%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA030-2 : 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 : n018.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 14.87s 8.31s
% Output : CNFRefutation 14.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of clauses : 62 ( 28 unt; 0 nHn; 28 RR)
% Number of literals : 105 ( 27 equ; 45 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 113 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_1,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('c$uOrderings$uOmax'('c$uminus'('v$uf'(X0),'v$ug'(X0),'t$ub'),'c$u0','t$ub'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ub'),'t$ub'),'t$ub') ).
cnf(cls_conjecture_2,negated_conjecture,
~ 'c$ulessequals'('v$uf'('v$ux'(X0)),'c$uplus'('v$ug'('v$ux'(X0)),'c$utimes'(X0,'c$uHOL$uOabs'('v$uh'('v$ux'(X0)),'t$ub'),'t$ub'),'t$ub'),'t$ub') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(cls_OrderedGroup_Oabs__of__nonneg_0,axiom,
( 'c$uHOL$uOabs'(X1,X0) = X1
| ~ 'c$ulessequals'('c$u0',X1,X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__1_0,axiom,
( 'c$uplus'(X1,'c$uuminus'(X2,X0),X0) = 'c$uminus'(X1,X2,X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_OrderedGroup_Ocompare__rls__8_0,axiom,
( 'c$ulessequals'(X1,'c$uplus'(X3,X2,X0),X0)
| ~ 'c$ulessequals'('c$uminus'(X1,X2,X0),X3,X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_OrderedGroup_Odiff__minus__eq__add_0,axiom,
( 'c$uminus'(X1,'c$uuminus'(X2,X0),X0) = 'c$uplus'(X1,X2,X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_OrderedGroup_Ominus__add__distrib_0,axiom,
( 'c$uuminus'('c$uplus'(X1,X2,X0),X0) = 'c$uplus'('c$uuminus'(X1,X0),'c$uuminus'(X2,X0),X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_OrderedGroup_Ominus__diff__eq_0,axiom,
( 'c$uuminus'('c$uminus'(X1,X2,X0),X0) = 'c$uminus'(X2,X1,X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_OrderedGroup_Ominus__minus_0,axiom,
( 'c$uuminus'('c$uuminus'(X1,X0),X0) = X1
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ) ).
cnf(cls_Orderings_Ole__maxI2_0,axiom,
( 'c$ulessequals'(X1,'c$uOrderings$uOmax'(X2,X1,X0),X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0,axiom,
( 'c$ulessequals'(X1,X3,X0)
| ~ 'c$ulessequals'('c$uOrderings$uOmax'(X1,X2,X0),X3,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(clsrel_OrderedGroup_Olordered__ab__group__abs_1,axiom,
( 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_33,axiom,
( 'class$uOrderings$uOlinorder'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(clsrel_Ring__and__Field_Oordered__idom_4,axiom,
( 'class$uOrderedGroup$uOab$u$ugroup$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$uHOL$uOabs'('c$uOrderings$uOmax'('c$uminus'('v$uf'(X0),'v$ug'(X0),'t$ub'),'c$u0','t$ub'),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c1,plain,
~ 'c$ulessequals'('v$uf'('v$ux'(X0)),'c$uplus'('v$ug'('v$ux'(X0)),'c$utimes'(X0,'c$uHOL$uOabs'('v$uh'('v$ux'(X0)),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c2,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c3,plain,
( 'c$uHOL$uOabs'(X1,X0) = X1
| ~ 'c$ulessequals'('c$u0',X1,X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__of__nonneg_0]) ).
cnf(c4,plain,
( 'c$uplus'(X1,'c$uuminus'(X2,X0),X0) = 'c$uminus'(X1,X2,X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Ocompare__rls__1_0]) ).
cnf(c5,plain,
( 'c$ulessequals'(X1,'c$uplus'(X3,X2,X0),X0)
| ~ 'c$ulessequals'('c$uminus'(X1,X2,X0),X3,X0)
| ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Ocompare__rls__8_0]) ).
cnf(c6,plain,
( 'c$uminus'(X1,'c$uuminus'(X2,X0),X0) = 'c$uplus'(X1,X2,X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Odiff__minus__eq__add_0]) ).
cnf(c7,plain,
( 'c$uuminus'('c$uplus'(X1,X2,X0),X0) = 'c$uplus'('c$uuminus'(X1,X0),'c$uuminus'(X2,X0),X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Ominus__add__distrib_0]) ).
cnf(c8,plain,
( 'c$uuminus'('c$uminus'(X1,X2,X0),X0) = 'c$uminus'(X2,X1,X0)
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Ominus__diff__eq_0]) ).
cnf(c9,plain,
( 'c$uuminus'('c$uuminus'(X1,X0),X0) = X1
| ~ 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Ominus__minus_0]) ).
cnf(c10,plain,
( 'c$ulessequals'(X1,'c$uOrderings$uOmax'(X2,X1,X0),X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Ole__maxI2_0]) ).
cnf(c11,plain,
( 'c$ulessequals'(X1,X3,X0)
| ~ 'c$ulessequals'('c$uOrderings$uOmax'(X1,X2,X0),X3,X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0]) ).
cnf(c12,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(c13,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(c14,plain,
( 'class$uOrderedGroup$uOab$u$ugroup$u$uadd'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_4]) ).
cnf(c15,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$uOrderedGroup$uOab$u$ugroup$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[c14,c2]) ).
cnf(d1,plain,
'c$uplus'(X0,'c$uuminus'(X1,'t$ub'),'t$ub') = 'c$uminus'(X0,X1,'t$ub'),
inference(resolution,[status(thm)],[d0,c4]) ).
cnf(d2,plain,
'c$uuminus'('c$uuminus'(X0,'t$ub'),'t$ub') = X0,
inference(resolution,[status(thm)],[c9,d0]) ).
cnf(d3,plain,
'c$uplus'(X1,X0,'t$ub') = 'c$uminus'(X1,'c$uuminus'(X0,'t$ub'),'t$ub'),
inference(superposition,[status(thm)],[d2,d1]) ).
cnf(d4,plain,
'c$uuminus'('c$uminus'(X0,X1,'t$ub'),'t$ub') = 'c$uminus'(X1,X0,'t$ub'),
inference(resolution,[status(thm)],[c8,d0]) ).
cnf(d5,plain,
'c$uminus'(X0,'c$uuminus'(X1,'t$ub'),'t$ub') = 'c$uplus'(X0,X1,'t$ub'),
inference(resolution,[status(thm)],[c6,d0]) ).
cnf(d6,plain,
'c$uuminus'('c$uplus'(X0,X1,'t$ub'),'t$ub') = 'c$uplus'('c$uuminus'(X0,'t$ub'),'c$uuminus'(X1,'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[c7,d0]) ).
cnf(d7,plain,
'c$uuminus'('c$uplus'(X0,X1,'t$ub'),'t$ub') = 'c$uminus'('c$uuminus'(X0,'t$ub'),X1,'t$ub'),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
'c$uuminus'('c$uplus'(X0,'c$uuminus'(X1,'t$ub'),'t$ub'),'t$ub') = 'c$uplus'('c$uuminus'(X0,'t$ub'),X1,'t$ub'),
inference(superposition,[status(thm)],[d7,d5]) ).
cnf(d9,plain,
'c$uuminus'('c$uminus'(X0,X1,'t$ub'),'t$ub') = 'c$uplus'('c$uuminus'(X0,'t$ub'),X1,'t$ub'),
inference(demodulation,[status(thm)],[d8,d1]) ).
cnf(d10,plain,
'c$uminus'(X1,X0,'t$ub') = 'c$uplus'('c$uuminus'(X0,'t$ub'),X1,'t$ub'),
inference(demodulation,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
'c$uminus'(X1,'c$uuminus'(X0,'t$ub'),'t$ub') = 'c$uplus'(X0,X1,'t$ub'),
inference(superposition,[status(thm)],[d2,d10]) ).
cnf(d12,plain,
'c$uplus'(X0,X1,'t$ub') = 'c$uplus'(X1,X0,'t$ub'),
inference(superposition,[status(thm)],[d11,d3]) ).
cnf(d13,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub')
| 'c$ulessequals'(X0,'c$uplus'(X2,'c$uuminus'(X1,'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uplus'(X0,X1,'t$ub'),X2,'t$ub') ),
inference(superposition,[status(thm)],[d5,c5]) ).
cnf(d14,plain,
( ~ 'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub')
| ~ 'c$ulessequals'('c$uplus'(X2,X1,'t$ub'),X0,'t$ub')
| 'c$ulessequals'(X2,'c$uminus'(X0,X1,'t$ub'),'t$ub') ),
inference(demodulation,[status(thm)],[d13,d1]) ).
cnf(d15,plain,
'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub'),
inference(resolution,[status(thm)],[c15,c2]) ).
cnf(d16,plain,
'class$uOrderedGroup$uOpordered$u$uab$u$ugroup$u$uadd'('t$ub'),
inference(resolution,[status(thm)],[d15,c12]) ).
cnf(d17,plain,
( ~ 'c$ulessequals'('c$uplus'(X0,X2,'t$ub'),X1,'t$ub')
| 'c$ulessequals'(X0,'c$uminus'(X1,X2,'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d16,d14]) ).
cnf(d18,plain,
( 'c$ulessequals'(X0,'c$uminus'(X2,'c$uuminus'(X1,'t$ub'),'t$ub'),'t$ub')
| ~ 'c$ulessequals'('c$uminus'(X0,X1,'t$ub'),X2,'t$ub') ),
inference(superposition,[status(thm)],[d1,d17]) ).
cnf(d19,plain,
( ~ 'c$ulessequals'('c$uminus'(X2,X1,'t$ub'),X0,'t$ub')
| 'c$ulessequals'(X2,'c$uplus'(X0,X1,'t$ub'),'t$ub') ),
inference(demodulation,[status(thm)],[d18,d5]) ).
cnf(d20,plain,
'class$uOrderings$uOlinorder'('t$ub'),
inference(resolution,[status(thm)],[c13,c2]) ).
cnf(d21,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0)
| 'c$uHOL$uOabs'('c$uOrderings$uOmax'(X1,'c$u0',X0),X0) = 'c$uOrderings$uOmax'(X1,'c$u0',X0)
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(resolution,[status(thm)],[c10,c3]) ).
cnf(d22,plain,
( ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ub')
| 'c$uHOL$uOabs'('c$uOrderings$uOmax'(X0,'c$u0','t$ub'),'t$ub') = 'c$uOrderings$uOmax'(X0,'c$u0','t$ub') ),
inference(resolution,[status(thm)],[d21,d20]) ).
cnf(d23,plain,
'c$uHOL$uOabs'('c$uOrderings$uOmax'(X0,'c$u0','t$ub'),'t$ub') = 'c$uOrderings$uOmax'(X0,'c$u0','t$ub'),
inference(resolution,[status(thm)],[d15,d22]) ).
cnf(d24,plain,
'c$ulessequals'('c$uOrderings$uOmax'('c$uminus'('v$uf'(X0),'v$ug'(X0),'t$ub'),'c$u0','t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[c0,d23]) ).
cnf(d25,plain,
( ~ 'class$uOrderings$uOlinorder'('t$ub')
| 'c$ulessequals'('c$uminus'('v$uf'(X0),'v$ug'(X0),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ub'),'t$ub'),'t$ub') ),
inference(resolution,[status(thm)],[d24,c11]) ).
cnf(d26,plain,
'c$ulessequals'('c$uminus'('v$uf'(X0),'v$ug'(X0),'t$ub'),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ub'),'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[d20,d25]) ).
cnf(d27,plain,
'c$ulessequals'('v$uf'(X0),'c$uplus'('c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ub'),'t$ub'),'v$ug'(X0),'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[d26,d19]) ).
cnf(d28,plain,
'c$ulessequals'('v$uf'(X0),'c$uplus'('v$ug'(X0),'c$utimes'('v$uc','c$uHOL$uOabs'('v$uh'(X0),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[d27,d12]) ).
cnf(d29,plain,
$false,
inference(resolution,[status(thm)],[d28,c1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : ANA030-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n018.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 22:10:13 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.87/8.31 % SZS status Unsatisfiable for theBenchmark.p
% 14.87/8.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------