%------------------------------------------------------------------------------
% File : LisaST---0.9
% Problem : COL081-2 : 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 : n009.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 06:56:53 AM UTC 2026
% Result : Unsatisfiable 18.16s 6.17s
% Output : CNFRefutation 18.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of clauses : 28 ( 22 unt; 0 nHn; 9 RR)
% Number of literals : 34 ( 33 equ; 9 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 : 48 ( 7 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_TRC2c,negated_conjecture,
k(k(b)) != apply(abstraction,k(k(b))) ).
cnf(c0,plain,
apply(k(X0),X1) = X0,
inference(clausification,[status(esa)],[k_definition]) ).
cnf(c1,plain,
apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(clausification,[status(esa)],[abstraction]) ).
cnf(c2,plain,
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(clausification,[status(esa)],[extensionality2]) ).
cnf(c3,plain,
apply(identity,X0) = X0,
inference(clausification,[status(esa)],[identity_definition]) ).
cnf(c4,plain,
k(k(b)) != apply(abstraction,k(k(b))),
inference(clausification,[status(esa)],[prove_TRC2c]) ).
cnf(d0,plain,
( X1 = k(X0)
| apply(X1,n(X1,k(X0))) != X0 ),
inference(superposition,[status(thm)],[c0,c2]) ).
cnf(d1,plain,
apply(apply(apply(abstraction,k(X0)),X2),X1) = apply(X0,apply(X2,X1)),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d2,plain,
( apply(apply(abstraction,k(X0)),X1) = k(X2)
| apply(X0,apply(X1,n(apply(apply(abstraction,k(X0)),X1),k(X2)))) != X2 ),
inference(superposition,[status(thm)],[d1,d0]) ).
cnf(d3,plain,
apply(apply(apply(abstraction,X2),k(X0)),X1) = apply(apply(X2,k(X1)),X0),
inference(superposition,[status(thm)],[c0,c1]) ).
cnf(d4,plain,
apply(apply(apply(abstraction,identity),X1),X0) = apply(k(X0),apply(X1,X0)),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d5,plain,
apply(apply(apply(abstraction,identity),X1),X0) = X0,
inference(demodulation,[status(thm)],[d4,c0]) ).
cnf(d6,plain,
X1 = apply(apply(identity,k(X1)),X0),
inference(superposition,[status(thm)],[d5,d3]) ).
cnf(d7,plain,
X0 = apply(k(X0),X1),
inference(demodulation,[status(thm)],[d6,c3]) ).
cnf(d8,plain,
( apply(apply(abstraction,k(k(X0))),X1) = k(X2)
| X0 != X2 ),
inference(superposition,[status(thm)],[d7,d2]) ).
cnf(d9,plain,
apply(apply(abstraction,k(k(X0))),X1) = k(X0),
inference(equality_resolution,[status(thm)],[d8]) ).
cnf(d10,plain,
( apply(abstraction,k(k(X0))) = k(X1)
| k(X0) != X1 ),
inference(superposition,[status(thm)],[d9,d0]) ).
cnf(d11,plain,
apply(abstraction,k(k(X0))) = k(k(X0)),
inference(equality_resolution,[status(thm)],[d10]) ).
cnf(d12,plain,
k(k(b)) != k(k(b)),
inference(demodulation,[status(thm)],[c4,d11]) ).
cnf(d13,plain,
apply(apply(apply(abstraction,X1),identity),X0) = apply(apply(X1,k(X0)),X0),
inference(superposition,[status(thm)],[c3,c1]) ).
cnf(d14,plain,
apply(apply(identity,k(X0)),X0) = X0,
inference(superposition,[status(thm)],[d13,d5]) ).
cnf(d15,plain,
apply(k(X0),X0) = X0,
inference(demodulation,[status(thm)],[d14,c3]) ).
cnf(d16,plain,
X0 = X0,
inference(demodulation,[status(thm)],[d15,c0]) ).
cnf(d17,plain,
$false,
inference(resolution,[status(thm)],[d16,d12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL081-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.06 % Command : casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.43 % Computer : n009.cluster.edu
% 0.09/0.43 % Model : x86_64 x86_64
% 0.09/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.43 % Memory : 8046.5625MB
% 0.09/0.43 % OS : Linux 6.8.0-71-generic
% 0.09/0.43 % CPULimit : 300
% 0.09/0.43 % WCLimit : 300
% 0.09/0.43 % DateTime : Sat Sep 26 23:13:14 UTC 2026
% 0.09/0.43 % CPUTime :
% 0.09/0.43 Running casc-portfolio.sh -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.16/6.17 % SZS status Unsatisfiable for theBenchmark.p
% 18.16/6.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
%------------------------------------------------------------------------------