%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU292+1 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 03:45:06 PM UTC 2025
% Result : Theorem 247.40s 31.45s
% Output : CNFRefutation 247.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 19 unt; 0 def)
% Number of atoms : 98 ( 24 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 86 ( 29 ~; 29 |; 9 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-3 aty)
% Number of variables : 49 ( 2 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t21_funct_2,plain,
! [A,B,C,D] :
( ( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B) )
=> ! [E] :
( ( relation(E)
& function(E) )
=> ( in(C,A)
=> ( B = empty_set
| apply(relation_composition(D,E),C) = apply(E,apply(D,C)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_2) ).
fof(t21_funct_2_negated,plain,
~ ! [A,B,C,D] :
( ( function(D)
& quasi_total(D,A,B)
& relation_of2_as_subset(D,A,B) )
=> ! [E] :
( ( relation(E)
& function(E) )
=> ( in(C,A)
=> ( B = empty_set
| apply(relation_composition(D,E),C) = apply(E,apply(D,C)) ) ) ) ),
inference(negate_conjecture,[status(cth)],[t21_funct_2]) ).
cnf(78,plain,
in(sK20,sK18),
inference(cnf,[status(esa)],[t21_funct_2_negated]) ).
cnf(l0,plain,
in(sK20,sK18),
inference(instantiation,[status(thm)],[78]) ).
fof(redefinition_k4_relset_1,plain,
! [A,B,C] :
( relation_of2(C,A,B)
=> relation_dom_as_subset(A,B,C) = relation_dom(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_k4_relset_1) ).
cnf(68,plain,
( ~ relation_of2(X0,X1,X2)
| relation_dom_as_subset(X1,X2,X0) = relation_dom(X0) ),
inference(cnf,[status(esa)],[redefinition_k4_relset_1]) ).
cnf(l269,plain,
( ~ relation_of2(sK21,sK18,sK19)
| relation_dom_as_subset(sK18,sK19,sK21) = relation_dom(sK21) ),
inference(instantiation,[status(thm)],[68]) ).
fof(redefinition_m2_relset_1,plain,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
cnf(69,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| relation_of2(X0,X1,X2) ),
inference(cnf,[status(esa)],[redefinition_m2_relset_1]) ).
cnf(l270,plain,
( ~ relation_of2_as_subset(sK21,sK18,sK19)
| relation_of2(sK21,sK18,sK19) ),
inference(instantiation,[status(thm)],[69]) ).
fof(t23_funct_1,plain,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(B))
=> apply(relation_composition(B,C),A) = apply(C,apply(B,A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
cnf(81,plain,
( ~ in(X0,relation_dom(X1))
| ~ function(X1)
| ~ function(X2)
| ~ relation(X1)
| ~ relation(X2)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf,[status(esa)],[t23_funct_1]) ).
cnf(l3,plain,
( ~ in(sK20,relation_dom(sK21))
| ~ function(sK21)
| ~ function(sK22)
| ~ relation(sK21)
| ~ relation(sK22)
| apply(relation_composition(sK21,sK22),sK20) = apply(sK22,apply(sK21,sK20)) ),
inference(instantiation,[status(thm)],[81]) ).
fof(d1_funct_2,plain,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( ( ( B = empty_set
=> A = empty_set )
=> ( quasi_total(C,A,B)
<=> A = relation_dom_as_subset(A,B,C) ) )
& ( B = empty_set
=> ( A = empty_set
| ( quasi_total(C,A,B)
<=> C = empty_set ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_2) ).
cnf(10,plain,
( ~ quasi_total(X0,X1,X2)
| X1 = relation_dom_as_subset(X1,X2,X0)
| ~ sP0(X2,X1,X0) ),
inference(cnf,[status(esa)],[d1_funct_2]) ).
cnf(l265,plain,
( ~ quasi_total(sK21,sK18,sK19)
| sK18 = relation_dom_as_subset(sK18,sK19,sK21)
| ~ sP0(sK19,sK18,sK21) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(74,plain,
quasi_total(sK21,sK18,sK19),
inference(cnf,[status(esa)],[t21_funct_2_negated]) ).
cnf(l273,plain,
quasi_total(sK21,sK18,sK19),
inference(instantiation,[status(thm)],[74]) ).
cnf(5,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| X2 = empty_set
| sP0(X2,X1,X0) ),
inference(cnf,[status(esa)],[d1_funct_2]) ).
cnf(l287,plain,
( ~ relation_of2_as_subset(sK21,sK18,sK19)
| sK19 = empty_set
| sP0(sK19,sK18,sK21) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(75,plain,
relation_of2_as_subset(sK21,sK18,sK19),
inference(cnf,[status(esa)],[t21_funct_2_negated]) ).
cnf(l353,plain,
relation_of2_as_subset(sK21,sK18,sK19),
inference(instantiation,[status(thm)],[75]) ).
cnf(80,plain,
apply(relation_composition(sK21,sK22),sK20) != apply(sK22,apply(sK21,sK20)),
inference(cnf,[status(esa)],[t21_funct_2_negated]) ).
cnf(l1084,plain,
apply(relation_composition(sK21,sK22),sK20) != apply(sK22,apply(sK21,sK20)),
inference(instantiation,[status(thm)],[80]) ).
cnf(73,plain,
function(sK21),
inference(cnf,[status(esa)],[t21_funct_2_negated]) ).
cnf(l23,plain,
function(sK21),
inference(instantiation,[status(thm)],[73]) ).
cnf(79,plain,
sK19 != empty_set,
inference(cnf,[status(esa)],[t21_funct_2_negated]) ).
cnf(l311,plain,
sK19 != empty_set,
inference(instantiation,[status(thm)],[79]) ).
cnf(76,plain,
relation(sK22),
inference(cnf,[status(esa)],[t21_funct_2_negated]) ).
cnf(l908,plain,
relation(sK22),
inference(instantiation,[status(thm)],[76]) ).
cnf(l320,plain,
relation_of2_as_subset(sK21,sK18,sK19),
inference(instantiation,[status(thm)],[75]) ).
fof(cc1_relset_1,plain,
! [A,B,C] :
( element(C,powerset(cartesian_product2(A,B)))
=> relation(C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relset_1) ).
cnf(3,plain,
( ~ element(X0,powerset(cartesian_product2(X1,X2)))
| relation(X0) ),
inference(cnf,[status(esa)],[cc1_relset_1]) ).
cnf(l336,plain,
( ~ element(sK21,powerset(cartesian_product2(sK18,sK19)))
| relation(sK21) ),
inference(instantiation,[status(thm)],[3]) ).
fof(dt_m2_relset_1,plain,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> element(C,powerset(cartesian_product2(A,B))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m2_relset_1) ).
cnf(13,plain,
( ~ relation_of2_as_subset(X0,X1,X2)
| element(X0,powerset(cartesian_product2(X1,X2))) ),
inference(cnf,[status(esa)],[dt_m2_relset_1]) ).
cnf(l338,plain,
( ~ relation_of2_as_subset(sK21,sK18,sK19)
| element(sK21,powerset(cartesian_product2(sK18,sK19))) ),
inference(instantiation,[status(thm)],[13]) ).
cnf(l339,plain,
relation_of2_as_subset(sK21,sK18,sK19),
inference(instantiation,[status(thm)],[75]) ).
cnf(77,plain,
function(sK22),
inference(cnf,[status(esa)],[t21_funct_2_negated]) ).
cnf(l337,plain,
function(sK22),
inference(instantiation,[status(thm)],[77]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l269,l270,l3,l265,l273,l287,l353,l1084,l23,l311,l908,l320,l336,l338,l339,l337]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU292+1 : TPTP v9.0.0. Released v3.3.0.
% 0.03/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/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 : Tue Jul 22 00:35:34 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 9
% 0.19/0.35 % launching worker at depth: 10
% 0.19/0.47 % launching worker at depth: 11
% 13.30/2.02 % launching worker at depth: 12
% 247.40/31.45 % SZS status Theorem for theBenchmark
% 247.40/31.45 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------