%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA016-2 : 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 : 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 06:50:37 AM UTC 2026
% Result : Unsatisfiable 13.87s 2.46s
% Output : CNFRefutation 13.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of clauses : 29 ( 13 unt; 5 nHn; 18 RR)
% Number of literals : 47 ( 23 equ; 18 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 31 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'v$uc' != 'c$u0' ).
cnf(cls_conjecture_2,negated_conjecture,
'v$ug'('v$ux') != 'c$utimes'('v$uc','c$utimes'('c$uHOL$uOinverse'('v$uc','t$ua'),'v$ug'('v$ux'),'t$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_Ring__and__Field_Oright__inverse_0,axiom,
( 'c$utimes'(X1,'c$uHOL$uOinverse'(X1,X0),X0) = 'c$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$ufield'(X0) ) ).
cnf(c0,plain,
'v$uc' != 'c$u0',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
'v$ug'('v$ux') != 'c$utimes'('v$uc','c$utimes'('c$uHOL$uOinverse'('v$uc','t$ua'),'v$ug'('v$ux'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
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$umult'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Osemigroup__mult__class_Omult__assoc_0]) ).
cnf(c5,plain,
( 'c$utimes'(X1,'c$uHOL$uOinverse'(X1,X0),X0) = 'c$u1'
| X1 = 'c$u0'
| ~ 'class$uRing$u$uand$u$uField$uOfield'(X0) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Oright__inverse_0]) ).
cnf(c6,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(c7,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(c8,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(d0,plain,
'class$uRing$u$uand$u$uField$uOfield'('t$ua'),
inference(resolution,[status(thm)],[c8,c2]) ).
cnf(d1,plain,
'class$uOrderedGroup$uOmonoid$u$umult'('t$ua'),
inference(resolution,[status(thm)],[c6,d0]) ).
cnf(d2,plain,
'c$utimes'('c$u1',X0,'t$ua') = X0,
inference(resolution,[status(thm)],[d1,c3]) ).
cnf(d3,plain,
'class$uOrderedGroup$uOsemigroup$u$umult'('t$ua'),
inference(resolution,[status(thm)],[c7,d0]) ).
cnf(d4,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)],[d3,c4]) ).
cnf(d5,plain,
( 'c$utimes'(X0,'c$uHOL$uOinverse'(X0,'t$ua'),'t$ua') = 'c$u1'
| X0 = 'c$u0' ),
inference(resolution,[status(thm)],[c5,d0]) ).
cnf(d6,plain,
( X0 = 'c$u0'
| 'c$utimes'('c$u1',X1,'t$ua') = 'c$utimes'(X0,'c$utimes'('c$uHOL$uOinverse'(X0,'t$ua'),X1,'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
( X0 = 'c$utimes'(X1,'c$utimes'('c$uHOL$uOinverse'(X1,'t$ua'),X0,'t$ua'),'t$ua')
| X1 = 'c$u0' ),
inference(demodulation,[status(thm)],[d6,d2]) ).
cnf(d8,plain,
( 'v$uc' = 'c$u0'
| 'v$ug'('v$ux') != 'v$ug'('v$ux') ),
inference(superposition,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
'v$ug'('v$ux') != 'v$ug'('v$ux'),
inference(resolution,[status(thm)],[c0,d8]) ).
cnf(d10,plain,
$false,
inference(equality_resolution,[status(thm)],[d9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA016-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n013.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 22:04:21 UTC 2026
% 0.21/0.42 % CPUTime :
% 0.21/0.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.87/2.46 % SZS status Unsatisfiable for theBenchmark.p
% 13.87/2.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------