%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL042-3 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 12:08:32 PM UTC 2026
% Result : Unsatisfiable 275.94s 35.22s
% Output : CNFRefutation 211.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 21 unt; 0 def)
% Number of atoms : 25 ( 20 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 14 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 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(w1,X),Y) = apply(apply(Y,X),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Strong_fixed_point] :
( fixed_point(Strong_fixed_point)
| apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f6,plain,
! [X0,X1] : apply(apply(w1,X0),X1) = apply(apply(X1,X0),X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
! [X0] :
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b))),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f24,plain,
apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt)),
inference(resolution,[status(thm)],[f7,f8]) ).
fof(f25,plain,
apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(apply(apply(b,b),b),fixed_pt)) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt)),
inference(forward_demodulation,[status(thm)],[f5,f24]) ).
fof(f26,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt))) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt)),
inference(forward_demodulation,[status(thm)],[f5,f25]) ).
fof(f27,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(apply(b,apply(w1,w1)),apply(b,w1))),apply(apply(b,b),b)),fixed_pt)),
inference(forward_demodulation,[status(thm)],[f5,f26]) ).
fof(f28,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(apply(b,apply(w1,w1)),apply(b,w1)),apply(apply(apply(b,b),b),fixed_pt))),
inference(forward_demodulation,[status(thm)],[f5,f27]) ).
fof(f29,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(apply(apply(b,b),b),fixed_pt)))),
inference(forward_demodulation,[status(thm)],[f5,f28]) ).
fof(f30,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt))))),
inference(forward_demodulation,[status(thm)],[f5,f29]) ).
fof(f37,plain,
! [X0,X1,X2] : apply(apply(w1,X0),apply(apply(b,X1),X2)) = apply(apply(X1,apply(X2,X0)),X0),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f265,plain,
! [X0,X1,X2] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),X2)) = apply(X1,apply(apply(X2,X0),X0)),
inference(paramodulation,[status(thm)],[f5,f37]) ).
fof(f300,plain,
apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,fixed_pt)))) != apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)),
inference(paramodulation,[status(thm)],[f37,f30]) ).
fof(f8419,plain,
apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1) != apply(fixed_pt,apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1)),
inference(paramodulation,[status(thm)],[f37,f300]) ).
fof(f12908,plain,
! [X0,X1,X2] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),X2)) = apply(X1,apply(apply(w1,X0),X2)),
inference(paramodulation,[status(thm)],[f6,f265]) ).
fof(f29045,plain,
! [X0,X1] : apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),w1) = apply(X0,apply(apply(w1,apply(apply(b,apply(b,X0)),X1)),X1)),
inference(paramodulation,[status(thm)],[f6,f12908]) ).
fof(f29232,plain,
apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1) != apply(apply(w1,apply(apply(b,apply(b,fixed_pt)),w1)),w1),
inference(backward_demodulation,[status(thm)],[f29045,f8419]) ).
fof(f29363,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f29232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL042-3 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n008.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 14:06:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 275.94/35.22 % Refutation found
% 275.94/35.22 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 275.94/35.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 211.34/36.60 % Elapsed time: 36.015108 seconds
% 211.34/36.60 % CPU time: 260.567019 seconds
% 211.34/36.60 % Total memory used: 817.654 MB
% 211.34/36.60 % Net memory used: 786.848 MB
%------------------------------------------------------------------------------