%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD037-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : 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 12:21:59 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.49s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 27
% Syntax : Number of formulae : 92 ( 21 unt; 11 def)
% Number of atoms : 206 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 209 ( 95 ~; 103 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 58 ( 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(f11,axiom,
defined(additive_identity),
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(f16,axiom,
! [X,Y] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| equalish(X,Y) ),
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(f21,axiom,
! [X] :
( ~ defined(X)
| equalish(X,X) ),
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(f26,axiom,
! [Y,Z,X] :
( ~ equalish(X,Y)
| ~ less_or_equal(X,Z)
| less_or_equal(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(a,additive_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| equalish(multiply(X0,multiplicative_inverse(X0)),multiplicative_identity) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f49,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f53,plain,
defined(multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f54,plain,
! [X0] :
( equalish(X0,additive_identity)
| ~ defined(X0)
| defined(multiplicative_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f55,plain,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f58,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f59,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f64,plain,
! [X0] :
( ~ defined(X0)
| equalish(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f65,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f66,plain,
! [Z,Y] :
( ~ equalish(Y,Z)
| ! [X] :
( ~ equalish(X,Y)
| equalish(X,Z) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X1)
| ~ equalish(X0,X2)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f70,plain,
! [X,Y] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ defined(Z)
| equalish(multiply(X,Z),multiply(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(multiply(X0,X1),multiply(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
! [Y,X] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f75,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f76,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f77,plain,
~ equalish(a,additive_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f78,plain,
equalish(a,b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f79,plain,
~ equalish(multiplicative_identity,multiply(b,multiplicative_inverse(a))),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f86,plain,
~ equalish(multiply(b,multiplicative_inverse(a)),multiplicative_identity),
inference(resolution,[status(thm)],[f65,f79]) ).
fof(f93,plain,
! [X0] :
( ~ equalish(X0,multiplicative_identity)
| ~ equalish(multiply(b,multiplicative_inverse(a)),X0) ),
inference(resolution,[status(thm)],[f67,f86]) ).
fof(f98,plain,
! [X0] :
( ~ equalish(X0,additive_identity)
| ~ equalish(a,X0) ),
inference(resolution,[status(thm)],[f67,f77]) ).
fof(f140,plain,
( ~ defined(a)
| ~ equalish(a,additive_identity) ),
inference(resolution,[status(thm)],[f98,f64]) ).
fof(f141,definition,
( sQ6_spl
<=> equalish(a,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f144,definition,
( sQ7_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f146,plain,
( sQ7_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f144]) ).
fof(f147,plain,
( ~ sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f140,f141,f144]) ).
fof(f162,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f146,f75]) ).
fof(f163,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f162]) ).
fof(f221,definition,
( sQ15_spl
<=> defined(multiplicative_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f223,plain,
( sQ15_spl
| ~ defined(multiplicative_inverse(a)) ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f244,plain,
! [X0] :
( ~ equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)
| ~ equalish(b,X0)
| ~ defined(multiplicative_inverse(a)) ),
inference(resolution,[status(thm)],[f71,f93]) ).
fof(f245,definition,
! [X0] :
( sQ18_spl
<=> ( ~ equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)
| ~ equalish(b,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f246,plain,
! [X0] :
( ~ sQ18_spl
| ~ equalish(multiply(X0,multiplicative_inverse(a)),multiplicative_identity)
| ~ equalish(b,X0) ),
inference(component_clause,[status(thm)],[f245]) ).
fof(f248,plain,
( sQ18_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f244,f221,f245]) ).
fof(f249,plain,
( sQ15_spl
| equalish(a,additive_identity)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f223,f54]) ).
fof(f250,plain,
( sQ15_spl
| sQ6_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f249,f144,f141,f221]) ).
fof(f265,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(b,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f59,f76]) ).
fof(f266,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(a,X0)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f59,f75]) ).
fof(f267,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(multiplicative_identity,X0)
| less_or_equal(X0,multiplicative_identity) ),
inference(resolution,[status(thm)],[f59,f53]) ).
fof(f268,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f59,f49]) ).
fof(f309,plain,
( less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(resolution,[status(thm)],[f265,f76]) ).
fof(f320,definition,
( sQ26_spl
<=> less_or_equal(b,b) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f321,plain,
( ~ sQ26_spl
| less_or_equal(b,b) ),
inference(component_clause,[status(thm)],[f320]) ).
fof(f323,plain,
sQ26_spl,
inference(split_clause,[status(thm)],[f309,f320]) ).
fof(f324,definition,
( sQ27_spl
<=> less_or_equal(a,b) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f325,plain,
( ~ sQ27_spl
| less_or_equal(a,b) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f326,plain,
( sQ27_spl
| ~ less_or_equal(a,b) ),
inference(component_clause,[status(thm)],[f324]) ).
fof(f327,definition,
( sQ28_spl
<=> less_or_equal(b,a) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f329,plain,
( sQ28_spl
| ~ less_or_equal(b,a) ),
inference(component_clause,[status(thm)],[f327]) ).
fof(f346,plain,
! [X0] :
( ~ sQ26_spl
| ~ equalish(b,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f321,f73]) ).
fof(f370,plain,
( ~ sQ27_spl
| ~ less_or_equal(b,a)
| equalish(b,a) ),
inference(resolution,[status(thm)],[f325,f55]) ).
fof(f371,definition,
( sQ35_spl
<=> equalish(b,a) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f374,plain,
( ~ sQ27_spl
| ~ sQ28_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f370,f371,f327,f324]) ).
fof(f512,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[status(thm)],[f266,f75]) ).
fof(f523,definition,
( sQ48_spl
<=> less_or_equal(a,a) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( ~ sQ48_spl
| less_or_equal(a,a) ),
inference(component_clause,[status(thm)],[f523]) ).
fof(f526,plain,
sQ48_spl,
inference(split_clause,[status(thm)],[f512,f523]) ).
fof(f548,plain,
( less_or_equal(multiplicative_identity,multiplicative_identity)
| less_or_equal(multiplicative_identity,multiplicative_identity) ),
inference(resolution,[status(thm)],[f267,f53]) ).
fof(f559,definition,
( sQ55_spl
<=> less_or_equal(multiplicative_identity,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f562,plain,
sQ55_spl,
inference(split_clause,[status(thm)],[f548,f559]) ).
fof(f578,plain,
! [X0] :
( ~ sQ48_spl
| ~ equalish(a,X0)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f524,f73]) ).
fof(f667,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f268,f49]) ).
fof(f678,definition,
( sQ63_spl
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f681,plain,
sQ63_spl,
inference(split_clause,[status(thm)],[f667,f678]) ).
fof(f880,plain,
( ~ sQ26_spl
| sQ27_spl
| ~ equalish(b,a) ),
inference(resolution,[status(thm)],[f326,f346]) ).
fof(f1021,plain,
( ~ sQ26_spl
| sQ27_spl
| ~ equalish(a,b) ),
inference(resolution,[status(thm)],[f880,f65]) ).
fof(f1022,plain,
( ~ sQ26_spl
| sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1021,f78]) ).
fof(f1023,plain,
( ~ sQ26_spl
| sQ27_spl ),
inference(contradiction_clause,[status(thm)],[f1022]) ).
fof(f1040,plain,
( ~ sQ48_spl
| sQ28_spl
| ~ equalish(a,b) ),
inference(resolution,[status(thm)],[f329,f578]) ).
fof(f1041,plain,
( ~ sQ48_spl
| sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1040,f78]) ).
fof(f1042,plain,
( ~ sQ48_spl
| sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f1041]) ).
fof(f1232,plain,
( ~ sQ18_spl
| equalish(a,additive_identity)
| ~ defined(a)
| ~ equalish(b,a) ),
inference(resolution,[status(thm)],[f246,f42]) ).
fof(f1235,plain,
( ~ sQ18_spl
| sQ6_spl
| ~ sQ7_spl
| ~ sQ35_spl ),
inference(split_clause,[status(thm)],[f1232,f371,f144,f141,f245]) ).
fof(f1236,plain,
$false,
inference(sat_refutation,[status(thm)],[f147,f163,f248,f250,f323,f374,f526,f562,f681,f1023,f1042,f1235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD037-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/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 15:39:35 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.49 % Refutation found
% 0.14/0.49 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.52 % Elapsed time: 0.142478 seconds
% 0.14/0.52 % CPU time: 0.944568 seconds
% 0.14/0.52 % Total memory used: 32.483 MB
% 0.14/0.52 % Net memory used: 30.625 MB
%------------------------------------------------------------------------------