%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD069-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 12:22:08 PM UTC 2026
% Result : Unsatisfiable 1.50s 0.76s
% Output : CNFRefutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 21
% Syntax : Number of formulae : 75 ( 18 unt; 8 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 181 ( 86 ~; 87 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 56 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X] :
( ~ defined(X)
| equalish(add(additive_identity,X),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( ~ less_or_equal(Y,X)
| ~ less_or_equal(X,Y)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Z,Y] :
( ~ less_or_equal(Y,Z)
| ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Z,Y] :
( ~ less_or_equal(X,Y)
| ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [X,Y] :
( ~ equalish(Y,X)
| equalish(X,Y) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
defined(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
less_or_equal(additive_identity,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
less_or_equal(additive_identity,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ equalish(b,additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
equalish(add(a,b),additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(additive_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f50,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f56,plain,
! [X0,X1] :
( ~ less_or_equal(X1,X0)
| ~ less_or_equal(X0,X1)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f57,plain,
! [Z,Y] :
( ~ less_or_equal(Y,Z)
| ! [X] :
( ~ less_or_equal(X,Y)
| less_or_equal(X,Z) ) ),
inference(miniscoping,[status(thm)],[f17]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X2,X1)
| ~ less_or_equal(X0,X2)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f59,plain,
! [Y] :
( ~ defined(Y)
| ! [X] :
( ~ defined(X)
| less_or_equal(Y,X)
| less_or_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f60,plain,
! [X0,X1] :
( ~ defined(X1)
| ~ defined(X0)
| less_or_equal(X1,X0)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f61,plain,
! [X,Y] :
( ~ less_or_equal(X,Y)
| ! [Z] :
( ~ defined(Z)
| less_or_equal(add(X,Z),add(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ less_or_equal(X0,X2)
| ~ defined(X1)
| less_or_equal(add(X0,X1),add(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f66,plain,
! [X0,X1] :
( ~ equalish(X1,X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f73,plain,
! [Y,X] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f77,plain,
defined(b),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f78,plain,
less_or_equal(additive_identity,a),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f79,plain,
less_or_equal(additive_identity,b),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f80,plain,
~ equalish(b,additive_identity),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f81,plain,
equalish(add(a,b),additive_identity),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f82,plain,
~ equalish(additive_identity,b),
inference(resolution,[status(thm)],[f66,f80]) ).
fof(f84,plain,
( ~ less_or_equal(b,additive_identity)
| ~ less_or_equal(additive_identity,b) ),
inference(resolution,[status(thm)],[f56,f82]) ).
fof(f86,definition,
( sQ0_spl
<=> less_or_equal(additive_identity,b) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f88,plain,
( sQ0_spl
| ~ less_or_equal(additive_identity,b) ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,definition,
( sQ1_spl
<=> less_or_equal(b,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( sQ1_spl
| ~ less_or_equal(b,additive_identity) ),
inference(component_clause,[status(thm)],[f89]) ).
fof(f92,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f84,f86,f89]) ).
fof(f94,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f88,f79]) ).
fof(f95,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f107,definition,
( sQ3_spl
<=> defined(additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f109,plain,
( sQ3_spl
| ~ defined(additive_identity) ),
inference(component_clause,[status(thm)],[f107]) ).
fof(f118,definition,
( sQ5_spl
<=> defined(b) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f120,plain,
( sQ5_spl
| ~ defined(b) ),
inference(component_clause,[status(thm)],[f118]) ).
fof(f132,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f77]) ).
fof(f133,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f132]) ).
fof(f137,definition,
( sQ7_spl
<=> less_or_equal(add(additive_identity,b),additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f139,plain,
( sQ7_spl
| ~ less_or_equal(add(additive_identity,b),additive_identity) ),
inference(component_clause,[status(thm)],[f137]) ).
fof(f148,plain,
! [X0] :
( sQ7_spl
| ~ less_or_equal(X0,additive_identity)
| ~ less_or_equal(add(additive_identity,b),X0) ),
inference(resolution,[status(thm)],[f139,f58]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( ~ less_or_equal(X3,X1)
| ~ less_or_equal(X2,X3)
| ~ equalish(X2,X0)
| less_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[f74,f58]) ).
fof(f175,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f109,f50]) ).
fof(f176,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f175]) ).
fof(f188,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f60,f50]) ).
fof(f197,definition,
( sQ14_spl
<=> less_or_equal(additive_identity,a) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f199,plain,
( sQ14_spl
| ~ less_or_equal(additive_identity,a) ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f206,definition,
( sQ16_spl
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f207,plain,
( ~ sQ16_spl
| less_or_equal(additive_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f208,plain,
( sQ16_spl
| ~ less_or_equal(additive_identity,additive_identity) ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f214,plain,
! [X0] :
( ~ sQ16_spl
| ~ equalish(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f207,f74]) ).
fof(f217,plain,
! [X0] :
( ~ sQ16_spl
| ~ equalish(X0,additive_identity)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f214,f66]) ).
fof(f412,plain,
! [X0,X1] :
( sQ1_spl
| ~ less_or_equal(X1,additive_identity)
| ~ less_or_equal(X0,X1)
| ~ equalish(X0,b) ),
inference(resolution,[status(thm)],[f151,f91]) ).
fof(f617,plain,
( sQ16_spl
| ~ defined(additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f208,f188]) ).
fof(f620,plain,
( ~ sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f617,f206,f107]) ).
fof(f658,plain,
( ~ sQ16_spl
| less_or_equal(add(a,b),additive_identity) ),
inference(resolution,[status(thm)],[f217,f81]) ).
fof(f766,plain,
! [X0] :
( sQ1_spl
| ~ defined(b)
| ~ less_or_equal(X0,additive_identity)
| ~ less_or_equal(add(additive_identity,b),X0) ),
inference(resolution,[status(thm)],[f412,f36]) ).
fof(f775,definition,
! [X0] :
( sQ76_spl
<=> ( ~ less_or_equal(X0,additive_identity)
| ~ less_or_equal(add(additive_identity,b),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f776,plain,
! [X0] :
( ~ sQ76_spl
| ~ less_or_equal(X0,additive_identity)
| ~ less_or_equal(add(additive_identity,b),X0) ),
inference(component_clause,[status(thm)],[f775]) ).
fof(f778,plain,
( sQ1_spl
| ~ sQ5_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f766,f775,f118,f89]) ).
fof(f781,plain,
( ~ sQ16_spl
| sQ7_spl
| ~ less_or_equal(add(additive_identity,b),add(a,b)) ),
inference(resolution,[status(thm)],[f148,f658]) ).
fof(f794,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f199,f78]) ).
fof(f795,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f794]) ).
fof(f1330,plain,
( ~ sQ16_spl
| ~ sQ76_spl
| ~ less_or_equal(add(additive_identity,b),additive_identity) ),
inference(resolution,[status(thm)],[f776,f207]) ).
fof(f1685,plain,
( ~ sQ16_spl
| sQ7_spl
| ~ less_or_equal(additive_identity,a)
| ~ defined(b) ),
inference(resolution,[status(thm)],[f781,f62]) ).
fof(f1692,plain,
( ~ sQ16_spl
| sQ7_spl
| ~ sQ14_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1685,f118,f197,f137,f206]) ).
fof(f1709,plain,
( ~ sQ16_spl
| ~ sQ76_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f1330,f137,f775,f206]) ).
fof(f1710,plain,
$false,
inference(sat_refutation,[status(thm)],[f92,f95,f133,f176,f620,f778,f795,f1692,f1709]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD069-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n019.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 15:45:04 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 1.50/0.76 % Refutation found
% 1.50/0.76 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 1.50/0.76 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.01/0.79 % Elapsed time: 0.403682 seconds
% 1.01/0.79 % CPU time: 2.924854 seconds
% 1.01/0.79 % Total memory used: 59.202 MB
% 1.01/0.79 % Net memory used: 54.745 MB
%------------------------------------------------------------------------------