%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO006-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 0.07s 0.36s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 25 ( 25 unt; 0 def)
% Number of atoms : 25 ( 24 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 : 4 ( 2 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 : 36 ( 36 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(multiply(X,Y),Z) = multiply(add(X,Z),add(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y,Z] : multiply(add(X,Y),Z) = add(multiply(X,Z),multiply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] : add(inverse(X),X) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X] : add(additive_identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
multiply(a,additive_identity) != additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
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(f20,plain,
! [X0,X1,X2] : multiply(add(X0,X1),X2) = add(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f5]) ).
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(f29,plain,
! [X0] : add(additive_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f30,plain,
multiply(a,additive_identity) != additive_identity,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f53,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(paramodulation,[status(thm)],[f17,f26]) ).
fof(f97,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),X0) = multiply(multiplicative_identity,add(X1,X0)),
inference(paramodulation,[status(thm)],[f23,f18]) ).
fof(f113,plain,
! [X0,X1] : add(multiply(inverse(X0),X1),X0) = add(X1,X0),
inference(forward_demodulation,[status(thm)],[f53,f97]) ).
fof(f126,plain,
! [X0] : add(inverse(X0),X0) = add(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f26,f113]) ).
fof(f140,plain,
! [X0] : multiplicative_identity = add(multiplicative_identity,X0),
inference(forward_demodulation,[status(thm)],[f23,f126]) ).
fof(f270,plain,
! [X0,X1] : multiply(add(multiplicative_identity,X0),X1) = add(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f53,f20]) ).
fof(f294,plain,
! [X0,X1] : multiply(multiplicative_identity,X0) = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f140,f270]) ).
fof(f295,plain,
! [X0,X1] : X0 = add(X0,multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f53,f294]) ).
fof(f351,plain,
! [X0] : additive_identity = multiply(X0,additive_identity),
inference(paramodulation,[status(thm)],[f29,f295]) ).
fof(f372,plain,
additive_identity != additive_identity,
inference(backward_demodulation,[status(thm)],[f351,f30]) ).
fof(f387,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f372]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n018.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 13:49:29 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.07/0.36 % Refutation found
% 0.07/0.36 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.07/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.027679 seconds
% 0.12/0.38 % CPU time: 0.044444 seconds
% 0.12/0.38 % Total memory used: 1.775 MB
% 0.12/0.38 % Net memory used: 1.746 MB
%------------------------------------------------------------------------------