%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD041-4 : 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 7.14s 1.40s
% Output : CNFRefutation 7.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 37
% Syntax : Number of formulae : 168 ( 56 unt; 13 def)
% Number of atoms : 364 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 363 ( 167 ~; 183 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 14 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-1 aty)
% Number of variables : 195 ( 195 !; 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(f12,axiom,
! [A,Z,B,X,Y,C,D] :
( ~ sum(C,D,B)
| ~ product(Y,Z,D)
| ~ product(X,Z,C)
| ~ sum(X,Y,A)
| product(A,Z,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(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,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ sum(additive_identity,a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ sum(additive_identity,b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
sum(additive_identity,c,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,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(f35,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)],[f34]) ).
fof(f36,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(f37,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)],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f39,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_inverse(X0),X0,additive_identity) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ sum(X1,X0,X2)
| sum(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f43,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(f44,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)],[f43]) ).
fof(f45,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f46,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f48,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(f49,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)],[f48]) ).
fof(f50,plain,
! [B,C,D] :
( ~ sum(C,D,B)
| ! [Z,Y] :
( ~ product(Y,Z,D)
| ! [X] :
( ~ product(X,Z,C)
| ! [A] :
( ~ sum(X,Y,A)
| product(A,Z,B) ) ) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ sum(X5,X6,X2)
| ~ product(X4,X1,X6)
| ~ product(X3,X1,X5)
| ~ sum(X3,X4,X0)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f54,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f55,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f58,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f67,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f68,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f72,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f73,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f74,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
defined(c),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
product(a,b,c),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f79,plain,
sum(additive_identity,c,additive_identity),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f80,plain,
defined(additive_inverse(multiplicative_identity)),
inference(resolution,[status(thm)],[f55,f58]) ).
fof(f81,plain,
defined(additive_inverse(c)),
inference(resolution,[status(thm)],[f55,f75]) ).
fof(f82,plain,
defined(additive_inverse(b)),
inference(resolution,[status(thm)],[f55,f74]) ).
fof(f83,plain,
defined(additive_inverse(a)),
inference(resolution,[status(thm)],[f55,f73]) ).
fof(f84,plain,
defined(additive_inverse(additive_identity)),
inference(resolution,[status(thm)],[f55,f54]) ).
fof(f85,plain,
defined(additive_inverse(additive_inverse(multiplicative_identity))),
inference(resolution,[status(thm)],[f80,f55]) ).
fof(f86,plain,
defined(additive_inverse(additive_inverse(c))),
inference(resolution,[status(thm)],[f81,f55]) ).
fof(f87,plain,
defined(additive_inverse(additive_inverse(b))),
inference(resolution,[status(thm)],[f82,f55]) ).
fof(f88,plain,
defined(additive_inverse(additive_inverse(a))),
inference(resolution,[status(thm)],[f83,f55]) ).
fof(f94,plain,
sum(additive_identity,c,c),
inference(resolution,[status(thm)],[f38,f75]) ).
fof(f95,plain,
sum(additive_identity,b,b),
inference(resolution,[status(thm)],[f38,f74]) ).
fof(f97,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f38,f54]) ).
fof(f104,plain,
sum(additive_inverse(b),b,additive_identity),
inference(resolution,[status(thm)],[f39,f74]) ).
fof(f110,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_inverse(multiplicative_identity),X0)
| less_or_equal(X0,additive_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[f68,f80]) ).
fof(f111,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(multiplicative_identity,X0)
| less_or_equal(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f68,f58]) ).
fof(f479,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolution,[status(thm)],[f46,f74]) ).
fof(f480,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f46,f73]) ).
fof(f524,definition,
( sQ89_spl
<=> product(multiplicative_inverse(b),b,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f525,plain,
( ~ sQ89_spl
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f527,definition,
( sQ90_spl
<=> sum(additive_identity,b,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f528,plain,
( ~ sQ90_spl
| sum(additive_identity,b,additive_identity) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,plain,
( sQ90_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f479,f524,f527]) ).
fof(f531,definition,
( sQ91_spl
<=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( ~ sQ91_spl
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f534,definition,
( sQ92_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f535,plain,
( ~ sQ92_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f534]) ).
fof(f537,plain,
( sQ92_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f480,f531,f534]) ).
fof(f590,plain,
( ~ sQ92_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f535,f76]) ).
fof(f591,plain,
~ sQ92_spl,
inference(contradiction_clause,[status(thm)],[f590]) ).
fof(f592,plain,
( ~ sQ90_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f528,f77]) ).
fof(f593,plain,
~ sQ90_spl,
inference(contradiction_clause,[status(thm)],[f592]) ).
fof(f598,plain,
( less_or_equal(multiplicative_identity,multiplicative_identity)
| less_or_equal(multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f111,f58]) ).
fof(f613,definition,
( sQ106_spl
<=> less_or_equal(multiplicative_identity,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f616,plain,
sQ106_spl,
inference(split_clause,[status(thm)],[f598,f613]) ).
fof(f624,plain,
( less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity))
| less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity)) ),
inference(resolution,[status(thm)],[f110,f80]) ).
fof(f633,definition,
( sQ107_spl
<=> less_or_equal(additive_inverse(multiplicative_identity),additive_inverse(multiplicative_identity)) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f636,plain,
sQ107_spl,
inference(split_clause,[status(thm)],[f624,f633]) ).
fof(f642,plain,
sum(c,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f79,f40]) ).
fof(f644,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_identity,X1)
| ~ sum(X2,additive_identity,X0)
| sum(X0,c,X1) ),
inference(resolution,[status(thm)],[f79,f37]) ).
fof(f646,plain,
! [X0,X1,X2] :
( ~ sum(X2,c,X1)
| ~ sum(X0,X2,additive_identity)
| sum(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f79,f35]) ).
fof(f648,plain,
! [X0,X1,X2] :
( ~ sum(X2,c,X1)
| ~ sum(X0,additive_identity,X2)
| sum(X0,additive_identity,X1) ),
inference(resolution,[status(thm)],[f79,f35]) ).
fof(f654,plain,
! [X0] :
( ~ sum(X0,c,c)
| sum(X0,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f642,f35]) ).
fof(f668,plain,
! [X0,X1,X2] :
( ~ product(X2,b,X1)
| ~ product(X0,a,X2)
| product(X0,c,X1) ),
inference(resolution,[status(thm)],[f42,f78]) ).
fof(f669,plain,
! [X0,X1,X2] :
( ~ product(X2,b,X1)
| ~ product(X0,X2,a)
| product(X0,X1,c) ),
inference(resolution,[status(thm)],[f42,f78]) ).
fof(f686,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_inverse(additive_identity),X0)
| less_or_equal(X0,additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[f84,f68]) ).
fof(f689,plain,
defined(additive_inverse(additive_inverse(additive_identity))),
inference(resolution,[status(thm)],[f84,f55]) ).
fof(f764,plain,
( less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity))
| less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity)) ),
inference(resolution,[status(thm)],[f686,f84]) ).
fof(f774,definition,
( sQ129_spl
<=> less_or_equal(additive_inverse(additive_identity),additive_inverse(additive_identity)) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f777,plain,
sQ129_spl,
inference(split_clause,[status(thm)],[f764,f774]) ).
fof(f1055,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_inverse(additive_inverse(c)),X0)
| less_or_equal(X0,additive_inverse(additive_inverse(c))) ),
inference(resolution,[status(thm)],[f86,f68]) ).
fof(f1156,plain,
( less_or_equal(additive_inverse(additive_inverse(c)),additive_inverse(additive_inverse(c)))
| less_or_equal(additive_inverse(additive_inverse(c)),additive_inverse(additive_inverse(c))) ),
inference(resolution,[status(thm)],[f1055,f86]) ).
fof(f1169,definition,
( sQ207_spl
<=> less_or_equal(additive_inverse(additive_inverse(c)),additive_inverse(additive_inverse(c))) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f1172,plain,
sQ207_spl,
inference(split_clause,[status(thm)],[f1156,f1169]) ).
fof(f1198,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_inverse(additive_inverse(b)),X0)
| less_or_equal(X0,additive_inverse(additive_inverse(b))) ),
inference(resolution,[status(thm)],[f87,f68]) ).
fof(f1306,plain,
( less_or_equal(additive_inverse(additive_inverse(b)),additive_inverse(additive_inverse(b)))
| less_or_equal(additive_inverse(additive_inverse(b)),additive_inverse(additive_inverse(b))) ),
inference(resolution,[status(thm)],[f1198,f87]) ).
fof(f1320,definition,
( sQ237_spl
<=> less_or_equal(additive_inverse(additive_inverse(b)),additive_inverse(additive_inverse(b))) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f1323,plain,
sQ237_spl,
inference(split_clause,[status(thm)],[f1306,f1320]) ).
fof(f1335,plain,
product(b,a,c),
inference(resolution,[status(thm)],[f47,f78]) ).
fof(f1342,plain,
! [X0,X1,X2] :
( ~ product(X2,a,X1)
| ~ product(X0,b,X2)
| product(X0,c,X1) ),
inference(resolution,[status(thm)],[f1335,f42]) ).
fof(f1364,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_inverse(additive_inverse(a)),X0)
| less_or_equal(X0,additive_inverse(additive_inverse(a))) ),
inference(resolution,[status(thm)],[f88,f68]) ).
fof(f1490,plain,
! [X0] :
( ~ sum(X0,additive_identity,additive_identity)
| sum(X0,c,additive_identity) ),
inference(resolution,[status(thm)],[f94,f646]) ).
fof(f1503,plain,
sum(b,additive_identity,b),
inference(resolution,[status(thm)],[f95,f40]) ).
fof(f1527,plain,
! [X0] :
( ~ sum(additive_identity,c,X0)
| sum(additive_identity,additive_identity,X0) ),
inference(resolution,[status(thm)],[f97,f648]) ).
fof(f1572,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),X0)
| less_or_equal(X0,additive_inverse(additive_inverse(multiplicative_identity))) ),
inference(resolution,[status(thm)],[f85,f68]) ).
fof(f1698,plain,
product(multiplicative_identity,b,b),
inference(resolution,[status(thm)],[f45,f74]) ).
fof(f1699,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[f45,f73]) ).
fof(f1736,plain,
( less_or_equal(additive_inverse(additive_inverse(a)),additive_inverse(additive_inverse(a)))
| less_or_equal(additive_inverse(additive_inverse(a)),additive_inverse(additive_inverse(a))) ),
inference(resolution,[status(thm)],[f1364,f88]) ).
fof(f1758,definition,
( sQ302_spl
<=> less_or_equal(additive_inverse(additive_inverse(a)),additive_inverse(additive_inverse(a))) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f1761,plain,
sQ302_spl,
inference(split_clause,[status(thm)],[f1736,f1758]) ).
fof(f1776,plain,
( less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),additive_inverse(additive_inverse(multiplicative_identity)))
| less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),additive_inverse(additive_inverse(multiplicative_identity))) ),
inference(resolution,[status(thm)],[f1572,f85]) ).
fof(f1792,definition,
( sQ303_spl
<=> less_or_equal(additive_inverse(additive_inverse(multiplicative_identity)),additive_inverse(additive_inverse(multiplicative_identity))) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f1795,plain,
sQ303_spl,
inference(split_clause,[status(thm)],[f1776,f1792]) ).
fof(f1809,plain,
sum(c,c,additive_identity),
inference(resolution,[status(thm)],[f1490,f642]) ).
fof(f1814,plain,
! [X0,X1,X2,X3] :
( ~ product(X3,X1,c)
| ~ product(X2,X1,c)
| ~ sum(X2,X3,X0)
| product(X0,X1,additive_identity) ),
inference(resolution,[status(thm)],[f1809,f51]) ).
fof(f1833,plain,
sum(additive_identity,additive_identity,c),
inference(resolution,[status(thm)],[f1527,f94]) ).
fof(f1843,plain,
! [X0] :
( ~ sum(additive_identity,additive_identity,X0)
| sum(X0,c,c) ),
inference(resolution,[status(thm)],[f1833,f644]) ).
fof(f1846,plain,
! [X0,X1,X2,X3] :
( ~ product(additive_identity,X3,X1)
| ~ product(additive_identity,X3,X0)
| ~ product(c,X3,X2)
| sum(X0,X1,X2) ),
inference(resolution,[status(thm)],[f1833,f49]) ).
fof(f1851,plain,
! [X0,X1,X2] :
( ~ sum(X2,additive_identity,X1)
| ~ sum(X0,X2,additive_identity)
| sum(X0,X1,c) ),
inference(resolution,[status(thm)],[f1833,f35]) ).
fof(f1981,plain,
sum(c,c,c),
inference(resolution,[status(thm)],[f1843,f1833]) ).
fof(f2068,plain,
! [X0] :
( ~ product(c,X0,c)
| ~ product(c,X0,c)
| product(c,X0,additive_identity) ),
inference(resolution,[status(thm)],[f1814,f1981]) ).
fof(f2081,plain,
! [X0] :
( ~ product(c,X0,c)
| product(c,X0,additive_identity) ),
inference(duplicate_literals_removal,[status(thm)],[f2068]) ).
fof(f2284,definition,
( sQ318_spl
<=> sum(additive_identity,additive_identity,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f2285,plain,
( ~ sQ318_spl
| sum(additive_identity,additive_identity,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f2284]) ).
fof(f2328,plain,
( ~ sQ318_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2285,f72]) ).
fof(f2329,plain,
~ sQ318_spl,
inference(contradiction_clause,[status(thm)],[f2328]) ).
fof(f2903,plain,
! [X0] :
( ~ sQ89_spl
| ~ product(multiplicative_identity,a,X0)
| product(multiplicative_inverse(b),c,X0) ),
inference(resolution,[status(thm)],[f525,f1342]) ).
fof(f2904,plain,
! [X0] :
( ~ sQ89_spl
| ~ product(X0,multiplicative_inverse(b),a)
| product(X0,multiplicative_identity,c) ),
inference(resolution,[status(thm)],[f525,f669]) ).
fof(f2972,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_inverse(additive_inverse(additive_identity)),X0)
| less_or_equal(X0,additive_inverse(additive_inverse(additive_identity))) ),
inference(resolution,[status(thm)],[f689,f68]) ).
fof(f3145,plain,
( less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_inverse(additive_identity)))
| less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_inverse(additive_identity))) ),
inference(resolution,[status(thm)],[f2972,f689]) ).
fof(f3162,definition,
( sQ374_spl
<=> less_or_equal(additive_inverse(additive_inverse(additive_identity)),additive_inverse(additive_inverse(additive_identity))) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f3165,plain,
sQ374_spl,
inference(split_clause,[status(thm)],[f3145,f3162]) ).
fof(f3663,plain,
! [X0] :
( ~ product(X0,a,multiplicative_identity)
| product(X0,c,b) ),
inference(resolution,[status(thm)],[f1698,f668]) ).
fof(f3675,plain,
( ~ sQ89_spl
| product(multiplicative_inverse(b),c,a) ),
inference(resolution,[status(thm)],[f1699,f2903]) ).
fof(f4366,plain,
( ~ sQ91_spl
| product(multiplicative_inverse(a),c,b) ),
inference(resolution,[status(thm)],[f3663,f532]) ).
fof(f4371,plain,
( ~ sQ89_spl
| product(c,multiplicative_inverse(b),a) ),
inference(resolution,[status(thm)],[f3675,f47]) ).
fof(f4382,plain,
( ~ sQ91_spl
| product(c,multiplicative_inverse(a),b) ),
inference(resolution,[status(thm)],[f4366,f47]) ).
fof(f4390,plain,
( ~ sQ89_spl
| product(c,multiplicative_identity,c) ),
inference(resolution,[status(thm)],[f4371,f2904]) ).
fof(f4401,plain,
( ~ sQ89_spl
| product(c,multiplicative_identity,additive_identity) ),
inference(resolution,[status(thm)],[f4390,f2081]) ).
fof(f4462,plain,
( ~ sQ89_spl
| product(multiplicative_identity,c,additive_identity) ),
inference(resolution,[status(thm)],[f4401,f47]) ).
fof(f4577,plain,
! [X0,X1,X2] :
( ~ sQ91_spl
| ~ product(X2,b,X1)
| ~ product(X2,c,X0)
| product(X0,multiplicative_inverse(a),X1) ),
inference(resolution,[status(thm)],[f4382,f44]) ).
fof(f4764,plain,
! [X0] :
( ~ sQ89_spl
| ~ sQ91_spl
| ~ product(multiplicative_identity,b,X0)
| product(additive_identity,multiplicative_inverse(a),X0) ),
inference(resolution,[status(thm)],[f4577,f4462]) ).
fof(f5074,plain,
( ~ sQ89_spl
| ~ sQ91_spl
| product(additive_identity,multiplicative_inverse(a),b) ),
inference(resolution,[status(thm)],[f4764,f1698]) ).
fof(f5076,plain,
! [X0] :
( ~ sQ89_spl
| ~ sQ91_spl
| ~ product(c,multiplicative_inverse(a),X0)
| sum(b,b,X0) ),
inference(resolution,[status(thm)],[f5074,f1846]) ).
fof(f5112,plain,
( ~ sQ91_spl
| ~ sQ89_spl
| sum(b,b,b) ),
inference(resolution,[status(thm)],[f5076,f4382]) ).
fof(f5294,plain,
! [X0] :
( ~ sum(X0,b,additive_identity)
| sum(X0,b,c) ),
inference(resolution,[status(thm)],[f1503,f1851]) ).
fof(f5644,plain,
sum(additive_inverse(b),b,c),
inference(resolution,[status(thm)],[f5294,f104]) ).
fof(f5654,plain,
sum(b,additive_inverse(b),c),
inference(resolution,[status(thm)],[f5644,f40]) ).
fof(f5674,plain,
! [X0] :
( ~ sum(X0,b,b)
| sum(X0,c,c) ),
inference(resolution,[status(thm)],[f5654,f35]) ).
fof(f6588,plain,
( ~ sQ91_spl
| ~ sQ89_spl
| sum(b,c,c) ),
inference(resolution,[status(thm)],[f5674,f5112]) ).
fof(f6603,plain,
( ~ sQ91_spl
| ~ sQ89_spl
| sum(b,additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f6588,f654]) ).
fof(f7020,plain,
( ~ sQ91_spl
| ~ sQ89_spl
| sum(additive_identity,b,additive_identity) ),
inference(resolution,[status(thm)],[f6603,f40]) ).
fof(f7035,plain,
( ~ sQ91_spl
| ~ sQ89_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f7020,f527,f524,f531]) ).
fof(f7036,plain,
$false,
inference(sat_refutation,[status(thm)],[f530,f537,f591,f593,f616,f636,f777,f1172,f1323,f1761,f1795,f2329,f3165,f7035]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD041-4 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n009.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 15:40:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 7.14/1.40 % Refutation found
% 7.14/1.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 7.14/1.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.71/1.44 % Elapsed time: 1.061209 seconds
% 7.71/1.44 % CPU time: 7.985344 seconds
% 7.71/1.44 % Total memory used: 66.998 MB
% 7.71/1.44 % Net memory used: 61.197 MB
%------------------------------------------------------------------------------