%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 06:50:37 AM UTC 2026
% Result : Unsatisfiable 10.81s 1.91s
% Output : CNFRefutation 10.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of clauses : 38 ( 17 unt; 0 nHn; 28 RR)
% Number of literals : 66 ( 6 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-3 aty)
% Number of variables : 54 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
( 'c$utimes'('c$utimes'(X1,X2,X0),X3,X0) = 'c$utimes'(X1,'c$utimes'(X2,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOsemigroup$u$umult'(X0) ) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( 'c$uHOL$uOabs'('c$utimes'(X1,X2,X0),X0) = 'c$utimes'('c$uHOL$uOabs'(X1,X0),'c$uHOL$uOabs'(X2,X0),X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( 'c$ulessequals'('c$utimes'(X3,X1,X0),'c$utimes'(X3,X2,X0),X0)
| ~ 'c$ulessequals'('c$u0',X3,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0) ) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$ug'(X0),'t$ua'),'c$utimes'('v$ud','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua') ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('c$utimes'('c$uHOL$uOinverse'('v$uc','t$ua'),'v$ug'('v$ux'(X0)),'t$ua'),'t$ua'),'c$utimes'(X0,'c$uHOL$uOabs'('v$uf'('v$ux'(X0)),'t$ua'),'t$ua'),'t$ua') ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( 'class$uOrderedGroup$uOsemigroup$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOfield'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_0,axiom,
( 'class$uRing$u$uand$u$uField$uOfield'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_34,axiom,
( 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_46,axiom,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_47,axiom,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ) ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$ufield'('t$ua') ).
cnf(c0,plain,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c1,plain,
( 'c$utimes'('c$utimes'(X1,X2,X0),X3,X0) = 'c$utimes'(X1,'c$utimes'(X2,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOsemigroup$u$umult'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0]) ).
cnf(c2,plain,
( 'c$uHOL$uOabs'('c$utimes'(X1,X2,X0),X0) = 'c$utimes'('c$uHOL$uOabs'(X1,X0),'c$uHOL$uOabs'(X2,X0),X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Oabs__mult_0]) ).
cnf(c3,plain,
( 'c$ulessequals'('c$utimes'(X3,X1,X0),'c$utimes'(X3,X2,X0),X0)
| ~ 'c$ulessequals'('c$u0',X3,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0]) ).
cnf(c4,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$ug'(X0),'t$ua'),'c$utimes'('v$ud','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c5,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('c$utimes'('c$uHOL$uOinverse'('v$uc','t$ua'),'v$ug'('v$ux'(X0)),'t$ua'),'t$ua'),'c$utimes'(X0,'c$uHOL$uOabs'('v$uf'('v$ux'(X0)),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c6,plain,
( 'class$uOrderedGroup$uOsemigroup$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOfield'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Ofield_21]) ).
cnf(c7,plain,
( 'class$uRing$u$uand$u$uField$uOfield'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__field_0]) ).
cnf(c8,plain,
( 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__field_34]) ).
cnf(c9,plain,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__field_46]) ).
cnf(c10,plain,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__field_47]) ).
cnf(c11,plain,
'class$uRing$u$uand$u$uField$uOordered$u$ufield'('t$ua'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(d0,plain,
'class$uRing$u$uand$u$uField$uOfield'('t$ua'),
inference(resolution,[status(thm)],[c7,c11]) ).
cnf(d1,plain,
'class$uOrderedGroup$uOsemigroup$u$umult'('t$ua'),
inference(resolution,[status(thm)],[d0,c6]) ).
cnf(d2,plain,
'c$utimes'('c$utimes'(X0,X1,'t$ua'),X2,'t$ua') = 'c$utimes'(X0,'c$utimes'(X1,X2,'t$ua'),'t$ua'),
inference(resolution,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('c$utimes'('c$uHOL$uOinverse'('v$uc','t$ua'),'v$ug'('v$ux'('c$utimes'(X0,X1,'t$ua'))),'t$ua'),'t$ua'),'c$utimes'(X0,'c$utimes'(X1,'c$uHOL$uOabs'('v$uf'('v$ux'('c$utimes'(X0,X1,'t$ua'))),'t$ua'),'t$ua'),'t$ua'),'t$ua'),
inference(superposition,[status(thm)],[d2,c5]) ).
cnf(d4,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua'),
inference(resolution,[status(thm)],[c8,c11]) ).
cnf(d5,plain,
'c$uHOL$uOabs'('c$utimes'(X0,X1,'t$ua'),'t$ua') = 'c$utimes'('c$uHOL$uOabs'(X0,'t$ua'),'c$uHOL$uOabs'(X1,'t$ua'),'t$ua'),
inference(resolution,[status(thm)],[d4,c2]) ).
cnf(d6,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X0,'t$ua'),'t$ua')
| ~ 'c$ulessequals'('c$uHOL$uOabs'(X1,'t$ua'),X2,'t$ua')
| 'c$ulessequals'('c$uHOL$uOabs'('c$utimes'(X0,X1,'t$ua'),'t$ua'),'c$utimes'('c$uHOL$uOabs'(X0,'t$ua'),X2,'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ua'),
inference(resolution,[status(thm)],[c9,c11]) ).
cnf(d8,plain,
( 'c$ulessequals'('c$uHOL$uOabs'('c$utimes'(X0,X1,'t$ua'),'t$ua'),'c$utimes'('c$uHOL$uOabs'(X0,'t$ua'),X2,'t$ua'),'t$ua')
| ~ 'c$ulessequals'('c$uHOL$uOabs'(X1,'t$ua'),X2,'t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X0,'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ 'c$ulessequals'('c$uHOL$uOabs'('v$ug'('v$ux'('c$utimes'('c$uHOL$uOabs'('c$uHOL$uOinverse'('v$uc','t$ua'),'t$ua'),X0,'t$ua'))),'t$ua'),'c$utimes'(X0,'c$uHOL$uOabs'('v$uf'('v$ux'('c$utimes'('c$uHOL$uOabs'('c$uHOL$uOinverse'('v$uc','t$ua'),'t$ua'),X0,'t$ua'))),'t$ua'),'t$ua'),'t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('c$uHOL$uOinverse'('v$uc','t$ua'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('c$uHOL$uOinverse'('v$uc','t$ua'),'t$ua'),'t$ua'),
inference(resolution,[status(thm)],[d9,c4]) ).
cnf(d11,plain,
~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[c10,c11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA015-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n004.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 22:04:21 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.81/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 10.81/1.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------