%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 0.20s 0.48s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 52 unt; 0 def)
% Number of atoms : 52 ( 51 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 : 4 ( 2 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 : 58 ( 58 !; 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(f6,axiom,
! [X] : multiply(X,multiplicative_identity) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] : add(X,inverse(X)) = multiplicative_identity,
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,hypothesis,
add(a,b) = multiplicative_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,hypothesis,
multiply(a,b) = additive_identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
b != inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [X0,X1] : add(X0,X1) = add(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f13,plain,
! [X0,X1] : multiply(X0,X1) = multiply(X1,X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
! [X0,X1,X2] : add(X0,multiply(X1,X2)) = multiply(add(X0,X1),add(X0,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f15,plain,
! [X0,X1,X2] : multiply(X0,add(X1,X2)) = add(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f16,plain,
! [X0] : add(X0,additive_identity) = X0,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f17,plain,
! [X0] : multiply(X0,multiplicative_identity) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f18,plain,
! [X0] : add(X0,inverse(X0)) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f19,plain,
! [X0] : multiply(X0,inverse(X0)) = additive_identity,
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f20,plain,
add(a,b) = multiplicative_identity,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f21,plain,
multiply(a,b) = additive_identity,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f22,plain,
b != inverse(a),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f25,plain,
! [X0] : X0 = add(additive_identity,X0),
inference(paramodulation,[status(thm)],[f16,f12]) ).
fof(f56,plain,
! [X0] : X0 = multiply(multiplicative_identity,X0),
inference(paramodulation,[status(thm)],[f17,f13]) ).
fof(f91,plain,
! [X0] : add(a,multiply(b,X0)) = multiply(multiplicative_identity,add(a,X0)),
inference(paramodulation,[status(thm)],[f20,f14]) ).
fof(f93,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = multiply(multiplicative_identity,add(X0,X1)),
inference(paramodulation,[status(thm)],[f18,f14]) ).
fof(f109,plain,
! [X0] : add(a,multiply(b,X0)) = add(a,X0),
inference(forward_demodulation,[status(thm)],[f56,f91]) ).
fof(f110,plain,
! [X0,X1] : add(X0,multiply(inverse(X0),X1)) = add(X0,X1),
inference(forward_demodulation,[status(thm)],[f56,f93]) ).
fof(f121,plain,
! [X0] : add(X0,inverse(X0)) = add(X0,multiplicative_identity),
inference(paramodulation,[status(thm)],[f17,f110]) ).
fof(f122,plain,
! [X0] : add(X0,additive_identity) = add(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f19,f110]) ).
fof(f135,plain,
! [X0] : multiplicative_identity = add(X0,multiplicative_identity),
inference(forward_demodulation,[status(thm)],[f18,f121]) ).
fof(f136,plain,
! [X0] : X0 = add(X0,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f16,f122]) ).
fof(f189,plain,
! [X0] : multiply(a,add(b,X0)) = add(additive_identity,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f21,f15]) ).
fof(f191,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = add(additive_identity,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f15]) ).
fof(f198,plain,
! [X0,X1] : multiply(X0,add(X1,multiplicative_identity)) = add(multiply(X0,X1),X0),
inference(paramodulation,[status(thm)],[f17,f15]) ).
fof(f211,plain,
! [X0] : multiply(a,add(b,X0)) = multiply(a,X0),
inference(forward_demodulation,[status(thm)],[f25,f189]) ).
fof(f214,plain,
! [X0,X1] : multiply(X0,add(inverse(X0),X1)) = multiply(X0,X1),
inference(forward_demodulation,[status(thm)],[f25,f191]) ).
fof(f218,plain,
! [X0,X1] : multiply(X0,multiplicative_identity) = add(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f135,f198]) ).
fof(f219,plain,
! [X0,X1] : X0 = add(multiply(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f17,f218]) ).
fof(f337,plain,
add(a,additive_identity) = add(a,inverse(b)),
inference(paramodulation,[status(thm)],[f19,f109]) ).
fof(f347,plain,
a = add(a,inverse(b)),
inference(forward_demodulation,[status(thm)],[f16,f337]) ).
fof(f385,plain,
! [X0,X1] : X0 = add(multiply(X1,X0),X0),
inference(paramodulation,[status(thm)],[f13,f219]) ).
fof(f757,plain,
multiply(a,multiplicative_identity) = multiply(a,inverse(b)),
inference(paramodulation,[status(thm)],[f18,f211]) ).
fof(f779,plain,
a = multiply(a,inverse(b)),
inference(forward_demodulation,[status(thm)],[f17,f757]) ).
fof(f954,plain,
! [X0] : multiply(X0,multiplicative_identity) = multiply(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f18,f214]) ).
fof(f986,plain,
! [X0] : X0 = multiply(X0,inverse(inverse(X0))),
inference(forward_demodulation,[status(thm)],[f17,f954]) ).
fof(f1045,plain,
! [X0] : inverse(inverse(X0)) = add(X0,inverse(inverse(X0))),
inference(paramodulation,[status(thm)],[f986,f385]) ).
fof(f1060,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f136,f1045]) ).
fof(f1084,plain,
inverse(b) = add(a,inverse(b)),
inference(paramodulation,[status(thm)],[f779,f385]) ).
fof(f1094,plain,
inverse(b) = a,
inference(forward_demodulation,[status(thm)],[f347,f1084]) ).
fof(f1101,plain,
inverse(a) = b,
inference(paramodulation,[status(thm)],[f1094,f1060]) ).
fof(f1109,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1101,f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : BOO013-4 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.44 % Computer : n011.cluster.edu
% 0.20/0.44 % Model : x86_64 x86_64
% 0.20/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.44 % Memory : 8046.5625MB
% 0.20/0.44 % OS : Linux 6.8.0-71-generic
% 0.20/0.44 % CPULimit : 300
% 0.20/0.44 % WCLimit : 300
% 0.20/0.44 % DateTime : Mon Sep 21 13:47:57 UTC 2026
% 0.20/0.44 % CPUTime :
% 0.20/0.45 % Drodi V4.1.1
% 0.20/0.48 % Refutation found
% 0.20/0.48 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.20/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.50 % Elapsed time: 0.049230 seconds
% 0.20/0.50 % CPU time: 0.198769 seconds
% 0.20/0.50 % Total memory used: 6.052 MB
% 0.20/0.50 % Net memory used: 5.879 MB
%------------------------------------------------------------------------------