%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU137+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/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 03:44:34 PM UTC 2025
% Result : Theorem 18.07s 2.57s
% Output : CNFRefutation 18.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 10 unt; 0 def)
% Number of atoms : 89 ( 29 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 92 ( 38 ~; 43 |; 1 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 3 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t45_xboole_1,plain,
! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t45_xboole_1) ).
fof(t45_xboole_1_negated,plain,
~ ! [A,B] :
( subset(A,B)
=> B = set_union2(A,set_difference(B,A)) ),
inference(negate_conjecture,[status(cth)],[t45_xboole_1]) ).
cnf(33,plain,
sK8 != set_union2(sK7,set_difference(sK8,sK7)),
inference(cnf,[status(esa)],[t45_xboole_1_negated]) ).
cnf(l0,plain,
sK8 != set_union2(sK7,set_difference(sK8,sK7)),
inference(instantiation,[status(thm)],[33]) ).
fof(t2_tarski,plain,
! [A,B] :
( ! [C] :
( in(C,A)
<=> in(C,B) )
=> A = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_tarski) ).
cnf(29,plain,
( X0 = X1
| in(sK6(X0,X1),X0)
| in(sK6(X0,X1),X1) ),
inference(cnf,[status(esa)],[t2_tarski]) ).
cnf(l1,plain,
( sK8 = set_union2(sK7,set_difference(sK8,sK7))
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK8)
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_union2(sK7,set_difference(sK8,sK7))) ),
inference(instantiation,[status(thm)],[29]) ).
fof(d2_xboole_0,plain,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_xboole_0) ).
cnf(2,plain,
( X0 != set_union2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l53,plain,
( set_union2(sK7,set_difference(sK8,sK7)) != set_union2(set_difference(sK8,sK7),sK7)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_union2(sK7,set_difference(sK8,sK7)))
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_difference(sK8,sK7))
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK7) ),
inference(instantiation,[status(thm)],[2]) ).
fof(d4_xboole_0,plain,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& ~ in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_xboole_0) ).
cnf(15,plain,
( X0 != set_difference(X1,X2)
| ~ in(X3,X1)
| in(X3,X2)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d4_xboole_0]) ).
cnf(l3,plain,
( set_difference(sK8,sK7) != set_difference(sK8,sK7)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK8)
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK7)
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_difference(sK8,sK7)) ),
inference(instantiation,[status(thm)],[15]) ).
fof(d3_tarski,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
cnf(10,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l58,plain,
( ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK7)
| ~ subset(sK7,sK8)
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK8) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(32,plain,
subset(sK7,sK8),
inference(cnf,[status(esa)],[t45_xboole_1_negated]) ).
cnf(l78,plain,
subset(sK7,sK8),
inference(instantiation,[status(thm)],[32]) ).
cnf(3,plain,
( X0 != set_union2(X1,X2)
| ~ in(X3,X1)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l47,plain,
( set_union2(sK7,set_difference(sK8,sK7)) != set_union2(set_difference(sK8,sK7),sK7)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_difference(sK8,sK7))
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_union2(sK7,set_difference(sK8,sK7))) ),
inference(instantiation,[status(thm)],[3]) ).
fof(commutativity_k2_xboole_0,plain,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
cnf(1,plain,
set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf,[status(esa)],[commutativity_k2_xboole_0]) ).
cnf(l73,plain,
set_union2(set_difference(sK8,sK7),sK7) = set_union2(sK7,set_difference(sK8,sK7)),
inference(instantiation,[status(thm)],[1]) ).
cnf(30,plain,
( ~ in(sK6(X0,X1),X0)
| ~ in(sK6(X0,X1),X1)
| X0 = X1 ),
inference(cnf,[status(esa)],[t2_tarski]) ).
cnf(l77,plain,
( ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK8)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_union2(sK7,set_difference(sK8,sK7)))
| sK8 = set_union2(sK7,set_difference(sK8,sK7)) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(13,plain,
( X0 != set_difference(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf,[status(esa)],[d4_xboole_0]) ).
cnf(l54,plain,
( set_difference(sK8,sK7) != set_difference(sK8,sK7)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_difference(sK8,sK7))
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK8) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l83,plain,
( ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK8)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_union2(sK7,set_difference(sK8,sK7)))
| sK8 = set_union2(sK7,set_difference(sK8,sK7)) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(l49,plain,
set_union2(sK7,set_difference(sK8,sK7)) = set_union2(set_difference(sK8,sK7),sK7),
inference(instantiation,[status(thm)],[1]) ).
cnf(l55,plain,
( ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK8)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_union2(sK7,set_difference(sK8,sK7)))
| sK8 = set_union2(sK7,set_difference(sK8,sK7)) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(4,plain,
( X0 != set_union2(X1,X2)
| ~ in(X3,X2)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d2_xboole_0]) ).
cnf(l5,plain,
( set_union2(sK7,set_difference(sK8,sK7)) != set_union2(set_difference(sK8,sK7),sK7)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK7)
| in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_union2(sK7,set_difference(sK8,sK7))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l33,plain,
( ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),sK8)
| ~ in(sK6(sK8,set_union2(sK7,set_difference(sK8,sK7))),set_union2(sK7,set_difference(sK8,sK7)))
| sK8 = set_union2(sK7,set_difference(sK8,sK7)) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(l22,plain,
set_union2(sK7,set_difference(sK8,sK7)) = set_union2(set_difference(sK8,sK7),sK7),
inference(instantiation,[status(thm)],[1]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l53,l3,l58,l78,l47,l73,l77,l54,l83,l49,l55,l5,l33,l22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09 % Problem : SEU137+1 : TPTP v9.0.0. Released v3.3.0.
% 0.08/0.09 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.29 % Computer : n024.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Mon Jul 21 23:34:19 EDT 2025
% 0.09/0.29 % CPUTime :
% 0.09/0.29 % launching worker at depth: 1
% 0.09/0.29 % launching worker at depth: 7
% 0.09/0.29 % launching worker at depth: 2
% 0.09/0.29 % launching worker at depth: 6
% 0.09/0.29 % launching worker at depth: 3
% 0.09/0.29 % launching worker at depth: 5
% 0.09/0.29 % launching worker at depth: 4
% 0.09/0.29 % launching worker at depth: 8
% 0.09/0.29 % launching worker at depth: 9
% 0.09/0.30 % launching worker at depth: 10
% 0.13/0.33 % launching worker at depth: 11
% 18.07/2.57 % SZS status Theorem for theBenchmark
% 18.07/2.57 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------