%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD040-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 12:22:00 PM UTC 2026
% Result : Unsatisfiable 1.06s 0.58s
% Output : CNFRefutation 1.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 73 ( 21 unt; 3 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 181 ( 90 ~; 88 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 103 ( 103 !; 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(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(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(f17,axiom,
defined(multiplicative_identity),
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,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
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(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(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(f54,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
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,
sum(additive_identity,multiplicative_inverse(a),additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
sum(additive_identity,a,a),
inference(resolution,[status(thm)],[f34,f69]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_identity,X1)
| ~ sum(X2,additive_identity,X0)
| sum(X0,multiplicative_inverse(a),X1) ),
inference(resolution,[status(thm)],[f33,f71]) ).
fof(f86,plain,
sum(a,additive_identity,a),
inference(resolution,[status(thm)],[f36,f75]) ).
fof(f88,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f54,f34]) ).
fof(f102,plain,
sum(additive_inverse(a),a,additive_identity),
inference(resolution,[status(thm)],[f35,f69]) ).
fof(f134,definition,
( sQ7_spl
<=> sum(additive_identity,multiplicative_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f135,plain,
( ~ sQ7_spl
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f141,definition,
( sQ9_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f142,plain,
( ~ sQ9_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f141]) ).
fof(f156,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f42,f69]) ).
fof(f174,definition,
( sQ16_spl
<=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ16_spl
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,plain,
( sQ9_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f156,f174,f141]) ).
fof(f182,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f142,f70]) ).
fof(f183,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f479,plain,
sum(multiplicative_identity,additive_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f88,f36]) ).
fof(f513,plain,
! [X0] :
( ~ sum(a,additive_identity,X0)
| sum(X0,multiplicative_inverse(a),a) ),
inference(resolution,[status(thm)],[f86,f83]) ).
fof(f521,plain,
sum(a,multiplicative_inverse(a),a),
inference(resolution,[status(thm)],[f513,f86]) ).
fof(f528,plain,
! [X0,X1,X2] :
( ~ sum(X2,a,X1)
| ~ sum(X2,a,X0)
| sum(X0,multiplicative_inverse(a),X1) ),
inference(resolution,[status(thm)],[f521,f33]) ).
fof(f543,plain,
! [X0] :
( ~ sum(additive_inverse(a),a,X0)
| sum(X0,multiplicative_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f528,f102]) ).
fof(f910,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[f41,f69]) ).
fof(f1105,plain,
! [X0] :
( ~ sum(multiplicative_identity,additive_identity,X0)
| sum(X0,multiplicative_inverse(a),multiplicative_identity) ),
inference(resolution,[status(thm)],[f479,f83]) ).
fof(f1114,plain,
sum(multiplicative_identity,multiplicative_inverse(a),multiplicative_identity),
inference(resolution,[status(thm)],[f1105,f479]) ).
fof(f1123,plain,
! [X0,X1,X2,X3] :
( ~ product(multiplicative_inverse(a),X3,X1)
| ~ product(multiplicative_identity,X3,X0)
| ~ product(multiplicative_identity,X3,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1114,f45]) ).
fof(f1126,plain,
! [X0,X1,X2] :
( ~ sum(X2,multiplicative_identity,X1)
| ~ sum(X2,multiplicative_identity,X0)
| sum(X0,multiplicative_inverse(a),X1) ),
inference(resolution,[status(thm)],[f1114,f33]) ).
fof(f1128,plain,
! [X0,X1,X2] :
( ~ sum(X2,multiplicative_inverse(a),X1)
| ~ sum(X0,X2,multiplicative_identity)
| sum(X0,X1,multiplicative_identity) ),
inference(resolution,[status(thm)],[f1114,f31]) ).
fof(f1130,plain,
! [X0,X1,X2] :
( ~ sum(X2,multiplicative_inverse(a),X1)
| ~ sum(X0,multiplicative_identity,X2)
| sum(X0,multiplicative_identity,X1) ),
inference(resolution,[status(thm)],[f1114,f31]) ).
fof(f1144,plain,
! [X0] :
( ~ sQ7_spl
| ~ sum(additive_identity,multiplicative_identity,X0)
| sum(X0,multiplicative_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f1126,f135]) ).
fof(f1147,plain,
( ~ sQ7_spl
| sum(multiplicative_identity,multiplicative_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f1144,f88]) ).
fof(f1148,plain,
! [X0,X1] :
( ~ sQ16_spl
| ~ product(multiplicative_identity,a,X0)
| ~ product(multiplicative_identity,a,X1)
| sum(X0,multiplicative_identity,X1) ),
inference(resolution,[status(thm)],[f1123,f175]) ).
fof(f1169,plain,
! [X0] :
( ~ sQ7_spl
| ~ sum(X0,multiplicative_identity,multiplicative_identity)
| sum(X0,additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f1147,f1128]) ).
fof(f1248,plain,
( ~ sQ7_spl
| sum(additive_identity,additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f1169,f88]) ).
fof(f1249,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1248,f68]) ).
fof(f1250,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f1249]) ).
fof(f1253,plain,
! [X0] :
( ~ sQ16_spl
| ~ product(multiplicative_identity,a,X0)
| sum(X0,multiplicative_identity,a) ),
inference(resolution,[status(thm)],[f1148,f910]) ).
fof(f1254,plain,
( ~ sQ16_spl
| sum(a,multiplicative_identity,a) ),
inference(resolution,[status(thm)],[f1253,f910]) ).
fof(f1263,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sum(X2,multiplicative_identity,X1)
| ~ sum(X0,a,X2)
| sum(X0,a,X1) ),
inference(resolution,[status(thm)],[f1254,f31]) ).
fof(f1296,plain,
! [X0] :
( ~ sQ16_spl
| ~ sum(X0,a,additive_identity)
| sum(X0,a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f1263,f88]) ).
fof(f1723,plain,
( ~ sQ16_spl
| sum(additive_inverse(a),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f1296,f102]) ).
fof(f1724,plain,
( ~ sQ16_spl
| sum(multiplicative_identity,multiplicative_inverse(a),additive_identity) ),
inference(resolution,[status(thm)],[f1723,f543]) ).
fof(f1742,plain,
! [X0] :
( ~ sQ16_spl
| ~ sum(X0,multiplicative_identity,multiplicative_identity)
| sum(X0,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[f1724,f1130]) ).
fof(f1859,plain,
( ~ sQ16_spl
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[f1742,f88]) ).
fof(f1860,plain,
( ~ sQ16_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1859,f134,f174]) ).
fof(f1861,plain,
$false,
inference(sat_refutation,[status(thm)],[f177,f183,f1250,f1860]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD040-5 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n009.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 15:39:58 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.37 % Drodi V4.1.1
% 1.06/0.58 % Refutation found
% 1.06/0.58 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.06/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.06/0.60 % Elapsed time: 0.227155 seconds
% 1.06/0.60 % CPU time: 1.622182 seconds
% 1.06/0.60 % Total memory used: 35.188 MB
% 1.06/0.60 % Net memory used: 32.955 MB
%------------------------------------------------------------------------------