%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA009-2 : 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 : n013.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 06:50:36 AM UTC 2026
% Result : Unsatisfiable 9.52s 1.76s
% Output : CNFRefutation 9.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 11 unt; 0 nHn; 14 RR)
% Number of literals : 34 ( 3 equ; 16 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oadd__le__cancel__right_1,axiom,
( 'c$ulessequals'('c$uplus'(X1,X3,X0),'c$uplus'(X2,X3,X0),X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$usemigroup$u$uadd$u$uimp$u$ule'(X0) ) ).
cnf(cls_OrderedGroup_Oright__minus_0,axiom,
( 'c$uplus'(X1,'c$uuminus'(X1,X0),X0) = 'c$u0'
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'('v$ulb'(X0),'v$uf'(X0),'t$ub') ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('c$u0','c$uplus'('v$uf'('v$ux'),'c$uuminus'('v$ulb'('v$ux'),'t$ub'),'t$ub'),'t$ub') ).
cnf(clsrel_Ring__and__Field_Oordered__idom_37,axiom,
( 'class$uOrderedGroup$uOpordered$u$uab$u$usemigroup$u$uadd$u$uimp$u$ule'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(c0,plain,
( 'c$ulessequals'('c$uplus'(X1,X3,X0),'c$uplus'(X2,X3,X0),X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$usemigroup$u$uadd$u$uimp$u$ule'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oadd__le__cancel__right_1]) ).
cnf(c1,plain,
( 'c$uplus'(X1,'c$uuminus'(X1,X0),X0) = 'c$u0'
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oright__minus_0]) ).
cnf(c2,plain,
'c$ulessequals'('v$ulb'(X0),'v$uf'(X0),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c3,plain,
~ 'c$ulessequals'('c$u0','c$uplus'('v$uf'('v$ux'),'c$uuminus'('v$ulb'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c4,plain,
( 'class$uOrderedGroup$uOpordered$u$uab$u$usemigroup$u$uadd$u$uimp$u$ule'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_37]) ).
cnf(c5,plain,
( 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
cnf(c6,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(d0,plain,
'class$uOrderedGroup$uOab$u$ugroup$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[c5,c6]) ).
cnf(d1,plain,
'c$uplus'(X0,'c$uuminus'(X0,'t$ub'),'t$ub') = 'c$u0',
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$usemigroup$u$uadd$u$uimp$u$ule'('t$ub')
| ~ 'c$ulessequals'(X0,X1,'t$ub')
| 'c$ulessequals'('c$u0','c$uplus'(X1,'c$uuminus'(X0,'t$ub'),'t$ub'),'t$ub') ),
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
'class$uOrderedGroup$uOpordered$u$uab$u$usemigroup$u$uadd$u$uimp$u$ule'('t$ub'),
inference(resolution,[status(thm)],[c4,c6]) ).
cnf(d4,plain,
( 'c$ulessequals'('c$u0','c$uplus'(X1,'c$uuminus'(X0,'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'(X0,X1,'t$ub') ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
~ 'c$ulessequals'('v$ulb'('v$ux'),'v$uf'('v$ux'),'t$ub'),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c2,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA009-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.53 % Computer : n013.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.53 % CPULimit : 300
% 0.10/0.53 % WCLimit : 300
% 0.10/0.53 % DateTime : Sat Sep 26 22:03:36 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.54 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.52/1.76 % SZS status Unsatisfiable for theBenchmark.p
% 9.52/1.76 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------