%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 17 unt; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 12 ( 12 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 10 ( 10 !; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : apply(apply(k,X),Y) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
file('/export/starexec/sandbox2/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,
apply(apply(apply(apply(s,apply(k,apply(s,apply(apply(s,k),k)))),apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k))),x),y) != apply(y,apply(apply(x,x),y)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
apply(apply(apply(apply(k,apply(s,apply(apply(s,k),k))),x),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f4,f6]) ).
fof(f24,plain,
apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x)),y) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f5,f23]) ).
fof(f25,plain,
apply(apply(apply(apply(s,k),k),y),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f4,f24]) ).
fof(f26,plain,
apply(apply(apply(k,y),apply(k,y)),apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f4,f25]) ).
fof(f27,plain,
apply(y,apply(apply(apply(apply(s,apply(apply(s,k),k)),apply(apply(s,k),k)),x),y)) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f5,f26]) ).
fof(f28,plain,
apply(y,apply(apply(apply(apply(apply(s,k),k),x),apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f4,f27]) ).
fof(f29,plain,
apply(y,apply(apply(apply(apply(k,x),apply(k,x)),apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f4,f28]) ).
fof(f30,plain,
apply(y,apply(apply(x,apply(apply(apply(s,k),k),x)),y)) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f5,f29]) ).
fof(f31,plain,
apply(y,apply(apply(x,apply(apply(k,x),apply(k,x))),y)) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f4,f30]) ).
fof(f32,plain,
apply(y,apply(apply(x,x),y)) != apply(y,apply(apply(x,x),y)),
inference(forward_demodulation,[status(thm)],[f5,f31]) ).
fof(f33,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL004-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.38 % Computer : n018.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 14:06:14 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 % Drodi V4.1.1
% 0.12/0.40 % Refutation found
% 0.12/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.44 % Elapsed time: 0.043451 seconds
% 0.12/0.44 % CPU time: 0.033002 seconds
% 0.12/0.44 % Total memory used: 968.624 KB
% 0.12/0.44 % Net memory used: 907.808 KB
%------------------------------------------------------------------------------