%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA012-2 : 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 : n012.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 10.14s 1.69s
% Output : CNFRefutation 10.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 12 unt; 3 nHn; 24 RR)
% Number of literals : 51 ( 19 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 21 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'v$uc' != 'c$u0' ).
cnf(cls_conjecture_1,negated_conjecture,
~ 'c$ulessequals'('c$u1','c$utimes'(X0,'c$uHOL$uOabs'('v$uc','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_Oabs__eq__0_0,axiom,
( X1 = 'c$u0'
| 'c$uHOL$uOabs'(X1,X0) != 'c$u0'
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_Orderings_Oorder__class_Oaxioms__1_0,axiom,
( 'c$ulessequals'(X1,X1,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_Ring__and__Field_Ofield__class_Oaxioms__1_0,axiom,
( 'c$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_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_47,axiom,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(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$ulessequals'('c$u1','c$utimes'(X0,'c$uHOL$uOabs'('v$uc','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,
( X1 = 'c$u0'
| 'c$uHOL$uOabs'(X1,X0) != 'c$u0'
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__eq__0_0]) ).
cnf(c4,plain,
( 'c$ulessequals'(X1,X1,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oaxioms__1_0]) ).
cnf(c5,plain,
( 'c$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(c6,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(c7,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(c8,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$uField$uOfield'('t$ua'),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d1,plain,
( 'c$utimes'('c$uHOL$uOinverse'(X0,'t$ua'),X0,'t$ua') = 'c$u1'
| X0 = 'c$u0' ),
inference(resolution,[status(thm)],[c5,d0]) ).
cnf(d2,plain,
( 'c$uHOL$uOabs'('v$uc','t$ua') = 'c$u0'
| ~ 'c$ulessequals'('c$u1','c$u1','t$ua') ),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
( ~ 'class$uOrderings$uOorder'('t$ua')
| 'c$uHOL$uOabs'('v$uc','t$ua') = 'c$u0' ),
inference(resolution,[status(thm)],[d2,c4]) ).
cnf(d4,plain,
'class$uOrderings$uOorder'('t$ua'),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d5,plain,
'c$uHOL$uOabs'('v$uc','t$ua') = 'c$u0',
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua')
| 'v$uc' = 'c$u0'
| 'c$u0' != 'c$u0' ),
inference(superposition,[status(thm)],[d5,c3]) ).
cnf(d7,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua')
| 'c$u0' != 'c$u0' ),
inference(resolution,[status(thm)],[c0,d6]) ).
cnf(d8,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[c7,c2]) ).
cnf(d9,plain,
'c$u0' != 'c$u0',
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA012-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Sat Sep 26 22:04:04 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.14/1.69 % SZS status Unsatisfiable for theBenchmark.p
% 10.14/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------