%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA037-1 : 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 : n008.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 192.66s 54.63s
% Output : CNFRefutation 192.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 40 ( 17 unt; 0 nHn; 38 RR)
% Number of literals : 81 ( 0 equ; 45 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 43 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Orderings_Ole__maxI1_0,axiom,
( 'c$ulessequals'(X1,'c$uOrderings$uOmax'(X1,X2,X0),X0)
| ~ 'class$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_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_2,negated_conjecture,
'c$ulessequals'('c$u0','v$uf'('v$uxa'),'t$ub') ).
cnf(cls_conjecture_4,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$uxa'),'t$ub'),'c$utimes'('v$uc','v$uf'('v$uxa'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_8,negated_conjecture,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$uxa'),'t$ub'),'c$utimes'('c$uOrderings$uOmax'('v$uc','v$uca','t$ub'),'v$uf'('v$uxa'),'t$ub'),'t$ub') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(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_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_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_48,axiom,
( 'class$uRing$u$uand$u$uField$uOlordered$u$uring'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(c3,plain,
( 'c$ulessequals'(X1,'c$uOrderings$uOmax'(X1,X2,X0),X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Ole__maxI1_0]) ).
cnf(c5,plain,
( 'c$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$ulessequals'('c$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) ),
inference(clausification,[status(esa)],[cls_Ring__and__Field_Opordered__semiring__class_Omult__right__mono_0]) ).
cnf(c14,plain,
'c$ulessequals'('c$u0','v$uf'('v$uxa'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c16,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$uxa'),'t$ub'),'c$utimes'('v$uc','v$uf'('v$uxa'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c20,plain,
~ 'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$uxa'),'t$ub'),'c$utimes'('c$uOrderings$uOmax'('v$uc','v$uca','t$ub'),'v$uf'('v$uxa'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_8]) ).
cnf(c21,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c1896,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ),
inference(clausification,[status(esa)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c2052,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(c2345,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(c2464,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(c2467,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(c2481,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'(X2)
| ~ 'c$ulessequals'(X4,'c$utimes'(X0,X3,X2),X2)
| 'c$ulessequals'(X4,'c$utimes'(X1,X3,X2),X2)
| ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'(X2)
| ~ 'c$ulessequals'('c$u0',X3,X2)
| ~ 'c$ulessequals'(X0,X1,X2) ),
inference(resolution,[status(thm)],[c7,c5]) ).
cnf(d1,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub')
| ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'('c$u0','v$uf'('v$uxa'),'t$ub')
| ~ 'c$ulessequals'('v$uc',X0,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$uxa'),'t$ub'),'c$utimes'(X0,'v$uf'('v$uxa'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d0,c16]) ).
cnf(d2,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub')
| ~ 'class$uOrderings$uOorder'('t$ub')
| ~ 'c$ulessequals'('v$uc',X0,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$uxa'),'t$ub'),'c$utimes'(X0,'v$uf'('v$uxa'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[c14,d1]) ).
cnf(d3,plain,
'class$uLOrder$uOjoin$u$usemilorder'('t$ub'),
inference(resolution,[status(thm)],[c2467,c21]) ).
cnf(d4,plain,
'class$uOrderings$uOorder'('t$ub'),
inference(resolution,[status(thm)],[c1896,d3]) ).
cnf(d5,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub')
| ~ 'c$ulessequals'('v$uc',X0,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$uxa'),'t$ub'),'c$utimes'(X0,'v$uf'('v$uxa'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d4,d2]) ).
cnf(d6,plain,
'class$uRing$u$uand$u$uField$uOlordered$u$uring'('t$ub'),
inference(resolution,[status(thm)],[c2481,c21]) ).
cnf(d7,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$usemiring'('t$ub'),
inference(resolution,[status(thm)],[c2345,d6]) ).
cnf(d8,plain,
( ~ 'c$ulessequals'('v$uc',X0,'t$ub')
| 'c$ulessequals'('c$uHOL$uOabs'('v$ua'('v$uxa'),'t$ub'),'c$utimes'(X0,'v$uf'('v$uxa'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
~ 'c$ulessequals'('v$uc','c$uOrderings$uOmax'('v$uc','v$uca','t$ub'),'t$ub'),
inference(resolution,[status(thm)],[d8,c20]) ).
cnf(d10,plain,
~ 'class$uOrderings$uOlinorder'('t$ub'),
inference(resolution,[status(thm)],[d9,c3]) ).
cnf(d11,plain,
'class$uOrderedGroup$uOordered$u$ucancel$u$uab$u$usemigroup$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[c2464,c21]) ).
cnf(d12,plain,
'class$uOrderings$uOlinorder'('t$ub'),
inference(resolution,[status(thm)],[c2052,d11]) ).
cnf(d13,plain,
$false,
inference(resolution,[status(thm)],[d12,d10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA037-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/10.58 % Computer : n008.cluster.edu
% 0.11/10.58 % Model : x86_64 x86_64
% 0.11/10.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.58 % Memory : 8046.5625MB
% 0.11/10.58 % OS : Linux 6.8.0-71-generic
% 0.11/10.58 % CPULimit : 300
% 0.11/10.58 % WCLimit : 300
% 0.11/10.58 % DateTime : Sat Sep 26 22:10:05 UTC 2026
% 0.11/10.58 % CPUTime :
% 0.11/10.58 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 192.66/54.63 % SZS status Unsatisfiable for theBenchmark.p
% 192.66/54.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------