%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/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 12:08:24 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.54s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 12 unt; 0 def)
% Number of atoms : 16 ( 10 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 4 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 28 !; 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,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : apply(apply(apply(c,X),Y),Z) = apply(apply(X,Z),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Weak_sage] :
( fixed_point(Weak_sage)
| Weak_sage != apply(fixed_pt,Weak_sage) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
! [X] : ~ fixed_point(apply(apply(apply(s,apply(c,apply(b,X))),apply(s,apply(c,apply(b,X)))),apply(s,apply(c,apply(b,X))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,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(f8,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f9,plain,
! [X0,X1,X2] : apply(apply(apply(c,X0),X1),X2) = apply(apply(X0,X2),X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f11,plain,
! [X0] :
( fixed_point(X0)
| X0 != apply(fixed_pt,X0) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f12,plain,
! [X0] : ~ fixed_point(apply(apply(apply(s,apply(c,apply(b,X0))),apply(s,apply(c,apply(b,X0)))),apply(s,apply(c,apply(b,X0))))),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(c,X0)),X1),X2) = apply(apply(X0,apply(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f9,f7]) ).
fof(f76,plain,
! [X0,X1,X2] : apply(apply(apply(s,apply(c,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f8,f15]) ).
fof(f1086,plain,
fixed_point(apply(apply(apply(s,apply(c,apply(b,fixed_pt))),apply(s,apply(c,apply(b,fixed_pt)))),apply(s,apply(c,apply(b,fixed_pt))))),
inference(resolution,[status(thm)],[f11,f76]) ).
fof(f1089,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1086,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n018.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 14:05:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.54 % Refutation found
% 0.12/0.54 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.63/0.57 % Elapsed time: 0.200059 seconds
% 0.63/0.57 % CPU time: 1.314633 seconds
% 0.63/0.57 % Total memory used: 96.734 MB
% 0.63/0.57 % Net memory used: 96.364 MB
%------------------------------------------------------------------------------