%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL042-8 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 110.12s 14.81s
% Output : CNFRefutation 110.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 22 unt; 0 def)
% Number of atoms : 22 ( 21 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 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 : 28 ( 28 !; 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 = apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,negated_conjecture,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
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,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b))),b),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f8,plain,
apply(strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(strong_fixed_point,fixed_pt)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
! [X0] : apply(apply(w1,X0),w1) = apply(apply(X0,X0),X0),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f21,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(f22,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(b,apply(w1,w1)),apply(apply(b,apply(b,w1)),b)),apply(b,X0)),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f24,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(apply(b,apply(b,w1)),b),apply(b,X0))),
inference(forward_demodulation,[status(thm)],[f5,f22]) ).
fof(f25,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,w1),apply(apply(b,w1),apply(b,apply(b,X0)))),
inference(forward_demodulation,[status(thm)],[f5,f24]) ).
fof(f176,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,f21]) ).
fof(f231,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1),
inference(paramodulation,[status(thm)],[f21,f25]) ).
fof(f15469,plain,
! [X0,X1] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),w1)) = apply(X1,apply(apply(X0,X0),X0)),
inference(paramodulation,[status(thm)],[f6,f176]) ).
fof(f16208,plain,
! [X0,X1] : apply(apply(w1,X0),apply(apply(b,apply(b,X1)),w1)) = apply(X1,apply(apply(w1,X0),w1)),
inference(paramodulation,[status(thm)],[f13,f15469]) ).
fof(f18842,plain,
! [X0] : apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1) = apply(X0,apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1)),
inference(paramodulation,[status(thm)],[f6,f16208]) ).
fof(f18942,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(apply(w1,apply(apply(b,apply(b,X0)),w1)),w1)),
inference(forward_demodulation,[status(thm)],[f231,f18842]) ).
fof(f18943,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(forward_demodulation,[status(thm)],[f231,f18942]) ).
fof(f20371,plain,
apply(strong_fixed_point,fixed_pt) != apply(strong_fixed_point,fixed_pt),
inference(backward_demodulation,[status(thm)],[f18943,f8]) ).
fof(f20615,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f20371]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL042-8 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n005.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 14:05:48 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 110.12/14.81 % Refutation found
% 110.12/14.81 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 110.12/14.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 55.84/16.08 % Elapsed time: 15.394338 seconds
% 55.84/16.08 % CPU time: 108.734399 seconds
% 55.84/16.08 % Total memory used: 442.381 MB
% 55.84/16.08 % Net memory used: 433.613 MB
%------------------------------------------------------------------------------