%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL062-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 5.87s 11.64s
% Output : CNFRefutation 5.87s
% 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 : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 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(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),x),y),z) != apply(apply(x,z),y) ).
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(apply(apply(b,apply(t,apply(apply(b,b),t))),apply(apply(b,b),t)),x),y),z) != apply(apply(x,z),y),
inference(clausification,[status(esa)],[prove_c_combinator]) ).
cnf(d0,plain,
apply(apply(apply(apply(t,apply(apply(b,b),t)),apply(apply(apply(b,b),t),x)),y),z) != apply(apply(x,z),y),
inference(demodulation,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
apply(apply(apply(apply(apply(apply(b,b),t),x),apply(apply(b,b),t)),y),z) != apply(apply(x,z),y),
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
apply(apply(apply(apply(b,apply(t,x)),apply(apply(b,b),t)),y),z) != apply(apply(x,z),y),
inference(demodulation,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
apply(apply(apply(t,x),apply(apply(apply(b,b),t),y)),z) != apply(apply(x,z),y),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
apply(apply(apply(apply(apply(b,b),t),y),x),z) != apply(apply(x,z),y),
inference(demodulation,[status(thm)],[d3,c1]) ).
cnf(d5,plain,
apply(apply(apply(b,apply(t,y)),x),z) != apply(apply(x,z),y),
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
apply(apply(t,y),apply(x,z)) != apply(apply(x,z),y),
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
apply(apply(x,z),y) != apply(apply(x,z),y),
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
$false,
inference(equality_resolution,[status(thm)],[d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL062-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/10.42 % Computer : n014.cluster.edu
% 0.15/10.42 % Model : x86_64 x86_64
% 0.15/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/10.42 % Memory : 8046.5625MB
% 0.15/10.42 % OS : Linux 6.8.0-71-generic
% 0.15/10.42 % CPULimit : 300
% 0.15/10.42 % WCLimit : 300
% 0.15/10.42 % DateTime : Sat Sep 26 23:10:12 UTC 2026
% 0.15/10.42 % CPUTime :
% 0.15/10.42 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.87/11.64 % SZS status Unsatisfiable for theBenchmark.p
% 5.87/11.64 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------