%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 06:56:39 AM UTC 2026
% Result : Unsatisfiable 8.97s 2.91s
% Output : CNFRefutation 8.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of clauses : 15 ( 15 unt; 0 nHn; 10 RR)
% Number of literals : 15 ( 14 equ; 9 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 12 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(s_definition,axiom,
apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)) ).
cnf(k_definition,axiom,
apply(apply(k,X0),X1) = X0 ).
cnf(prove_u_combinator,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)) ).
cnf(c0,plain,
apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(clausification,[status(esa)],[s_definition]) ).
cnf(c1,plain,
apply(apply(k,X0),X1) = X0,
inference(clausification,[status(esa)],[k_definition]) ).
cnf(c2,plain,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
inference(clausification,[status(esa)],[prove_u_combinator]) ).
cnf(d0,plain,
apply(apply(apply(s,k),X1),X0) = X0,
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm)],[c2,c0]) ).
cnf(d2,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
apply(y,apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm)],[d3,d0]) ).
cnf(d5,plain,
apply(y,apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
apply(y,apply(apply(x,apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
apply(y,apply(apply(x,x),y)) != apply(y,apply(apply(x,x),y)),
inference(demodulation,[status(thm)],[d6,d0]) ).
cnf(d8,plain,
$false,
inference(equality_resolution,[status(thm)],[d7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.42 % Computer : n001.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8046.5625MB
% 0.11/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Sat Sep 26 23:10:29 UTC 2026
% 0.11/0.43 % CPUTime :
% 0.11/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.97/2.91 % SZS status Unsatisfiable for theBenchmark.p
% 8.97/2.91 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------