%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO013-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 12:06:21 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.41s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 31 unt; 0 def)
% Number of atoms : 31 ( 30 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 20 ( 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] : add(X,Y) = add(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(f12,axiom,
! [X] : multiply(multiplicative_identity,X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X] : add(X,additive_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
add(a,c) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
multiply(a,c) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : add(multiply(X0,X1),X2) = multiply(add(X0,X2),add(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f31,plain,
! [X0] : multiply(multiplicative_identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f32,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f34,plain,
add(a,b) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f35,plain,
add(a,c) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f36,plain,
multiply(a,b) = additive_identity,
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f37,plain,
multiply(a,c) = additive_identity,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f38,plain,
b != c,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f80,plain,
! [X0] : add(multiply(a,X0),c) = multiply(multiplicative_identity,add(X0,c)),
inference(paramodulation,[status(thm)],[f35,f22]) ).
fof(f81,plain,
! [X0] : add(multiply(a,X0),b) = multiply(multiplicative_identity,add(X0,b)),
inference(paramodulation,[status(thm)],[f34,f22]) ).
fof(f97,plain,
! [X0] : add(c,multiply(a,X0)) = multiply(multiplicative_identity,add(X0,c)),
inference(forward_demodulation,[status(thm)],[f20,f80]) ).
fof(f98,plain,
! [X0] : add(c,multiply(a,X0)) = add(X0,c),
inference(forward_demodulation,[status(thm)],[f31,f97]) ).
fof(f99,plain,
! [X0] : add(b,multiply(a,X0)) = multiply(multiplicative_identity,add(X0,b)),
inference(forward_demodulation,[status(thm)],[f20,f81]) ).
fof(f100,plain,
! [X0] : add(b,multiply(a,X0)) = add(X0,b),
inference(forward_demodulation,[status(thm)],[f31,f99]) ).
fof(f116,plain,
add(c,additive_identity) = add(b,c),
inference(paramodulation,[status(thm)],[f36,f98]) ).
fof(f124,plain,
c = add(b,c),
inference(forward_demodulation,[status(thm)],[f32,f116]) ).
fof(f131,plain,
add(b,additive_identity) = add(c,b),
inference(paramodulation,[status(thm)],[f37,f100]) ).
fof(f139,plain,
b = add(c,b),
inference(forward_demodulation,[status(thm)],[f32,f131]) ).
fof(f140,plain,
b = add(b,c),
inference(forward_demodulation,[status(thm)],[f20,f139]) ).
fof(f141,plain,
b = c,
inference(forward_demodulation,[status(thm)],[f124,f140]) ).
fof(f142,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f141,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : BOO013-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n001.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 13:53:30 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.40 % 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
% 0.15/0.46 % Elapsed time: 0.072573 seconds
% 0.15/0.46 % CPU time: 0.066529 seconds
% 0.15/0.46 % Total memory used: 1.618 MB
% 0.15/0.46 % Net memory used: 1.589 MB
%------------------------------------------------------------------------------