%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL061-2 : 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 : n005.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 10.57s 3.04s
% Output : CNFRefutation 10.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of clauses : 13 ( 13 unt; 0 nHn; 9 RR)
% Number of literals : 13 ( 12 equ; 8 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 : 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_q1_combinator,negated_conjecture,
apply(apply(apply(apply(apply(b,apply(t,t)),apply(apply(b,b),b)),x),y),z) != apply(x,apply(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,t)),apply(apply(b,b),b)),x),y),z) != apply(x,apply(z,y)),
inference(clausification,[status(esa)],[prove_q1_combinator]) ).
cnf(d0,plain,
apply(apply(apply(apply(t,t),apply(apply(apply(b,b),b),x)),y),z) != apply(x,apply(z,y)),
inference(demodulation,[status(thm)],[c2,c0]) ).
cnf(d1,plain,
apply(apply(apply(apply(apply(apply(b,b),b),x),t),y),z) != apply(x,apply(z,y)),
inference(demodulation,[status(thm)],[d0,c1]) ).
cnf(d2,plain,
apply(apply(apply(apply(b,apply(b,x)),t),y),z) != apply(x,apply(z,y)),
inference(demodulation,[status(thm)],[d1,c0]) ).
cnf(d3,plain,
apply(apply(apply(b,x),apply(t,y)),z) != apply(x,apply(z,y)),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
apply(x,apply(apply(t,y),z)) != apply(x,apply(z,y)),
inference(demodulation,[status(thm)],[d3,c0]) ).
cnf(d5,plain,
apply(x,apply(z,y)) != apply(x,apply(z,y)),
inference(demodulation,[status(thm)],[d4,c1]) ).
cnf(d6,plain,
$false,
inference(equality_resolution,[status(thm)],[d5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL061-2 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.07 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.45 % Computer : n005.cluster.edu
% 0.11/0.45 % Model : x86_64 x86_64
% 0.11/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.45 % Memory : 8046.5625MB
% 0.11/0.45 % OS : Linux 6.8.0-71-generic
% 0.11/0.45 % CPULimit : 300
% 0.11/0.45 % WCLimit : 300
% 0.11/0.45 % DateTime : Sat Sep 26 23:10:02 UTC 2026
% 0.11/0.45 % CPUTime :
% 0.11/0.45 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.57/3.04 % SZS status Unsatisfiable for theBenchmark.p
% 10.57/3.04 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------