%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA039-1 : 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 : n012.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 17.87s 12.11s
% Output : CNFRefutation 17.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 41 ( 15 unt; 0 nHn; 35 RR)
% Number of literals : 79 ( 0 equ; 44 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 46 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_OrderedGroup_Oabs__ge__self_0,axiom,
( 'c$ulessequals'(X1,'c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$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$uabs'(X0) ) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( 'c$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(cls_conjecture_0,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua') ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'c$utimes'('c$uHOL$uOabs'('v$uc','t$ua'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'t$ua'),'t$ua') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua') ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ) ).
cnf(clsrel_Orderings_Olinorder_1,axiom,
( 'class$uLOrder$uOjoin$u$usemilorder'(X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_24,axiom,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOlordered$u$uring'(X0) ) ).
cnf(clsrel_Ring__and__Field_Olordered__ring_8,axiom,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOlordered$u$uring'(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_48,axiom,
( 'class$uRing$u$uand$u$uField$uOlordered$u$uring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(c0,plain,
( 'c$ulessequals'(X1,'c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__self_0]) ).
cnf(c1,plain,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c2,plain,
( 'c$ulessequals'(X0,X3,X2)
| ~ 'c$ulessequals'(X1,X3,X2)
| ~ 'class$uOrderings$uOorder'(X2)
| ~ 'c$ulessequals'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c3,plain,
( 'c$ulessequals'('c$utimes'(X2,X0,X1),'c$utimes'(X3,X0,X1),X1)
| ~ 'c$ulessequals'(X2,X3,X1)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X1)
| ~ 'c$ulessequals'('c$u0',X0,X1) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0]) ).
cnf(c4,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c6,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$uh'('v$ux'),'t$ua'),'c$utimes'('c$uHOL$uOabs'('v$uc','t$ua'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c7,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c512,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ),
inference(clausification,[status(esa)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c708,plain,
( 'class$uLOrder$uOjoin$u$usemilorder'(X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[clsrel_Orderings_Olinorder_1]) ).
cnf(c949,plain,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOlordered$u$uring'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Olordered__ring_24]) ).
cnf(c961,plain,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOlordered$u$uring'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Olordered__ring_8]) ).
cnf(c1081,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(c1097,plain,
( 'class$uRing$u$uand$u$uField$uOlordered$u$uring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_48]) ).
cnf(d0,plain,
( ~ 'class$uOrderings$uOorder'('t$ua')
| 'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),X1,'t$ua')
| ~ 'c$ulessequals'('c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),X1,'t$ua') ),
inference(resolution,[status(thm)],[c4,c2]) ).
cnf(d1,plain,
'class$uOrderings$uOlinorder'('t$ua'),
inference(resolution,[status(thm)],[c1081,c7]) ).
cnf(d2,plain,
'class$uLOrder$uOjoin$u$usemilorder'('t$ua'),
inference(resolution,[status(thm)],[d1,c708]) ).
cnf(d3,plain,
'class$uOrderings$uOorder'('t$ua'),
inference(resolution,[status(thm)],[c512,d2]) ).
cnf(d4,plain,
( ~ 'c$ulessequals'('c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),X1,'t$ua')
| 'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),X1,'t$ua') ),
inference(resolution,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua')
| ~ 'c$ulessequals'('v$uc',X1,'t$ua')
| 'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'(X1,'c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
'class$uRing$u$uand$u$uField$uOlordered$u$uring'('t$ua'),
inference(resolution,[status(thm)],[c1097,c7]) ).
cnf(d7,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ua'),
inference(resolution,[status(thm)],[c961,d6]) ).
cnf(d8,plain,
( ~ 'c$ulessequals'('v$uc',X1,'t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua')
| 'c$ulessequals'('c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'c$utimes'(X1,'c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
( ~ 'c$ulessequals'('v$uc','c$uHOL$uOabs'('v$uc','t$ua'),'t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d8,c6]) ).
cnf(d10,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua')
| ~ 'c$ulessequals'('v$uc','c$uHOL$uOabs'('v$uc','t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d9,c1]) ).
cnf(d11,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[c949,d6]) ).
cnf(d12,plain,
~ 'c$ulessequals'('v$uc','c$uHOL$uOabs'('v$uc','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,c0]) ).
cnf(d14,plain,
$false,
inference(resolution,[status(thm)],[d11,d13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : ANA039-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.04/0.29 % Computer : n012.cluster.edu
% 0.04/0.29 % Model : x86_64 x86_64
% 0.04/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.29 % Memory : 8046.5625MB
% 0.04/0.29 % OS : Linux 6.8.0-71-generic
% 0.04/0.29 % CPULimit : 300
% 0.04/0.29 % WCLimit : 300
% 0.04/0.29 % DateTime : Sat Sep 26 22:09:29 UTC 2026
% 0.04/0.29 % CPUTime :
% 0.04/0.29 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.87/12.11 % SZS status Unsatisfiable for theBenchmark.p
% 17.87/12.11 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------