%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL003-16 : TPTP v9.3.1. Released v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:08:25 PM UTC 2026
% Result : Unsatisfiable 279.59s 35.80s
% Output : CNFRefutation 280.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 29 unt; 2 def)
% Number of atoms : 29 ( 28 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 : 8 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 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(w,X),Y) = apply(apply(X,Y),Y),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),w)),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(w,X0),X1) = apply(apply(X0,X1),X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f7,plain,
strong_fixed_point = apply(apply(b,apply(apply(b,apply(apply(b,apply(w,w)),w)),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(f9,definition,
sF0_fnc = apply(strong_fixed_point,fixed_pt),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f10,definition,
sF1_fnc = apply(fixed_pt,sF0_fnc),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f11,plain,
sF0_fnc != sF1_fnc,
inference(definition_folding,[],[f8,f10,f9]) ).
fof(f14,plain,
! [X0] : apply(apply(w,w),X0) = apply(apply(X0,X0),X0),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f17,plain,
! [X0,X1] : apply(apply(w,apply(X0,X1)),X1) = apply(apply(apply(w,X0),X1),X1),
inference(paramodulation,[status(thm)],[f6,f6]) ).
fof(f32,plain,
! [X0,X1] : apply(apply(w,apply(b,X0)),X1) = apply(X0,apply(X1,X1)),
inference(paramodulation,[status(thm)],[f5,f6]) ).
fof(f49,plain,
! [X0,X1,X2] : apply(apply(apply(w,apply(b,apply(b,X0))),X1),X2) = apply(X0,apply(apply(X1,X1),X2)),
inference(paramodulation,[status(thm)],[f32,f5]) ).
fof(f114,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(b,apply(apply(b,apply(w,w)),w)),b),apply(b,X0)),
inference(paramodulation,[status(thm)],[f7,f5]) ).
fof(f117,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(apply(b,apply(w,w)),w),apply(b,apply(b,X0))),
inference(forward_demodulation,[status(thm)],[f5,f114]) ).
fof(f118,plain,
! [X0] : apply(strong_fixed_point,X0) = apply(apply(w,w),apply(w,apply(b,apply(b,X0)))),
inference(forward_demodulation,[status(thm)],[f5,f117]) ).
fof(f137,plain,
! [X0] : apply(apply(w,apply(X0,apply(w,X0))),apply(w,X0)) = apply(apply(w,w),apply(w,X0)),
inference(paramodulation,[status(thm)],[f14,f17]) ).
fof(f3220,plain,
! [X0,X1] : apply(apply(apply(w,apply(b,apply(b,X0))),X1),X1) = apply(X0,apply(apply(w,X1),X1)),
inference(paramodulation,[status(thm)],[f6,f49]) ).
fof(f3401,plain,
! [X0,X1] : apply(apply(w,apply(apply(b,apply(b,X0)),X1)),X1) = apply(X0,apply(apply(w,X1),X1)),
inference(forward_demodulation,[status(thm)],[f17,f3220]) ).
fof(f25266,plain,
! [X0] : apply(X0,apply(apply(w,apply(w,apply(b,apply(b,X0)))),apply(w,apply(b,apply(b,X0))))) = apply(apply(w,w),apply(w,apply(b,apply(b,X0)))),
inference(paramodulation,[status(thm)],[f3401,f137]) ).
fof(f25344,plain,
! [X0] : apply(X0,apply(apply(w,apply(w,apply(b,apply(b,X0)))),apply(w,apply(b,apply(b,X0))))) = apply(strong_fixed_point,X0),
inference(forward_demodulation,[status(thm)],[f118,f25266]) ).
fof(f26946,plain,
! [X0] : apply(X0,apply(apply(w,w),apply(w,apply(b,apply(b,X0))))) = apply(strong_fixed_point,X0),
inference(paramodulation,[status(thm)],[f6,f25344]) ).
fof(f27212,plain,
! [X0] : apply(X0,apply(strong_fixed_point,X0)) = apply(strong_fixed_point,X0),
inference(forward_demodulation,[status(thm)],[f118,f26946]) ).
fof(f27243,plain,
apply(fixed_pt,sF0_fnc) = apply(strong_fixed_point,fixed_pt),
inference(paramodulation,[status(thm)],[f9,f27212]) ).
fof(f27516,plain,
sF1_fnc = apply(strong_fixed_point,fixed_pt),
inference(forward_demodulation,[status(thm)],[f10,f27243]) ).
fof(f27517,plain,
sF1_fnc = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f9,f27516]) ).
fof(f27518,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f27517,f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-16 : 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 : n014.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 14:03:20 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 279.59/35.80 % Refutation found
% 279.59/35.80 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 279.59/35.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 263.98/37.06 % Elapsed time: 36.476988 seconds
% 263.98/37.06 % CPU time: 276.459503 seconds
% 263.98/37.06 % Total memory used: 712.521 MB
% 263.98/37.06 % Net memory used: 643.947 MB
%------------------------------------------------------------------------------