%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 06:48:24 AM UTC 2026
% Result : Unsatisfiable 34.90s 21.26s
% Output : CNFRefutation 34.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of clauses : 30 ( 16 unt; 0 nHn; 19 RR)
% Number of literals : 46 ( 19 equ; 21 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 23 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_sup__idem_0,axiom,
( 'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X1,X1,X0) = X1
| ~ 'class$uLattices$uOupper$u$usemilattice'(X0) ) ).
cnf(cls_sup__absorb1_0,axiom,
( ~ 'c$ulessequals'(X2,X1,X0)
| 'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X1,X2,X0) = X1
| ~ 'class$uLattices$uOupper$u$usemilattice'(X0) ) ).
cnf(cls_norm__zero_0,axiom,
( 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ) ).
cnf(cls_rp_0,axiom,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal') ).
cnf(cls_real__le__refl_0,axiom,
'c$ulessequals'(X0,X0,'tc$uRealDef$uOreal') ).
cnf(cls_minus__equation__iff_1,axiom,
( 'c$uHOL$uOuminus$u$uclass$uOuminus'('c$uHOL$uOuminus$u$uclass$uOuminus'(X1,X0),X0) = X1
| ~ 'class$uOrderedGroup$uOgroup$u$uadd'(X0) ) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ 'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$ur','tc$uRealDef$uOreal')
| 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uHOL$uOuminus$u$uclass$uOuminus'('c$uHOL$uOuminus$u$uclass$uOuminus'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ) ).
cnf(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice,axiom,
'class$uLattices$uOupper$u$usemilattice'('tc$uRealDef$uOreal') ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
'class$uOrderedGroup$uOgroup$u$uadd'('tc$uRealDef$uOreal') ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex') ).
cnf(c154,plain,
( 'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X1,X1,X0) = X1
| ~ 'class$uLattices$uOupper$u$usemilattice'(X0) ),
inference(clausification,[status(esa)],[cls_sup__idem_0]) ).
cnf(c286,plain,
( ~ 'c$ulessequals'(X2,X1,X0)
| 'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X1,X2,X0) = X1
| ~ 'class$uLattices$uOupper$u$usemilattice'(X0) ),
inference(clausification,[status(esa)],[cls_sup__absorb1_0]) ).
cnf(c683,plain,
( 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'(X0),X0) = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal')
| ~ 'class$uRealVector$uOreal$u$unormed$u$uvector'(X0) ),
inference(clausification,[status(esa)],[cls_norm__zero_0]) ).
cnf(c698,plain,
'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_rp_0]) ).
cnf(c711,plain,
'c$ulessequals'(X0,X0,'tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[cls_real__le__refl_0]) ).
cnf(c743,plain,
( 'c$uHOL$uOuminus$u$uclass$uOuminus'('c$uHOL$uOuminus$u$uclass$uOuminus'(X1,X0),X0) = X1
| ~ 'class$uOrderedGroup$uOgroup$u$uadd'(X0) ),
inference(clausification,[status(esa)],[cls_minus__equation__iff_1]) ).
cnf(c753,plain,
( ~ 'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$ur','tc$uRealDef$uOreal')
| 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uHOL$uOuminus$u$uclass$uOuminus'('c$uHOL$uOuminus$u$uclass$uOuminus'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(c840,plain,
'class$uLattices$uOupper$u$usemilattice'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__Lattices_Oupper__semilattice]) ).
cnf(c854,plain,
'class$uOrderedGroup$uOgroup$u$uadd'('tc$uRealDef$uOreal'),
inference(clausification,[status(esa)],[clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add]) ).
cnf(c879,plain,
'class$uRealVector$uOreal$u$unormed$u$uvector'('tc$uComplex$uOcomplex'),
inference(clausification,[status(esa)],[clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
cnf(d0,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c683,c879]) ).
cnf(d1,plain,
'c$uHOL$uOuminus$u$uclass$uOuminus'('c$uHOL$uOuminus$u$uclass$uOuminus'(X0,'tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') = X0,
inference(resolution,[status(thm)],[c743,c854]) ).
cnf(d2,plain,
( ~ 'c$ulessequals'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'v$ur','tc$uRealDef$uOreal')
| 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ),
inference(demodulation,[status(thm)],[c753,d1]) ).
cnf(d3,plain,
( ~ 'c$ulessequals'('c$uHOL$uOzero$u$uclass$uOzero'('tc$uRealDef$uOreal'),'v$ur','tc$uRealDef$uOreal')
| 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') ),
inference(demodulation,[status(thm)],[d2,d0]) ).
cnf(d4,plain,
'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex') != 'c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uPolynomial$uOpoly'('v$up','c$uHOL$uOzero$u$uclass$uOzero'('tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),
inference(resolution,[status(thm)],[c698,d3]) ).
cnf(d5,plain,
'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X0,X0,'tc$uRealDef$uOreal') = X0,
inference(resolution,[status(thm)],[c154,c840]) ).
cnf(d6,plain,
( ~ 'class$uLattices$uOupper$u$usemilattice'('tc$uRealDef$uOreal')
| 'c$uLattices$uOupper$u$usemilattice$u$uclass$uOsup'(X0,X0,'tc$uRealDef$uOreal') = X0 ),
inference(resolution,[status(thm)],[c286,c711]) ).
cnf(d7,plain,
( ~ 'class$uLattices$uOupper$u$usemilattice'('tc$uRealDef$uOreal')
| X0 = X0 ),
inference(demodulation,[status(thm)],[d6,d5]) ).
cnf(d8,plain,
X0 = X0,
inference(resolution,[status(thm)],[c840,d7]) ).
cnf(d9,plain,
$false,
inference(resolution,[status(thm)],[d8,d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG372-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/15.40 % Computer : n026.cluster.edu
% 0.10/15.40 % Model : x86_64 x86_64
% 0.10/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.40 % Memory : 8046.5625MB
% 0.10/15.40 % OS : Linux 6.8.0-71-generic
% 0.14/15.40 % CPULimit : 300
% 0.14/15.40 % WCLimit : 300
% 0.14/15.40 % DateTime : Sat Sep 26 21:58:40 UTC 2026
% 0.14/15.40 % CPUTime :
% 0.14/15.40 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.90/21.26 % SZS status Unsatisfiable for theBenchmark.p
% 34.90/21.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------