%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA018-2 : 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 : n011.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 17.73s 2.74s
% Output : CNFRefutation 17.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 41 ( 19 unt; 0 nHn; 34 RR)
% Number of literals : 77 ( 3 equ; 40 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 55 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$uf'(X0),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$ug'(X0),'t$ub'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_2,negated_conjecture,
'c$uless'('c$u0','v$uca','t$ub') ).
cnf(cls_conjecture_3,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$ux'(X0),'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$uf'(X0),'t$ub'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_4,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$ux'('v$uxa'),'t$ub'),'c$utimes'('c$utimes'('v$uca','v$uc','t$ub'),'c$uHOL$uOabs'('v$ug'('v$uxa'),'t$ub'),'t$ub'),'t$ub') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(cls_OrderedGroup_Omult__ac__1_0,axiom,
( 'c$utimes'('c$utimes'(X1,X2,X0),X3,X0) = 'c$utimes'(X1,'c$utimes'(X2,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOsemigroup$u$umult'(X0) ) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_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_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(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(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_35,axiom,
( 'class$uLOrder$uOjoin$u$usemilorder'(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(c0,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$uf'(X0),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$ug'(X0),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c1,plain,
'c$uless'('c$u0','v$uca','t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c2,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$ux'(X0),'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$uf'(X0),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c3,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$ux'('v$uxa'),'t$ub'),'c$utimes'('c$utimes'('v$uca','v$uc','t$ub'),'c$uHOL$uOabs'('v$ug'('v$uxa'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c4,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c5,plain,
( 'c$utimes'('c$utimes'(X1,X2,X0),X3,X0) = 'c$utimes'(X1,'c$utimes'(X2,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOsemigroup$u$umult'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Omult__ac__1_0]) ).
cnf(c6,plain,
( 'c$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(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$ulessequals'('c$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(c9,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ),
inference(clausification,[status(esa)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c10,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(c11,plain,
( 'class$uLOrder$uOjoin$u$usemilorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_35]) ).
cnf(c12,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(d0,plain,
'class$uOrderedGroup$uOsemigroup$u$umult'('t$ub'),
inference(resolution,[status(thm)],[c10,c4]) ).
cnf(d1,plain,
'c$utimes'('c$utimes'(X0,X1,'t$ub'),X2,'t$ub') = 'c$utimes'(X0,'c$utimes'(X1,X2,'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[c5,d0]) ).
cnf(d2,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$ux'('v$uxa'),'t$ub'),'c$utimes'('v$uca','c$utimes'('v$uc','c$uHOL$uOabs'('v$ug'('v$uxa'),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[c3,d1]) ).
cnf(d3,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ux'(X0),'t$ub'),X1,'t$ub')
| ~ 'c$ulessequals'('c$utimes'('v$uca','c$uHOL$uOabs'('v$uf'(X0),'t$ub'),'t$ub'),X1,'t$ub') ),
inference(resolution,[status(thm)],[c6,c2]) ).
cnf(d4,plain,
'class$uLOrder$uOjoin$u$usemilorder'('t$ub'),
inference(resolution,[status(thm)],[c11,c4]) ).
cnf(d5,plain,
'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[c9,d4]) ).
cnf(d6,plain,
( ~ 'c$ulessequals'('c$utimes'('v$uca','c$uHOL$uOabs'('v$uf'(X0),'t$ub'),'t$ub'),X1,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ux'(X0),'t$ub'),X1,'t$ub') ),
inference(resolution,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub')
| ~ 'c$ulessequals'('c$u0','v$uca','t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'(X0),'t$ub'),X1,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ux'(X0),'t$ub'),'c$utimes'('v$uca',X1,'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d6,c8]) ).
cnf(d8,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub'),
inference(resolution,[status(thm)],[c12,c4]) ).
cnf(d9,plain,
( ~ 'c$ulessequals'('c$u0','v$uca','t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ux'(X0),'t$ub'),'c$utimes'('v$uca',X1,'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'(X0),'t$ub'),X1,'t$ub') ),
inference(resolution,[status(thm)],[d8,d7]) ).
cnf(d10,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| 'c$ulessequals'('c$u0','v$uca','t$ub') ),
inference(resolution,[status(thm)],[c7,c1]) ).
cnf(d11,plain,
'c$ulessequals'('c$u0','v$uca','t$ub'),
inference(resolution,[status(thm)],[d5,d10]) ).
cnf(d12,plain,
( 'c$ulessequals'('c$uHOL$uOabs'('v$ux'(X0),'t$ub'),'c$utimes'('v$uca',X1,'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'(X0),'t$ub'),X1,'t$ub') ),
inference(resolution,[status(thm)],[d11,d9]) ).
cnf(d13,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$uxa'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$ug'('v$uxa'),'t$ub'),'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[c0,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA018-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n011.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 22:05:15 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.73/2.74 % SZS status Unsatisfiable for theBenchmark.p
% 17.73/2.74 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------