%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO003-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:06:17 PM UTC 2026
% Result : Unsatisfiable 0.21s 0.51s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 20 ( 20 unt; 1 def)
% Number of atoms : 20 ( 19 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 : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 15 ( 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : add(X,additive_identity) = 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(f7,axiom,
! [X] : add(X,inverse(X)) = multiplicative_identity,
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,
multiply(a,a) != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f14,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f15,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f16,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f17,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
multiply(a,a) != a,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,definition,
sF0_fnc = multiply(a,a),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f20,plain,
sF0_fnc != a,
inference(definition_folding,[],[f18,f19]) ).
fof(f166,plain,
! [X0] : multiply(a,add(a,X0)) = add(sF0_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f19,f13]) ).
fof(f238,plain,
multiply(a,add(a,inverse(a))) = add(sF0_fnc,additive_identity),
inference(paramodulation,[status(thm)],[f17,f166]) ).
fof(f246,plain,
multiply(a,multiplicative_identity) = add(sF0_fnc,additive_identity),
inference(forward_demodulation,[status(thm)],[f16,f238]) ).
fof(f247,plain,
a = add(sF0_fnc,additive_identity),
inference(forward_demodulation,[status(thm)],[f15,f246]) ).
fof(f248,plain,
a = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f14,f247]) ).
fof(f249,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f248,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO003-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.46 % Computer : n009.cluster.edu
% 0.21/0.46 % Model : x86_64 x86_64
% 0.21/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.46 % Memory : 8046.5625MB
% 0.21/0.46 % OS : Linux 6.8.0-71-generic
% 0.21/0.47 % CPULimit : 300
% 0.21/0.47 % WCLimit : 300
% 0.21/0.47 % DateTime : Mon Sep 21 13:45:58 UTC 2026
% 0.21/0.47 % CPUTime :
% 0.21/0.49 % Drodi V4.1.1
% 0.21/0.51 % Refutation found
% 0.21/0.51 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.21/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.25/0.57 % Elapsed time: 0.075435 seconds
% 0.25/0.57 % CPU time: 0.093470 seconds
% 0.25/0.57 % Total memory used: 2.221 MB
% 0.25/0.57 % Net memory used: 2.167 MB
%------------------------------------------------------------------------------