%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 0.20s 0.66s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 13
% Syntax : Number of formulae : 35 ( 35 unt; 7 def)
% Number of atoms : 35 ( 34 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 5 con; 0-4 aty)
% Number of variables : 52 ( 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B,C] : ifeq(A,A,B,C) = B,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,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(f3,axiom,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : apply(i,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Weak_sage] : ifeq(Weak_sage,apply(fixed_pt,Weak_sage),fixed_point(Weak_sage),true) = true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
! [X] : fixed_point(apply(apply(apply(s,apply(b,X)),i),apply(apply(s,apply(b,X)),i))) != true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,plain,
! [X0,X1,X2] : ifeq(X0,X0,X1,X2) = X1,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
! [X0,X1,X2] : apply(apply(apply(s,X0),X1),X2) = apply(apply(X0,X2),apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] : apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0] : apply(i,X0) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f13,plain,
! [X0] : ifeq(X0,apply(fixed_pt,X0),fixed_point(X0),true) = true,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f14,plain,
! [X0] : fixed_point(apply(apply(apply(s,apply(b,X0)),i),apply(apply(s,apply(b,X0)),i))) != true,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f15,definition,
! [X0] : sF4_fnc(X0) = apply(b,X0),
introduced(definition,[new_symbols(definition,[sF4_fnc(X0)])],[function_definition]) ).
fof(f16,definition,
! [X0] : sF3_fnc(X0) = apply(s,sF4_fnc(X0)),
introduced(definition,[new_symbols(definition,[sF3_fnc(X0)])],[function_definition]) ).
fof(f17,definition,
! [X0] : sF2_fnc(X0) = apply(sF3_fnc(X0),i),
introduced(definition,[new_symbols(definition,[sF2_fnc(X0)])],[function_definition]) ).
fof(f18,definition,
! [X0] : sF6_fnc(X0) = apply(s,sF4_fnc(X0)),
introduced(definition,[new_symbols(definition,[sF6_fnc(X0)])],[function_definition]) ).
fof(f19,definition,
! [X0] : sF5_fnc(X0) = apply(sF6_fnc(X0),i),
introduced(definition,[new_symbols(definition,[sF5_fnc(X0)])],[function_definition]) ).
fof(f20,definition,
! [X0] : sF1_fnc(X0) = apply(sF2_fnc(X0),sF5_fnc(X0)),
introduced(definition,[new_symbols(definition,[sF1_fnc(X0)])],[function_definition]) ).
fof(f21,definition,
! [X0] : sF0_fnc(X0) = fixed_point(sF1_fnc(X0)),
introduced(definition,[new_symbols(definition,[sF0_fnc(X0)])],[function_definition]) ).
fof(f22,plain,
! [X0] : sF0_fnc(X0) != true,
inference(definition_folding,[],[f14,f21,f20,f19,f18,f17,f16,f15]) ).
fof(f23,plain,
! [X0] : sF6_fnc(X0) = sF3_fnc(X0),
inference(forward_demodulation,[status(thm)],[f16,f18]) ).
fof(f24,plain,
! [X0] : sF5_fnc(X0) = apply(sF3_fnc(X0),i),
inference(forward_demodulation,[status(thm)],[f23,f19]) ).
fof(f25,plain,
! [X0] : sF5_fnc(X0) = sF2_fnc(X0),
inference(forward_demodulation,[status(thm)],[f17,f24]) ).
fof(f26,plain,
! [X0] : sF1_fnc(X0) = apply(sF2_fnc(X0),sF2_fnc(X0)),
inference(forward_demodulation,[status(thm)],[f25,f20]) ).
fof(f27,plain,
! [X0,X1,X2] : apply(apply(sF4_fnc(X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(forward_demodulation,[status(thm)],[f15,f10]) ).
fof(f30,plain,
! [X0,X1,X2] : apply(apply(sF3_fnc(X0),X1),X2) = apply(apply(sF4_fnc(X0),X2),apply(X1,X2)),
inference(paramodulation,[status(thm)],[f16,f9]) ).
fof(f48,plain,
! [X0,X1,X2] : apply(apply(sF3_fnc(X0),X1),X2) = apply(X0,apply(X2,apply(X1,X2))),
inference(forward_demodulation,[status(thm)],[f27,f30]) ).
fof(f121,plain,
! [X0,X1] : apply(apply(sF3_fnc(X0),i),X1) = apply(X0,apply(X1,X1)),
inference(paramodulation,[status(thm)],[f12,f48]) ).
fof(f146,plain,
! [X0,X1] : apply(sF2_fnc(X0),X1) = apply(X0,apply(X1,X1)),
inference(forward_demodulation,[status(thm)],[f17,f121]) ).
fof(f169,plain,
! [X0,X1] : apply(sF2_fnc(X0),sF2_fnc(X1)) = apply(X0,sF1_fnc(X1)),
inference(paramodulation,[status(thm)],[f26,f146]) ).
fof(f543,plain,
! [X0] : sF1_fnc(X0) = apply(X0,sF1_fnc(X0)),
inference(backward_demodulation,[status(thm)],[f169,f26]) ).
fof(f576,plain,
ifeq(sF1_fnc(fixed_pt),sF1_fnc(fixed_pt),fixed_point(sF1_fnc(fixed_pt)),true) = true,
inference(paramodulation,[status(thm)],[f543,f13]) ).
fof(f603,plain,
fixed_point(sF1_fnc(fixed_pt)) = true,
inference(forward_demodulation,[status(thm)],[f8,f576]) ).
fof(f604,plain,
sF0_fnc(fixed_pt) = true,
inference(forward_demodulation,[status(thm)],[f21,f603]) ).
fof(f605,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f604,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COL002-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.62 % Computer : n007.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Mon Sep 21 14:00:51 UTC 2026
% 0.15/0.62 % CPUTime :
% 0.15/0.63 % Drodi V4.1.1
% 0.20/0.66 % Refutation found
% 0.20/0.66 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.68 % Elapsed time: 0.053165 seconds
% 0.20/0.68 % CPU time: 0.219310 seconds
% 0.20/0.68 % Total memory used: 7.636 MB
% 0.20/0.68 % Net memory used: 7.475 MB
%------------------------------------------------------------------------------