%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO018-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 12:06:23 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 5
% Syntax : Number of formulae : 14 ( 14 unt; 1 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 9 ( 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
inverse(multiplicative_identity) != additive_identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f15,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f17,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
inverse(multiplicative_identity) != additive_identity,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,definition,
sF0_fnc = inverse(multiplicative_identity),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f20,plain,
sF0_fnc != additive_identity,
inference(definition_folding,[],[f18,f19]) ).
fof(f22,plain,
multiply(multiplicative_identity,sF0_fnc) = additive_identity,
inference(paramodulation,[status(thm)],[f19,f17]) ).
fof(f41,plain,
! [X0] : X0 = multiply(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f15,f11]) ).
fof(f49,plain,
sF0_fnc = additive_identity,
inference(backward_demodulation,[status(thm)],[f41,f22]) ).
fof(f58,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f49,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO018-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:46:21 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.36 % Drodi V4.1.1
% 0.12/0.37 % Refutation found
% 0.12/0.37 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.39 % Elapsed time: 0.031040 seconds
% 0.12/0.39 % CPU time: 0.035708 seconds
% 0.12/0.39 % Total memory used: 419.152 KB
% 0.12/0.39 % Net memory used: 404.512 KB
%------------------------------------------------------------------------------