%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL075-2 : TPTP v9.3.1. Released 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 06:56:52 AM UTC 2026
% Result : Unsatisfiable 13.92s 7.05s
% Output : CNFRefutation 13.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of clauses : 14 ( 14 unt; 0 nHn; 4 RR)
% Number of literals : 14 ( 13 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 25 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(apply(k,X0),X1) = X0 ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)) ).
cnf(prove_diagonal_combinator,negated_conjecture,
apply(apply(X0,b(X0)),c(X0)) != apply(b(X0),b(X0)) ).
cnf(c0,plain,
apply(apply(k,X0),X1) = X0,
inference(clausification,[status(esa)],[k_definition]) ).
cnf(c1,plain,
apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
inference(clausification,[status(esa)],[abstraction]) ).
cnf(c2,plain,
apply(apply(X0,b(X0)),c(X0)) != apply(b(X0),b(X0)),
inference(clausification,[status(esa)],[prove_diagonal_combinator]) ).
cnf(d0,plain,
apply(apply(apply(abstraction,apply(k,X0)),X2),X1) = apply(X0,apply(X2,X1)),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d1,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),X0),X2) = apply(X0,apply(apply(X1,X0),X2)),
inference(superposition,[status(thm)],[c1,d0]) ).
cnf(d2,plain,
apply(apply(apply(apply(abstraction,abstraction),k),X0),X1) = apply(X0,X0),
inference(superposition,[status(thm)],[c0,d1]) ).
cnf(d3,plain,
apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))) != apply(b(apply(apply(abstraction,abstraction),k)),b(apply(apply(abstraction,abstraction),k))),
inference(superposition,[status(thm)],[d2,c2]) ).
cnf(d4,plain,
apply(apply(apply(apply(abstraction,abstraction),X1),apply(k,X0)),X2) = X0,
inference(superposition,[status(thm)],[d1,c0]) ).
cnf(d5,plain,
apply(apply(k,X0),apply(k,X0)) = X0,
inference(superposition,[status(thm)],[d2,d4]) ).
cnf(d6,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d5,c0]) ).
cnf(d7,plain,
$false,
inference(resolution,[status(thm)],[d6,d3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n014.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 23:11:32 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.92/7.05 % SZS status Unsatisfiable for theBenchmark.p
% 13.92/7.05 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------