%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% 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 12:08:34 PM UTC 2026
% Result : Unsatisfiable 5.60s 1.29s
% Output : CNFRefutation 5.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 24 unt; 0 def)
% Number of atoms : 24 ( 23 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 12 ( 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 : 44 ( 44 !; 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,Z] : apply(apply(apply(n,X),Y),Z) = apply(apply(apply(X,Z),Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),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,X2] : apply(apply(apply(n,X0),X1),X2) = apply(apply(apply(X0,X2),X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),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(f12,plain,
! [X0] : apply(apply(apply(b,apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n)),b),apply(b,X0)) = apply(strong_fixed_point,X0),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f13,plain,
! [X0] : apply(apply(apply(n,apply(apply(b,b),apply(apply(n,apply(apply(b,b),n)),n))),n),apply(b,apply(b,X0))) = apply(strong_fixed_point,X0),
inference(forward_demodulation,[status(thm)],[f5,f12]) ).
fof(f16,plain,
! [X0,X1,X2] : apply(apply(apply(n,apply(n,X0)),X1),X2) = apply(apply(apply(apply(X0,X1),X2),X1),X2),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f17,plain,
! [X0,X1,X2] : apply(apply(apply(n,apply(b,X0)),X1),X2) = apply(apply(X0,apply(X2,X1)),X2),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f22,plain,
! [X0,X1,X2,X3] : apply(apply(apply(n,apply(apply(b,X0),X1)),X2),X3) = apply(apply(apply(X0,apply(X1,X3)),X2),X3),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f165,plain,
! [X0,X1,X2] : apply(apply(apply(n,apply(n,X0)),X1),X2) = apply(apply(apply(n,apply(X0,X1)),X1),X2),
inference(forward_demodulation,[status(thm)],[f6,f16]) ).
fof(f229,plain,
! [X0,X1,X2] : apply(apply(apply(n,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X2,X1),X2)),
inference(paramodulation,[status(thm)],[f5,f17]) ).
fof(f295,plain,
! [X0,X1,X2] : apply(apply(X0,X1),apply(X0,X2)) = apply(apply(apply(apply(n,apply(b,b)),X1),X0),X2),
inference(paramodulation,[status(thm)],[f17,f5]) ).
fof(f575,plain,
! [X0,X1] : apply(apply(X0,X1),apply(X0,X1)) = apply(apply(apply(n,apply(n,apply(b,b))),X0),X1),
inference(paramodulation,[status(thm)],[f6,f295]) ).
fof(f881,plain,
! [X0,X1,X2] : apply(apply(apply(n,apply(apply(b,b),X0)),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(paramodulation,[status(thm)],[f5,f22]) ).
fof(f1386,plain,
! [X0] : apply(apply(apply(apply(n,apply(apply(b,b),n)),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
inference(paramodulation,[status(thm)],[f13,f881]) ).
fof(f2695,plain,
! [X0] : apply(apply(apply(apply(n,apply(n,apply(b,b))),n),apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))) = apply(strong_fixed_point,X0),
inference(forward_demodulation,[status(thm)],[f165,f1386]) ).
fof(f2697,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X0)))),apply(n,apply(b,apply(b,X0)))),
inference(paramodulation,[status(thm)],[f575,f2695]) ).
fof(f3273,plain,
! [X0,X1] : apply(apply(apply(n,apply(b,apply(b,X0))),apply(n,apply(b,apply(b,X1)))),apply(n,apply(b,apply(b,X1)))) = apply(X0,apply(strong_fixed_point,X1)),
inference(paramodulation,[status(thm)],[f2697,f229]) ).
fof(f4006,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(X0,apply(strong_fixed_point,X0)),
inference(backward_demodulation,[status(thm)],[f3273,f2697]) ).
fof(f4050,plain,
$false,
inference(resolution,[status(thm)],[f4006,f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL044-6 : TPTP v9.3.1. Released v2.1.0.
% 0.00/0.04 % 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 14:07:24 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 5.60/1.29 % Refutation found
% 5.60/1.29 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 5.60/1.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.95/2.51 % Elapsed time: 1.932021 seconds
% 9.95/2.51 % CPU time: 6.145390 seconds
% 9.95/2.51 % Total memory used: 137.941 MB
% 9.95/2.51 % Net memory used: 136.305 MB
%------------------------------------------------------------------------------