%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU141+2 : 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 : n019.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 03:44:35 PM UTC 2025
% Result : Theorem 33.21s 4.51s
% Output : CNFRefutation 33.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 12 unt; 0 def)
% Number of atoms : 127 ( 35 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 52 ~; 57 |; 7 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 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 : 67 ( 4 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t83_xboole_1,plain,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t83_xboole_1) ).
fof(t83_xboole_1_negated,plain,
~ ! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
inference(negate_conjecture,[status(cth)],[t83_xboole_1]) ).
cnf(85,plain,
( set_difference(sK11,sK12) = sK11
| disjoint(sK11,sK12) ),
inference(cnf,[status(esa)],[t83_xboole_1_negated]) ).
cnf(l0,plain,
( set_difference(sK11,sK12) = sK11
| disjoint(sK11,sK12) ),
inference(instantiation,[status(thm)],[85]) ).
fof(t3_xboole_0,plain,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] :
~ ( in(C,A)
& in(C,B) ) )
& ~ ( ? [C] :
( in(C,A)
& in(C,B) )
& disjoint(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_xboole_0) ).
cnf(71,plain,
( in(sK9(X0,X1),X1)
| disjoint(X0,X1) ),
inference(cnf,[status(esa)],[t3_xboole_0]) ).
cnf(l11,plain,
( in(sK9(sK12,set_difference(sK11,sK12)),set_difference(sK11,sK12))
| disjoint(sK12,set_difference(sK11,sK12)) ),
inference(instantiation,[status(thm)],[71]) ).
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(29,plain,
( X0 != set_difference(X1,X2)
| ~ in(X3,X2)
| ~ in(X3,X0) ),
inference(cnf,[status(esa)],[d4_xboole_0]) ).
cnf(l13,plain,
( set_difference(sK11,sK12) != set_difference(sK11,sK12)
| ~ in(sK9(sK12,set_difference(sK11,sK12)),sK12)
| ~ in(sK9(sK12,set_difference(sK11,sK12)),set_difference(sK11,sK12)) ),
inference(instantiation,[status(thm)],[29]) ).
cnf(70,plain,
( in(sK9(X0,X1),X0)
| disjoint(X0,X1) ),
inference(cnf,[status(esa)],[t3_xboole_0]) ).
cnf(l22,plain,
( in(sK9(sK12,set_difference(sK11,sK12)),sK12)
| disjoint(sK12,set_difference(sK11,sK12)) ),
inference(instantiation,[status(thm)],[70]) ).
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(62,plain,
( ~ in(sK8(X0,X1),X0)
| ~ in(sK8(X0,X1),X1)
| X0 = X1 ),
inference(cnf,[status(esa)],[t2_tarski]) ).
cnf(l94,plain,
( ~ in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),sK12)
| ~ in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),set_difference(sK12,set_difference(sK12,sK12)))
| sK12 = set_difference(sK12,set_difference(sK12,sK12)) ),
inference(instantiation,[status(thm)],[62]) ).
fof(d3_xboole_0,plain,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_xboole_0) ).
cnf(21,plain,
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X2) ),
inference(cnf,[status(esa)],[d3_xboole_0]) ).
cnf(l127,plain,
( set_difference(sK12,set_difference(sK12,sK12)) != set_intersection2(sK12,sK12)
| ~ in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),set_difference(sK12,set_difference(sK12,sK12)))
| in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),sK12) ),
inference(instantiation,[status(thm)],[21]) ).
cnf(61,plain,
( X0 = X1
| in(sK8(X0,X1),X0)
| in(sK8(X0,X1),X1) ),
inference(cnf,[status(esa)],[t2_tarski]) ).
cnf(l129,plain,
( sK12 = set_difference(sK12,set_difference(sK12,sK12))
| in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),sK12)
| in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),set_difference(sK12,set_difference(sK12,sK12))) ),
inference(instantiation,[status(thm)],[61]) ).
fof(t48_xboole_1,plain,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).
cnf(76,plain,
set_difference(X0,set_difference(X0,X1)) = set_intersection2(X0,X1),
inference(cnf,[status(esa)],[t48_xboole_1]) ).
cnf(l128,plain,
set_difference(sK12,set_difference(sK12,sK12)) = set_intersection2(sK12,sK12),
inference(instantiation,[status(thm)],[76]) ).
cnf(22,plain,
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X1)
| ~ in(X3,X2)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d3_xboole_0]) ).
cnf(l98,plain,
( set_difference(sK12,set_difference(sK12,sK12)) != set_intersection2(sK12,sK12)
| ~ in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),sK12)
| ~ in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),sK12)
| in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),set_difference(sK12,set_difference(sK12,sK12))) ),
inference(instantiation,[status(thm)],[22]) ).
cnf(l132,plain,
set_difference(sK12,set_difference(sK12,sK12)) = set_intersection2(sK12,sK12),
inference(instantiation,[status(thm)],[76]) ).
cnf(l135,plain,
( sK12 = set_difference(sK12,set_difference(sK12,sK12))
| in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),sK12)
| in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),set_difference(sK12,set_difference(sK12,sK12))) ),
inference(instantiation,[status(thm)],[61]) ).
cnf(l133,plain,
( sK12 = set_difference(sK12,set_difference(sK12,sK12))
| in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),sK12)
| in(sK8(sK12,set_difference(sK12,set_difference(sK12,sK12))),set_difference(sK12,set_difference(sK12,sK12))) ),
inference(instantiation,[status(thm)],[61]) ).
fof(symmetry_r1_xboole_0,plain,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetry_r1_xboole_0) ).
cnf(52,plain,
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf,[status(esa)],[symmetry_r1_xboole_0]) ).
cnf(l144,plain,
( ~ disjoint(sK12,sK11)
| disjoint(sK11,sK12) ),
inference(instantiation,[status(thm)],[52]) ).
cnf(86,plain,
( set_difference(sK11,sK12) != sK11
| ~ disjoint(sK11,sK12) ),
inference(cnf,[status(esa)],[t83_xboole_1_negated]) ).
cnf(l146,plain,
( set_difference(sK11,sK12) != sK11
| ~ disjoint(sK11,sK12) ),
inference(instantiation,[status(thm)],[86]) ).
cnf(l2,plain,
( set_difference(sK11,sK12) != sK11
| ~ disjoint(sK11,sK12) ),
inference(instantiation,[status(thm)],[86]) ).
cnf(l4,plain,
( set_difference(sK11,sK12) = sK11
| in(sK8(set_difference(sK11,sK12),sK11),set_difference(sK11,sK12))
| in(sK8(set_difference(sK11,sK12),sK11),sK11) ),
inference(instantiation,[status(thm)],[61]) ).
cnf(30,plain,
( X0 != set_difference(X1,X2)
| ~ in(X3,X1)
| in(X3,X2)
| in(X3,X0) ),
inference(cnf,[status(esa)],[d4_xboole_0]) ).
cnf(l57,plain,
( set_difference(sK11,sK12) != set_difference(sK11,sK12)
| ~ in(sK8(set_difference(sK11,sK12),sK11),sK11)
| in(sK8(set_difference(sK11,sK12),sK11),sK12)
| in(sK8(set_difference(sK11,sK12),sK11),set_difference(sK11,sK12)) ),
inference(instantiation,[status(thm)],[30]) ).
cnf(l97,plain,
set_difference(sK12,set_difference(sK12,sK12)) = set_intersection2(sK12,sK12),
inference(instantiation,[status(thm)],[76]) ).
fof(idempotence_k3_xboole_0,plain,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k3_xboole_0) ).
cnf(45,plain,
set_intersection2(X0,X0) = X0,
inference(cnf,[status(esa)],[idempotence_k3_xboole_0]) ).
cnf(l96,plain,
set_intersection2(sK12,sK12) = sK12,
inference(instantiation,[status(thm)],[45]) ).
cnf(72,plain,
( ~ in(X0,X1)
| ~ in(X0,X2)
| ~ disjoint(X1,X2) ),
inference(cnf,[status(esa)],[t3_xboole_0]) ).
cnf(l61,plain,
( ~ in(sK8(set_difference(sK11,sK12),sK11),sK11)
| ~ in(sK8(set_difference(sK11,sK12),sK11),sK12)
| ~ disjoint(sK11,sK12) ),
inference(instantiation,[status(thm)],[72]) ).
cnf(l58,plain,
( ~ in(sK8(set_difference(sK11,sK12),sK11),set_difference(sK11,sK12))
| ~ in(sK8(set_difference(sK11,sK12),sK11),sK11)
| set_difference(sK11,sK12) = sK11 ),
inference(instantiation,[status(thm)],[62]) ).
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(17,plain,
( ~ in(X0,X1)
| ~ subset(X1,X2)
| in(X0,X2) ),
inference(cnf,[status(esa)],[d3_tarski]) ).
cnf(l7,plain,
( ~ in(sK8(set_difference(sK11,sK12),sK11),set_difference(sK11,sK12))
| ~ subset(set_difference(sK11,sK12),sK11)
| in(sK8(set_difference(sK11,sK12),sK11),sK11) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l14,plain,
( ~ in(sK8(set_difference(sK11,sK12),sK11),set_difference(sK11,sK12))
| ~ in(sK8(set_difference(sK11,sK12),sK11),sK11)
| set_difference(sK11,sK12) = sK11 ),
inference(instantiation,[status(thm)],[62]) ).
fof(t36_xboole_1,plain,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).
cnf(65,plain,
subset(set_difference(X0,X1),X0),
inference(cnf,[status(esa)],[t36_xboole_1]) ).
cnf(l17,plain,
subset(set_difference(sK11,sK12),sK11),
inference(instantiation,[status(thm)],[65]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l11,l13,l22,l94,l127,l129,l128,l98,l132,l135,l133,l144,l146,l2,l4,l57,l97,l96,l61,l58,l7,l14,l17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SEU141+2 : TPTP v9.0.0. Released v3.3.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Jul 21 23:35:19 EDT 2025
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % launching worker at depth: 4
% 0.14/0.35 % launching worker at depth: 5
% 0.14/0.35 % launching worker at depth: 3
% 0.14/0.35 % launching worker at depth: 1
% 0.14/0.35 % launching worker at depth: 8
% 0.14/0.35 % launching worker at depth: 6
% 0.14/0.35 % launching worker at depth: 7
% 0.14/0.35 % launching worker at depth: 2
% 0.14/0.35 % launching worker at depth: 9
% 0.14/0.37 % launching worker at depth: 10
% 2.49/0.68 % launching worker at depth: 11
% 33.21/4.51 % SZS status Theorem for theBenchmark
% 33.21/4.51 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------