%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA035-2 : 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 06:50:41 AM UTC 2026
% Result : Unsatisfiable 15.63s 2.46s
% Output : CNFRefutation 15.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of clauses : 25 ( 17 unt; 0 nHn; 15 RR)
% Number of literals : 33 ( 19 equ; 17 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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$ub') ).
cnf(tfree_tcs,negated_conjecture,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub') ).
cnf(cls_OrderedGroup_Omult__ac__2_0,axiom,
( 'c$utimes'(X1,X2,X0) = 'c$utimes'(X2,X1,X0)
| ~ 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0) ) ).
cnf(cls_OrderedGroup_Omult__ac__3_0,axiom,
( 'c$utimes'(X1,'c$utimes'(X2,X3,X0),X0) = 'c$utimes'(X2,'c$utimes'(X1,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0) ) ).
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(clsrel_Ring__and__Field_Oordered__idom_17,axiom,
( 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ) ).
cnf(c0,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$ub'),
inference(clausification,[status(esa)],[cls_conjecture_4]) ).
cnf(c1,plain,
'class$uRing$u$uand$u$uField$uOordered$u$uidom'('t$ub'),
inference(clausification,[status(esa)],[tfree_tcs]) ).
cnf(c2,plain,
( 'c$utimes'(X1,X2,X0) = 'c$utimes'(X2,X1,X0)
| ~ 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Omult__ac__2_0]) ).
cnf(c3,plain,
( 'c$utimes'(X1,'c$utimes'(X2,X3,X0),X0) = 'c$utimes'(X2,'c$utimes'(X1,X3,X0),X0)
| ~ 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0) ),
inference(clausification,[status(esa)],[cls_OrderedGroup_Omult__ac__3_0]) ).
cnf(c4,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(c5,plain,
( 'class$uOrderedGroup$uOab$u$usemigroup$u$umult'(X0)
| ~ 'class$uRing$u$uand$u$uField$uOordered$u$uidom'(X0) ),
inference(clausification,[status(esa)],[clsrel_Ring__and__Field_Oordered__idom_17]) ).
cnf(d0,plain,
'class$uOrderedGroup$uOab$u$usemigroup$u$umult'('t$ub'),
inference(resolution,[status(thm)],[c5,c1]) ).
cnf(d1,plain,
'c$utimes'(X0,X1,'t$ub') = 'c$utimes'(X1,X0,'t$ub'),
inference(resolution,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
'c$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)],[c4,c1]) ).
cnf(d3,plain,
'c$utimes'(X0,'c$utimes'(X1,X2,'t$ub'),'t$ub') = 'c$utimes'(X1,'c$utimes'(X0,X2,'t$ub'),'t$ub'),
inference(resolution,[status(thm)],[c3,d0]) ).
cnf(d4,plain,
'c$utimes'(X1,'c$utimes'(X0,X2,'t$ub'),'t$ub') = 'c$utimes'('c$utimes'(X1,X2,'t$ub'),X0,'t$ub'),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,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'('v$uca','c$utimes'('c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[c0,d3]) ).
cnf(d6,plain,
'c$utimes'('v$uc','c$utimes'('c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'v$uca','t$ub'),'t$ub') != 'c$utimes'('v$uca','c$utimes'('c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[d5,d4]) ).
cnf(d7,plain,
'c$utimes'('v$uc','c$utimes'('v$uca','c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') != 'c$utimes'('v$uca','c$utimes'('c$utimes'('v$uc','c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[d6,d1]) ).
cnf(d8,plain,
'c$utimes'('v$uc','c$utimes'('v$uca','c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') != 'c$utimes'('v$uca','c$utimes'('v$uc','c$utimes'('c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[d7,d4]) ).
cnf(d9,plain,
'c$utimes'('v$uc','c$utimes'('v$uca','c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') != 'c$utimes'('v$uc','c$utimes'('v$uca','c$utimes'('c$uHOL$uOabs'('v$ug'('v$ux'),'t$ub'),'c$uHOL$uOabs'('v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[d8,d3]) ).
cnf(d10,plain,
'c$utimes'('v$uc','c$utimes'('v$uca','c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') != 'c$utimes'('v$uc','c$utimes'('v$uca','c$uHOL$uOabs'('c$utimes'('v$ug'('v$ux'),'v$uf'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[d9,d2]) ).
cnf(d11,plain,
'c$utimes'('v$uc','c$utimes'('v$uca','c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub') != 'c$utimes'('v$uc','c$utimes'('v$uca','c$uHOL$uOabs'('c$utimes'('v$uf'('v$ux'),'v$ug'('v$ux'),'t$ub'),'t$ub'),'t$ub'),'t$ub'),
inference(demodulation,[status(thm)],[d10,d1]) ).
cnf(d12,plain,
$false,
inference(equality_resolution,[status(thm)],[d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : ANA035-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n007.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 22:06:39 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 15.63/2.46 % SZS status Unsatisfiable for theBenchmark.p
% 15.63/2.46 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------