%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12.18s 2.90s
% Output : CNFRefutation 12.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of clauses : 43 ( 19 unt; 5 nHn; 27 RR)
% Number of literals : 69 ( 22 equ; 29 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'v$uc' != 'c$u0' ).
cnf(cls_conjecture_1,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'(X0)),'t$ua'),'c$utimes'(X0,'c$utimes'('c$uHOL$uOabs'('v$uc','t$ua'),'c$uHOL$uOabs'('v$uf'('v$ux'(X0)),'t$ua'),'t$ua'),'t$ua'),'t$ua') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$ufield'('t$ua') ).
cnf(cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0,axiom,
( 'c$utimes'('c$u1',X1,X0) = X1
| ~ 'class$uOrderedGroup$uOmonoid$u$umult'(X0) ) ).
cnf(cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0,axiom,
( 'c$utimes'('c$utimes'(X1,X2,X0),X3,X0) = 'c$utimes'(X1,'c$utimes'(X2,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOsemigroup$u$umult'(X0) ) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( 'c$ulessequals'(X1,X1,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_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
( 'c$utimes'('c$uHOL$uOinverse'(X1,X0),X1,X0) = 'c$u1'
| X1 = 'c$u0'
| ~ 'class$uRing$u$uand$u$uField$uOfield'(X0) ) ).
cnf(clsrel_Ring__and__Field_Ofield_12,axiom,
( 'class$uOrderedGroup$uOmonoid$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOfield'(X0) ) ).
cnf(clsrel_Ring__and__Field_Ofield_21,axiom,
( 'class$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$ufield'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__field_58,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ) ).
cnf(c0,plain,
'v$uc' != 'c$u0',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'(X0)),'t$ua'),'c$utimes'(X0,'c$utimes'('c$uHOL$uOabs'('v$uc','t$ua'),'c$uHOL$uOabs'('v$uf'('v$ux'(X0)),'t$ua'),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
'class$uRing$u$uand$u$uField$uOordered$u$ufield'('t$ua'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c3,plain,
( 'c$utimes'('c$u1',X1,X0) = X1
| ~ 'class$uOrderedGroup$uOmonoid$u$umult'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0]) ).
cnf(c4,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(c5,plain,
( 'c$ulessequals'(X1,X1,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
cnf(c6,plain,
( 'c$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$uidom'(X0) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Oabs__mult_0]) ).
cnf(c7,plain,
( 'c$utimes'('c$uHOL$uOinverse'(X1,X0),X1,X0) = 'c$u1'
| X1 = 'c$u0'
| ~ 'class$uRing$u$uand$u$uField$uOfield'(X0) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Ofield__class_Oaxioms__1_0]) ).
cnf(c8,plain,
( 'class$uOrderedGroup$uOmonoid$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOfield'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Ofield_12]) ).
cnf(c9,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(c10,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(c11,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(c12,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$ufield'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__field_58]) ).
cnf(d0,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua'),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d1,plain,
'c$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)],[c6,d0]) ).
cnf(d2,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'(X0)),'t$ua'),'c$utimes'(X0,'c$uHOL$uOabs'('c$utimes'('v$uc','v$uf'('v$ux'(X0)),'t$ua'),'t$ua'),'t$ua'),'t$ua'),
inference(demodulation,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'('c$uHOL$uOabs'(X0,'t$ua'))),'t$ua'),'c$uHOL$uOabs'('c$utimes'(X0,'c$utimes'('v$uc','v$uf'('v$ux'('c$uHOL$uOabs'(X0,'t$ua'))),'t$ua'),'t$ua'),'t$ua'),'t$ua'),
inference(superposition,[status(thm)],[d1,d2]) ).
cnf(d4,plain,
'class$uRing$u$uand$u$uField$uOfield'('t$ua'),
inference(resolution,[status(thm)],[c10,c2]) ).
cnf(d5,plain,
'class$uOrderedGroup$uOmonoid$u$umult'('t$ua'),
inference(resolution,[status(thm)],[c8,d4]) ).
cnf(d6,plain,
'c$utimes'('c$u1',X0,'t$ua') = X0,
inference(resolution,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
'class$uOrderedGroup$uOsemigroup$u$umult'('t$ua'),
inference(resolution,[status(thm)],[c9,d4]) ).
cnf(d8,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)],[d7,c4]) ).
cnf(d9,plain,
( 'c$utimes'('c$uHOL$uOinverse'(X0,'t$ua'),X0,'t$ua') = 'c$u1'
| X0 = 'c$u0' ),
inference(resolution,[status(thm)],[c7,d4]) ).
cnf(d10,plain,
( X0 = 'c$u0'
| 'c$utimes'('c$u1',X1,'t$ua') = 'c$utimes'('c$uHOL$uOinverse'(X0,'t$ua'),'c$utimes'(X0,X1,'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( X0 = 'c$utimes'('c$uHOL$uOinverse'(X1,'t$ua'),'c$utimes'(X1,X0,'t$ua'),'t$ua')
| X1 = 'c$u0' ),
inference(demodulation,[status(thm)],[d10,d6]) ).
cnf(d12,plain,
( 'v$uc' = 'c$u0'
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'('c$uHOL$uOabs'('c$uHOL$uOinverse'('v$uc','t$ua'),'t$ua'))),'t$ua'),'c$uHOL$uOabs'('v$uf'('v$ux'('c$uHOL$uOabs'('c$uHOL$uOinverse'('v$uc','t$ua'),'t$ua'))),'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'('c$uHOL$uOabs'('c$uHOL$uOinverse'('v$uc','t$ua'),'t$ua'))),'t$ua'),'c$uHOL$uOabs'('v$uf'('v$ux'('c$uHOL$uOabs'('c$uHOL$uOinverse'('v$uc','t$ua'),'t$ua'))),'t$ua'),'t$ua'),
inference(resolution,[status(thm)],[c0,d12]) ).
cnf(d14,plain,
~ 'class$uOrderings$uOorder'('t$ua'),
inference(resolution,[status(thm)],[d13,c5]) ).
cnf(d15,plain,
'class$uOrderings$uOorder'('t$ua'),
inference(resolution,[status(thm)],[c12,c2]) ).
cnf(d16,plain,
$false,
inference(resolution,[status(thm)],[d15,d14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA014-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n005.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 22:04:31 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.18/2.90 % SZS status Unsatisfiable for theBenchmark.p
% 12.18/2.90 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------