%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA010-2 : 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 : n015.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 11.27s 3.15s
% Output : CNFRefutation 11.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 15 unt; 0 nHn; 21 RR)
% Number of literals : 51 ( 8 equ; 26 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 38 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( 'c$uHOL$uOabs'(X1,X0) = X1
| ~ 'c$ulessequals'('c$u0',X1,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$uOorder'(X0) ) ).
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( 'c$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$uidom'(X0) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'('c$u0','v$uf'(X0),'t$ub') ).
cnf(cls_conjecture_1,negated_conjecture,
'c$ulessequals'('v$uf'(X0),'c$utimes'('v$uc','v$ug'(X0),'t$ub'),'t$ub') ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('v$uf'('v$ux'(X0)),'c$utimes'(X0,'c$uHOL$uOabs'('v$ug'('v$ux'(X0)),'t$ub'),'t$ub'),'t$ub') ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_50,axiom,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(c0,plain,
( 'c$uHOL$uOabs'(X1,X0) = X1
| ~ 'c$ulessequals'('c$u0',X1,X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__of__nonneg_0]) ).
cnf(c1,plain,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c2,plain,
( 'c$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$u0','v$uf'(X0),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c4,plain,
'c$ulessequals'('v$uf'(X0),'c$utimes'('v$uc','v$ug'(X0),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c5,plain,
~ 'c$ulessequals'('v$uf'('v$ux'(X0)),'c$utimes'(X0,'c$uHOL$uOabs'('v$ug'('v$ux'(X0)),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c6,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Olordered__ab__group__abs_17]) ).
cnf(c7,plain,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(c8,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(d0,plain,
'c$uHOL$uOabs'('c$utimes'(X0,X1,'t$ub'),'t$ub') = 'c$utimes'('c$uHOL$uOabs'(X0,'t$ub'),'c$uHOL$uOabs'(X1,'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[c2,c8]) ).
cnf(d1,plain,
~ 'c$ulessequals'('v$uf'('v$ux'('c$uHOL$uOabs'(X0,'t$ub'))),'c$uHOL$uOabs'('c$utimes'(X0,'v$ug'('v$ux'('c$uHOL$uOabs'(X0,'t$ub'))),'t$ub'),'t$ub'),'t$ub'),
inference(superposition,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'(X0,'v$uf'(X1),'t$ub')
| 'c$ulessequals'(X0,'c$utimes'('v$uc','v$ug'(X1),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[c4,c1]) ).
cnf(d3,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[c7,c8]) ).
cnf(d4,plain,
'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[d3,c6]) ).
cnf(d5,plain,
( ~ 'c$ulessequals'(X0,'v$uf'(X1),'t$ub')
| 'c$ulessequals'(X0,'c$utimes'('v$uc','v$ug'(X1),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub')
| 'c$uHOL$uOabs'('c$utimes'('v$uc','v$ug'(X0),'t$ub'),'t$ub') = 'c$utimes'('v$uc','v$ug'(X0),'t$ub')
| ~ 'c$ulessequals'('c$u0','v$uf'(X0),'t$ub') ),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
( ~ 'c$ulessequals'('c$u0','v$uf'(X0),'t$ub')
| 'c$uHOL$uOabs'('c$utimes'('v$uc','v$ug'(X0),'t$ub'),'t$ub') = 'c$utimes'('v$uc','v$ug'(X0),'t$ub') ),
inference(resolution,[status(thm)],[d3,d6]) ).
cnf(d8,plain,
'c$uHOL$uOabs'('c$utimes'('v$uc','v$ug'(X0),'t$ub'),'t$ub') = 'c$utimes'('v$uc','v$ug'(X0),'t$ub'),
inference(resolution,[status(thm)],[c3,d7]) ).
cnf(d9,plain,
~ 'c$ulessequals'('v$uf'('v$ux'('c$uHOL$uOabs'('v$uc','t$ub'))),'c$utimes'('v$uc','v$ug'('v$ux'('c$uHOL$uOabs'('v$uc','t$ub'))),'t$ub'),'t$ub'),
inference(superposition,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[c4,d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA010-2 : 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 : n015.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 22:07:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.27/3.15 % SZS status Unsatisfiable for theBenchmark.p
% 11.27/3.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------