%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD011-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.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 12:21:52 PM UTC 2026
% Result : Unsatisfiable 112.09s 14.82s
% Output : CNFRefutation 112.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 96 ( 31 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 261 ( 125 ~; 136 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 177 ( 177 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,V,W,Y,U,Z] :
( ~ sum(U,Z,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [U,Z,W,X,Y,V] :
( ~ sum(X,V,W)
| ~ sum(Y,Z,V)
| ~ sum(X,Y,U)
| sum(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,V,W,Y,U,Z] :
( ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(X,V,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U,Z,W,X,Y,V] :
( ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U)
| product(U,Z,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,additive_identity)
| product(multiplicative_inverse(X),X,multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [C,D,B,X,Y,A,Z] :
( ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] :
( sum(additive_identity,X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,plain,
! [W,U,Z] :
( ~ sum(U,Z,W)
| ! [V,Y] :
( ~ sum(Y,Z,V)
| ! [X] :
( ~ sum(X,Y,U)
| sum(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X4,X5,X2)
| ~ sum(X3,X5,X1)
| ~ sum(X0,X3,X4)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
! [W,X,V] :
( ~ sum(X,V,W)
| ! [Z,Y] :
( ~ sum(Y,Z,V)
| ! [U] :
( ~ sum(X,Y,U)
| sum(U,Z,W) ) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sum(X3,X5,X2)
| ~ sum(X4,X1,X5)
| ~ sum(X3,X4,X0)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f37,plain,
! [W,U,Z] :
( ~ product(U,Z,W)
| ! [V,Y] :
( ~ product(Y,Z,V)
| ! [X] :
( ~ product(X,Y,U)
| product(X,V,W) ) ) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f38,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X1)
| ~ product(X0,X3,X4)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f39,plain,
! [W,X,V] :
( ~ product(X,V,W)
| ! [Z,Y] :
( ~ product(Y,Z,V)
| ! [U] :
( ~ product(X,Y,U)
| product(U,Z,W) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f40,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X3,X5,X2)
| ~ product(X4,X1,X5)
| ~ product(X3,X4,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f42,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
! [D,Y,Z] :
( ~ product(Y,Z,D)
| ! [C,X] :
( ~ product(X,Z,C)
| ! [B,A] :
( ~ product(A,Z,B)
| ~ sum(X,Y,A)
| sum(C,D,B) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ product(X4,X6,X1)
| ~ product(X3,X6,X0)
| ~ product(X5,X6,X2)
| ~ sum(X3,X4,X5)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f50,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f55,plain,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f58,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| product(X,Y,multiply(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f59,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f68,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f69,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
~ product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f77,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_identity,X0) ),
inference(resolution,[status(thm)],[f36,f34]) ).
fof(f79,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f77,f54]) ).
fof(f80,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f77,f50]) ).
fof(f86,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f79,f36]) ).
fof(f124,plain,
! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(X0,multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f33,f86]) ).
fof(f129,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_identity,X1)
| ~ sum(X2,additive_identity,X0)
| sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f33,f80]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( ~ defined(X2)
| ~ sum(X3,X1,X2)
| ~ sum(additive_identity,X3,X0)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f33,f34]) ).
fof(f147,plain,
! [X0,X1,X2,X3] :
( ~ defined(X2)
| ~ product(X3,X2,X1)
| ~ product(X0,X3,multiplicative_identity)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f38,f41]) ).
fof(f152,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[status(thm)],[f35,f69]) ).
fof(f160,plain,
sum(a,additive_inverse(a),additive_identity),
inference(resolution,[status(thm)],[f152,f36]) ).
fof(f193,plain,
! [X0] :
( ~ sum(X0,a,a)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f160,f31]) ).
fof(f313,plain,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f42,f43]) ).
fof(f317,plain,
! [X0,X1,X2,X3,X4] :
( ~ defined(X2)
| ~ product(X4,X2,X1)
| ~ product(X3,X2,X0)
| ~ sum(X3,X4,multiplicative_identity)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f41]) ).
fof(f485,plain,
! [X0] :
( sum(multiplicative_inverse(X0),additive_identity,multiplicative_inverse(X0))
| sum(additive_identity,X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f55,f77]) ).
fof(f555,plain,
! [X0] :
( ~ defined(X0)
| product(X0,multiplicative_identity,multiply(X0,multiplicative_identity)) ),
inference(resolution,[status(thm)],[f59,f54]) ).
fof(f619,plain,
product(a,multiplicative_identity,multiply(a,multiplicative_identity)),
inference(resolution,[status(thm)],[f555,f69]) ).
fof(f631,plain,
product(multiplicative_identity,a,multiply(a,multiplicative_identity)),
inference(resolution,[status(thm)],[f619,f43]) ).
fof(f1132,plain,
! [X0,X1,X2,X3] :
( sum(additive_identity,X2,additive_identity)
| ~ defined(X2)
| ~ sum(X3,X1,multiplicative_inverse(X2))
| ~ sum(additive_identity,X3,X0)
| sum(X0,X1,multiplicative_inverse(X2)) ),
inference(resolution,[status(thm)],[f137,f55]) ).
fof(f1272,plain,
! [X0,X1] :
( ~ defined(multiplicative_identity)
| ~ defined(X1)
| ~ product(multiplicative_identity,X1,X0)
| product(multiplicative_identity,X0,X1) ),
inference(resolution,[status(thm)],[f147,f41]) ).
fof(f1274,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ product(multiplicative_identity,X1,X0)
| product(multiplicative_identity,X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1272,f54]) ).
fof(f1280,plain,
! [X0] :
( ~ product(multiplicative_identity,a,X0)
| product(multiplicative_identity,X0,a) ),
inference(resolution,[status(thm)],[f1274,f69]) ).
fof(f1283,plain,
product(multiplicative_identity,multiply(a,multiplicative_identity),a),
inference(resolution,[status(thm)],[f1280,f631]) ).
fof(f1290,plain,
! [X0] :
( ~ product(X0,multiplicative_identity,multiplicative_identity)
| product(X0,a,a) ),
inference(resolution,[status(thm)],[f1283,f38]) ).
fof(f1381,plain,
( ~ defined(multiplicative_identity)
| product(multiplicative_identity,a,a) ),
inference(resolution,[status(thm)],[f1290,f41]) ).
fof(f1384,plain,
product(multiplicative_identity,a,a),
inference(forward_subsumption_resolution,[status(thm)],[f1381,f54]) ).
fof(f1399,plain,
product(a,multiplicative_identity,a),
inference(resolution,[status(thm)],[f1384,f43]) ).
fof(f1402,plain,
! [X0,X1,X2] :
( ~ product(X2,X1,multiplicative_identity)
| ~ product(a,X2,X0)
| product(X0,X1,a) ),
inference(resolution,[status(thm)],[f1399,f40]) ).
fof(f2116,plain,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| product(multiplicative_inverse(X0),multiplicative_inverse(multiplicative_inverse(X0)),multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(X0),additive_identity) ),
inference(resolution,[status(thm)],[f313,f55]) ).
fof(f2120,plain,
( product(a,multiplicative_inverse(a),multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[f313,f69]) ).
fof(f2123,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[f2120,f70]) ).
fof(f2277,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,a,X1)
| ~ product(X2,a,X0)
| ~ sum(X2,X3,multiplicative_identity)
| sum(X0,X1,a) ),
inference(resolution,[status(thm)],[f317,f69]) ).
fof(f3815,plain,
! [X0] :
( ~ sum(multiplicative_identity,additive_identity,X0)
| sum(X0,additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f129,f79]) ).
fof(f5300,plain,
( sum(multiplicative_inverse(a),additive_identity,multiplicative_inverse(a))
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[f485,f69]) ).
fof(f5303,plain,
sum(multiplicative_inverse(a),additive_identity,multiplicative_inverse(a)),
inference(forward_subsumption_resolution,[status(thm)],[f5300,f70]) ).
fof(f5438,plain,
! [X0] :
( ~ product(multiplicative_inverse(a),X0,multiplicative_identity)
| product(multiplicative_identity,X0,a) ),
inference(resolution,[status(thm)],[f1402,f2123]) ).
fof(f6987,plain,
! [X0,X1,X2] :
( sum(additive_identity,a,additive_identity)
| ~ sum(X2,X1,multiplicative_inverse(a))
| ~ sum(additive_identity,X2,X0)
| sum(X0,X1,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f1132,f69]) ).
fof(f6990,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,multiplicative_inverse(a))
| ~ sum(additive_identity,X2,X0)
| sum(X0,X1,multiplicative_inverse(a)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6987,f70]) ).
fof(f8612,plain,
! [X0] :
( ~ sum(additive_identity,multiplicative_inverse(a),X0)
| sum(X0,additive_identity,multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f6990,f5303]) ).
fof(f13549,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f2116,f69]) ).
fof(f13552,plain,
( product(multiplicative_inverse(a),multiplicative_inverse(multiplicative_inverse(a)),multiplicative_identity)
| sum(additive_identity,multiplicative_inverse(a),additive_identity) ),
inference(forward_subsumption_resolution,[status(thm)],[f13549,f70]) ).
fof(f13939,plain,
! [X0,X1] :
( ~ defined(a)
| sum(additive_identity,a,additive_identity)
| ~ product(X1,a,X0)
| ~ sum(multiplicative_inverse(a),X1,multiplicative_identity)
| sum(multiplicative_identity,X0,a) ),
inference(resolution,[status(thm)],[f2277,f42]) ).
fof(f13982,plain,
! [X0,X1] :
( ~ defined(a)
| ~ product(X1,a,X0)
| ~ sum(multiplicative_inverse(a),X1,multiplicative_identity)
| sum(multiplicative_identity,X0,a) ),
inference(forward_subsumption_resolution,[status(thm)],[f13939,f70]) ).
fof(f14006,plain,
( product(multiplicative_identity,multiplicative_inverse(multiplicative_inverse(a)),a)
| sum(additive_identity,multiplicative_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f13552,f5438]) ).
fof(f14028,plain,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f14006,f71]) ).
fof(f14033,plain,
sum(additive_identity,additive_identity,multiplicative_inverse(a)),
inference(resolution,[status(thm)],[f14028,f8612]) ).
fof(f14118,plain,
sum(multiplicative_inverse(a),multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f14033,f124]) ).
fof(f16061,plain,
! [X0,X1] :
( ~ product(X1,a,X0)
| ~ sum(multiplicative_inverse(a),X1,multiplicative_identity)
| sum(multiplicative_identity,X0,a) ),
inference(forward_subsumption_resolution,[status(thm)],[f13982,f69]) ).
fof(f16064,plain,
! [X0] :
( ~ product(multiplicative_identity,a,X0)
| sum(multiplicative_identity,X0,a) ),
inference(resolution,[status(thm)],[f16061,f14118]) ).
fof(f16113,plain,
sum(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[f16064,f1384]) ).
fof(f16136,plain,
sum(multiplicative_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f16113,f193]) ).
fof(f16173,plain,
sum(additive_identity,additive_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f16136,f3815]) ).
fof(f16228,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f16173,f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD011-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.57 % Computer : n007.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 15:35:36 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.15/0.58 % Drodi V4.1.1
% 112.09/14.82 % Refutation found
% 112.09/14.82 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 112.09/14.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 74.28/16.11 % Elapsed time: 15.316361 seconds
% 74.28/16.11 % CPU time: 110.289205 seconds
% 74.28/16.11 % Total memory used: 492.827 MB
% 74.28/16.11 % Net memory used: 442.319 MB
%------------------------------------------------------------------------------