%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 12:06:20 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% 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 : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] : multiply(X,Y) = multiply(Y,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : add(X,multiply(Y,Z)) = multiply(add(X,Y),add(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y,Z] : multiply(X,add(Y,Z)) = add(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] : add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : multiply(X,inverse(X)) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
multiply(a,add(a,b)) != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f12,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
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(f17,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f18,plain,
multiply(a,add(a,b)) != a,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f19,definition,
sF1_fnc = add(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f20,definition,
sF0_fnc = multiply(a,sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f21,plain,
sF0_fnc != a,
inference(definition_folding,[],[f18,f20,f19]) ).
fof(f30,plain,
sF0_fnc = multiply(sF1_fnc,a),
inference(paramodulation,[status(thm)],[f20,f11]) ).
fof(f41,plain,
! [X0] : add(a,multiply(b,X0)) = multiply(sF1_fnc,add(a,X0)),
inference(paramodulation,[status(thm)],[f19,f12]) ).
fof(f74,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(paramodulation,[status(thm)],[f10,f14]) ).
fof(f122,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = add(multiply(X0,X1),additive_identity),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f126,plain,
! [X0,X1] : multiply(X0,add(X1,inverse(X0))) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f14,f122]) ).
fof(f640,plain,
! [X0] : multiply(X0,inverse(X0)) = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f74,f126]) ).
fof(f665,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(forward_demodulation,[status(thm)],[f17,f640]) ).
fof(f715,plain,
add(a,additive_identity) = multiply(sF1_fnc,add(a,additive_identity)),
inference(paramodulation,[status(thm)],[f665,f41]) ).
fof(f726,plain,
a = multiply(sF1_fnc,add(a,additive_identity)),
inference(forward_demodulation,[status(thm)],[f14,f715]) ).
fof(f727,plain,
a = multiply(sF1_fnc,a),
inference(forward_demodulation,[status(thm)],[f14,f726]) ).
fof(f728,plain,
a = sF0_fnc,
inference(forward_demodulation,[status(thm)],[f30,f727]) ).
fof(f729,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f728,f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO009-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:49:16 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.41 % Refutation found
% 0.11/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.46 % Elapsed time: 0.066296 seconds
% 0.11/0.46 % CPU time: 0.083804 seconds
% 0.11/0.46 % Total memory used: 2.472 MB
% 0.11/0.46 % Net memory used: 2.414 MB
%------------------------------------------------------------------------------