%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD027-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 0.18s 5.94s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 37
% Syntax : Number of formulae : 142 ( 46 unt; 18 def)
% Number of atoms : 280 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 244 ( 106 ~; 120 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 23 ( 22 usr; 19 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 98 ( 98 !; 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( ~ defined(X)
| sum(additive_identity,X,X) ),
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(f13,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| defined(add(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
~ sum(additive_identity,additive_identity,multiplicative_identity),
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,
~ sum(additive_identity,b,additive_identity),
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(f32,negated_conjecture,
~ product(multiplicative_identity,a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,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(f34,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)],[f33]) ).
fof(f37,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f40,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(f41,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)],[f40]) ).
fof(f42,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(f43,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)],[f42]) ).
fof(f44,plain,
! [X0] :
( ~ defined(X0)
| product(multiplicative_identity,X0,X0) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f45,plain,
! [X0] :
( ~ defined(X0)
| sum(additive_identity,X0,additive_identity)
| product(multiplicative_inverse(X0),X0,multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ product(X1,X0,X2)
| product(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f51,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| defined(add(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f52,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(add(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f53,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f57,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f66,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f67,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f71,plain,
~ sum(additive_identity,additive_identity,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f72,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f73,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f74,plain,
~ sum(additive_identity,a,additive_identity),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f75,plain,
~ sum(additive_identity,b,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f76,plain,
product(multiplicative_identity,multiplicative_inverse(a),multiplicative_inverse(b)),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f77,plain,
~ product(multiplicative_identity,a,b),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f78,plain,
product(multiplicative_inverse(a),multiplicative_identity,multiplicative_inverse(b)),
inference(resolution,[status(thm)],[f46,f76]) ).
fof(f84,plain,
sum(additive_identity,additive_identity,additive_identity),
inference(resolution,[status(thm)],[f37,f53]) ).
fof(f86,plain,
defined(additive_inverse(additive_identity)),
inference(resolution,[status(thm)],[f54,f53]) ).
fof(f95,plain,
defined(additive_inverse(multiplicative_identity)),
inference(resolution,[status(thm)],[f57,f54]) ).
fof(f97,plain,
sum(additive_identity,multiplicative_identity,multiplicative_identity),
inference(resolution,[status(thm)],[f57,f37]) ).
fof(f102,plain,
defined(additive_inverse(a)),
inference(resolution,[status(thm)],[f72,f54]) ).
fof(f103,plain,
product(multiplicative_identity,a,a),
inference(resolution,[status(thm)],[f72,f44]) ).
fof(f109,plain,
defined(additive_inverse(b)),
inference(resolution,[status(thm)],[f73,f54]) ).
fof(f110,plain,
product(multiplicative_identity,b,b),
inference(resolution,[status(thm)],[f73,f44]) ).
fof(f122,plain,
! [X0] :
( ~ defined(X0)
| defined(add(X0,additive_inverse(multiplicative_identity))) ),
inference(resolution,[status(thm)],[f95,f52]) ).
fof(f129,plain,
! [X0] :
( ~ defined(X0)
| defined(add(X0,additive_inverse(a))) ),
inference(resolution,[status(thm)],[f102,f52]) ).
fof(f184,plain,
( sum(additive_identity,b,additive_identity)
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(resolution,[status(thm)],[f45,f73]) ).
fof(f185,plain,
( sum(additive_identity,a,additive_identity)
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f45,f72]) ).
fof(f216,definition,
( sQ11_spl
<=> product(multiplicative_inverse(b),b,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f217,plain,
( ~ sQ11_spl
| product(multiplicative_inverse(b),b,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f216]) ).
fof(f219,definition,
( sQ12_spl
<=> sum(additive_identity,b,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f220,plain,
( ~ sQ12_spl
| sum(additive_identity,b,additive_identity) ),
inference(component_clause,[status(thm)],[f219]) ).
fof(f222,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f184,f216,f219]) ).
fof(f223,definition,
( sQ13_spl
<=> product(multiplicative_inverse(a),a,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ13_spl
| product(multiplicative_inverse(a),a,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,definition,
( sQ14_spl
<=> sum(additive_identity,a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( ~ sQ14_spl
| sum(additive_identity,a,additive_identity) ),
inference(component_clause,[status(thm)],[f226]) ).
fof(f229,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f185,f223,f226]) ).
fof(f233,definition,
( sQ16_spl
<=> sum(additive_identity,multiplicative_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( ~ sQ16_spl
| sum(additive_identity,multiplicative_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f284,plain,
( ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f74]) ).
fof(f285,plain,
~ sQ14_spl,
inference(contradiction_clause,[status(thm)],[f284]) ).
fof(f286,plain,
( ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f220,f75]) ).
fof(f287,plain,
~ sQ12_spl,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f318,definition,
( sQ29_spl
<=> defined(additive_inverse(additive_identity)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( sQ29_spl
| ~ defined(additive_inverse(additive_identity)) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f427,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(b,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f67,f73]) ).
fof(f428,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(a,X0)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f67,f72]) ).
fof(f429,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(multiplicative_identity,X0)
| less_or_equal(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f67,f57]) ).
fof(f430,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f67,f53]) ).
fof(f491,plain,
! [X0,X1,X2] :
( ~ sum(X2,multiplicative_identity,X1)
| ~ sum(X0,X2,additive_identity)
| sum(X0,X1,multiplicative_identity) ),
inference(resolution,[status(thm)],[f97,f34]) ).
fof(f495,definition,
( sQ37_spl
<=> defined(multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f497,plain,
( sQ37_spl
| ~ defined(multiplicative_identity) ),
inference(component_clause,[status(thm)],[f495]) ).
fof(f502,plain,
( sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f497,f57]) ).
fof(f503,plain,
sQ37_spl,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f525,definition,
( sQ42_spl
<=> defined(additive_inverse(multiplicative_identity)) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ42_spl
| ~ defined(additive_inverse(multiplicative_identity)) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f539,plain,
! [X0,X1,X2] :
( ~ product(X2,a,X1)
| ~ product(X2,multiplicative_identity,X0)
| product(X0,a,X1) ),
inference(resolution,[status(thm)],[f103,f43]) ).
fof(f594,definition,
( sQ44_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ44_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f601,plain,
( sQ44_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f72]) ).
fof(f602,plain,
sQ44_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f634,definition,
( sQ49_spl
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ49_spl
| ~ defined(additive_inverse(a)) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f650,plain,
! [X0,X1,X2] :
( ~ product(X2,b,X1)
| ~ product(X0,X2,multiplicative_identity)
| product(X0,X1,b) ),
inference(resolution,[status(thm)],[f110,f41]) ).
fof(f693,definition,
( sQ51_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( sQ51_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f700,plain,
( sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f695,f73]) ).
fof(f701,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f700]) ).
fof(f723,definition,
( sQ56_spl
<=> defined(additive_inverse(b)) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f725,plain,
( sQ56_spl
| ~ defined(additive_inverse(b)) ),
inference(component_clause,[status(thm)],[f723]) ).
fof(f903,plain,
! [X0] :
( ~ sQ16_spl
| ~ sum(X0,additive_identity,additive_identity)
| sum(X0,additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f234,f491]) ).
fof(f1002,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f320,f86]) ).
fof(f1003,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f1002]) ).
fof(f1163,plain,
! [X0] :
( ~ sQ13_spl
| ~ product(multiplicative_inverse(a),multiplicative_identity,X0)
| product(X0,a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f224,f539]) ).
fof(f1177,plain,
( ~ sQ13_spl
| product(multiplicative_inverse(b),a,multiplicative_identity) ),
inference(resolution,[status(thm)],[f1163,f78]) ).
fof(f1194,plain,
( ~ sQ13_spl
| product(a,multiplicative_inverse(b),multiplicative_identity) ),
inference(resolution,[status(thm)],[f1177,f46]) ).
fof(f1203,plain,
! [X0] :
( ~ sQ11_spl
| ~ product(X0,multiplicative_inverse(b),multiplicative_identity)
| product(X0,multiplicative_identity,b) ),
inference(resolution,[status(thm)],[f217,f650]) ).
fof(f1233,plain,
( less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(resolution,[status(thm)],[f427,f73]) ).
fof(f1314,definition,
( sQ116_spl
<=> less_or_equal(b,b) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1317,plain,
sQ116_spl,
inference(split_clause,[status(thm)],[f1233,f1314]) ).
fof(f1364,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[status(thm)],[f428,f72]) ).
fof(f1445,definition,
( sQ145_spl
<=> less_or_equal(a,a) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1448,plain,
sQ145_spl,
inference(split_clause,[status(thm)],[f1364,f1445]) ).
fof(f1476,plain,
( less_or_equal(multiplicative_identity,multiplicative_identity)
| less_or_equal(multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f429,f57]) ).
fof(f1557,definition,
( sQ172_spl
<=> less_or_equal(multiplicative_identity,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1560,plain,
sQ172_spl,
inference(split_clause,[status(thm)],[f1476,f1557]) ).
fof(f1582,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f430,f53]) ).
fof(f1663,definition,
( sQ197_spl
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f1666,plain,
sQ197_spl,
inference(split_clause,[status(thm)],[f1582,f1663]) ).
fof(f1760,plain,
( sQ56_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f725,f109]) ).
fof(f1761,plain,
sQ56_spl,
inference(contradiction_clause,[status(thm)],[f1760]) ).
fof(f1769,plain,
( ~ sQ16_spl
| sum(additive_identity,additive_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f903,f84]) ).
fof(f1774,plain,
( ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1769,f71]) ).
fof(f1775,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f1774]) ).
fof(f1841,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| product(a,multiplicative_identity,b) ),
inference(resolution,[status(thm)],[f1194,f1203]) ).
fof(f2109,definition,
( sQ227_spl
<=> defined(add(b,additive_inverse(multiplicative_identity))) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2111,plain,
( sQ227_spl
| ~ defined(add(b,additive_inverse(multiplicative_identity))) ),
inference(component_clause,[status(thm)],[f2109]) ).
fof(f2144,plain,
( sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f527,f95]) ).
fof(f2145,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f2144]) ).
fof(f2204,plain,
defined(add(b,additive_inverse(multiplicative_identity))),
inference(resolution,[status(thm)],[f122,f73]) ).
fof(f2208,plain,
( sQ227_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2204,f2111]) ).
fof(f2209,plain,
sQ227_spl,
inference(contradiction_clause,[status(thm)],[f2208]) ).
fof(f2399,definition,
( sQ256_spl
<=> defined(add(b,additive_inverse(a))) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f2401,plain,
( sQ256_spl
| ~ defined(add(b,additive_inverse(a))) ),
inference(component_clause,[status(thm)],[f2399]) ).
fof(f2434,plain,
( sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f636,f102]) ).
fof(f2435,plain,
sQ49_spl,
inference(contradiction_clause,[status(thm)],[f2434]) ).
fof(f2463,plain,
defined(add(b,additive_inverse(a))),
inference(resolution,[status(thm)],[f129,f73]) ).
fof(f2467,plain,
( sQ256_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2463,f2401]) ).
fof(f2468,plain,
sQ256_spl,
inference(contradiction_clause,[status(thm)],[f2467]) ).
fof(f2491,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| product(multiplicative_identity,a,b) ),
inference(resolution,[status(thm)],[f1841,f46]) ).
fof(f2492,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2491,f77]) ).
fof(f2493,plain,
( ~ sQ11_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f2492]) ).
fof(f2494,plain,
$false,
inference(sat_refutation,[status(thm)],[f222,f229,f285,f287,f503,f602,f701,f1003,f1317,f1448,f1560,f1666,f1761,f1775,f2145,f2209,f2435,f2468,f2493]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD027-3 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/5.41 % Computer : n017.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Mon Sep 21 15:34:18 UTC 2026
% 0.15/5.42 % CPUTime :
% 0.15/5.43 % Drodi V4.1.1
% 0.18/5.94 % Refutation found
% 0.18/5.94 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.18/5.94 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/5.97 % Elapsed time: 0.530591 seconds
% 0.18/5.97 % CPU time: 3.950335 seconds
% 0.18/5.97 % Total memory used: 45.189 MB
% 0.18/5.97 % Net memory used: 42.265 MB
%------------------------------------------------------------------------------