%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL066-3 : 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 : n004.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 06:56:51 AM UTC 2026
% Result : Unsatisfiable 36.03s 5.70s
% Output : CNFRefutation 36.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of clauses : 21 ( 21 unt; 0 nHn; 10 RR)
% Number of literals : 21 ( 20 equ; 9 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 27 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(b_definition,axiom,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)) ).
cnf(q_definition,axiom,
apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)) ).
cnf(w_definition,axiom,
apply(apply(w,X0),X1) = apply(apply(X0,X1),X1) ).
cnf(prove_p_combinator,negated_conjecture,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)) ).
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(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)),
inference(clausification,[status(esa)],[q_definition]) ).
cnf(c2,plain,
apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
inference(clausification,[status(esa)],[w_definition]) ).
cnf(c3,plain,
apply(apply(apply(apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x),y),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(clausification,[status(esa)],[prove_p_combinator]) ).
cnf(d0,plain,
apply(apply(w,apply(apply(q,X0),X1)),X2) = apply(apply(X1,apply(X0,X2)),X2),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d1,plain,
apply(apply(w,apply(q,X0)),X1) = apply(X1,apply(X0,X1)),
inference(superposition,[status(thm)],[c1,c2]) ).
cnf(d2,plain,
apply(apply(apply(w,apply(apply(apply(b,apply(w,apply(q,apply(q,q)))),q),x)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[c3,c2]) ).
cnf(d3,plain,
apply(apply(apply(w,apply(apply(w,apply(q,apply(q,q))),apply(q,x))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
apply(apply(apply(w,apply(apply(q,x),apply(apply(q,q),apply(q,x)))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[d3,d1]) ).
cnf(d5,plain,
apply(apply(apply(apply(apply(q,q),apply(q,x)),apply(x,y)),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[d4,d0]) ).
cnf(d6,plain,
apply(apply(apply(apply(q,x),apply(q,apply(x,y))),y),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[d5,c1]) ).
cnf(d7,plain,
apply(apply(apply(q,apply(x,y)),apply(x,y)),z) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[d6,c1]) ).
cnf(d8,plain,
apply(apply(x,y),apply(apply(x,y),z)) != apply(apply(x,y),apply(apply(x,y),z)),
inference(demodulation,[status(thm)],[d7,c1]) ).
cnf(d9,plain,
apply(apply(apply(w,b),X0),X1) = apply(X0,apply(X0,X1)),
inference(superposition,[status(thm)],[c2,c0]) ).
cnf(d10,plain,
apply(apply(apply(b,X0),X0),X1) = apply(X0,apply(X0,X1)),
inference(superposition,[status(thm)],[c2,d9]) ).
cnf(d11,plain,
apply(X0,apply(X0,X1)) = apply(X0,apply(X0,X1)),
inference(demodulation,[status(thm)],[d10,c0]) ).
cnf(d12,plain,
$false,
inference(resolution,[status(thm)],[d11,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL066-3 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.49 % Computer : n004.cluster.edu
% 0.08/0.49 % Model : x86_64 x86_64
% 0.08/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.49 % Memory : 8046.5625MB
% 0.08/0.49 % OS : Linux 6.8.0-71-generic
% 0.08/0.49 % CPULimit : 300
% 0.08/0.49 % WCLimit : 300
% 0.08/0.49 % DateTime : Sat Sep 26 23:11:07 UTC 2026
% 0.08/0.50 % CPUTime :
% 0.08/0.50 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 36.03/5.70 % SZS status Unsatisfiable for theBenchmark.p
% 36.03/5.70 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------