%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU097+1 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n021.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 03:44:28 PM UTC 2025
% Result : Theorem 3.53s 0.80s
% Output : CNFRefutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 39 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 24 ( 10 ~; 7 |; 3 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 1 sgn 13 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t28_finset_1,plain,
! [A,B] :
( ( finite(A)
& finite(B) )
=> finite(symmetric_difference(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_finset_1) ).
fof(t28_finset_1_negated,plain,
~ ! [A,B] :
( ( finite(A)
& finite(B) )
=> finite(symmetric_difference(A,B)) ),
inference(negate_conjecture,[status(cth)],[t28_finset_1]) ).
cnf(138,plain,
finite(sK27),
inference(cnf,[status(esa)],[t28_finset_1_negated]) ).
cnf(l0,plain,
finite(sK27),
inference(instantiation,[status(thm)],[138]) ).
fof(fc12_finset_1,plain,
! [A,B] :
( finite(A)
=> finite(set_difference(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc12_finset_1) ).
cnf(25,plain,
( ~ finite(X0)
| finite(set_difference(X0,X1)) ),
inference(cnf,[status(esa)],[fc12_finset_1]) ).
cnf(l1,plain,
( ~ finite(sK27)
| finite(set_difference(sK27,sK28)) ),
inference(instantiation,[status(thm)],[25]) ).
fof(l3_finset_1,plain,
! [A,B] :
( ( finite(A)
& finite(B) )
=> finite(set_union2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_finset_1) ).
cnf(48,plain,
( ~ finite(X0)
| ~ finite(X1)
| finite(set_union2(X0,X1)) ),
inference(cnf,[status(esa)],[l3_finset_1]) ).
cnf(l36,plain,
( ~ finite(set_difference(sK28,sK27))
| ~ finite(set_difference(sK27,sK28))
| finite(set_union2(set_difference(sK28,sK27),set_difference(sK27,sK28))) ),
inference(instantiation,[status(thm)],[48]) ).
fof(d6_xboole_0,plain,
! [A,B] : symmetric_difference(A,B) = set_union2(set_difference(A,B),set_difference(B,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_xboole_0) ).
cnf(23,plain,
symmetric_difference(X0,X1) = set_union2(set_difference(X0,X1),set_difference(X1,X0)),
inference(cnf,[status(esa)],[d6_xboole_0]) ).
cnf(l44,plain,
symmetric_difference(sK28,sK27) = set_union2(set_difference(sK28,sK27),set_difference(sK27,sK28)),
inference(instantiation,[status(thm)],[23]) ).
fof(commutativity_k5_xboole_0,plain,
! [A,B] : symmetric_difference(A,B) = symmetric_difference(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k5_xboole_0) ).
cnf(22,plain,
symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf,[status(esa)],[commutativity_k5_xboole_0]) ).
cnf(l40,plain,
symmetric_difference(sK28,sK27) = symmetric_difference(sK27,sK28),
inference(instantiation,[status(thm)],[22]) ).
cnf(140,plain,
~ finite(symmetric_difference(sK27,sK28)),
inference(cnf,[status(esa)],[t28_finset_1_negated]) ).
cnf(l39,plain,
~ finite(symmetric_difference(sK27,sK28)),
inference(instantiation,[status(thm)],[140]) ).
cnf(l54,plain,
( ~ finite(sK28)
| finite(set_difference(sK28,set_difference(sK27,empty_set))) ),
inference(instantiation,[status(thm)],[25]) ).
fof(t3_boole,plain,
! [A] : set_difference(A,empty_set) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).
cnf(142,plain,
set_difference(X0,empty_set) = X0,
inference(cnf,[status(esa)],[t3_boole]) ).
cnf(l53,plain,
set_difference(sK27,empty_set) = sK27,
inference(instantiation,[status(thm)],[142]) ).
cnf(139,plain,
finite(sK28),
inference(cnf,[status(esa)],[t28_finset_1_negated]) ).
cnf(l56,plain,
finite(sK28),
inference(instantiation,[status(thm)],[139]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l36,l44,l40,l39,l54,l53,l56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : SEU097+1 : TPTP v9.0.0. Released v3.2.0.
% 0.03/0.12 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n021.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 23:27:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.19/0.40 % launching worker at depth: 11
% 3.53/0.80 % SZS status Theorem for theBenchmark
% 3.53/0.80 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------