%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL080-2 : 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 12.26s 6.18s
% Output : CNFRefutation 12.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of clauses : 26 ( 21 unt; 0 nHn; 9 RR)
% Number of literals : 31 ( 30 equ; 8 neg)
% Maximal clause size : 2 ( 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; 3 con; 0-2 aty)
% Number of variables : 44 ( 5 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,axiom,
apply(k(X0),X1) = X0 ).
cnf(abstraction,axiom,
apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)) ).
cnf(extensionality2,axiom,
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ) ).
cnf(identity_definition,axiom,
apply(identity,X0) = X0 ).
cnf(prove_TRC2b,negated_conjecture,
k(b) != apply(abstraction,apply(abstraction,k(b))) ).
cnf(c0,plain,
apply(k(X0),X1) = X0,
inference(clausification,[status(esa)],[k_definition]) ).
cnf(c1,plain,
apply(apply(X0,k(X1)),apply(X2,X1)) = apply(apply(apply(abstraction,X0),X2),X1),
inference(clausification,[status(esa)],[abstraction]) ).
cnf(c2,plain,
( apply(X0,n(X1,X0)) != apply(X1,n(X1,X0))
| X0 = X1 ),
inference(clausification,[status(esa)],[extensionality2]) ).
cnf(c3,plain,
apply(identity,X0) = X0,
inference(clausification,[status(esa)],[identity_definition]) ).
cnf(c4,plain,
apply(abstraction,apply(abstraction,k(b))) != k(b),
inference(clausification,[status(esa)],[prove_TRC2b]) ).
cnf(d0,plain,
( k(X0) = X1
| X0 != apply(X1,n(X1,k(X0))) ),
inference(superposition,[status(thm)],[c0,c2]) ).
cnf(d1,plain,
apply(X0,apply(X2,X1)) = apply(apply(apply(abstraction,k(X0)),X2),X1),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d2,plain,
apply(X0,apply(k(X1),apply(X2,X1))) = apply(apply(apply(abstraction,apply(abstraction,k(X0))),X2),X1),
inference(superposition,[status(thm)],[d1,c1]) ).
cnf(d3,plain,
apply(X2,X0) = apply(apply(apply(abstraction,apply(abstraction,k(X2))),X1),X0),
inference(demodulation,[status(thm)],[d2,c0]) ).
cnf(d4,plain,
( X2 = apply(apply(abstraction,apply(abstraction,k(X0))),X1)
| apply(X2,n(apply(apply(abstraction,apply(abstraction,k(X0))),X1),X2)) != apply(X0,n(apply(apply(abstraction,apply(abstraction,k(X0))),X1),X2)) ),
inference(superposition,[status(thm)],[d3,c2]) ).
cnf(d5,plain,
X0 = apply(apply(abstraction,apply(abstraction,k(X0))),X1),
inference(equality_resolution,[status(thm)],[d4]) ).
cnf(d6,plain,
( k(X1) = apply(abstraction,apply(abstraction,k(X0)))
| X1 != X0 ),
inference(superposition,[status(thm)],[d5,d0]) ).
cnf(d7,plain,
k(X0) = apply(abstraction,apply(abstraction,k(X0))),
inference(equality_resolution,[status(thm)],[d6]) ).
cnf(d8,plain,
k(b) != k(b),
inference(demodulation,[status(thm)],[c4,d7]) ).
cnf(d9,plain,
apply(k(X0),apply(X1,X0)) = apply(apply(apply(abstraction,identity),X1),X0),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d10,plain,
X0 = apply(apply(apply(abstraction,identity),X1),X0),
inference(demodulation,[status(thm)],[d9,c0]) ).
cnf(d11,plain,
apply(apply(X1,k(X0)),X0) = apply(apply(apply(abstraction,X1),identity),X0),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d12,plain,
X0 = apply(apply(identity,k(X0)),X0),
inference(superposition,[status(thm)],[d11,d10]) ).
cnf(d13,plain,
X0 = apply(k(X0),X0),
inference(demodulation,[status(thm)],[d12,c3]) ).
cnf(d14,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d13,c0]) ).
cnf(d15,plain,
$false,
inference(resolution,[status(thm)],[d14,d8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL080-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 23:12:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.26/6.18 % SZS status Unsatisfiable for theBenchmark.p
% 12.26/6.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------