%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:06:18 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.58s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 21 ( 21 unt; 1 def)
% Number of atoms : 21 ( 20 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 : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 23 ( 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : add(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : add(inverse(X),X) = multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : multiply(multiplicative_identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
add(a,multiplicative_identity) != multiplicative_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f23,plain,
! [X0] : add(inverse(X0),X0) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f26,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f27,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
add(a,multiplicative_identity) != multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f31,definition,
sF0_fnc = add(a,multiplicative_identity),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f32,plain,
sF0_fnc != multiplicative_identity,
inference(definition_folding,[],[f30,f31]) ).
fof(f79,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),X0) = multiply(multiplicative_identity,add(X1,X0)),
inference(paramodulation,[status(thm)],[f23,f18]) ).
fof(f97,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),X0) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f27,f79]) ).
fof(f109,plain,
! [X0] : add(inverse(X0),X0) = add(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f26,f97]) ).
fof(f122,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(forward_demodulation,[status(thm)],[f23,f109]) ).
fof(f131,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f16,f122]) ).
fof(f141,plain,
sF0_fnc = multiplicative_identity,
inference(backward_demodulation,[status(thm)],[f131,f31]) ).
fof(f156,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f141,f32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO005-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.56 % Computer : n003.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Mon Sep 21 13:47:33 UTC 2026
% 0.10/0.56 % CPUTime :
% 0.10/0.57 % Drodi V4.1.1
% 0.13/0.58 % Refutation found
% 0.13/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.59 % Elapsed time: 0.023975 seconds
% 0.13/0.59 % CPU time: 0.035051 seconds
% 0.13/0.59 % Total memory used: 1.013 MB
% 0.13/0.59 % Net memory used: 984.880 KB
%------------------------------------------------------------------------------