%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ALG354-1 : 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 : n002.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 06:48:22 AM UTC 2026
% Result : Unsatisfiable 23.75s 4.01s
% Output : CNFRefutation 23.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of clauses : 14 ( 9 unt; 3 nHn; 14 RR)
% Number of literals : 21 ( 5 equ; 9 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-3 aty)
% Number of variables : 3 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_that_0,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$ub','c$uPower$uOpower$u$uclass$uOpower'(X0,'v$um','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| 'v$uthesis' ) ).
cnf(cls_CHAINED_0,axiom,
'c$uHOL$uOord$u$uclass$uOless'('v$um','v$una','tc$unat') ).
cnf(cls_CHAINED_0_01,axiom,
'v$um' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ).
cnf(cls_CHAINED_0_02,axiom,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('v$um','v$una','tc$unat')
| 'v$um' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')
| 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$ub','c$uPower$uOpower$u$uclass$uOpower'('v$usko$u$uCHAINED$u$u1'('v$ub','v$um'),'v$um','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ) ).
cnf(cls_conjecture_0,negated_conjecture,
~ 'v$uthesis' ).
cnf(c369,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$ub','c$uPower$uOpower$u$uclass$uOpower'(X0,'v$um','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| 'v$uthesis' ),
inference(clausification,[status(esa)],[cls_that_0]) ).
cnf(c371,plain,
'c$uHOL$uOord$u$uclass$uOless'('v$um','v$una','tc$unat'),
inference(clausification,[status(esa)],[cls_CHAINED_0]) ).
cnf(c372,plain,
'v$um' != 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat'),
inference(clausification,[status(esa)],[cls_CHAINED_0_01]) ).
cnf(c373,plain,
( ~ 'c$uHOL$uOord$u$uclass$uOless'('v$um','v$una','tc$unat')
| 'v$um' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat')
| 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$ub','c$uPower$uOpower$u$uclass$uOpower'('v$usko$u$uCHAINED$u$u1'('v$ub','v$um'),'v$um','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal') ),
inference(clausification,[status(esa)],[cls_CHAINED_0_02]) ).
cnf(c374,plain,
~ 'v$uthesis',
inference(clausification,[status(esa)],[cls_conjecture_0]) ).
cnf(d0,plain,
( 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$ub','c$uPower$uOpower$u$uclass$uOpower'('v$usko$u$uCHAINED$u$u1'('v$ub','v$um'),'v$um','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal')
| 'v$um' = 'c$uHOL$uOzero$u$uclass$uOzero'('tc$unat') ),
inference(resolution,[status(thm)],[c371,c373]) ).
cnf(d1,plain,
'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$ub','c$uPower$uOpower$u$uclass$uOpower'('v$usko$u$uCHAINED$u$u1'('v$ub','v$um'),'v$um','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c372,d0]) ).
cnf(d2,plain,
~ 'c$uHOL$uOord$u$uclass$uOless'('c$uRealVector$uOnorm$u$uclass$uOnorm'('c$uHOL$uOplus$u$uclass$uOplus'('c$uHOL$uOone$u$uclass$uOone'('tc$uComplex$uOcomplex'),'c$uHOL$uOtimes$u$uclass$uOtimes'('v$ub','c$uPower$uOpower$u$uclass$uOpower'(X0,'v$um','tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'tc$uComplex$uOcomplex'),'c$uHOL$uOone$u$uclass$uOone'('tc$uRealDef$uOreal'),'tc$uRealDef$uOreal'),
inference(resolution,[status(thm)],[c374,c369]) ).
cnf(d3,plain,
$false,
inference(resolution,[status(thm)],[d2,d1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ALG354-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n002.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sat Sep 26 21:57:06 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.75/4.01 % SZS status Unsatisfiable for theBenchmark.p
% 23.75/4.01 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------