%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL033-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 06:56:43 AM UTC 2026
% Result : Unsatisfiable 44.20s 6.63s
% Output : CNFRefutation 44.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 6 RR)
% Number of literals : 14 ( 13 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)) ).
cnf(l_definition,axiom,
apply(apply(l,X0),X1) = apply(X0,apply(X1,X1)) ).
cnf(m_definition,axiom,
apply(m,X0) = apply(X0,X0) ).
cnf(prove_fixed_point,negated_conjecture,
apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))) ).
cnf(c0,plain,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(clausification,[status(esa)],[b_definition]) ).
cnf(c1,plain,
apply(apply(l,X0),X1) = apply(X0,apply(X1,X1)),
inference(clausification,[status(esa)],[l_definition]) ).
cnf(c2,plain,
apply(m,X0) = apply(X0,X0),
inference(clausification,[status(esa)],[m_definition]) ).
cnf(c3,plain,
apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
inference(clausification,[status(esa)],[prove_fixed_point]) ).
cnf(d0,plain,
apply(apply(apply(b,X0),X1),f(apply(apply(b,X0),X1))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))),
inference(superposition,[status(thm)],[c0,c3]) ).
cnf(d1,plain,
apply(X0,apply(X1,f(apply(apply(b,X0),X1)))) != apply(f(apply(apply(b,X0),X1)),apply(X0,apply(X1,f(apply(apply(b,X0),X1))))),
inference(demodulation,[status(thm)],[d0,c0]) ).
cnf(d2,plain,
apply(apply(l,X1),X0) = apply(X1,apply(m,X0)),
inference(superposition,[status(thm)],[c2,c1]) ).
cnf(d3,plain,
apply(m,apply(l,X0)) = apply(X0,apply(m,apply(l,X0))),
inference(superposition,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
apply(m,apply(l,f(apply(apply(b,m),l)))) != apply(m,apply(l,f(apply(apply(b,m),l)))),
inference(superposition,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
$false,
inference(equality_resolution,[status(thm)],[d4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL033-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 23:11:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 44.20/6.63 % SZS status Unsatisfiable for theBenchmark.p
% 44.20/6.63 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------