%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL006-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n002.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 12:08:27 PM UTC 2026
% Result : Unsatisfiable 35.08s 4.94s
% Output : CNFRefutation 35.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 15 unt; 0 def)
% Number of atoms : 15 ( 14 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 33 ( 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] : apply(apply(apply(s,X),Y),Z) = apply(apply(X,Z),apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
! [Y] : apply(Y,f(Y)) != apply(f(Y),apply(Y,f(Y))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : apply(apply(X0,X1),apply(X2,X1)) = apply(apply(apply(s,X0),X2),X1),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : X0 = apply(apply(k,X0),X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
! [X0] : apply(X0,f(X0)) != apply(f(X0),apply(X0,f(X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f14,plain,
! [X0,X1,X2] : apply(X0,apply(X1,X2)) = apply(apply(apply(s,apply(k,X0)),X1),X2),
inference(paramodulation,[status(thm)],[f5,f4]) ).
fof(f20,plain,
! [X0,X1] : X0 = apply(apply(apply(s,k),X1),X0),
inference(paramodulation,[status(thm)],[f4,f5]) ).
fof(f26,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),apply(apply(s,k),X1)),X2) = apply(apply(X0,X2),X2),
inference(paramodulation,[status(thm)],[f20,f4]) ).
fof(f27,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(apply(s,k),X0)),X1),X2) = apply(X2,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f20,f4]) ).
fof(f36,plain,
! [X0,X1,X2,X3] : apply(apply(X0,apply(X1,X2)),apply(X3,X2)) = apply(apply(apply(s,apply(apply(s,apply(k,X0)),X1)),X3),X2),
inference(paramodulation,[status(thm)],[f14,f4]) ).
fof(f913,plain,
! [X0,X1] : apply(X0,f(X0)) != apply(apply(apply(s,apply(apply(s,k),X1)),X0),f(X0)),
inference(paramodulation,[status(thm)],[f27,f6]) ).
fof(f1123,plain,
! [X0,X1] : apply(apply(X0,X1),f(apply(X0,X1))) != apply(apply(apply(apply(s,apply(apply(s,apply(k,s)),apply(s,k))),X0),X1),f(apply(X0,X1))),
inference(paramodulation,[status(thm)],[f36,f913]) ).
fof(f9107,plain,
! [X0,X1] : apply(apply(X0,X0),f(apply(X0,X0))) != apply(apply(apply(apply(s,apply(s,apply(apply(s,apply(k,s)),apply(s,k)))),apply(apply(s,k),X1)),X0),f(apply(X0,X0))),
inference(paramodulation,[status(thm)],[f26,f1123]) ).
fof(f9229,plain,
$false,
inference(equality_resolution,[status(thm)],[f9107]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL006-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n002.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 14:07:01 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 35.08/4.94 % Refutation found
% 35.08/4.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 35.08/4.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.80/5.02 % Elapsed time: 4.628967 seconds
% 7.80/5.02 % CPU time: 36.393550 seconds
% 7.80/5.02 % Total memory used: 526.413 MB
% 7.80/5.02 % Net memory used: 509.687 MB
%------------------------------------------------------------------------------