%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET720+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n022.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 03:32:34 PM UTC 2025
% Result : Theorem 130.97s 16.84s
% Output : CNFRefutation 130.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 5 unt; 0 def)
% Number of atoms : 86 ( 6 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 83 ( 26 ~; 35 |; 11 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-4 aty)
% Number of variables : 61 ( 0 sgn 25 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thII11,plain,
! [F,A,B] :
( ( maps(F,A,B)
& one_to_one(F,A,B) )
=> equal_maps(inverse_function(inverse_function(F,A,B),B,A),F,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thII11) ).
fof(thII11_negated,plain,
~ ! [F,A,B] :
( ( maps(F,A,B)
& one_to_one(F,A,B) )
=> equal_maps(inverse_function(inverse_function(F,A,B),B,A),F,A,B) ),
inference(negate_conjecture,[status(cth)],[thII11]) ).
cnf(138,plain,
~ equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),
inference(cnf,[status(esa)],[thII11_negated]) ).
cnf(l0,plain,
~ equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),
inference(instantiation,[status(thm)],[138]) ).
fof(equal_maps,plain,
! [F,G,A,B] :
( equal_maps(F,G,A,B)
<=> ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(G,X,Y2) )
=> Y1 = Y2 ) ) ),
file('Axioms/SET006+1.ax',equal_maps) ).
cnf(58,plain,
( member(sK20(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf,[status(esa)],[equal_maps]) ).
cnf(l1,plain,
( member(sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK53)
| equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) ),
inference(instantiation,[status(thm)],[58]) ).
fof(inverse_function,plain,
! [F,A,B,X,Y] :
( ( member(X,A)
& member(Y,B) )
=> ( apply(F,X,Y)
<=> apply(inverse_function(F,A,B),Y,X) ) ),
file('Axioms/SET006+1.ax',inverse_function) ).
cnf(89,plain,
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ apply(inverse_function(X4,X1,X3),X2,X0)
| apply(X4,X0,X2) ),
inference(cnf,[status(esa)],[inverse_function]) ).
cnf(l82,plain,
( ~ member(sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK52)
| ~ member(sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK53)
| ~ apply(inverse_function(sK51,sK52,sK53),sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53))
| apply(sK51,sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53)) ),
inference(instantiation,[status(thm)],[89]) ).
fof(maps,plain,
! [F,A,B] :
( maps(F,A,B)
<=> ( ! [X] :
( member(X,A)
=> ? [Y] :
( member(Y,B)
& apply(F,X,Y) ) )
& ! [X,Y1,Y2] :
( ( member(X,A)
& member(Y1,B)
& member(Y2,B) )
=> ( ( apply(F,X,Y1)
& apply(F,X,Y2) )
=> Y1 = Y2 ) ) ) ),
file('Axioms/SET006+1.ax',maps) ).
cnf(31,plain,
( ~ member(X0,X1)
| ~ member(X2,X3)
| ~ member(X4,X3)
| ~ maps(X5,X1,X3)
| ~ apply(X5,X0,X2)
| ~ apply(X5,X0,X4)
| X2 = X4 ),
inference(cnf,[status(esa)],[maps]) ).
cnf(l334,plain,
( ~ member(sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK52)
| ~ member(sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK53)
| ~ member(sK21(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK53)
| ~ maps(sK51,sK52,sK53)
| ~ apply(sK51,sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53))
| ~ apply(sK51,sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK21(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53))
| sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) = sK21(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) ),
inference(instantiation,[status(thm)],[31]) ).
cnf(l263,plain,
( ~ member(sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK53)
| ~ member(sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK52)
| ~ apply(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53))
| apply(inverse_function(sK51,sK52,sK53),sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53)) ),
inference(instantiation,[status(thm)],[89]) ).
cnf(57,plain,
( member(sK19(X0,X1,X2,X3),X2)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf,[status(esa)],[equal_maps]) ).
cnf(l264,plain,
( member(sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK52)
| equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(61,plain,
( equal_maps(X0,X1,X2,X3)
| apply(X1,sK19(X0,X1,X2,X3),sK21(X0,X1,X2,X3)) ),
inference(cnf,[status(esa)],[equal_maps]) ).
cnf(l335,plain,
( equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53)
| apply(sK51,sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK21(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53)) ),
inference(instantiation,[status(thm)],[61]) ).
cnf(136,plain,
maps(sK51,sK52,sK53),
inference(cnf,[status(esa)],[thII11_negated]) ).
cnf(l342,plain,
maps(sK51,sK52,sK53),
inference(instantiation,[status(thm)],[136]) ).
cnf(60,plain,
( equal_maps(X0,X1,X2,X3)
| apply(X0,sK19(X0,X1,X2,X3),sK20(X0,X1,X2,X3)) ),
inference(cnf,[status(esa)],[equal_maps]) ).
cnf(l266,plain,
( equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53)
| apply(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53)) ),
inference(instantiation,[status(thm)],[60]) ).
cnf(62,plain,
( sK20(X0,X1,X2,X3) != sK21(X0,X1,X2,X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf,[status(esa)],[equal_maps]) ).
cnf(l340,plain,
( sK20(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) != sK21(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53)
| equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) ),
inference(instantiation,[status(thm)],[62]) ).
cnf(59,plain,
( member(sK21(X0,X1,X2,X3),X3)
| equal_maps(X0,X1,X2,X3) ),
inference(cnf,[status(esa)],[equal_maps]) ).
cnf(l341,plain,
( member(sK21(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK53)
| equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) ),
inference(instantiation,[status(thm)],[59]) ).
cnf(l338,plain,
( member(sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK52)
| equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(l84,plain,
( member(sK19(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53),sK52)
| equal_maps(inverse_function(inverse_function(sK51,sK52,sK53),sK53,sK52),sK51,sK52,sK53) ),
inference(instantiation,[status(thm)],[57]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l82,l334,l263,l264,l335,l342,l266,l340,l341,l338,l84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : SET720+4 : TPTP v9.0.0. Bugfixed v2.2.1.
% 0.08/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n022.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 22:25:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 7
% 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: 4
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.37 % launching worker at depth: 10
% 3.57/0.80 % launching worker at depth: 11
% 130.97/16.84 % SZS status Theorem for theBenchmark
% 130.97/16.84 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------