%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET185+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 : n017.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 03:31:45 PM UTC 2025
% Result : Theorem 8.35s 1.42s
% Output : CNFRefutation 8.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 39 ( 13 unt; 0 def)
% Number of atoms : 79 ( 20 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 71 ( 31 ~; 33 |; 0 &)
% ( 4 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 40 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subset_union,plain,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_subset_union) ).
fof(prove_subset_union_negated,plain,
~ ! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
inference(negate_conjecture,[status(cth)],[prove_subset_union]) ).
cnf(17,plain,
subset(sK3,sK4),
inference(cnf,[status(esa)],[prove_subset_union_negated]) ).
cnf(l0,plain,
subset(sK3,sK4),
inference(instantiation,[status(thm)],[17]) ).
fof(subset_defn,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subset_defn) ).
cnf(3,plain,
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf,[status(esa)],[subset_defn]) ).
cnf(l1,plain,
( ~ subset(sK3,sK4)
| ~ member(sK2(union(sK4,sK3),sK4),sK3)
| member(sK2(union(sK4,sK3),sK4),sK4) ),
inference(instantiation,[status(thm)],[3]) ).
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(l2,plain,
( ~ member(sK2(union(sK4,sK3),sK4),union(sK4,sK3))
| member(sK2(union(sK4,sK3),sK4),sK4)
| member(sK2(union(sK4,sK3),sK4),sK3) ),
inference(instantiation,[status(thm)],[0]) ).
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(13,plain,
( member(sK2(X0,X1),X0)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l4,plain,
( member(sK2(union(sK4,sK3),sK4),union(sK4,sK3))
| union(sK4,sK3) = sK4
| sP0(sK4,union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(16,plain,
( member(sK2(X0,X1),X1)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l34,plain,
( member(sK2(union(sK4,sK3),sK4),sK4)
| ~ sP0(sK4,union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[16]) ).
fof(commutativity_of_union,plain,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_of_union) ).
cnf(9,plain,
union(X0,X1) = union(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_union]) ).
cnf(l14,plain,
union(sK3,sK4) = union(sK4,sK3),
inference(instantiation,[status(thm)],[9]) ).
cnf(18,plain,
union(sK3,sK4) != sK4,
inference(cnf,[status(esa)],[prove_subset_union_negated]) ).
cnf(l18,plain,
union(sK3,sK4) != sK4,
inference(instantiation,[status(thm)],[18]) ).
cnf(1,plain,
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l36,plain,
( ~ member(sK2(union(sK4,sK3),sK4),sK4)
| member(sK2(union(sK4,sK3),sK4),union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(14,plain,
( ~ member(sK2(X0,X1),X1)
| X0 = X1
| sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l43,plain,
( ~ member(sK2(union(sK4,sK3),sK4),sK4)
| union(sK4,sK3) = sK4
| sP0(sK4,union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(l3,plain,
( ~ member(sK2(union(sK4,sK3),sK4),sK4)
| union(sK4,sK3) = sK4
| sP0(sK4,union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[14]) ).
cnf(15,plain,
( ~ member(sK2(X0,X1),X0)
| ~ sP0(X1,X0) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l5,plain,
( ~ member(sK2(union(sK4,sK3),sK4),union(sK4,sK3))
| ~ sP0(sK4,union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(l49,plain,
( ~ member(sK2(union(sK4,sK3),sK4),union(sK4,sK3))
| ~ sP0(sK4,union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[15]) ).
cnf(11,plain,
( ~ member(X0,X1)
| X1 != X2
| member(X0,X2) ),
inference(cnf,[status(esa)],[equal_member_defn]) ).
cnf(l22,plain,
( ~ member(sK2(union(sK4,sK3),sK4),union(sK3,sK4))
| union(sK3,sK4) != union(sK4,sK3)
| member(sK2(union(sK4,sK3),sK4),union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l50,plain,
( ~ member(sK2(union(sK4,sK3),sK4),sK4)
| member(sK2(union(sK4,sK3),sK4),union(sK4,sK3)) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(2,plain,
( ~ member(X0,X1)
| member(X0,union(X2,X1)) ),
inference(cnf,[status(esa)],[union_defn]) ).
cnf(l23,plain,
( ~ member(sK2(union(sK4,sK3),sK4),sK4)
| member(sK2(union(sK4,sK3),sK4),union(sK3,sK4)) ),
inference(instantiation,[status(thm)],[2]) ).
cnf(l31,plain,
union(sK3,sK4) = union(sK4,sK3),
inference(instantiation,[status(thm)],[9]) ).
cnf(l167,plain,
union(sK3,sK4) != sK4,
inference(instantiation,[status(thm)],[18]) ).
cnf(l48,plain,
union(sK3,sK4) = union(sK4,sK3),
inference(instantiation,[status(thm)],[9]) ).
cnf(l160,plain,
union(sK3,sK4) = union(sK4,sK3),
inference(instantiation,[status(thm)],[9]) ).
cnf(l62,plain,
union(sK3,sK4) != sK4,
inference(instantiation,[status(thm)],[18]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l4,l34,l14,l18,l36,l43,l3,l5,l49,l22,l50,l23,l31,l167,l48,l160,l62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET185+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n017.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 20:21:19 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % launching worker at depth: 1
% 0.13/0.34 % launching worker at depth: 4
% 0.13/0.34 % launching worker at depth: 6
% 0.13/0.34 % launching worker at depth: 2
% 0.13/0.34 % launching worker at depth: 3
% 0.13/0.34 % launching worker at depth: 8
% 0.13/0.34 % launching worker at depth: 7
% 0.13/0.34 % launching worker at depth: 5
% 0.13/0.34 % launching worker at depth: 9
% 0.13/0.34 % launching worker at depth: 10
% 0.13/0.37 % launching worker at depth: 11
% 0.19/0.56 % launching worker at depth: 12
% 8.35/1.42 % SZS status Theorem for theBenchmark
% 8.35/1.42 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------