)))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l496,plain,
union(sK4,sK3) = union(sK3,sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(l452,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| union(sK3,difference(sK4,sK3)) != union(difference(sK4,sK3),sK3)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l320,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK3)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3)),union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3))))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(sK3,union(union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3)),union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3))))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(3,plain,
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l497,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(sK3,union(union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3)),union(union(difference(sK4,sK3),sK3),union(difference(sK4,sK3),sK3)))))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK3) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l465,plain,
union(sK3,difference(sK4,sK3)) = union(difference(sK4,sK3),sK3),
inference(instantiation,[status(thm)],[9]) ).
cnf(19,plain,
( member(sK2(X0,X1),X1)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l463,plain,
( member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| ~ sP0(union(difference(sK4,sK3),sK3),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(l455,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(union(sK3,difference(sK4,sK3)),union(union(sK3,difference(sK4,sK3)),X2_459)))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,difference(sK4,sK3))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l459,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,difference(sK4,sK3)))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(union(sK3,difference(sK4,sK3)),X2_459)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l325,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,sK4))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK3)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK4) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(16,plain,
( member(sK2(X0,X1),X0)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l329,plain,
( member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,sK4))
| union(sK3,sK4) = union(difference(sK4,sK3),sK3)
| sP0(union(difference(sK4,sK3),sK3),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[16]) ).
cnf(2,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l498,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK3)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l563,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK4)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK3)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(sK4,sK3)) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l570,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(sK4,sK3))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(l373,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(union(union(sK3,difference(sK4,sK3)),X2_459),sK4))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(difference(union(union(sK3,difference(sK4,sK3)),X2_459),sK4),union(difference(sK4,sK3),sK3))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l567,plain,
( member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| ~ sP0(union(difference(sK4,sK3),sK3),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(4,plain,
( ~ member(X0,X1)
| ~ member(X0,difference(X2,X1)) ),
inference(cnf,[status(esa)],[difference_defn]) ).
cnf(l380,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(difference(union(union(sK3,difference(sK4,sK3)),X2_459),sK4),union(difference(sK4,sK3),sK3))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l382,plain,
( member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| ~ sP0(union(difference(sK4,sK3),sK3),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[19]) ).
cnf(l381,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(difference(sK4,sK3),sK3))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(sK4,sK3))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l564,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),difference(sK4,sK3))
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK4) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l565,plain,
( ~ member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),sK3)
| member(sK2(union(sK3,sK4),union(difference(sK4,sK3),sK3)),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l302,l303,l331,l492,l493,l499,l500,l2,l367,l416,l310,l317,l496,l452,l320,l497,l465,l463,l455,l459,l325,l329,l498,l563,l570,l373,l567,l380,l382,l381,l564,l565]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SET607+3 : TPTP v9.0.0. Released v2.2.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n024.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Jul 21 22:06:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % launching worker at depth: 3
% 0.13/0.35 % launching worker at depth: 8
% 0.13/0.35 % launching worker at depth: 1
% 0.13/0.35 % launching worker at depth: 2
% 0.13/0.35 % launching worker at depth: 4
% 0.13/0.35 % launching worker at depth: 6
% 0.13/0.35 % launching worker at depth: 7
% 0.13/0.35 % launching worker at depth: 5
% 0.13/0.35 % launching worker at depth: 9
% 0.13/0.35 % launching worker at depth: 10
% 0.13/0.38 % launching worker at depth: 11
% 2.06/0.59 % launching worker at depth: 12
% 29.12/3.99 % SZS status Theorem for theBenchmark
% 29.12/3.99 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------