%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA020-2 : 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 : n014.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 06:50:38 AM UTC 2026
% Result : Unsatisfiable 8.81s 2.36s
% Output : CNFRefutation 8.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of clauses : 39 ( 22 unt; 0 nHn; 37 RR)
% Number of literals : 63 ( 7 equ; 34 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 24 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'v$uf'('c$u0') = 'c$u0' ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uless'('c$u0','v$uc','t$ua') ).
cnf(cls_conjecture_3,negated_conjecture,
'v$ux' = 'c$u0' ).
cnf(cls_conjecture_4,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'t$ua'),'t$ua') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua') ).
cnf(cls_OrderedGroup_Oabs__eq__0_1,axiom,
( 'c$uHOL$uOabs'('c$u0',X0) = 'c$u0'
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( 'c$ulessequals'(X1,X2,X0)
| ~ 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( 'c$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_44,axiom,
( 'class$uOrderings$uOorder'(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,
'v$uf'('c$u0') = 'c$u0',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
'c$uless'('c$u0','v$uc','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
'v$ux' = 'c$u0',
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c3,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c4,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c5,plain,
( 'c$uHOL$uOabs'('c$u0',X0) = 'c$u0'
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__eq__0_1]) ).
cnf(c6,plain,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c7,plain,
( 'c$ulessequals'(X1,X2,X0)
| ~ 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(c8,plain,
( 'c$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(c9,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(c10,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(c11,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'('t$ua'),
inference(resolution,[status(thm)],[c11,c4]) ).
cnf(d1,plain,
'c$uHOL$uOabs'('c$u0','t$ua') = 'c$u0',
inference(resolution,[status(thm)],[d0,c5]) ).
cnf(d2,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('c$u0'),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'t$ua'),'t$ua'),
inference(demodulation,[status(thm)],[c3,c2]) ).
cnf(d3,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('c$u0','t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'t$ua'),'t$ua'),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('c$u0','t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),'t$ua'),
inference(demodulation,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
~ 'c$ulessequals'('c$u0','c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),'t$ua'),
inference(demodulation,[status(thm)],[d4,d1]) ).
cnf(d6,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua')
| ~ 'c$ulessequals'('c$u0','v$uc','t$ua') ),
inference(resolution,[status(thm)],[d5,c8]) ).
cnf(d7,plain,
( ~ 'class$uOrderings$uOorder'('t$ua')
| 'c$ulessequals'('c$u0','v$uc','t$ua') ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d8,plain,
'class$uOrderings$uOorder'('t$ua'),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d9,plain,
'c$ulessequals'('c$u0','v$uc','t$ua'),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d9,d6]) ).
cnf(d11,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ua'),
inference(resolution,[status(thm)],[c9,c4]) ).
cnf(d12,plain,
~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),
inference(resolution,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[d12,c6]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d0,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA020-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 22:05:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.81/2.36 % SZS status Unsatisfiable for theBenchmark.p
% 8.81/2.36 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------