%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL062-1 : 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 : n018.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 06:56:48 AM UTC 2026
% Result : Unsatisfiable 6.94s 5.28s
% Output : CNFRefutation 6.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 11 RR)
% Number of literals : 15 ( 14 equ; 10 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 13 ( 3 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)) ).
cnf(t_definition,axiom,
apply(apply(t,X0),X1) = apply(X1,X0) ).
cnf(prove_c_combinator,negated_conjecture,
apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(apply(f(X0),h(X0)),g(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(t,X0),X1) = apply(X1,X0),
inference(clausification,[status(esa)],[t_definition]) ).
cnf(c2,plain,
apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(apply(f(X0),h(X0)),g(X0)),
inference(clausification,[status(esa)],[prove_c_combinator]) ).
cnf(d0,plain,
apply(apply(apply(X0,apply(X1,f(apply(apply(b,X0),X1)))),g(apply(apply(b,X0),X1))),h(apply(apply(b,X0),X1))) != apply(apply(f(apply(apply(b,X0),X1)),h(apply(apply(b,X0),X1))),g(apply(apply(b,X0),X1))),
inference(superposition,[status(thm)],[c0,c2]) ).
cnf(d1,plain,
apply(apply(apply(X0,apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,X0),X1)),X2))))),g(apply(apply(b,apply(apply(b,X0),X1)),X2))),h(apply(apply(b,apply(apply(b,X0),X1)),X2))) != apply(apply(f(apply(apply(b,apply(apply(b,X0),X1)),X2)),h(apply(apply(b,apply(apply(b,X0),X1)),X2))),g(apply(apply(b,apply(apply(b,X0),X1)),X2))),
inference(superposition,[status(thm)],[c0,d0]) ).
cnf(d2,plain,
apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(apply(b,apply(t,X0)),X1)),X2)))),X0),g(apply(apply(b,apply(apply(b,apply(t,X0)),X1)),X2))),h(apply(apply(b,apply(apply(b,apply(t,X0)),X1)),X2))) != apply(apply(f(apply(apply(b,apply(apply(b,apply(t,X0)),X1)),X2)),h(apply(apply(b,apply(apply(b,apply(t,X0)),X1)),X2))),g(apply(apply(b,apply(apply(b,apply(t,X0)),X1)),X2))),
inference(superposition,[status(thm)],[c1,d1]) ).
cnf(d3,plain,
apply(apply(apply(X0,f(apply(apply(b,apply(apply(b,apply(t,X1)),b)),X0))),apply(X1,g(apply(apply(b,apply(apply(b,apply(t,X1)),b)),X0)))),h(apply(apply(b,apply(apply(b,apply(t,X1)),b)),X0))) != apply(apply(f(apply(apply(b,apply(apply(b,apply(t,X1)),b)),X0)),h(apply(apply(b,apply(apply(b,apply(t,X1)),b)),X0))),g(apply(apply(b,apply(apply(b,apply(t,X1)),b)),X0))),
inference(superposition,[status(thm)],[c0,d2]) ).
cnf(d4,plain,
apply(apply(apply(X0,g(apply(apply(b,apply(apply(b,apply(t,X0)),b)),t))),f(apply(apply(b,apply(apply(b,apply(t,X0)),b)),t))),h(apply(apply(b,apply(apply(b,apply(t,X0)),b)),t))) != apply(apply(f(apply(apply(b,apply(apply(b,apply(t,X0)),b)),t)),h(apply(apply(b,apply(apply(b,apply(t,X0)),b)),t))),g(apply(apply(b,apply(apply(b,apply(t,X0)),b)),t))),
inference(superposition,[status(thm)],[c1,d3]) ).
cnf(d5,plain,
apply(apply(apply(X0,apply(X1,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X0),X1))),b)),t)))),f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X0),X1))),b)),t))),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X0),X1))),b)),t))) != apply(apply(f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X0),X1))),b)),t)),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X0),X1))),b)),t))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,X0),X1))),b)),t))),
inference(superposition,[status(thm)],[c0,d4]) ).
cnf(d6,plain,
apply(apply(X0,g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X0))),b)),t))),apply(f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X0))),b)),t)),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X0))),b)),t)))) != apply(apply(f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X0))),b)),t)),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X0))),b)),t))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),X0))),b)),t))),
inference(superposition,[status(thm)],[c0,d5]) ).
cnf(d7,plain,
apply(apply(f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t))) != apply(apply(f(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t)),h(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t))),g(apply(apply(b,apply(apply(b,apply(t,apply(apply(b,b),t))),b)),t))),
inference(superposition,[status(thm)],[c1,d6]) ).
cnf(d8,plain,
$false,
inference(equality_resolution,[status(thm)],[d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL062-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n018.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 23:12:22 UTC 2026
% 0.16/0.44 % CPUTime :
% 0.16/0.44 Running casc-portfolio.sh -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.94/5.28 % SZS status Unsatisfiable for theBenchmark.p
% 6.94/5.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------