%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SEU215+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 : 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 03:44:51 PM UTC 2025
% Result : Theorem 22.28s 3.15s
% Output : CNFRefutation 22.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 26 unt; 0 def)
% Number of atoms : 136 ( 21 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 147 ( 57 ~; 55 |; 16 &)
% ( 3 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(t23_funct_1_negated,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)) ) ) ),
inference(negate_conjecture,[status(cth)],[t23_funct_1]) ).
cnf(46,plain,
relation(sK10),
inference(cnf,[status(esa)],[t23_funct_1_negated]) ).
cnf(l0,plain,
relation(sK10),
inference(instantiation,[status(thm)],[46]) ).
fof(d4_funct_1,plain,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B,C] :
( ( in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> in(ordered_pair(B,C),A) ) )
& ( ~ in(B,relation_dom(A))
=> ( C = apply(A,B)
<=> C = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
cnf(7,plain,
( ~ function(X0)
| ~ relation(X0)
| X1 != empty_set
| in(X2,relation_dom(X0))
| X1 = apply(X0,X2) ),
inference(cnf,[status(esa)],[d4_funct_1]) ).
cnf(l1,plain,
( ~ function(sK10)
| ~ relation(sK10)
| apply(relation_composition(sK9,sK10),sK8) != empty_set
| in(apply(sK9,sK8),relation_dom(sK10))
| apply(relation_composition(sK9,sK10),sK8) = apply(sK10,apply(sK9,sK8)) ),
inference(instantiation,[status(thm)],[7]) ).
fof(t21_funct_1,plain,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
<=> ( in(A,relation_dom(C))
& in(apply(C,A),relation_dom(B)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t21_funct_1) ).
cnf(42,plain,
( ~ in(X0,relation_dom(X1))
| ~ in(apply(X1,X0),relation_dom(X2))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| in(X0,relation_dom(relation_composition(X1,X2))) ),
inference(cnf,[status(esa)],[t21_funct_1]) ).
cnf(l139,plain,
( ~ in(sK8,relation_dom(sK9))
| ~ in(apply(sK9,sK8),relation_dom(sK10))
| ~ function(sK10)
| ~ function(sK9)
| ~ relation(sK10)
| ~ relation(sK9)
| in(sK8,relation_dom(relation_composition(sK9,sK10))) ),
inference(instantiation,[status(thm)],[42]) ).
fof(t22_funct_1,plain,
! [A,B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( in(A,relation_dom(relation_composition(C,B)))
=> apply(relation_composition(C,B),A) = apply(B,apply(C,A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
cnf(43,plain,
( ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ function(X2)
| ~ function(X1)
| ~ relation(X2)
| ~ relation(X1)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf,[status(esa)],[t22_funct_1]) ).
cnf(l146,plain,
( ~ in(sK8,relation_dom(relation_composition(sK9,sK10)))
| ~ function(sK10)
| ~ function(sK9)
| ~ relation(sK10)
| ~ relation(sK9)
| apply(relation_composition(sK9,sK10),sK8) = apply(sK10,apply(sK9,sK8)) ),
inference(instantiation,[status(thm)],[43]) ).
cnf(49,plain,
apply(relation_composition(sK9,sK10),sK8) != apply(sK10,apply(sK9,sK8)),
inference(cnf,[status(esa)],[t23_funct_1_negated]) ).
cnf(l149,plain,
apply(relation_composition(sK9,sK10),sK8) != apply(sK10,apply(sK9,sK8)),
inference(instantiation,[status(thm)],[49]) ).
cnf(48,plain,
in(sK8,relation_dom(sK9)),
inference(cnf,[status(esa)],[t23_funct_1_negated]) ).
cnf(l169,plain,
in(sK8,relation_dom(sK9)),
inference(instantiation,[status(thm)],[48]) ).
cnf(44,plain,
relation(sK9),
inference(cnf,[status(esa)],[t23_funct_1_negated]) ).
cnf(l177,plain,
relation(sK9),
inference(instantiation,[status(thm)],[44]) ).
cnf(l160,plain,
relation(sK9),
inference(instantiation,[status(thm)],[44]) ).
cnf(45,plain,
function(sK9),
inference(cnf,[status(esa)],[t23_funct_1_negated]) ).
cnf(l153,plain,
function(sK9),
inference(instantiation,[status(thm)],[45]) ).
cnf(47,plain,
function(sK10),
inference(cnf,[status(esa)],[t23_funct_1_negated]) ).
cnf(l158,plain,
function(sK10),
inference(instantiation,[status(thm)],[47]) ).
cnf(l148,plain,
function(sK9),
inference(instantiation,[status(thm)],[45]) ).
cnf(l3,plain,
function(sK10),
inference(instantiation,[status(thm)],[47]) ).
cnf(l144,plain,
function(sK10),
inference(instantiation,[status(thm)],[47]) ).
cnf(6,plain,
( ~ function(X0)
| ~ relation(X0)
| X1 != apply(X0,X2)
| in(X2,relation_dom(X0))
| X1 = empty_set ),
inference(cnf,[status(esa)],[d4_funct_1]) ).
cnf(l10,plain,
( ~ function(relation_composition(sK9,sK10))
| ~ relation(relation_composition(sK9,sK10))
| apply(relation_composition(sK9,sK10),sK8) != apply(relation_composition(sK9,sK10),sK8)
| in(sK8,relation_dom(relation_composition(sK9,sK10)))
| apply(relation_composition(sK9,sK10),sK8) = empty_set ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l60,plain,
( ~ in(sK8,relation_dom(relation_composition(sK9,sK10)))
| ~ function(sK10)
| ~ function(sK9)
| ~ relation(sK10)
| ~ relation(sK9)
| apply(relation_composition(sK9,sK10),sK8) = apply(sK10,apply(sK9,sK8)) ),
inference(instantiation,[status(thm)],[43]) ).
fof(fc1_funct_1,plain,
! [A,B] :
( ( relation(A)
& function(A)
& relation(B)
& function(B) )
=> ( relation(relation_composition(A,B))
& function(relation_composition(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
cnf(17,plain,
( ~ function(X0)
| ~ function(X1)
| ~ relation(X0)
| ~ relation(X1)
| function(relation_composition(X0,X1)) ),
inference(cnf,[status(esa)],[fc1_funct_1]) ).
cnf(l39,plain,
( ~ function(sK9)
| ~ function(sK10)
| ~ relation(sK9)
| ~ relation(sK10)
| function(relation_composition(sK9,sK10)) ),
inference(instantiation,[status(thm)],[17]) ).
cnf(l136,plain,
apply(relation_composition(sK9,sK10),sK8) != apply(sK10,apply(sK9,sK8)),
inference(instantiation,[status(thm)],[49]) ).
cnf(l41,plain,
relation(sK9),
inference(instantiation,[status(thm)],[44]) ).
cnf(l40,plain,
function(sK9),
inference(instantiation,[status(thm)],[45]) ).
cnf(l137,plain,
relation(sK9),
inference(instantiation,[status(thm)],[44]) ).
fof(dt_k5_relat_1,plain,
! [A,B] :
( ( relation(A)
& relation(B) )
=> relation(relation_composition(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
cnf(9,plain,
( ~ relation(X0)
| ~ relation(X1)
| relation(relation_composition(X0,X1)) ),
inference(cnf,[status(esa)],[dt_k5_relat_1]) ).
cnf(l59,plain,
( ~ relation(sK9)
| ~ relation(sK10)
| relation(relation_composition(sK9,sK10)) ),
inference(instantiation,[status(thm)],[9]) ).
cnf(l106,plain,
relation(sK9),
inference(instantiation,[status(thm)],[44]) ).
cnf(l134,plain,
function(sK9),
inference(instantiation,[status(thm)],[45]) ).
cnf(l42,plain,
function(sK10),
inference(instantiation,[status(thm)],[47]) ).
cnf(l76,plain,
function(sK10),
inference(instantiation,[status(thm)],[47]) ).
cnf(l45,plain,
apply(relation_composition(sK9,sK10),sK8) != apply(sK10,apply(sK9,sK8)),
inference(instantiation,[status(thm)],[49]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l139,l146,l149,l169,l177,l160,l153,l158,l148,l3,l144,l10,l60,l39,l136,l41,l40,l137,l59,l106,l134,l42,l76,l45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU215+1 : TPTP v9.0.0. Released v3.3.0.
% 0.00/0.12 % 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 23:59:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.33 % launching worker at depth: 1
% 0.12/0.33 % launching worker at depth: 7
% 0.12/0.33 % launching worker at depth: 2
% 0.12/0.33 % launching worker at depth: 5
% 0.12/0.33 % launching worker at depth: 4
% 0.12/0.33 % launching worker at depth: 6
% 0.12/0.33 % launching worker at depth: 8
% 0.12/0.33 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 9
% 0.19/0.35 % launching worker at depth: 10
% 0.19/0.51 % launching worker at depth: 11
% 22.28/3.15 % SZS status Theorem for theBenchmark
% 22.28/3.15 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------