%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA044-2 : 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 : 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 06:50:43 AM UTC 2026
% Result : Unsatisfiable 4.55s 2.80s
% Output : CNFRefutation 4.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 8
% Syntax : Number of clauses : 25 ( 13 unt; 0 nHn; 17 RR)
% Number of literals : 49 ( 10 equ; 27 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 32 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'c$ulessequals'('c$u0','v$ul'(X0,X1),'t$ub') ).
cnf(cls_conjecture_1,negated_conjecture,
'c$ulessequals'('c$u0','v$uh'(X0),'t$ub') ).
cnf(cls_conjecture_3,negated_conjecture,
'c$utimes'('v$ul'('v$ux','v$uxa'),'v$uh'('v$uk'('v$ux','v$uxa')),'t$ub') != 'c$uHOL$uOabs'('c$utimes'('v$ul'('v$ux','v$uxa'),'v$uh'('v$uk'('v$ux','v$uxa')),'t$ub'),'t$ub') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
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_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( 'c$ulessequals'('c$u0','c$utimes'(X2,X1,X0),X0)
| ~ 'c$ulessequals'('c$u0',X2,X0)
| ~ 'c$ulessequals'('c$u0',X1,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_40,axiom,
( 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$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$uidom'(X0) ) ).
cnf(c0,plain,
'c$ulessequals'('c$u0','v$ul'(X0,X1),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
'c$ulessequals'('c$u0','v$uh'(X0),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
'c$utimes'('v$ul'('v$ux','v$uxa'),'v$uh'('v$uk'('v$ux','v$uxa')),'t$ub') != 'c$uHOL$uOabs'('c$utimes'('v$ul'('v$ux','v$uxa'),'v$uh'('v$uk'('v$ux','v$uxa')),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c3,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c4,plain,
( 'c$uHOL$uOabs'(X1,X0) = X1
| ~ 'c$ulessequals'('c$u0',X1,X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__of__nonneg_0]) ).
cnf(c5,plain,
( 'c$ulessequals'('c$u0','c$utimes'(X2,X1,X0),X0)
| ~ 'c$ulessequals'('c$u0',X2,X0)
| ~ 'c$ulessequals'('c$u0',X1,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'(X0) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Omult__nonneg__nonneg_0]) ).
cnf(c6,plain,
( 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_40]) ).
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(d0,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X1)
| 'c$uHOL$uOabs'('c$utimes'(X2,X0,X1),X1) = 'c$utimes'(X2,X0,X1)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'(X1)
| ~ 'c$ulessequals'('c$u0',X2,X1)
| ~ 'c$ulessequals'('c$u0',X0,X1) ),
inference(resolution,[status(thm)],[c5,c4]) ).
cnf(d1,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ub')
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub')
| ~ 'c$ulessequals'('c$u0',X0,'t$ub')
| 'c$uHOL$uOabs'('c$utimes'(X0,'v$uh'(X1),'t$ub'),'t$ub') = 'c$utimes'(X0,'v$uh'(X1),'t$ub') ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ub'),
inference(resolution,[status(thm)],[c6,c3]) ).
cnf(d3,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub')
| ~ 'c$ulessequals'('c$u0',X0,'t$ub')
| 'c$uHOL$uOabs'('c$utimes'(X0,'v$uh'(X1),'t$ub'),'t$ub') = 'c$utimes'(X0,'v$uh'(X1),'t$ub') ),
inference(resolution,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d5,plain,
( ~ 'c$ulessequals'('c$u0',X0,'t$ub')
| 'c$uHOL$uOabs'('c$utimes'(X0,'v$uh'(X1),'t$ub'),'t$ub') = 'c$utimes'(X0,'v$uh'(X1),'t$ub') ),
inference(resolution,[status(thm)],[d4,d3]) ).
cnf(d6,plain,
'c$uHOL$uOabs'('c$utimes'('v$ul'(X0,X1),'v$uh'(X2),'t$ub'),'t$ub') = 'c$utimes'('v$ul'(X0,X1),'v$uh'(X2),'t$ub'),
inference(resolution,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
'c$utimes'('v$ul'('v$ux','v$uxa'),'v$uh'('v$uk'('v$ux','v$uxa')),'t$ub') != 'c$utimes'('v$ul'('v$ux','v$uxa'),'v$uh'('v$uk'('v$ux','v$uxa')),'t$ub'),
inference(demodulation,[status(thm)],[c2,d6]) ).
cnf(d8,plain,
$false,
inference(equality_resolution,[status(thm)],[d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA044-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n006.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 22:10:11 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.55/2.80 % SZS status Unsatisfiable for theBenchmark.p
% 4.55/2.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------