%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL001-2 : 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 : 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 06:56:37 AM UTC 2026
% Result : Unsatisfiable 24.49s 3.80s
% Output : CNFRefutation 24.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 4
% Syntax : Number of clauses : 12 ( 12 unt; 0 nHn; 4 RR)
% Number of literals : 12 ( 11 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 21 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)) ).
cnf(b_definition,axiom,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)) ).
cnf(i_definition,axiom,
apply(i,X0) = X0 ).
cnf(prove_fixed_point,negated_conjecture,
X0 != apply(combinator,X0) ).
cnf(c0,plain,
apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(clausification,[status(esa)],[s_definition]) ).
cnf(c2,plain,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(clausification,[status(esa)],[b_definition]) ).
cnf(c3,plain,
apply(i,X0) = X0,
inference(clausification,[status(esa)],[i_definition]) ).
cnf(c5,plain,
X0 != apply(combinator,X0),
inference(clausification,[status(esa)],[prove_fixed_point]) ).
cnf(d0,plain,
apply(apply(apply(s,X1),i),X0) = apply(apply(X1,X0),X0),
inference(superposition,[status(thm)],[c3,c0]) ).
cnf(d1,plain,
apply(apply(apply(s,apply(b,X0)),i),X1) = apply(X0,apply(X1,X1)),
inference(superposition,[status(thm)],[d0,c2]) ).
cnf(d2,plain,
apply(X0,X0) != apply(apply(apply(s,apply(b,combinator)),i),X0),
inference(superposition,[status(thm)],[d1,c5]) ).
cnf(d3,plain,
$false,
inference(equality_resolution,[status(thm)],[d2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL001-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n002.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 23:05:20 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 24.49/3.80 % SZS status Unsatisfiable for theBenchmark.p
% 24.49/3.80 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------