%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 06:50:35 AM UTC 2026
% Result : Unsatisfiable 7.62s 1.91s
% Output : CNFRefutation 7.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of clauses : 39 ( 4 unt; 17 nHn; 35 RR)
% Number of literals : 94 ( 0 equ; 35 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-2 aty)
% Number of variables : 57 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(absolute_sum_less_or_equal_sum_of_absolutes2,axiom,
( 'less$uor$uequal'(absolute(add(X0,X1)),X2)
| ~ 'less$uor$uequal'(add(absolute(X0),absolute(X1)),X2) ) ).
cnf(minimum3,axiom,
( 'less$uor$uequal'(X0,X1)
| ~ 'less$uor$uequal'(X0,minimum(X1,X2)) ) ).
cnf(minimum7,axiom,
( 'less$uor$uequal'(X0,X2)
| ~ 'less$uor$uequal'(X0,minimum(X1,X2)) ) ).
cnf(minimum9,axiom,
( ~ 'less$uor$uequal'(minimum(X0,X1),n0)
| 'less$uor$uequal'(X1,n0)
| 'less$uor$uequal'(X0,n0) ) ).
cnf(less_or_equal_sum_of_halves,axiom,
( 'less$uor$uequal'(add(X0,X2),X1)
| ~ 'less$uor$uequal'(X2,half(X1))
| ~ 'less$uor$uequal'(X0,half(X1)) ) ).
cnf(zero_and_half,axiom,
( ~ 'less$uor$uequal'(half(X0),n0)
| 'less$uor$uequal'(X0,n0) ) ).
cnf(clause_1,hypothesis,
( ~ 'less$uor$uequal'('delta$u1'(X0),n0)
| 'less$uor$uequal'(X0,n0) ) ).
cnf(clause_2,hypothesis,
( ~ 'less$uor$uequal'('delta$u2'(X0),n0)
| 'less$uor$uequal'(X0,n0) ) ).
cnf(clause_3,hypothesis,
( 'less$uor$uequal'(absolute(add(f(X1),negate(f('a$ureal$unumber')))),X0)
| ~ 'less$uor$uequal'(absolute(add(X1,negate('a$ureal$unumber'))),'delta$u1'(X0))
| 'less$uor$uequal'(X0,n0) ) ).
cnf(clause_4,hypothesis,
( 'less$uor$uequal'(absolute(add(g(X1),negate(g('a$ureal$unumber')))),X0)
| ~ 'less$uor$uequal'(absolute(add(X1,negate('a$ureal$unumber'))),'delta$u2'(X0))
| 'less$uor$uequal'(X0,n0) ) ).
cnf(clause_5,hypothesis,
~ 'less$uor$uequal'('epsilon$u0',n0) ).
cnf(clause_6,hypothesis,
( 'less$uor$uequal'(absolute(add(xs(X0),negate('a$ureal$unumber'))),X0)
| 'less$uor$uequal'(X0,n0) ) ).
cnf(clause_7_1,negated_conjecture,
( ~ 'less$uor$uequal'(absolute(add(add(f(xs(X0)),negate(f('a$ureal$unumber'))),add(g(xs(X0)),negate(g('a$ureal$unumber'))))),'epsilon$u0')
| 'less$uor$uequal'(X0,n0) ) ).
cnf(c0,plain,
( 'less$uor$uequal'(absolute(add(X0,X1)),X2)
| ~ 'less$uor$uequal'(add(absolute(X0),absolute(X1)),X2) ),
inference(clausification,[status(esa)],[absolute_sum_less_or_equal_sum_of_absolutes2]) ).
cnf(c1,plain,
( 'less$uor$uequal'(X0,X1)
| ~ 'less$uor$uequal'(X0,minimum(X1,X2)) ),
inference(clausification,[status(esa)],[minimum3]) ).
cnf(c2,plain,
( 'less$uor$uequal'(X0,X2)
| ~ 'less$uor$uequal'(X0,minimum(X1,X2)) ),
inference(clausification,[status(esa)],[minimum7]) ).
cnf(c3,plain,
( ~ 'less$uor$uequal'(minimum(X0,X1),n0)
| 'less$uor$uequal'(X1,n0)
| 'less$uor$uequal'(X0,n0) ),
inference(clausification,[status(esa)],[minimum9]) ).
cnf(c4,plain,
( 'less$uor$uequal'(add(X0,X2),X1)
| ~ 'less$uor$uequal'(X2,half(X1))
| ~ 'less$uor$uequal'(X0,half(X1)) ),
inference(clausification,[status(esa)],[less_or_equal_sum_of_halves]) ).
cnf(c5,plain,
( ~ 'less$uor$uequal'(half(X0),n0)
| 'less$uor$uequal'(X0,n0) ),
inference(clausification,[status(esa)],[zero_and_half]) ).
cnf(c6,plain,
( ~ 'less$uor$uequal'('delta$u1'(X0),n0)
| 'less$uor$uequal'(X0,n0) ),
inference(clausification,[status(esa)],[clause_1]) ).
cnf(c7,plain,
( ~ 'less$uor$uequal'('delta$u2'(X0),n0)
| 'less$uor$uequal'(X0,n0) ),
inference(clausification,[status(esa)],[clause_2]) ).
cnf(c8,plain,
( 'less$uor$uequal'(absolute(add(f(X1),negate(f('a$ureal$unumber')))),X0)
| ~ 'less$uor$uequal'(absolute(add(X1,negate('a$ureal$unumber'))),'delta$u1'(X0))
| 'less$uor$uequal'(X0,n0) ),
inference(clausification,[status(esa)],[clause_3]) ).
cnf(c9,plain,
( 'less$uor$uequal'(absolute(add(g(X1),negate(g('a$ureal$unumber')))),X0)
| ~ 'less$uor$uequal'(absolute(add(X1,negate('a$ureal$unumber'))),'delta$u2'(X0))
| 'less$uor$uequal'(X0,n0) ),
inference(clausification,[status(esa)],[clause_4]) ).
cnf(c10,plain,
~ 'less$uor$uequal'('epsilon$u0',n0),
inference(clausification,[status(esa)],[clause_5]) ).
cnf(c11,plain,
( 'less$uor$uequal'(absolute(add(xs(X0),negate('a$ureal$unumber'))),X0)
| 'less$uor$uequal'(X0,n0) ),
inference(clausification,[status(esa)],[clause_6]) ).
cnf(c12,plain,
( ~ 'less$uor$uequal'(absolute(add(add(f(xs(X0)),negate(f('a$ureal$unumber'))),add(g(xs(X0)),negate(g('a$ureal$unumber'))))),'epsilon$u0')
| 'less$uor$uequal'(X0,n0) ),
inference(clausification,[status(esa)],[clause_7_1]) ).
cnf(d0,plain,
( 'less$uor$uequal'(absolute(add(xs(minimum(X0,X1)),negate('a$ureal$unumber'))),X1)
| 'less$uor$uequal'(minimum(X0,X1),n0) ),
inference(resolution,[status(thm)],[c11,c2]) ).
cnf(d1,plain,
( 'less$uor$uequal'(absolute(add(xs(minimum(X0,X1)),negate('a$ureal$unumber'))),X0)
| 'less$uor$uequal'(minimum(X0,X1),n0) ),
inference(resolution,[status(thm)],[c11,c1]) ).
cnf(d2,plain,
( 'less$uor$uequal'(absolute(add(X0,X2)),X1)
| ~ 'less$uor$uequal'(absolute(X2),half(X1))
| ~ 'less$uor$uequal'(absolute(X0),half(X1)) ),
inference(resolution,[status(thm)],[c4,c0]) ).
cnf(d3,plain,
( ~ 'less$uor$uequal'(absolute(add(f(xs(X0)),negate(f('a$ureal$unumber')))),half('epsilon$u0'))
| ~ 'less$uor$uequal'(absolute(add(g(xs(X0)),negate(g('a$ureal$unumber')))),half('epsilon$u0'))
| 'less$uor$uequal'(X0,n0) ),
inference(resolution,[status(thm)],[c12,d2]) ).
cnf(d4,plain,
( ~ 'less$uor$uequal'(absolute(add(xs(X0),negate('a$ureal$unumber'))),'delta$u2'(half('epsilon$u0')))
| 'less$uor$uequal'(half('epsilon$u0'),n0)
| ~ 'less$uor$uequal'(absolute(add(f(xs(X0)),negate(f('a$ureal$unumber')))),half('epsilon$u0'))
| 'less$uor$uequal'(X0,n0) ),
inference(resolution,[status(thm)],[d3,c9]) ).
cnf(d5,plain,
( ~ 'less$uor$uequal'(absolute(add(xs(X0),negate('a$ureal$unumber'))),'delta$u1'(half('epsilon$u0')))
| 'less$uor$uequal'(half('epsilon$u0'),n0)
| 'less$uor$uequal'(half('epsilon$u0'),n0)
| ~ 'less$uor$uequal'(absolute(add(xs(X0),negate('a$ureal$unumber'))),'delta$u2'(half('epsilon$u0')))
| 'less$uor$uequal'(X0,n0) ),
inference(resolution,[status(thm)],[d4,c8]) ).
cnf(d6,plain,
( 'less$uor$uequal'(minimum('delta$u2'(half('epsilon$u0')),X0),n0)
| 'less$uor$uequal'(half('epsilon$u0'),n0)
| ~ 'less$uor$uequal'(absolute(add(xs(minimum('delta$u2'(half('epsilon$u0')),X0)),negate('a$ureal$unumber'))),'delta$u1'(half('epsilon$u0')))
| 'less$uor$uequal'(minimum('delta$u2'(half('epsilon$u0')),X0),n0) ),
inference(resolution,[status(thm)],[d5,d1]) ).
cnf(d7,plain,
( 'less$uor$uequal'(minimum('delta$u2'(half('epsilon$u0')),'delta$u1'(half('epsilon$u0'))),n0)
| 'less$uor$uequal'(half('epsilon$u0'),n0)
| 'less$uor$uequal'(minimum('delta$u2'(half('epsilon$u0')),'delta$u1'(half('epsilon$u0'))),n0) ),
inference(resolution,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
( 'less$uor$uequal'('delta$u2'(half('epsilon$u0')),n0)
| 'less$uor$uequal'('delta$u1'(half('epsilon$u0')),n0)
| 'less$uor$uequal'(half('epsilon$u0'),n0) ),
inference(resolution,[status(thm)],[d7,c3]) ).
cnf(d9,plain,
( 'less$uor$uequal'(half('epsilon$u0'),n0)
| 'less$uor$uequal'('delta$u1'(half('epsilon$u0')),n0)
| 'less$uor$uequal'(half('epsilon$u0'),n0) ),
inference(resolution,[status(thm)],[d8,c7]) ).
cnf(d10,plain,
( 'less$uor$uequal'(half('epsilon$u0'),n0)
| 'less$uor$uequal'(half('epsilon$u0'),n0) ),
inference(resolution,[status(thm)],[d9,c6]) ).
cnf(d11,plain,
'less$uor$uequal'('epsilon$u0',n0),
inference(resolution,[status(thm)],[d10,c5]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[c10,d11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : ANA004-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n006.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Sat Sep 26 22:02:25 UTC 2026
% 0.12/0.35 % CPUTime :
% 0.12/0.35 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.62/1.91 % SZS status Unsatisfiable for theBenchmark.p
% 7.62/1.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------