%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL035-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:08:31 PM UTC 2026
% Result : Unsatisfiable 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : apply(apply(l,X),Y) = apply(X,apply(Y,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : apply(apply(apply(q,X),Y),Z) = apply(Y,apply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
! [Y] : apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1] : apply(apply(l,X0),X1) = apply(X0,apply(X1,X1)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1] : apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0,X1,X2] : apply(apply(apply(q,X0),X1),X2) = apply(X1,apply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f49,plain,
! [X0,X1] : apply(apply(w,apply(q,X0)),X1) = apply(X1,apply(X0,X1)),
inference(paramodulation,[status(thm)],[f6,f7]) ).
fof(f113,plain,
! [X0] : apply(X0,f(X0)) != apply(apply(w,apply(q,X0)),f(X0)),
inference(paramodulation,[status(thm)],[f49,f8]) ).
fof(f183,plain,
! [X0] : apply(apply(X0,X0),f(apply(X0,X0))) != apply(apply(w,apply(apply(l,q),X0)),f(apply(X0,X0))),
inference(paramodulation,[status(thm)],[f5,f113]) ).
fof(f371,plain,
! [X0,X1] : apply(apply(X0,apply(X1,apply(apply(q,X1),X0))),f(apply(apply(apply(q,X1),X0),apply(apply(q,X1),X0)))) != apply(apply(w,apply(apply(l,q),apply(apply(q,X1),X0))),f(apply(apply(apply(q,X1),X0),apply(apply(q,X1),X0)))),
inference(paramodulation,[status(thm)],[f7,f183]) ).
fof(f385,plain,
! [X0,X1] : apply(apply(X0,apply(X1,apply(apply(q,X1),X0))),f(apply(X0,apply(X1,apply(apply(q,X1),X0))))) != apply(apply(w,apply(apply(l,q),apply(apply(q,X1),X0))),f(apply(apply(apply(q,X1),X0),apply(apply(q,X1),X0)))),
inference(forward_demodulation,[status(thm)],[f7,f371]) ).
fof(f386,plain,
! [X0,X1] : apply(apply(X0,apply(X1,apply(apply(q,X1),X0))),f(apply(X0,apply(X1,apply(apply(q,X1),X0))))) != apply(apply(w,apply(apply(l,q),apply(apply(q,X1),X0))),f(apply(X0,apply(X1,apply(apply(q,X1),X0))))),
inference(forward_demodulation,[status(thm)],[f7,f385]) ).
fof(f387,plain,
$false,
inference(destructive_equality_resolution,[status(thm)],[f386]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL035-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:07:17 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.45 % Elapsed time: 0.069702 seconds
% 0.14/0.45 % CPU time: 0.132536 seconds
% 0.14/0.45 % Total memory used: 4.382 MB
% 0.14/0.45 % Net memory used: 4.301 MB
%------------------------------------------------------------------------------