%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA038-2 : 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 : n018.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 06:50:42 AM UTC 2026
% Result : Unsatisfiable 10.03s 6.85s
% Output : CNFRefutation 10.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of clauses : 31 ( 14 unt; 0 nHn; 29 RR)
% Number of literals : 66 ( 0 equ; 39 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 37 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_3,negated_conjecture,
'c$ulessequals'('c$u0','v$ug'('v$uxa'),'t$ub') ).
cnf(cls_conjecture_5,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$uxa'),'t$ub'),'c$utimes'('v$uca','v$ug'('v$uxa'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_8,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$uxa'),'t$ub'),'c$utimes'('c$uOrderings$uOmax'('v$uc','v$uca','t$ub'),'v$ug'('v$uxa'),'t$ub'),'t$ub') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(cls_Orderings_Ole__maxI2_0,axiom,
( 'c$ulessequals'(X1,'c$uOrderings$uOmax'(X2,X1,X0),X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0,axiom,
( 'c$ulessequals'('c$utimes'(X1,X3,X0),'c$utimes'(X2,X3,X0),X0)
| ~ 'c$ulessequals'('c$u0',X3,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( 'class$uOrderings$uOlinorder'(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_44,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(c0,plain,
'c$ulessequals'('c$u0','v$ug'('v$uxa'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c1,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$uxa'),'t$ub'),'c$utimes'('v$uca','v$ug'('v$uxa'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(c2,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$uxa'),'t$ub'),'c$utimes'('c$uOrderings$uOmax'('v$uc','v$uca','t$ub'),'v$ug'('v$uxa'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_8]) ).
cnf(c3,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c4,plain,
( 'c$ulessequals'(X1,'c$uOrderings$uOmax'(X2,X1,X0),X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Ole__maxI2_0]) ).
cnf(c5,plain,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c6,plain,
( 'c$ulessequals'('c$utimes'(X1,X3,X0),'c$utimes'(X2,X3,X0),X0)
| ~ 'c$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__right__mono_0]) ).
cnf(c7,plain,
( 'class$uOrderings$uOlinorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_33]) ).
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$uOrderings$uOorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_44]) ).
cnf(d0,plain,
( ~ 'class$uOrderings$uOorder'(X2)
| ~ 'c$ulessequals'(X4,'c$utimes'(X0,X3,X2),X2)
| 'c$ulessequals'(X4,'c$utimes'(X1,X3,X2),X2)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X2)
| ~ 'c$ulessequals'('c$u0',X3,X2)
| ~ 'c$ulessequals'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d1,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub')
| ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'('c$u0','v$ug'('v$uxa'),'t$ub')
| ~ 'c$ulessequals'('v$uca',X0,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$uxa'),'t$ub'),'c$utimes'(X0,'v$ug'('v$uxa'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub')
| ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'('v$uca',X0,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$uxa'),'t$ub'),'c$utimes'(X0,'v$ug'('v$uxa'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub'),
inference(resolution,[status(thm)],[c8,c3]) ).
cnf(d4,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'('v$uca',X0,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$uxa'),'t$ub'),'c$utimes'(X0,'v$ug'('v$uxa'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[c9,c3]) ).
cnf(d6,plain,
( ~ 'c$ulessequals'('v$uca',X0,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$uxa'),'t$ub'),'c$utimes'(X0,'v$ug'('v$uxa'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
~ 'c$ulessequals'('v$uca','c$uOrderings$uOmax'('v$uc','v$uca','t$ub'),'t$ub'),
inference(resolution,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
~ 'class$uOrderings$uOlinorder'('t$ub'),
inference(resolution,[status(thm)],[d7,c4]) ).
cnf(d9,plain,
'class$uOrderings$uOlinorder'('t$ub'),
inference(resolution,[status(thm)],[c7,c3]) ).
cnf(d10,plain,
$false,
inference(resolution,[status(thm)],[d9,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA038-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.52 % Computer : n018.cluster.edu
% 0.09/5.52 % Model : x86_64 x86_64
% 0.09/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.52 % Memory : 8046.5625MB
% 0.09/5.52 % OS : Linux 6.8.0-71-generic
% 0.09/5.52 % CPULimit : 300
% 0.09/5.52 % WCLimit : 300
% 0.09/5.52 % DateTime : Sat Sep 26 22:11:59 UTC 2026
% 0.09/5.53 % CPUTime :
% 0.09/5.53 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.03/6.85 % SZS status Unsatisfiable for theBenchmark.p
% 10.03/6.85 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------