%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA034-2 : 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 : 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 06:50:41 AM UTC 2026
% Result : Unsatisfiable 12.20s 28.37s
% Output : CNFRefutation 12.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of clauses : 50 ( 21 unt; 0 nHn; 45 RR)
% Number of literals : 109 ( 5 equ; 70 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-3 aty)
% Number of variables : 48 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Ring__and__Field_Oabs__mult_0,axiom,
( 'c$uHOL$uOabs'('c$utimes'(X1,X2,X0),X0) = 'c$utimes'('c$uHOL$uOabs'(X1,X0),'c$uHOL$uOabs'(X2,X0),X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(cls_Ring__and__Field_Omult__mono_0,axiom,
( 'c$ulessequals'('c$utimes'(X3,X1,X0),'c$utimes'(X4,X2,X0),X0)
| ~ 'c$ulessequals'('c$u0',X4,X0)
| ~ 'c$ulessequals'('c$u0',X1,X0)
| ~ 'c$ulessequals'(X3,X4,X0)
| ~ 'c$ulessequals'(X1,X2,X0)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X0) ) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( 'c$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(cls_Orderings_Oorder__less__imp__le_0,axiom,
( 'c$ulessequals'(X1,X2,X0)
| ~ 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(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_conjecture_0,negated_conjecture,
'c$uless'('c$u0','v$uc','t$ub') ).
cnf(cls_conjecture_2,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$ux'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_3,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_4,negated_conjecture,
'c$utimes'('c$utimes'('v$uc','v$uca','t$ub'),'c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') = 'c$utimes'('c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_5,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('c$utimes'('v$ua'('v$ux'),'v$ub'('v$ux'),'t$ub'),'t$ub'),'c$utimes'('c$utimes'('v$uc','v$uca','t$ub'),'c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_17,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(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_42,axiom,
( 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(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$uHOL$uOabs'('c$utimes'(X1,X2,X0),X0) = 'c$utimes'('c$uHOL$uOabs'(X1,X0),'c$uHOL$uOabs'(X2,X0),X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Oabs__mult_0]) ).
cnf(c1,plain,
( ~ 'c$ulessequals'(X4,X3,X2)
| 'c$ulessequals'('c$utimes'(X4,X0,X2),'c$utimes'(X3,X1,X2),X2)
| ~ 'c$ulessequals'('c$u0',X0,X2)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X2)
| ~ 'c$ulessequals'('c$u0',X3,X2)
| ~ 'c$ulessequals'(X0,X1,X2) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Omult__mono_0]) ).
cnf(c2,plain,
( 'c$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(c3,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(c4,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(c5,plain,
'c$uless'('c$u0','v$uc','t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c6,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$ux'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c7,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c8,plain,
'c$utimes'('c$utimes'('v$uc','v$uca','t$ub'),'c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') = 'c$utimes'('c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c9,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('c$utimes'('v$ua'('v$ux'),'v$ub'('v$ux'),'t$ub'),'t$ub'),'c$utimes'('c$utimes'('v$uc','v$uca','t$ub'),'c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_5]) ).
cnf(c10,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c11,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[clsrel_OrderedGroup_Olordered__ab__group__abs_17]) ).
cnf(c12,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(c13,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(c14,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$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub')
| ~ 'c$ulessequals'('c$u0',X1,'t$ub')
| ~ 'c$ulessequals'('c$u0','c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'(X1,'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'(X0,'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| 'c$ulessequals'('c$utimes'(X0,X1,'t$ub'),'c$utimes'('c$utimes'('v$uc','v$uca','t$ub'),'c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') ),
inference(superposition,[status(thm)],[c8,c1]) ).
cnf(d1,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub'),
inference(resolution,[status(thm)],[c13,c10]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'('c$u0','c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0',X0,'t$ub')
| 'c$ulessequals'('c$utimes'(X1,X0,'t$ub'),'c$utimes'('c$utimes'('v$uc','v$uca','t$ub'),'c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'(X1,'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'(X0,'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
'c$uHOL$uOabs'('c$utimes'(X0,X1,'t$ub'),'t$ub') = 'c$utimes'('c$uHOL$uOabs'(X0,'t$ub'),'c$uHOL$uOabs'(X1,'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[c0,c10]) ).
cnf(d4,plain,
( ~ 'c$ulessequals'('c$u0','c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'(X1,'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'(X0,'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('c$utimes'(X0,X1,'t$ub'),'t$ub'),'c$utimes'('c$utimes'('v$uc','v$uca','t$ub'),'c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') ),
inference(superposition,[status(thm)],[d3,d2]) ).
cnf(d5,plain,
( ~ 'c$ulessequals'('c$u0','c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$ux'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d4,c9]) ).
cnf(d6,plain,
( ~ 'c$ulessequals'('c$u0','c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'c$utimes'('v$uca','c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[c6,d5]) ).
cnf(d7,plain,
( ~ 'c$ulessequals'('c$u0','c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[c7,d6]) ).
cnf(d8,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0','v$uc','t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d7,c2]) ).
cnf(d9,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ub'),
inference(resolution,[status(thm)],[c12,c10]) ).
cnf(d10,plain,
( ~ 'c$ulessequals'('c$u0','v$uc','t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d9,d8]) ).
cnf(d11,plain,
( ~ 'class$uOrderings$uOorder'('t$ub')
| 'c$ulessequals'('c$u0','v$uc','t$ub') ),
inference(resolution,[status(thm)],[c5,c3]) ).
cnf(d12,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[c14,c10]) ).
cnf(d13,plain,
'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[c11,d12]) ).
cnf(d14,plain,
'c$ulessequals'('c$u0','v$uc','t$ub'),
inference(resolution,[status(thm)],[d13,d11]) ).
cnf(d15,plain,
( ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$ub'('v$ux'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d14,d10]) ).
cnf(d16,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d15,c4]) ).
cnf(d17,plain,
~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[d12,d16]) ).
cnf(d18,plain,
~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[d17,c4]) ).
cnf(d19,plain,
$false,
inference(resolution,[status(thm)],[d12,d18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA034-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/25.38 % Computer : n012.cluster.edu
% 0.09/25.38 % Model : x86_64 x86_64
% 0.09/25.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/25.38 % Memory : 8046.5625MB
% 0.09/25.38 % OS : Linux 6.8.0-71-generic
% 0.09/25.39 % CPULimit : 300
% 0.09/25.39 % WCLimit : 300
% 0.09/25.39 % DateTime : Sat Sep 26 22:08:23 UTC 2026
% 0.09/25.39 % CPUTime :
% 0.09/25.39 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 12.20/28.37 % SZS status Unsatisfiable for theBenchmark.p
% 12.20/28.37 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------