%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA032-2 : 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 : n006.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 06:50:41 AM UTC 2026
% Result : Unsatisfiable 28.75s 4.59s
% Output : CNFRefutation 28.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of clauses : 37 ( 17 unt; 0 nHn; 28 RR)
% Number of literals : 65 ( 7 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 52 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_OrderedGroup_Omult__ac__1_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_OrderedGroup_Omult__ac__2_0,axiom,
( 'c$utimes'(X1,X2,X0) = 'c$utimes'(X2,X1,X0)
| ~ 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0) ) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0,axiom,
( 'c$ulessequals'('c$utimes'(X3,X1,X0),'c$utimes'(X3,X2,X0),X0)
| ~ 'c$ulessequals'('c$u0',X3,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0) ) ).
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_1,negated_conjecture,
~ 'c$ulessequals'('c$utimes'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'c$utimes'('v$uc','c$utimes'('c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') ).
cnf(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
( 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_21,axiom,
( 'class$uOrderedGroup$uOsemigroup$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_42,axiom,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(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$ub') ).
cnf(c0,plain,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c1,plain,
( 'c$utimes'('c$utimes'(X1,X2,X0),X3,X0) = 'c$utimes'(X1,'c$utimes'(X2,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOsemigroup$u$umult'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Omult__ac__1_0]) ).
cnf(c2,plain,
( 'c$utimes'(X1,X2,X0) = 'c$utimes'(X2,X1,X0)
| ~ 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Omult__ac__2_0]) ).
cnf(c3,plain,
( 'c$ulessequals'('c$utimes'(X3,X1,X0),'c$utimes'(X3,X2,X0),X0)
| ~ 'c$ulessequals'('c$u0',X3,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__left__mono_0]) ).
cnf(c4,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c5,plain,
~ 'c$ulessequals'('c$utimes'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'c$utimes'('v$uc','c$utimes'('c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c6,plain,
( 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_17]) ).
cnf(c7,plain,
( 'class$uOrderedGroup$uOsemigroup$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_21]) ).
cnf(c8,plain,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_42]) ).
cnf(c9,plain,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_50]) ).
cnf(c10,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(d0,plain,
'class$uOrderedGroup$uOab$u$usemigroup$u$umult'('t$ub'),
inference(resolution,[status(thm)],[c6,c10]) ).
cnf(d1,plain,
'c$utimes'(X0,X1,'t$ub') = 'c$utimes'(X1,X0,'t$ub'),
inference(resolution,[status(thm)],[c2,d0]) ).
cnf(d2,plain,
~ 'c$ulessequals'('c$utimes'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'c$utimes'('v$uc','c$utimes'('c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[c5,d1]) ).
cnf(d3,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub')
| ~ 'c$ulessequals'('c$u0',X0,'t$ub')
| ~ 'c$ulessequals'(X1,X2,'t$ub')
| 'c$ulessequals'('c$utimes'(X1,X0,'t$ub'),'c$utimes'(X0,X2,'t$ub'),'t$ub') ),
inference(superposition,[status(thm)],[d1,c3]) ).
cnf(d4,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub'),
inference(resolution,[status(thm)],[c8,c10]) ).
cnf(d5,plain,
( 'c$ulessequals'('c$utimes'(X0,X2,'t$ub'),'c$utimes'(X2,X1,'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0',X2,'t$ub')
| ~ 'c$ulessequals'(X0,X1,'t$ub') ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'class$uOrderedGroup$uOsemigroup$u$umult'('t$ub'),
inference(resolution,[status(thm)],[c7,c10]) ).
cnf(d7,plain,
'c$utimes'('c$utimes'(X0,X1,'t$ub'),X2,'t$ub') = 'c$utimes'(X0,'c$utimes'(X1,X2,'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
'c$utimes'(X2,'c$utimes'(X0,X1,'t$ub'),'t$ub') = 'c$utimes'(X0,'c$utimes'(X1,X2,'t$ub'),'t$ub'),
inference(superposition,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
( ~ 'c$ulessequals'('c$u0',X0,'t$ub')
| ~ 'c$ulessequals'(X3,'c$utimes'(X1,X2,'t$ub'),'t$ub')
| 'c$ulessequals'('c$utimes'(X3,X0,'t$ub'),'c$utimes'(X1,'c$utimes'(X2,X0,'t$ub'),'t$ub'),'t$ub') ),
inference(superposition,[status(thm)],[d8,d5]) ).
cnf(d10,plain,
( ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[c4,d10]) ).
cnf(d12,plain,
~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[d11,c0]) ).
cnf(d13,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[c9,c10]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d13,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA032-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.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 22:08:29 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.75/4.59 % SZS status Unsatisfiable for theBenchmark.p
% 28.75/4.59 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------