%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 : Thu Sep 24 12:08:41 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 10 ( 10 unt; 0 def)
% Number of atoms : 10 ( 9 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 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 : 19 ( 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,apply(k,Z)),apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y] : apply(apply(Y,b(Y)),c(Y)) != apply(b(Y),b(Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,apply(k,X2)),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
! [X0] : apply(apply(X0,b(X0)),c(X0)) != apply(b(X0),b(X0)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),apply(k,X1)),X2) = apply(apply(X0,apply(k,X2)),X1),
inference(paramodulation,[status(thm)],[f4,f5]) ).
fof(f54,plain,
! [X0,X1] : apply(apply(apply(k,X0),apply(k,X1)),X0) = apply(apply(apply(apply(abstraction,abstraction),k),X0),X1),
inference(paramodulation,[status(thm)],[f5,f14]) ).
fof(f63,plain,
! [X0,X1] : apply(X0,X0) = apply(apply(apply(apply(abstraction,abstraction),k),X0),X1),
inference(forward_demodulation,[status(thm)],[f4,f54]) ).
fof(f64,plain,
$false,
inference(resolution,[status(thm)],[f63,f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL075-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.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 : Mon Sep 21 14:08:30 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.037984 seconds
% 0.11/0.42 % CPU time: 0.048016 seconds
% 0.11/0.42 % Total memory used: 1.899 MB
% 0.11/0.42 % Net memory used: 1.873 MB
%------------------------------------------------------------------------------