%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA019-2 : 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 : n007.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 06:50:38 AM UTC 2026
% Result : Unsatisfiable 10.30s 1.71s
% Output : CNFRefutation 10.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of clauses : 52 ( 19 unt; 5 nHn; 43 RR)
% Number of literals : 93 ( 16 equ; 46 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 37 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_conjecture_0,negated_conjecture,
'v$uf'('c$u0') = 'c$u0' ).
cnf(cls_conjecture_1,negated_conjecture,
'c$uless'('c$u0','v$ux','t$ua') ).
cnf(cls_conjecture_2,negated_conjecture,
'c$ulessequals'('c$uHOL$uOabs'('v$uf'('c$uSuc'(X0)),'t$ua'),'c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'('c$uSuc'(X0)),'t$ua'),'t$ua'),'t$ua') ).
cnf(cls_conjecture_3,negated_conjecture,
( ~ 'c$uless'('c$u0',X0,'t$ua')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$uxa'(X0)),'t$ua'),'c$utimes'(X0,'c$uHOL$uOabs'('v$uh'('v$uxa'(X0)),'t$ua'),'t$ua'),'t$ua') ) ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua') ).
cnf(cls_NatBin_OSuc__pred_H_0,axiom,
( X0 = 'c$uSuc'('c$uminus'(X0,'c$u1','tc$unat'))
| ~ 'c$uless'('c$u0',X0,'tc$unat') ) ).
cnf(cls_Nat_Onot__gr0_0,axiom,
( X0 = 'c$u0'
| 'c$uless'('c$u0',X0,'tc$unat') ) ).
cnf(cls_OrderedGroup_Oabs__eq__0_1,axiom,
( 'c$uHOL$uOabs'('c$u0',X0) = 'c$u0'
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_OrderedGroup_Oabs__ge__zero_0,axiom,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ) ).
cnf(cls_Orderings_Oorder__less__imp__le_0,axiom,
( 'c$ulessequals'(X1,X2,X0)
| ~ 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ) ).
cnf(cls_Ring__and__Field_Omult__nonneg__nonneg_0,axiom,
( 'c$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(clsrel_LOrder_Ojoin__semilorder_1,axiom,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(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_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_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,
'v$uf'('c$u0') = 'c$u0',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c1,plain,
'c$uless'('c$u0','v$ux','t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_1]) ).
cnf(c2,plain,
'c$ulessequals'('c$uHOL$uOabs'('v$uf'('c$uSuc'(X0)),'t$ua'),'c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'('c$uSuc'(X0)),'t$ua'),'t$ua'),'t$ua'),
inference(clausification,[status(esa)],[cls_conjecture_2]) ).
cnf(c3,plain,
( ~ 'c$uless'('c$u0',X0,'t$ua')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$uxa'(X0)),'t$ua'),'c$utimes'(X0,'c$uHOL$uOabs'('v$uh'('v$uxa'(X0)),'t$ua'),'t$ua'),'t$ua') ),
inference(clausification,[status(esa)],[cls_conjecture_3]) ).
cnf(c4,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ua'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c5,plain,
( X0 = 'c$uSuc'('c$uminus'(X0,'c$u1','tc$unat'))
| ~ 'c$uless'('c$u0',X0,'tc$unat') ),
inference(clausification,[status(esa)],[cls_NatBin_OSuc__pred_H_0]) ).
cnf(c6,plain,
( X0 = 'c$u0'
| 'c$uless'('c$u0',X0,'tc$unat') ),
inference(clausification,[status(esa)],[cls_Nat_Onot__gr0_0]) ).
cnf(c7,plain,
( 'c$uHOL$uOabs'('c$u0',X0) = 'c$u0'
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__eq__0_1]) ).
cnf(c8,plain,
( 'c$ulessequals'('c$u0','c$uHOL$uOabs'(X1,X0),X0)
| ~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Oabs__ge__zero_0]) ).
cnf(c9,plain,
( 'c$ulessequals'(X1,X2,X0)
| ~ 'c$uless'(X1,X2,X0)
| ~ 'class$uOrderings$uOorder'(X0) ),
inference(clausification,[status(esa)],[cls_Orderings_Oorder__less__imp__le_0]) ).
cnf(c10,plain,
( 'c$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(c11,plain,
( 'class$uOrderings$uOorder'(X0)
| ~ 'class$uLOrder$uOjoin$u$usemilorder'(X0) ),
inference(clausification,[status(esa)],[clsrel_LOrder_Ojoin__semilorder_1]) ).
cnf(c12,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(c13,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(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$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[c14,c4]) ).
cnf(d1,plain,
'c$uHOL$uOabs'('c$u0','t$ua') = 'c$u0',
inference(resolution,[status(thm)],[d0,c7]) ).
cnf(d2,plain,
( X0 = 'c$uSuc'('c$uminus'(X0,'c$u1','tc$unat'))
| X0 = 'c$u0' ),
inference(resolution,[status(thm)],[c6,c5]) ).
cnf(d3,plain,
( X0 = 'c$u0'
| 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('c$uSuc'('c$uminus'(X0,'c$u1','tc$unat'))),'t$ua'),'c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
( X0 = 'c$u0'
| X0 = 'c$u0'
| 'c$ulessequals'('c$uHOL$uOabs'('v$uf'(X0),'t$ua'),'c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'(X0),'t$ua'),'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d2,d3]) ).
cnf(d5,plain,
( ~ 'c$uless'('c$u0','v$ux','t$ua')
| 'v$uxa'('v$ux') = 'c$u0' ),
inference(resolution,[status(thm)],[d4,c3]) ).
cnf(d6,plain,
'v$uxa'('v$ux') = 'c$u0',
inference(resolution,[status(thm)],[c1,d5]) ).
cnf(d7,plain,
( ~ 'c$uless'('c$u0','v$ux','t$ua')
| ~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('v$uxa'('v$ux')),'t$ua'),'c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),'t$ua') ),
inference(superposition,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
( ~ 'c$ulessequals'('c$uHOL$uOabs'('v$uf'('c$u0'),'t$ua'),'c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),'t$ua')
| ~ 'c$uless'('c$u0','v$ux','t$ua') ),
inference(demodulation,[status(thm)],[d7,d6]) ).
cnf(d9,plain,
( ~ 'c$ulessequals'('c$uHOL$uOabs'('c$u0','t$ua'),'c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),'t$ua')
| ~ 'c$uless'('c$u0','v$ux','t$ua') ),
inference(demodulation,[status(thm)],[d8,c0]) ).
cnf(d10,plain,
( ~ 'c$ulessequals'('c$u0','c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),'t$ua')
| ~ 'c$uless'('c$u0','v$ux','t$ua') ),
inference(demodulation,[status(thm)],[d9,d1]) ).
cnf(d11,plain,
~ 'c$ulessequals'('c$u0','c$utimes'('v$ux','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),'t$ua'),
inference(resolution,[status(thm)],[c1,d10]) ).
cnf(d12,plain,
( ~ 'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ua')
| ~ 'c$ulessequals'('c$u0','v$ux','t$ua')
| ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua') ),
inference(resolution,[status(thm)],[d11,c10]) ).
cnf(d13,plain,
'class$uRing$u$uand$u$uField$uOpordered$u$ucancel$u$usemiring'('t$ua'),
inference(resolution,[status(thm)],[c13,c4]) ).
cnf(d14,plain,
( ~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua')
| ~ 'c$ulessequals'('c$u0','v$ux','t$ua') ),
inference(resolution,[status(thm)],[d13,d12]) ).
cnf(d15,plain,
( ~ 'class$uOrderings$uOorder'('t$ua')
| 'c$ulessequals'('c$u0','v$ux','t$ua') ),
inference(resolution,[status(thm)],[c9,c1]) ).
cnf(d16,plain,
'class$uLOrder$uOjoin$u$usemilorder'('t$ua'),
inference(resolution,[status(thm)],[c12,c4]) ).
cnf(d17,plain,
'class$uOrderings$uOorder'('t$ua'),
inference(resolution,[status(thm)],[c11,d16]) ).
cnf(d18,plain,
'c$ulessequals'('c$u0','v$ux','t$ua'),
inference(resolution,[status(thm)],[d17,d15]) ).
cnf(d19,plain,
~ 'c$ulessequals'('c$u0','c$uHOL$uOabs'('v$uh'('c$u0'),'t$ua'),'t$ua'),
inference(resolution,[status(thm)],[d18,d14]) ).
cnf(d20,plain,
~ 'class$uOrderedGroup$uOlordered$u$uab$u$ugroup$u$uabs'('t$ua'),
inference(resolution,[status(thm)],[d19,c8]) ).
cnf(d21,plain,
$false,
inference(resolution,[status(thm)],[d0,d20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ANA019-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 22:02:54 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.30/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 10.30/1.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------