%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD026-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 12:21:56 PM UTC 2026
% Result : Unsatisfiable 257.68s 32.94s
% Output : CNFRefutation 161.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 18
% Syntax : Number of formulae : 90 ( 31 unt; 0 def)
% Number of atoms : 199 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 219 ( 110 ~; 109 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 156 ( 156 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( ~ defined(X)
| sum(additive_inverse(X),X,additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Y,X,Z] :
( ~ sum(X,Y,Z)
| sum(Y,X,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X] :
( ~ defined(X)
| product(multiplicative_identity,X,X) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Y,X,Z] :
( ~ product(X,Y,Z)
| product(Y,X,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X] :
( sum(additive_identity,X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| product(X,Y,multiply(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
defined(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,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(f35,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)],[f34]) ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f39,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(f40,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)],[f39]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f43,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f44,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f45,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f46,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(f47,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)],[f46]) ).
fof(f56,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f57,plain,
! [X0] :
( sum(additive_identity,X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f60,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| product(X,Y,multiply(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f20]) ).
fof(f61,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| product(X0,X1,multiply(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f71,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f72,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f73,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f74,plain,
product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f75,plain,
~ product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f83,plain,
! [X0,X1,X2,X3] :
( ~ defined(X2)
| ~ sum(X3,X1,X2)
| ~ sum(additive_identity,X3,X0)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f35,f36]) ).
fof(f85,plain,
! [X0] :
( ~ defined(X0)
| sum(X0,additive_identity,X0) ),
inference(resolution,[status(thm)],[f38,f36]) ).
fof(f87,plain,
sum(b,additive_identity,b),
inference(resolution,[status(thm)],[f85,f72]) ).
fof(f91,plain,
sum(additive_identity,b,b),
inference(resolution,[status(thm)],[f87,f38]) ).
fof(f122,plain,
! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(X0,b,b) ),
inference(resolution,[status(thm)],[f91,f35]) ).
fof(f141,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[status(thm)],[f37,f71]) ).
fof(f145,plain,
! [X0,X1,X2] :
( ~ product(X0,X2,multiplicative_inverse(b))
| ~ product(X1,multiplicative_inverse(a),X2)
| ~ product(X0,X1,multiplicative_identity) ),
inference(resolution,[status(thm)],[f42,f75]) ).
fof(f167,plain,
product(a,multiplicative_identity,b),
inference(resolution,[status(thm)],[f45,f74]) ).
fof(f168,plain,
! [X0] :
( ~ defined(X0)
| product(X0,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f45,f43]) ).
fof(f169,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X3,X5,X2)
| ~ product(X4,X0,X5)
| ~ product(X3,X4,X1)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f42]) ).
fof(f170,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ product(X4,X5,X2)
| ~ product(X3,X5,X0)
| ~ product(X1,X3,X4)
| product(X0,X1,X2) ),
inference(resolution,[status(thm)],[f45,f40]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,a)
| ~ sum(additive_inverse(a),X2,X0)
| sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f141,f35]) ).
fof(f191,plain,
! [X0] :
( product(X0,multiplicative_inverse(X0),multiplicative_identity)
| ~ defined(X0)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f44,f45]) ).
fof(f439,plain,
! [X0,X1] :
( product(X1,X0,multiply(X0,X1))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f61,f45]) ).
fof(f670,plain,
! [X0,X1,X2] :
( ~ sum(X2,X1,b)
| ~ sum(additive_identity,X2,X0)
| sum(X0,X1,b) ),
inference(resolution,[status(thm)],[f83,f72]) ).
fof(f753,plain,
! [X0,X1] :
( ~ defined(X0)
| ~ product(multiplicative_identity,multiplicative_identity,X1)
| product(X0,X1,X0) ),
inference(resolution,[status(thm)],[f169,f43]) ).
fof(f776,plain,
! [X0,X1,X2] :
( ~ product(X2,multiplicative_identity,X1)
| ~ product(X0,a,X2)
| product(b,X0,X1) ),
inference(resolution,[status(thm)],[f170,f167]) ).
fof(f797,plain,
! [X0,X1,X2,X3] :
( ~ product(X2,X3,X0)
| ~ product(X1,X2,X2)
| product(X0,X1,X0) ),
inference(factoring,[status(thm)],[f170]) ).
fof(f888,plain,
( product(a,multiplicative_inverse(a),multiplicative_identity)
| sum(additive_identity,a,additive_identity) ),
inference(resolution,[status(thm)],[f191,f71]) ).
fof(f891,plain,
product(a,multiplicative_inverse(a),multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[f888,f73]) ).
fof(f893,plain,
! [X0] :
( ~ product(X0,a,a)
| product(multiplicative_identity,X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f891,f170]) ).
fof(f906,plain,
product(multiplicative_inverse(a),a,multiplicative_identity),
inference(resolution,[status(thm)],[f891,f45]) ).
fof(f1178,plain,
( ~ defined(a)
| product(multiplicative_identity,multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f893,f43]) ).
fof(f1181,plain,
product(multiplicative_identity,multiplicative_identity,multiplicative_identity),
inference(forward_subsumption_resolution,[status(thm)],[f1178,f71]) ).
fof(f1407,plain,
! [X0] :
( product(multiplicative_identity,X0,multiply(X0,multiplicative_identity))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f439,f56]) ).
fof(f1925,plain,
product(multiplicative_identity,multiplicative_identity,multiply(multiplicative_identity,multiplicative_identity)),
inference(resolution,[status(thm)],[f1407,f56]) ).
fof(f3283,plain,
! [X0] :
( ~ defined(X0)
| product(X0,multiply(multiplicative_identity,multiplicative_identity),X0) ),
inference(resolution,[status(thm)],[f753,f1925]) ).
fof(f3297,plain,
product(a,multiply(multiplicative_identity,multiplicative_identity),a),
inference(resolution,[status(thm)],[f3283,f71]) ).
fof(f3550,plain,
! [X0,X1,X2] :
( ~ defined(X1)
| ~ product(X1,X2,X0)
| product(X0,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f797,f43]) ).
fof(f3833,plain,
! [X0,X1] :
( ~ product(a,X1,X0)
| product(X0,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f3550,f71]) ).
fof(f3836,plain,
product(a,multiplicative_identity,a),
inference(resolution,[status(thm)],[f3833,f3297]) ).
fof(f3904,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[f3836,f45]) ).
fof(f5676,plain,
! [X0] :
( ~ sum(a,X0,a)
| sum(additive_identity,X0,additive_identity) ),
inference(resolution,[status(thm)],[f184,f141]) ).
fof(f10750,plain,
! [X0] :
( ~ sum(additive_identity,b,X0)
| sum(X0,additive_identity,b) ),
inference(resolution,[status(thm)],[f670,f87]) ).
fof(f14160,plain,
! [X0] :
( ~ product(multiplicative_identity,multiplicative_identity,X0)
| product(b,multiplicative_inverse(a),X0) ),
inference(resolution,[status(thm)],[f776,f906]) ).
fof(f14163,plain,
! [X0] :
( ~ product(a,multiplicative_identity,X0)
| product(b,multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f776,f3904]) ).
fof(f14283,plain,
product(b,multiplicative_identity,a),
inference(resolution,[status(thm)],[f14163,f3836]) ).
fof(f14375,plain,
( ~ sum(b,b,b)
| sum(a,a,a) ),
inference(resolution,[status(thm)],[f14283,f47]) ).
fof(f18974,plain,
product(b,multiplicative_inverse(a),multiplicative_identity),
inference(resolution,[status(thm)],[f14160,f1181]) ).
fof(f18988,plain,
! [X0] :
( ~ product(X0,multiplicative_identity,multiplicative_inverse(b))
| ~ product(X0,b,multiplicative_identity) ),
inference(resolution,[status(thm)],[f18974,f145]) ).
fof(f21284,plain,
( ~ defined(multiplicative_inverse(b))
| ~ product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolution,[status(thm)],[f18988,f168]) ).
fof(f21855,plain,
( sum(additive_identity,b,additive_identity)
| ~ defined(b)
| ~ product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolution,[status(thm)],[f21284,f57]) ).
fof(f21856,plain,
( sum(additive_identity,b,additive_identity)
| ~ defined(b) ),
inference(forward_subsumption_resolution,[status(thm)],[f21855,f44]) ).
fof(f21857,plain,
sum(additive_identity,b,additive_identity),
inference(forward_subsumption_resolution,[status(thm)],[f21856,f72]) ).
fof(f21860,plain,
sum(additive_identity,additive_identity,b),
inference(resolution,[status(thm)],[f21857,f10750]) ).
fof(f21891,plain,
sum(b,b,b),
inference(resolution,[status(thm)],[f21860,f122]) ).
fof(f22009,plain,
sum(a,a,a),
inference(backward_subsumption_resolution,[status(thm)],[f14375,f21891]) ).
fof(f22146,plain,
sum(additive_identity,a,additive_identity),
inference(resolution,[status(thm)],[f22009,f5676]) ).
fof(f22179,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f22146,f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD026-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n004.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 15:38:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 257.68/32.94 % Refutation found
% 257.68/32.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 257.68/32.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 32.62/33.11 % Elapsed time: 32.695218 seconds
% 32.62/33.11 % CPU time: 258.902787 seconds
% 32.62/33.11 % Total memory used: 995.681 MB
% 32.62/33.11 % Net memory used: 895.346 MB
%------------------------------------------------------------------------------