%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL061-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 12:08:37 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.43s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 13 unt; 0 def)
% Number of atoms : 13 ( 12 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 8 ( 8 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 22 ( 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : apply(apply(t,X),Y) = apply(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [X] : apply(apply(apply(X,f(X)),g(X)),h(X)) != apply(f(X),apply(h(X),g(X))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : apply(apply(t,X0),X1) = apply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
! [X0] : apply(apply(apply(X0,f(X0)),g(X0)),h(X0)) != apply(f(X0),apply(h(X0),g(X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f17,plain,
! [X0,X1] : apply(f(apply(apply(b,X0),X1)),apply(h(apply(apply(b,X0),X1)),g(apply(apply(b,X0),X1)))) != apply(apply(apply(X0,apply(X1,f(apply(apply(b,X0),X1)))),g(apply(apply(b,X0),X1))),h(apply(apply(b,X0),X1))),
inference(paramodulation,[status(thm)],[f4,f6]) ).
fof(f26,plain,
! [X0,X1] : apply(f(apply(apply(b,apply(t,X0)),X1)),apply(h(apply(apply(b,apply(t,X0)),X1)),g(apply(apply(b,apply(t,X0)),X1)))) != apply(apply(apply(apply(X1,f(apply(apply(b,apply(t,X0)),X1))),X0),g(apply(apply(b,apply(t,X0)),X1))),h(apply(apply(b,apply(t,X0)),X1))),
inference(paramodulation,[status(thm)],[f5,f17]) ).
fof(f54,plain,
! [X0,X1,X2] : apply(f(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2))),apply(h(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2))),g(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2))))) != apply(apply(apply(apply(X1,apply(X2,f(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2))))),X0),g(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2)))),h(apply(apply(b,apply(t,X0)),apply(apply(b,X1),X2)))),
inference(paramodulation,[status(thm)],[f4,f26]) ).
fof(f204,plain,
! [X0,X1] : apply(f(apply(apply(b,apply(t,X0)),apply(apply(b,b),X1))),apply(h(apply(apply(b,apply(t,X0)),apply(apply(b,b),X1))),g(apply(apply(b,apply(t,X0)),apply(apply(b,b),X1))))) != apply(apply(apply(X1,f(apply(apply(b,apply(t,X0)),apply(apply(b,b),X1)))),apply(X0,g(apply(apply(b,apply(t,X0)),apply(apply(b,b),X1))))),h(apply(apply(b,apply(t,X0)),apply(apply(b,b),X1)))),
inference(paramodulation,[status(thm)],[f4,f54]) ).
fof(f481,plain,
! [X0] : apply(f(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))),apply(apply(X0,g(apply(apply(b,apply(t,X0)),apply(apply(b,b),b)))),h(apply(apply(b,apply(t,X0)),apply(apply(b,b),b))))),
inference(paramodulation,[status(thm)],[f4,f204]) ).
fof(f642,plain,
apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))) != apply(f(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),apply(h(apply(apply(b,apply(t,t)),apply(apply(b,b),b))),g(apply(apply(b,apply(t,t)),apply(apply(b,b),b))))),
inference(paramodulation,[status(thm)],[f5,f481]) ).
fof(f645,plain,
$false,
inference(equality_resolution,[status(thm)],[f642]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL061-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n010.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 14:07:55 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Drodi V4.1.1
% 0.13/0.43 % Refutation found
% 0.13/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.45 % Elapsed time: 0.087089 seconds
% 0.13/0.45 % CPU time: 0.541847 seconds
% 0.13/0.45 % Total memory used: 54.389 MB
% 0.13/0.45 % Net memory used: 54.152 MB
%------------------------------------------------------------------------------