%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD004-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 12:21:50 PM UTC 2026
% Result : Unsatisfiable 54.89s 7.33s
% Output : CNFRefutation 54.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 30
% Syntax : Number of formulae : 107 ( 22 unt; 14 def)
% Number of atoms : 257 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 277 ( 127 ~; 136 |; 0 &)
% ( 14 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 90 ( 90 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( equalish(X,additive_identity)
| ~ defined(X)
| equalish(multiply(X,multiplicative_inverse(X)),multiplicative_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| equalish(multiply(X,Y),multiply(Y,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y] :
( ~ defined(Y)
| ~ defined(X)
| defined(multiply(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
defined(multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X] :
( equalish(X,additive_identity)
| ~ defined(X)
| defined(multiplicative_inverse(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,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(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [X,Z,Y] :
( ~ equalish(Y,Z)
| ~ equalish(X,Y)
| equalish(X,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f40,plain,
! [X0] :
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f41,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| equalish(multiply(X,Y),multiply(Y,X)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f43,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| equalish(multiply(X0,X1),multiply(X1,X0)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f48,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f50,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| defined(multiply(X,Y)) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f51,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| defined(multiply(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f52,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f53,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f57,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f58,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f64,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f65,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
fof(f69,plain,
! [X,Y] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f74,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f75,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f76,plain,
~ equalish(b,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),a),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f86,plain,
! [X0,X1] :
( ~ equalish(X1,multiply(X0,multiplicative_inverse(X0)))
| equalish(X1,multiplicative_identity)
| equalish(X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f41,f66]) ).
fof(f89,plain,
! [X0,X1] :
( ~ equalish(X1,multiply(multiplicative_identity,X0))
| equalish(X1,X0)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f40,f66]) ).
fof(f95,plain,
! [X0] :
( ~ equalish(X0,multiply(multiplicative_identity,a))
| equalish(X0,a) ),
inference(resolution,[status(thm)],[f89,f74]) ).
fof(f110,plain,
! [X0,X1] :
( ~ equalish(X1,add(X0,additive_inverse(X0)))
| equalish(X1,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f35,f66]) ).
fof(f111,plain,
! [X0] :
( equalish(additive_identity,add(X0,additive_inverse(X0)))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f35,f64]) ).
fof(f118,definition,
( sQ1_spl
<=> defined(additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ1_spl
| ~ defined(additive_identity) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f130,definition,
( sQ3_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f132,plain,
( sQ3_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f130]) ).
fof(f142,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f132,f75]) ).
fof(f143,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f142]) ).
fof(f151,definition,
( sQ7_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f153,plain,
( sQ7_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f163,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f153,f74]) ).
fof(f164,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f182,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f48]) ).
fof(f183,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f182]) ).
fof(f184,plain,
! [X0,X1,X2] :
( ~ equalish(X2,multiply(X0,X1))
| equalish(X2,multiply(X1,X0))
| ~ defined(X1)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f43,f66]) ).
fof(f346,plain,
! [X0,X1,X2] :
( equalish(multiply(X2,X0),multiply(X1,X0))
| ~ equalish(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f70,f64]) ).
fof(f449,plain,
! [X0,X1] :
( equalish(multiplicative_identity,X1)
| ~ equalish(X1,multiply(X0,multiplicative_inverse(X0)))
| equalish(X0,additive_identity)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f86,f64]) ).
fof(f530,definition,
( sQ45_spl
<=> defined(multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ45_spl
| ~ defined(multiplicative_identity) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f621,definition,
( sQ56_spl
<=> equalish(b,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f675,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| equalish(X2,additive_identity)
| ~ equalish(X1,add(X0,additive_inverse(X0)))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f110,f66]) ).
fof(f747,plain,
( sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f52]) ).
fof(f748,plain,
sQ45_spl,
inference(contradiction_clause,[status(thm)],[f747]) ).
fof(f845,plain,
! [X0,X1,X2,X3] :
( ~ equalish(X3,multiply(X2,X0))
| equalish(X3,multiply(X1,X0))
| ~ equalish(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f346,f66]) ).
fof(f939,definition,
( sQ93_spl
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1641,plain,
~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),multiply(multiplicative_identity,a)),
inference(resolution,[status(thm)],[f95,f77]) ).
fof(f2055,plain,
! [X0] :
( equalish(multiplicative_identity,X0)
| ~ equalish(X0,multiply(b,multiplicative_inverse(b)))
| ~ defined(b) ),
inference(resolution,[status(thm)],[f449,f76]) ).
fof(f2067,definition,
! [X0] :
( sQ199_spl
<=> ( equalish(multiplicative_identity,X0)
| ~ equalish(X0,multiply(b,multiplicative_inverse(b))) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2068,plain,
! [X0] :
( ~ sQ199_spl
| equalish(multiplicative_identity,X0)
| ~ equalish(X0,multiply(b,multiplicative_inverse(b))) ),
inference(component_clause,[status(thm)],[f2067]) ).
fof(f2070,plain,
( sQ199_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2055,f130,f2067]) ).
fof(f2121,plain,
! [X0] :
( ~ sQ199_spl
| ~ equalish(X0,multiply(multiplicative_inverse(b),b))
| ~ defined(b)
| ~ defined(multiplicative_inverse(b))
| equalish(multiplicative_identity,X0) ),
inference(resolution,[status(thm)],[f2068,f184]) ).
fof(f2134,definition,
( sQ210_spl
<=> defined(multiplicative_inverse(b)) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2158,definition,
! [X0] :
( sQ216_spl
<=> ( ~ equalish(X0,multiply(multiplicative_inverse(b),b))
| equalish(multiplicative_identity,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2159,plain,
! [X0] :
( ~ sQ216_spl
| ~ equalish(X0,multiply(multiplicative_inverse(b),b))
| equalish(multiplicative_identity,X0) ),
inference(component_clause,[status(thm)],[f2158]) ).
fof(f2161,plain,
( ~ sQ199_spl
| ~ sQ3_spl
| ~ sQ210_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f2121,f2158,f2134,f130,f2067]) ).
fof(f2162,definition,
( sQ217_spl
<=> equalish(multiplicative_identity,multiply(b,multiplicative_inverse(b))) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2544,plain,
! [X0,X1] :
( ~ equalish(b,X1)
| ~ equalish(X1,add(X0,additive_inverse(X0)))
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f675,f76]) ).
fof(f2633,plain,
! [X0] :
( ~ equalish(b,X0)
| ~ equalish(X0,add(b,additive_inverse(b))) ),
inference(resolution,[status(thm)],[f2544,f75]) ).
fof(f3001,plain,
! [X0] :
( ~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),multiply(X0,a))
| ~ equalish(multiplicative_identity,X0)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f845,f1641]) ).
fof(f3018,definition,
! [X0] :
( sQ277_spl
<=> ( ~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),multiply(X0,a))
| ~ equalish(multiplicative_identity,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3019,plain,
! [X0] :
( ~ sQ277_spl
| ~ equalish(multiply(a,multiply(b,multiplicative_inverse(b))),multiply(X0,a))
| ~ equalish(multiplicative_identity,X0) ),
inference(component_clause,[status(thm)],[f3018]) ).
fof(f3021,plain,
( sQ277_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f3001,f151,f3018]) ).
fof(f5006,plain,
( ~ sQ216_spl
| ~ defined(multiplicative_inverse(b))
| ~ defined(b)
| equalish(multiplicative_identity,multiply(b,multiplicative_inverse(b))) ),
inference(resolution,[status(thm)],[f2159,f43]) ).
fof(f5035,plain,
( ~ sQ216_spl
| ~ sQ210_spl
| ~ sQ3_spl
| sQ217_spl ),
inference(split_clause,[status(thm)],[f5006,f2162,f130,f2134,f2158]) ).
fof(f8008,plain,
( equalish(b,additive_identity)
| defined(multiplicative_inverse(b)) ),
inference(resolution,[status(thm)],[f53,f75]) ).
fof(f8061,plain,
( sQ56_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f8008,f2134,f621]) ).
fof(f8409,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(multiplicative_identity,X0)
| less_or_equal(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f58,f52]) ).
fof(f8411,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f58,f48]) ).
fof(f8412,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(a,X0)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f58,f74]) ).
fof(f8413,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(b,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f58,f75]) ).
fof(f8440,plain,
! [X0,X1,X2] :
( ~ defined(X2)
| ~ defined(X1)
| ~ defined(X0)
| equalish(multiply(X0,multiply(X1,X2)),multiply(multiply(X1,X2),X0)) ),
inference(resolution,[status(thm)],[f43,f51]) ).
fof(f9713,plain,
( ~ defined(b)
| ~ equalish(b,additive_identity) ),
inference(resolution,[status(thm)],[f2633,f111]) ).
fof(f9714,plain,
( ~ sQ3_spl
| ~ sQ56_spl ),
inference(split_clause,[status(thm)],[f9713,f621,f130]) ).
fof(f10045,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f8411,f48]) ).
fof(f10095,plain,
sQ93_spl,
inference(split_clause,[status(thm)],[f10045,f939]) ).
fof(f10471,plain,
( less_or_equal(multiplicative_identity,multiplicative_identity)
| less_or_equal(multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f8409,f52]) ).
fof(f10513,definition,
( sQ826_spl
<=> less_or_equal(multiplicative_identity,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ826_spl])],[split_symbol_definition]) ).
fof(f10516,plain,
sQ826_spl,
inference(split_clause,[status(thm)],[f10471,f10513]) ).
fof(f10559,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[status(thm)],[f8412,f74]) ).
fof(f10612,definition,
( sQ849_spl
<=> less_or_equal(a,a) ),
introduced(definition,[new_symbols(definition,[sQ849_spl])],[split_symbol_definition]) ).
fof(f10615,plain,
sQ849_spl,
inference(split_clause,[status(thm)],[f10559,f10612]) ).
fof(f10637,plain,
( less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(resolution,[status(thm)],[f8413,f75]) ).
fof(f10690,definition,
( sQ866_spl
<=> less_or_equal(b,b) ),
introduced(definition,[new_symbols(definition,[sQ866_spl])],[split_symbol_definition]) ).
fof(f10693,plain,
sQ866_spl,
inference(split_clause,[status(thm)],[f10637,f10690]) ).
fof(f12163,plain,
( ~ sQ277_spl
| ~ defined(multiplicative_inverse(b))
| ~ defined(b)
| ~ defined(a)
| ~ equalish(multiplicative_identity,multiply(b,multiplicative_inverse(b))) ),
inference(resolution,[status(thm)],[f3019,f8440]) ).
fof(f12169,plain,
( ~ sQ277_spl
| ~ sQ210_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f12163,f2162,f151,f130,f2134,f3018]) ).
fof(f12178,plain,
$false,
inference(sat_refutation,[status(thm)],[f143,f164,f183,f748,f2070,f2161,f3021,f5035,f8061,f9714,f10095,f10516,f10615,f10693,f12169]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : FLD004-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n014.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 21 15:36:19 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.35 % Drodi V4.1.1
% 54.89/7.33 % Refutation found
% 54.89/7.33 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 54.89/7.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.51/8.32 % Elapsed time: 7.962545 seconds
% 4.51/8.32 % CPU time: 56.437039 seconds
% 4.51/8.32 % Total memory used: 351.165 MB
% 4.51/8.32 % Net memory used: 297.132 MB
%------------------------------------------------------------------------------