%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA027-2 : 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 : n003.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 06:50:40 AM UTC 2026
% Result : Unsatisfiable 9.69s 1.69s
% Output : CNFRefutation 9.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 42 ( 18 unt; 0 nHn; 39 RR)
% Number of literals : 76 ( 3 equ; 37 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 45 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
'c$ulessequals'('c$u0','c$uminus'('v$uf'('v$ux'),'v$uk'('v$ux'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_2,negated_conjecture,
'c$ulessequals'('v$ug'('v$ux'),'v$uk'('v$ux'),'t$ub') ).
cnf(cls_conjecture_3,negated_conjecture,
~ 'c$ulessequals'('c$u0','c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0,axiom,
( 'c$uplus'('c$u0',X1,X0) = X1
| ~ 'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_0,axiom,
( 'c$ulessequals'('c$uplus'(X1,X3,X0),X2,X0)
| ~ 'c$ulessequals'(X1,'c$uminus'(X2,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__9_1,axiom,
( 'c$ulessequals'(X1,'c$uminus'(X3,X2,X0),X0)
| ~ 'c$ulessequals'('c$uplus'(X1,X2,X0),X3,X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_Orderings_Oorder__class_Oorder__trans_0,axiom,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
( 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_15,axiom,
( 'class$uLOrder$uOjoin$u$usemilorder'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_23,axiom,
( 'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(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','c$uminus'('v$uf'('v$ux'),'v$uk'('v$ux'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c1,plain,
'c$ulessequals'('v$ug'('v$ux'),'v$uk'('v$ux'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c2,plain,
~ 'c$ulessequals'('c$u0','c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c3,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c4,plain,
( 'c$uplus'('c$u0',X1,X0) = X1
| ~ 'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0]) ).
cnf(c5,plain,
( 'c$ulessequals'('c$uplus'(X1,X3,X0),X2,X0)
| ~ 'c$ulessequals'(X1,'c$uminus'(X2,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Ocompare__rls__9_0]) ).
cnf(c6,plain,
( 'c$ulessequals'(X1,'c$uminus'(X3,X2,X0),X0)
| ~ 'c$ulessequals'('c$uplus'(X1,X2,X0),X3,X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Ocompare__rls__9_1]) ).
cnf(c7,plain,
( 'c$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(c8,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ),
inference(clausification,[status(esa)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c9,plain,
( 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Olordered__ab__group__abs_1]) ).
cnf(c10,plain,
( 'class$uLOrder$uOjoin$u$usemilorder'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Olordered__ab__group__abs_15]) ).
cnf(c11,plain,
( 'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_23]) ).
cnf(c12,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$uOrderedGroup$uOcomm$u$umonoid$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[c11,c3]) ).
cnf(d1,plain,
'c$uplus'('c$u0',X0,'t$ub') = X0,
inference(resolution,[status(thm)],[c4,d0]) ).
cnf(d2,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub')
| 'c$ulessequals'('c$u0','c$uminus'(X1,X0,'t$ub'),'t$ub')
| ~ 'c$ulessequals'(X0,X1,'t$ub') ),
inference(superposition,[status(thm)],[d1,c6]) ).
cnf(d3,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[c12,c3]) ).
cnf(d4,plain,
'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[c9,d3]) ).
cnf(d5,plain,
( 'c$ulessequals'('c$u0','c$uminus'(X1,X0,'t$ub'),'t$ub')
| ~ 'c$ulessequals'(X0,X1,'t$ub') ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
~ 'c$ulessequals'('v$ug'('v$ux'),'v$uf'('v$ux'),'t$ub'),
inference(resolution,[status(thm)],[d5,c2]) ).
cnf(d7,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub')
| 'c$ulessequals'('c$uplus'('c$u0','v$uk'('v$ux'),'t$ub'),'v$uf'('v$ux'),'t$ub') ),
inference(resolution,[status(thm)],[c5,c0]) ).
cnf(d8,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub')
| 'c$ulessequals'('v$uk'('v$ux'),'v$uf'('v$ux'),'t$ub') ),
inference(demodulation,[status(thm)],[d7,d1]) ).
cnf(d9,plain,
'c$ulessequals'('v$uk'('v$ux'),'v$uf'('v$ux'),'t$ub'),
inference(resolution,[status(thm)],[d4,d8]) ).
cnf(d10,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'(X0,'v$uk'('v$ux'),'t$ub')
| 'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub') ),
inference(resolution,[status(thm)],[d9,c7]) ).
cnf(d11,plain,
'class$uLOrder$uOjoin$u$usemilorder'('t$ub'),
inference(resolution,[status(thm)],[c10,d3]) ).
cnf(d12,plain,
'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[d11,c8]) ).
cnf(d13,plain,
( ~ 'c$ulessequals'(X0,'v$uk'('v$ux'),'t$ub')
| 'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub') ),
inference(resolution,[status(thm)],[d12,d10]) ).
cnf(d14,plain,
'c$ulessequals'('v$ug'('v$ux'),'v$uf'('v$ux'),'t$ub'),
inference(resolution,[status(thm)],[d13,c1]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA027-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 22:08:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.69/1.69 % SZS status Unsatisfiable for theBenchmark.p
% 9.69/1.69 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------