%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 12:08:26 PM UTC 2026
% Result : Unsatisfiable 6.17s 1.34s
% Output : CNFRefutation 6.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 16 ( 16 unt; 0 def)
% Number of atoms : 16 ( 15 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 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 : 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,
! [Z] : apply(apply(Z,f(Z)),g(Z)) != apply(g(Z),apply(apply(f(Z),f(Z)),g(Z))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
! [X0,X1] : apply(apply(k,X0),X1) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f6,plain,
! [X0] : apply(apply(X0,f(X0)),g(X0)) != apply(g(X0),apply(apply(f(X0),f(X0)),g(X0))),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f13,plain,
! [X0,X1,X2] : apply(apply(X0,X1),apply(apply(X2,X0),X1)) = apply(apply(apply(apply(s,s),X2),X0),X1),
inference(paramodulation,[status(thm)],[f4,f4]) ).
fof(f14,plain,
! [X0,X1] : apply(apply(apply(s,k),X0),X1) = X1,
inference(paramodulation,[status(thm)],[f5,f4]) ).
fof(f16,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(k,X0)),X1),X2) = apply(X0,apply(X1,X2)),
inference(paramodulation,[status(thm)],[f5,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)],[f14,f4]) ).
fof(f38,plain,
! [X0,X1] : apply(apply(apply(apply(s,s),apply(s,k)),X0),X1) = apply(apply(X0,X1),X1),
inference(paramodulation,[status(thm)],[f14,f13]) ).
fof(f85,plain,
! [X0,X1,X2,X3] : apply(apply(apply(s,apply(apply(s,apply(k,X0)),X1)),X2),X3) = apply(apply(X0,apply(X1,X3)),apply(X2,X3)),
inference(paramodulation,[status(thm)],[f16,f4]) ).
fof(f469,plain,
! [X0,X1] : apply(apply(X0,f(X0)),g(X0)) != apply(apply(apply(s,apply(apply(s,k),X1)),apply(f(X0),f(X0))),g(X0)),
inference(paramodulation,[status(thm)],[f27,f6]) ).
fof(f13742,plain,
! [X0] : apply(apply(X0,f(X0)),g(X0)) != apply(apply(apply(apply(s,apply(apply(s,apply(k,s)),apply(s,k))),f(X0)),f(X0)),g(X0)),
inference(paramodulation,[status(thm)],[f85,f469]) ).
fof(f14988,plain,
! [X0] : apply(apply(X0,f(X0)),g(X0)) != apply(apply(apply(apply(apply(s,s),apply(s,k)),apply(s,apply(apply(s,apply(k,s)),apply(s,k)))),f(X0)),g(X0)),
inference(paramodulation,[status(thm)],[f38,f13742]) ).
fof(f14990,plain,
$false,
inference(equality_resolution,[status(thm)],[f14988]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : COL004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n004.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Mon Sep 21 14:04:04 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.48 % Drodi V4.1.1
% 6.17/1.34 % Refutation found
% 6.17/1.34 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 6.17/1.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.87/1.38 % Elapsed time: 0.892010 seconds
% 3.87/1.38 % CPU time: 6.696161 seconds
% 3.87/1.38 % Total memory used: 136.385 MB
% 3.87/1.38 % Net memory used: 130.550 MB
%------------------------------------------------------------------------------