%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA039-2 : 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 : n007.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 06:50:42 AM UTC 2026
% Result : Unsatisfiable 10.07s 1.98s
% Output : CNFRefutation 10.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of clauses : 32 ( 12 unt; 0 nHn; 26 RR)
% Number of literals : 70 ( 0 equ; 44 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 43 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua') ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'c$utimes'('c$uHOL$uOabs'('v$uc','t$ua'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'t$ua'),'t$ua') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua') ).
cnf(cls_OrderedGroup_Oabs__ge__self_0,axiom,
( 'c$ulessequals'(X1,'c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0,axiom,
( 'c$ulessequals'('c$utimes'(X1,X3,X0),'c$utimes'(X2,X3,X0),X0)
| ~ 'c$ulessequals'('c$u0',X3,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_44,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(c0,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'c$utimes'('c$uHOL$uOabs'('v$uc','t$ua'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c2,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c3,plain,
( 'c$ulessequals'(X1,'c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__self_0]) ).
cnf(c4,plain,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c5,plain,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c6,plain,
( 'c$ulessequals'('c$utimes'(X1,X3,X0),'c$utimes'(X2,X3,X0),X0)
| ~ 'c$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__right__mono_0]) ).
cnf(c7,plain,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
cnf(c8,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
cnf(c9,plain,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(d0,plain,
( ~ 'class$uOrderings$uOorder'(X2)
| ~ 'c$ulessequals'(X4,'c$utimes'(X0,X3,X2),X2)
| 'c$ulessequals'(X4,'c$utimes'(X1,X3,X2),X2)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X2)
| ~ 'c$ulessequals'('c$u0',X3,X2)
| ~ 'c$ulessequals'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d1,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ua')
| ~ 'class$uOrderings$uOorder'('t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua')
| ~ 'c$ulessequals'('v$uc',X1,'t$ua')
| 'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'(X1,'c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ua'),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d3,plain,
( ~ 'class$uOrderings$uOorder'('t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua')
| ~ 'c$ulessequals'('v$uc',X1,'t$ua')
| 'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'(X1,'c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'class$uOrderings$uOorder'('t$ua'),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d5,plain,
( ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua')
| ~ 'c$ulessequals'('v$uc',X1,'t$ua')
| 'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'(X1,'c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'t$ua')
| ~ 'c$ulessequals'('v$uc','c$uHOL$uOabs'('v$uc','t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua')
| ~ 'c$ulessequals'('v$uc','c$uHOL$uOabs'('v$uc','t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d6,c4]) ).
cnf(d8,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[c9,c2]) ).
cnf(d9,plain,
~ 'c$ulessequals'('v$uc','c$uHOL$uOabs'('v$uc','t$ua'),'t$ua'),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[d9,c3]) ).
cnf(d11,plain,
$false,
inference(resolution,[status(thm)],[d8,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA039-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:07:26 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.07/1.98 % SZS status Unsatisfiable for theBenchmark.p
% 10.07/1.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------