%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:08:42 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 16 ( 14 unt; 0 def)
% Number of atoms : 18 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 8 ( 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 : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : apply(k(X),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] : apply(apply(apply(abstraction,X),Y),Z) = apply(apply(X,k(Z)),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( apply(X,n(X,Y)) != apply(Y,n(X,Y))
| X = Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1] : apply(k(X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1] :
( apply(X0,n(X0,X1)) != apply(X1,n(X0,X1))
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
apply(abstraction,apply(abstraction,apply(abstraction,b))) != apply(abstraction,b),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f9,plain,
apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))) != apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),
inference(resolution,[status(thm)],[f8,f7]) ).
fof(f13,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,X0),k(X1)),X2) = apply(apply(X0,k(X2)),X1),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f28,plain,
apply(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))) != apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),
inference(resolution,[status(thm)],[f9,f7]) ).
fof(f31,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(abstraction,X0)),X1),X2) = apply(apply(X0,k(apply(X1,X2))),X2),
inference(paramodulation,[status(thm)],[f6,f13]) ).
fof(f122,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X0))),X1),X2) = apply(apply(X0,k(X2)),apply(X1,X2)),
inference(paramodulation,[status(thm)],[f13,f31]) ).
fof(f169,plain,
apply(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))) != apply(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),n(apply(apply(abstraction,b),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))),apply(apply(abstraction,apply(abstraction,apply(abstraction,b))),n(apply(abstraction,apply(abstraction,apply(abstraction,b))),apply(abstraction,b))))),
inference(backward_demodulation,[status(thm)],[f172,f28]) ).
fof(f172,plain,
! [X0,X1,X2] : apply(apply(apply(abstraction,apply(abstraction,apply(abstraction,X0))),X1),X2) = apply(apply(apply(abstraction,X0),X1),X2),
inference(forward_demodulation,[status(thm)],[f6,f122]) ).
fof(f189,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL079-2 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 14:09:10 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.48 % Refutation found
% 0.12/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.51 % Elapsed time: 0.140151 seconds
% 0.12/0.51 % CPU time: 0.805612 seconds
% 0.12/0.51 % Total memory used: 92.744 MB
% 0.12/0.51 % Net memory used: 92.252 MB
%------------------------------------------------------------------------------