%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG428-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 06:48:29 AM UTC 2026
% Result : Unsatisfiable 16.35s 15.09s
% Output : CNFRefutation 16.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 21 ( 11 unt; 5 nHn; 16 RR)
% Number of literals : 38 ( 18 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 17 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| 'c$uHOL$uOord$u$uclass$uOless'(X2,X1,X0)
| X1 = X2
| ~ 'class$uOrderings$uOlinorder'(X0) ) ).
cnf(cls_Suc__pred_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),X0,'tc$unat')
| 'c$uSuc'('c$uHOL$uOminus$u$uclass$uOminus'(X0,'c$uSuc'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'tc$unat')) = X0 ) ).
cnf(cls_gr__implies__not0_0,axiom,
~ 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'tc$unat') ).
cnf(cls_that_0,axiom,
( 'v$uthesis'
| 'c$uPolynomial$uOdegree'('v$up','tc$uComplex$uOcomplex') != 'c$uSuc'(X0) ) ).
cnf(cls_dp_0,axiom,
'c$uPolynomial$uOdegree'('v$up','tc$uComplex$uOcomplex') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'v$uthesis' ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
'class$uOrderings$uOlinorder'('tc$unat') ).
cnf(c19,plain,
( 'c$uHOL$uOord$u$uclass$uOless'(X1,X2,X0)
| 'c$uHOL$uOord$u$uclass$uOless'(X2,X1,X0)
| X1 = X2
| ~ 'class$uOrderings$uOlinorder'(X0) ),
inference(clausification,[status(esa)],[cls_not__less__iff__gr__or__eq_0]) ).
cnf(c77,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),X0,'tc$unat')
| 'c$uSuc'('c$uHOL$uOminus$u$uclass$uOminus'(X0,'c$uSuc'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'tc$unat')) = X0 ),
inference(clausification,[status(esa)],[cls_Suc__pred_0]) ).
cnf(c318,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'tc$unat'),
inference(clausification,[status(esa)],[cls_gr__implies__not0_0]) ).
cnf(c772,plain,
( 'v$uthesis'
| 'c$uPolynomial$uOdegree'('v$up','tc$uComplex$uOcomplex') != 'c$uSuc'(X0) ),
inference(clausification,[status(esa)],[cls_that_0]) ).
cnf(c786,plain,
'c$uPolynomial$uOdegree'('v$up','tc$uComplex$uOcomplex') != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),
inference(clausification,[status(esa)],[cls_dp_0]) ).
cnf(c791,plain,
~ 'v$uthesis',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c827,plain,
'class$uOrderings$uOlinorder'('tc$unat'),
inference(clausification,[status(esa)],[clsarity_nat__Orderings_Olinorder]) ).
cnf(d0,plain,
'c$uPolynomial$uOdegree'('v$up','tc$uComplex$uOcomplex') != 'c$uSuc'(X0),
inference(resolution,[status(thm)],[c791,c772]) ).
cnf(d1,plain,
( ~ 'class$uOrderings$uOlinorder'('tc$unat')
| 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'tc$unat')
| X0 = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')
| 'c$uSuc'('c$uHOL$uOminus$u$uclass$uOminus'(X0,'c$uSuc'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'tc$unat')) = X0 ),
inference(resolution,[status(thm)],[c77,c19]) ).
cnf(d2,plain,
( 'c$uHOL$uOord$u$uclass$uOless'(X0,'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),'tc$unat')
| 'c$uSuc'('c$uHOL$uOminus$u$uclass$uOminus'(X0,'c$uSuc'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'tc$unat')) = X0
| X0 = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ),
inference(resolution,[status(thm)],[c827,d1]) ).
cnf(d3,plain,
( 'c$uSuc'('c$uHOL$uOminus$u$uclass$uOminus'(X0,'c$uSuc'('c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')),'tc$unat')) = X0
| X0 = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ),
inference(resolution,[status(thm)],[c318,d2]) ).
cnf(d4,plain,
( X0 = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')
| 'c$uPolynomial$uOdegree'('v$up','tc$uComplex$uOcomplex') != X0 ),
inference(superposition,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
'c$uPolynomial$uOdegree'('v$up','tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
$false,
inference(resolution,[status(thm)],[c786,d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG428-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.37 % Computer : n005.cluster.edu
% 0.06/0.37 % Model : x86_64 x86_64
% 0.06/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.37 % Memory : 8046.5625MB
% 0.06/0.37 % OS : Linux 6.8.0-71-generic
% 0.06/0.37 % CPULimit : 300
% 0.06/0.37 % WCLimit : 300
% 0.06/0.37 % DateTime : Sat Sep 26 22:00:17 UTC 2026
% 0.06/0.37 % CPUTime :
% 0.06/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.35/15.09 % SZS status Unsatisfiable for theBenchmark.p
% 16.35/15.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------