%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : SWV019-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/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 09:01:16 AM UTC 2026
% Result : Unsatisfiable 8.77s 2.89s
% Output : CNFRefutation 8.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of clauses : 43 ( 16 unt; 14 nHn; 39 RR)
% Number of literals : 100 ( 11 equ; 46 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 18 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(in_bounds,axiom,
( 'in$uarray$ubounds'(array,X0)
| 'less$uthan'('upper$ubound',X0)
| 'less$uthan'(X0,'lower$ubound') ) ).
cnf(predecessor_less,axiom,
( 'less$uthan'(X0,X1)
| ~ 'less$uthan'(successor(X0),successor(X1)) ) ).
cnf(transitivity_of_less,axiom,
( 'less$uthan'(X0,X2)
| ~ 'less$uthan'(X1,X2)
| ~ 'less$uthan'(X0,X1) ) ).
cnf(successor_greater,axiom,
'less$uthan'(X0,successor(X0)) ).
cnf(this_is_maximal,axiom,
( 'maximal$uvalue' = 'array$uvalue$uat'(array,'index$uof$umaximal')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal') ) ).
cnf(maximal_before_somewhere,axiom,
'less$uthan'('index$uof$umaximal','an$uindex') ).
cnf(somewhere_above_lower_bound,axiom,
~ 'less$uthan'('an$uindex','lower$ubound') ).
cnf(somewhere_below_upper_bound,axiom,
~ 'less$uthan'('upper$ubound','an$uindex') ).
cnf(maximal_above_lower_bound,axiom,
~ 'less$uthan'('index$uof$umaximal','lower$ubound') ).
cnf(prove_this,negated_conjecture,
( 'maximal$uvalue' != 'array$uvalue$uat'(array,'index$uof$umaximal')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal')
| ~ 'less$uthan'('index$uof$umaximal',successor('an$uindex'))
| 'less$uthan'('index$uof$umaximal','lower$ubound')
| 'less$uthan'(successor('upper$ubound'),successor('an$uindex'))
| 'less$uthan'(successor('an$uindex'),'lower$ubound')
| ~ 'in$uarray$ubounds'(array,'an$uindex') ) ).
cnf(c0,plain,
( 'in$uarray$ubounds'(array,X0)
| 'less$uthan'('upper$ubound',X0)
| 'less$uthan'(X0,'lower$ubound') ),
inference(clausification,[status(esa)],[in_bounds]) ).
cnf(c1,plain,
( 'less$uthan'(X0,X1)
| ~ 'less$uthan'(successor(X0),successor(X1)) ),
inference(clausification,[status(esa)],[predecessor_less]) ).
cnf(c2,plain,
( 'less$uthan'(X0,X2)
| ~ 'less$uthan'(X1,X2)
| ~ 'less$uthan'(X0,X1) ),
inference(clausification,[status(esa)],[transitivity_of_less]) ).
cnf(c3,plain,
'less$uthan'(X0,successor(X0)),
inference(clausification,[status(esa)],[successor_greater]) ).
cnf(c4,plain,
( 'maximal$uvalue' = 'array$uvalue$uat'(array,'index$uof$umaximal')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal') ),
inference(clausification,[status(esa)],[this_is_maximal]) ).
cnf(c5,plain,
'less$uthan'('index$uof$umaximal','an$uindex'),
inference(clausification,[status(esa)],[maximal_before_somewhere]) ).
cnf(c6,plain,
~ 'less$uthan'('an$uindex','lower$ubound'),
inference(clausification,[status(esa)],[somewhere_above_lower_bound]) ).
cnf(c7,plain,
~ 'less$uthan'('upper$ubound','an$uindex'),
inference(clausification,[status(esa)],[somewhere_below_upper_bound]) ).
cnf(c8,plain,
~ 'less$uthan'('index$uof$umaximal','lower$ubound'),
inference(clausification,[status(esa)],[maximal_above_lower_bound]) ).
cnf(c9,plain,
( 'maximal$uvalue' != 'array$uvalue$uat'(array,'index$uof$umaximal')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal')
| 'less$uthan'('index$uof$umaximal','lower$ubound')
| 'less$uthan'(successor('upper$ubound'),successor('an$uindex'))
| 'less$uthan'(successor('an$uindex'),'lower$ubound')
| ~ 'less$uthan'('index$uof$umaximal',successor('an$uindex'))
| ~ 'in$uarray$ubounds'(array,'an$uindex') ),
inference(clausification,[status(esa)],[prove_this]) ).
cnf(d0,plain,
( 'less$uthan'('index$uof$umaximal',X0)
| ~ 'less$uthan'('an$uindex',X0) ),
inference(resolution,[status(thm)],[c2,c5]) ).
cnf(d1,plain,
'less$uthan'('index$uof$umaximal',successor('an$uindex')),
inference(resolution,[status(thm)],[d0,c3]) ).
cnf(d2,plain,
( 'less$uthan'('index$uof$umaximal',X0)
| ~ 'less$uthan'(successor('an$uindex'),X0) ),
inference(resolution,[status(thm)],[d1,c2]) ).
cnf(d3,plain,
( ~ 'in$uarray$ubounds'(array,'an$uindex')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal')
| ~ 'less$uthan'('index$uof$umaximal',successor('an$uindex'))
| 'less$uthan'(successor('an$uindex'),'lower$ubound')
| 'less$uthan'(successor('upper$ubound'),successor('an$uindex'))
| 'maximal$uvalue' != 'array$uvalue$uat'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[c8,c9]) ).
cnf(d4,plain,
( ~ 'in$uarray$ubounds'(array,'an$uindex')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal')
| 'less$uthan'(successor('an$uindex'),'lower$ubound')
| 'less$uthan'(successor('upper$ubound'),successor('an$uindex'))
| 'maximal$uvalue' != 'array$uvalue$uat'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[d1,d3]) ).
cnf(d5,plain,
( 'less$uthan'('upper$ubound','index$uof$umaximal')
| 'less$uthan'('index$uof$umaximal','lower$ubound')
| 'maximal$uvalue' = 'array$uvalue$uat'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d6,plain,
( 'less$uthan'('upper$ubound','index$uof$umaximal')
| 'maximal$uvalue' = 'array$uvalue$uat'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[c8,d5]) ).
cnf(d7,plain,
( 'less$uthan'('upper$ubound',X0)
| ~ 'less$uthan'('index$uof$umaximal',X0)
| 'maximal$uvalue' = 'array$uvalue$uat'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[d6,c2]) ).
cnf(d8,plain,
( 'less$uthan'('upper$ubound','an$uindex')
| 'maximal$uvalue' = 'array$uvalue$uat'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[d7,c5]) ).
cnf(d9,plain,
'maximal$uvalue' = 'array$uvalue$uat'(array,'index$uof$umaximal'),
inference(resolution,[status(thm)],[c7,d8]) ).
cnf(d10,plain,
( ~ 'in$uarray$ubounds'(array,'an$uindex')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal')
| 'less$uthan'(successor('an$uindex'),'lower$ubound')
| 'less$uthan'(successor('upper$ubound'),successor('an$uindex')) ),
inference(resolution,[status(thm)],[d9,d4]) ).
cnf(d11,plain,
( 'less$uthan'('upper$ubound','an$uindex')
| ~ 'in$uarray$ubounds'(array,'an$uindex')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal')
| 'less$uthan'(successor('an$uindex'),'lower$ubound') ),
inference(resolution,[status(thm)],[d10,c1]) ).
cnf(d12,plain,
( ~ 'in$uarray$ubounds'(array,'an$uindex')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal')
| 'less$uthan'(successor('an$uindex'),'lower$ubound') ),
inference(resolution,[status(thm)],[c7,d11]) ).
cnf(d13,plain,
( 'less$uthan'('index$uof$umaximal','lower$ubound')
| ~ 'in$uarray$ubounds'(array,'an$uindex')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[d12,d2]) ).
cnf(d14,plain,
( ~ 'in$uarray$ubounds'(array,'an$uindex')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[c8,d13]) ).
cnf(d15,plain,
( 'less$uthan'('upper$ubound','an$uindex')
| 'less$uthan'('an$uindex','lower$ubound')
| ~ 'in$uarray$ubounds'(array,'index$uof$umaximal') ),
inference(resolution,[status(thm)],[d14,c0]) ).
cnf(d16,plain,
( ~ 'in$uarray$ubounds'(array,'index$uof$umaximal')
| 'less$uthan'('upper$ubound','an$uindex') ),
inference(resolution,[status(thm)],[c6,d15]) ).
cnf(d17,plain,
~ 'in$uarray$ubounds'(array,'index$uof$umaximal'),
inference(resolution,[status(thm)],[c7,d16]) ).
cnf(d18,plain,
( 'less$uthan'('upper$ubound','index$uof$umaximal')
| 'less$uthan'('index$uof$umaximal','lower$ubound') ),
inference(resolution,[status(thm)],[d17,c0]) ).
cnf(d19,plain,
'less$uthan'('upper$ubound','index$uof$umaximal'),
inference(resolution,[status(thm)],[c8,d18]) ).
cnf(d20,plain,
( 'less$uthan'('upper$ubound',X0)
| ~ 'less$uthan'('index$uof$umaximal',X0) ),
inference(resolution,[status(thm)],[d19,c2]) ).
cnf(d21,plain,
'less$uthan'('upper$ubound','an$uindex'),
inference(resolution,[status(thm)],[d20,c5]) ).
cnf(d22,plain,
$false,
inference(resolution,[status(thm)],[c7,d21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV019-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.65 % Computer : n026.cluster.edu
% 0.18/0.65 % Model : x86_64 x86_64
% 0.18/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.65 % Memory : 8046.5625MB
% 0.18/0.65 % OS : Linux 6.8.0-71-generic
% 0.18/0.65 % CPULimit : 300
% 0.18/0.65 % WCLimit : 300
% 0.18/0.65 % DateTime : Sat Sep 26 13:08:58 UTC 2026
% 0.18/0.65 % CPUTime :
% 0.18/0.66 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.77/2.89 % SZS status Unsatisfiable for theBenchmark.p
% 8.77/2.89 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------