%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET617+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 : 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 03:32:23 PM UTC 2025
% Result : Theorem 24.73s 3.48s
% Output : CNFRefutation 24.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 9
% Syntax : Number of formulae : 42 ( 34 unt; 0 def)
% Number of atoms : 54 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 8 |; 3 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 1 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th92,plain,
! [B] :
( symmetric_difference(B,empty_set) = B
& symmetric_difference(empty_set,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th92) ).
fof(prove_th92_negated,plain,
~ ! [B] :
( symmetric_difference(B,empty_set) = B
& symmetric_difference(empty_set,B) = B ),
inference(negate_conjecture,[status(cth)],[prove_th92]) ).
cnf(22,plain,
( symmetric_difference(empty_set,sK4) != sK4
| symmetric_difference(sK4,empty_set) != sK4 ),
inference(cnf,[status(esa)],[prove_th92_negated]) ).
cnf(l0,plain,
( symmetric_difference(empty_set,sK4) != sK4
| symmetric_difference(sK4,empty_set) != sK4 ),
inference(instantiation,[status(thm)],[22]) ).
fof(equal_defn,plain,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_defn) ).
cnf(7,plain,
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf,[status(esa)],[equal_defn]) ).
cnf(l50,plain,
( ~ subset(union(empty_set,sK4),sK4)
| ~ subset(sK4,union(empty_set,sK4))
| union(empty_set,sK4) = sK4 ),
inference(instantiation,[status(thm)],[7]) ).
fof(commutativity_of_union,plain,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_union) ).
cnf(8,plain,
union(X0,X1) = union(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_union]) ).
cnf(l65,plain,
union(sK4,empty_set) = union(empty_set,sK4),
inference(instantiation,[status(thm)],[8]) ).
fof(union_empty_set,plain,
! [B] : union(B,empty_set) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',union_empty_set) ).
cnf(1,plain,
union(X0,empty_set) = X0,
inference(cnf,[status(esa)],[union_empty_set]) ).
cnf(l54,plain,
union(sK4,empty_set) = sK4,
inference(instantiation,[status(thm)],[1]) ).
fof(reflexivity_of_subset,plain,
! [B] : subset(B,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_of_subset) ).
cnf(19,plain,
subset(X0,X0),
inference(cnf,[status(esa)],[reflexivity_of_subset]) ).
cnf(l64,plain,
subset(union(sK4,empty_set),union(sK4,empty_set)),
inference(instantiation,[status(thm)],[19]) ).
cnf(l68,plain,
subset(union(sK4,empty_set),union(sK4,empty_set)),
inference(instantiation,[status(thm)],[19]) ).
cnf(l8,plain,
( ~ subset(symmetric_difference(sK4,empty_set),union(difference(empty_set,sK4),difference(sK4,empty_set)))
| ~ subset(union(difference(empty_set,sK4),difference(sK4,empty_set)),symmetric_difference(sK4,empty_set))
| symmetric_difference(sK4,empty_set) = union(difference(empty_set,sK4),difference(sK4,empty_set)) ),
inference(instantiation,[status(thm)],[7]) ).
fof(no_difference_with_empty_set2,plain,
! [B] : difference(empty_set,B) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set2) ).
cnf(3,plain,
difference(empty_set,X0) = empty_set,
inference(cnf,[status(esa)],[no_difference_with_empty_set2]) ).
cnf(l20,plain,
difference(empty_set,sK4) = empty_set,
inference(instantiation,[status(thm)],[3]) ).
fof(no_difference_with_empty_set1,plain,
! [B] : difference(B,empty_set) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_difference_with_empty_set1) ).
cnf(2,plain,
difference(X0,empty_set) = X0,
inference(cnf,[status(esa)],[no_difference_with_empty_set1]) ).
cnf(l9,plain,
difference(sK4,empty_set) = sK4,
inference(instantiation,[status(thm)],[2]) ).
cnf(l69,plain,
union(sK4,empty_set) = sK4,
inference(instantiation,[status(thm)],[1]) ).
cnf(l67,plain,
union(sK4,empty_set) = union(empty_set,sK4),
inference(instantiation,[status(thm)],[8]) ).
cnf(l11,plain,
subset(symmetric_difference(empty_set,sK4),symmetric_difference(empty_set,sK4)),
inference(instantiation,[status(thm)],[19]) ).
fof(symmetric_difference_defn,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
cnf(0,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf,[status(esa)],[symmetric_difference_defn]) ).
cnf(l23,plain,
symmetric_difference(empty_set,sK4) = union(difference(empty_set,sK4),difference(sK4,empty_set)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l14,plain,
symmetric_difference(empty_set,sK4) = union(difference(empty_set,sK4),difference(sK4,empty_set)),
inference(instantiation,[status(thm)],[0]) ).
fof(commutativity_of_symmetric_difference,plain,
! [B,C] : symmetric_difference(B,C) = symmetric_difference(C,B),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_of_symmetric_difference) ).
cnf(9,plain,
symmetric_difference(X0,X1) = symmetric_difference(X1,X0),
inference(cnf,[status(esa)],[commutativity_of_symmetric_difference]) ).
cnf(l16,plain,
symmetric_difference(empty_set,sK4) = symmetric_difference(sK4,empty_set),
inference(instantiation,[status(thm)],[9]) ).
cnf(l19,plain,
difference(sK4,empty_set) = sK4,
inference(instantiation,[status(thm)],[2]) ).
cnf(l15,plain,
subset(symmetric_difference(empty_set,sK4),symmetric_difference(empty_set,sK4)),
inference(instantiation,[status(thm)],[19]) ).
cnf(l13,plain,
symmetric_difference(empty_set,sK4) = symmetric_difference(sK4,empty_set),
inference(instantiation,[status(thm)],[9]) ).
cnf(l17,plain,
symmetric_difference(empty_set,sK4) = union(difference(empty_set,sK4),difference(sK4,empty_set)),
inference(instantiation,[status(thm)],[0]) ).
cnf(l40,plain,
difference(empty_set,sK4) = empty_set,
inference(instantiation,[status(thm)],[3]) ).
cnf(l39,plain,
union(sK4,empty_set) = sK4,
inference(instantiation,[status(thm)],[1]) ).
cnf(l30,plain,
union(empty_set,sK4) = union(sK4,empty_set),
inference(instantiation,[status(thm)],[8]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l50,l65,l54,l64,l68,l8,l20,l9,l69,l67,l11,l23,l14,l16,l19,l15,l13,l17,l40,l39,l30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET617+3 : TPTP v9.0.0. Released v2.2.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.30 % Computer : n017.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Jul 21 22:08:04 EDT 2025
% 0.09/0.30 % CPUTime :
% 0.09/0.30 % launching worker at depth: 1
% 0.09/0.30 % launching worker at depth: 5
% 0.09/0.30 % launching worker at depth: 3
% 0.09/0.30 % launching worker at depth: 6
% 0.09/0.30 % launching worker at depth: 4
% 0.09/0.30 % launching worker at depth: 7
% 0.09/0.30 % launching worker at depth: 8
% 0.09/0.30 % launching worker at depth: 2
% 0.09/0.30 % launching worker at depth: 9
% 0.09/0.30 % launching worker at depth: 10
% 0.14/0.33 % launching worker at depth: 11
% 24.73/3.48 % SZS status Theorem for theBenchmark
% 24.73/3.48 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------