%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA027-1 : 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 : 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 06:50:40 AM UTC 2026
% Result : Unsatisfiable 263.33s 54.51s
% Output : CNFRefutation 263.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 18
% Syntax : Number of clauses : 58 ( 23 unt; 2 nHn; 53 RR)
% Number of literals : 107 ( 3 equ; 53 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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_Orderings_Olinorder__not__le_0,axiom,
( 'c$ulessequals'(X2,X1,X0)
| 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_Orderings_Olinorder__not__le_1,axiom,
( ~ 'c$ulessequals'(X2,X1,X0)
| ~ 'c$uless'(X1,X2,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$uOorder'(X0) ) ).
cnf(cls_conjecture_1,negated_conjecture,
'c$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_Odiff__less__0__iff__less_0,axiom,
( 'c$uless'(X1,X2,X0)
| ~ 'c$uless'('c$uminus'(X1,X2,X0),'c$u0',X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ) ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group_0,axiom,
( 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup'(X0) ) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_0,axiom,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9,axiom,
( 'class$uOrderings$uOlinorder'(X0)
| ~ 'class$uOrderedGroup$uOordered$u$ucancel$u$uab$u$usemigroup$u$uadd'(X0) ) ).
cnf(clsrel_OrderedGroup_Opordered__ab__group__add_2,axiom,
( 'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_32,axiom,
( 'class$uOrderedGroup$uOordered$u$ucancel$u$uab$u$usemigroup$u$uadd'(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_50,axiom,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(c15,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(c20,plain,
( 'c$ulessequals'(X2,X1,X0)
| 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Olinorder__not__le_0]) ).
cnf(c21,plain,
( ~ 'c$ulessequals'(X2,X1,X0)
| ~ 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Olinorder__not__le_1]) ).
cnf(c22,plain,
( 'c$ulessequals'(X3,X2,X0)
| ~ 'c$ulessequals'(X3,X1,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__class_Oorder__trans_0]) ).
cnf(c25,plain,
'c$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(c26,plain,
'c$ulessequals'('v$ug'('v$ux'),'v$uk'('v$ux'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c27,plain,
~ 'c$ulessequals'('c$u0','c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c28,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c1118,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(c1124,plain,
( 'c$uless'(X1,X2,X0)
| ~ 'c$uless'('c$uminus'(X1,X2,X0),'c$u0',X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Odiff__less__0__iff__less_0]) ).
cnf(c1903,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ),
inference(clausification,[status(esa)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c1968,plain,
( 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Olordered__ab__group_0]) ).
cnf(c1986,plain,
( 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Olordered__ab__group__abs_0]) ).
cnf(c2059,plain,
( 'class$uOrderings$uOlinorder'(X0)
| ~ 'class$uOrderedGroup$uOordered$u$ucancel$u$uab$u$usemigroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9]) ).
cnf(c2066,plain,
( 'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'(X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Opordered__ab__group__add_2]) ).
cnf(c2471,plain,
( 'class$uOrderedGroup$uOordered$u$ucancel$u$uab$u$usemigroup$u$uadd'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_32]) ).
cnf(c2474,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(c2491,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$ub'),
inference(resolution,[status(thm)],[c2491,c28]) ).
cnf(d1,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup'('t$ub'),
inference(resolution,[status(thm)],[d0,c1986]) ).
cnf(d2,plain,
'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[c1968,d1]) ).
cnf(d3,plain,
'class$uOrderedGroup$uOcomm$u$umonoid$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[d2,c2066]) ).
cnf(d4,plain,
'c$uplus'('c$u0',X0,'t$ub') = X0,
inference(resolution,[status(thm)],[c1118,d3]) ).
cnf(d5,plain,
( 'c$ulessequals'('c$uplus'('c$u0','v$uk'('v$ux'),'t$ub'),'v$uf'('v$ux'),'t$ub')
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub') ),
inference(resolution,[status(thm)],[c25,c15]) ).
cnf(d6,plain,
'c$ulessequals'('c$uplus'('c$u0','v$uk'('v$ux'),'t$ub'),'v$uf'('v$ux'),'t$ub'),
inference(resolution,[status(thm)],[d2,d5]) ).
cnf(d7,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'(X0,'c$uplus'('c$u0','v$uk'('v$ux'),'t$ub'),'t$ub')
| 'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub') ),
inference(resolution,[status(thm)],[d6,c22]) ).
cnf(d8,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| 'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub')
| ~ 'c$ulessequals'(X0,'v$uk'('v$ux'),'t$ub') ),
inference(demodulation,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
'class$uLOrder$uOjoin$u$usemilorder'('t$ub'),
inference(resolution,[status(thm)],[c2474,c28]) ).
cnf(d10,plain,
'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[c1903,d9]) ).
cnf(d11,plain,
( 'c$ulessequals'(X0,'v$uf'('v$ux'),'t$ub')
| ~ 'c$ulessequals'(X0,'v$uk'('v$ux'),'t$ub') ),
inference(resolution,[status(thm)],[d10,d8]) ).
cnf(d12,plain,
'c$ulessequals'('v$ug'('v$ux'),'v$uf'('v$ux'),'t$ub'),
inference(resolution,[status(thm)],[d11,c26]) ).
cnf(d13,plain,
( ~ 'class$uOrderings$uOlinorder'('t$ub')
| ~ 'c$uless'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub') ),
inference(resolution,[status(thm)],[d12,c21]) ).
cnf(d14,plain,
'class$uOrderedGroup$uOordered$u$ucancel$u$uab$u$usemigroup$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[c2471,c28]) ).
cnf(d15,plain,
'class$uOrderings$uOlinorder'('t$ub'),
inference(resolution,[status(thm)],[c2059,d14]) ).
cnf(d16,plain,
~ 'c$uless'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),
inference(resolution,[status(thm)],[d15,d13]) ).
cnf(d17,plain,
( ~ 'class$uOrderings$uOlinorder'('t$ub')
| 'c$uless'('c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub') ),
inference(resolution,[status(thm)],[c27,c20]) ).
cnf(d18,plain,
'c$uless'('c$uminus'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'c$u0','t$ub'),
inference(resolution,[status(thm)],[d15,d17]) ).
cnf(d19,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub')
| 'c$uless'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub') ),
inference(resolution,[status(thm)],[d18,c1124]) ).
cnf(d20,plain,
'c$uless'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),
inference(resolution,[status(thm)],[d2,d19]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d20,d16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA027-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n014.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 22:07:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 263.33/54.51 % SZS status Unsatisfiable for theBenchmark.p
% 263.33/54.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------