%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD067-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:22:07 PM UTC 2026
% Result : Unsatisfiable 0.08s 0.40s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 19
% Syntax : Number of formulae : 61 ( 16 unt; 8 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 122 ( 55 ~; 59 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 41 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
defined(additive_identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(X)) ),
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(f21,axiom,
! [X] :
( ~ defined(X)
| equalish(X,X) ),
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(f28,hypothesis,
defined(a),
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(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,plain,
! [X0] :
( ~ defined(X0)
| equalish(add(X0,additive_inverse(X0)),additive_identity) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f48,plain,
defined(additive_identity),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f49,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
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(f59,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(f60,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)],[f59]) ).
fof(f63,plain,
! [X0] :
( ~ defined(X0)
| equalish(X0,X0) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f71,plain,
! [Y,X] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ less_or_equal(X,Z)
| less_or_equal(Y,Z) ) ),
inference(miniscoping,[status(thm)],[f26]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ~ equalish(X2,X0)
| ~ less_or_equal(X2,X1)
| less_or_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
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,
less_or_equal(a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
~ less_or_equal(additive_identity,add(b,additive_inverse(a))),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f89,plain,
! [X0] :
( ~ equalish(a,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f72,f76]) ).
fof(f91,plain,
( ~ defined(a)
| less_or_equal(a,b) ),
inference(resolution,[status(thm)],[f89,f63]) ).
fof(f92,definition,
( sQ2_spl
<=> less_or_equal(a,b) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f95,definition,
( sQ3_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f97,plain,
( sQ3_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f95]) ).
fof(f98,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f91,f92,f95]) ).
fof(f106,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(b,X0)
| less_or_equal(X0,b) ),
inference(resolution,[status(thm)],[f58,f75]) ).
fof(f107,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(a,X0)
| less_or_equal(X0,a) ),
inference(resolution,[status(thm)],[f58,f74]) ).
fof(f108,plain,
! [X0] :
( ~ defined(X0)
| less_or_equal(additive_identity,X0)
| less_or_equal(X0,additive_identity) ),
inference(resolution,[status(thm)],[f58,f48]) ).
fof(f171,plain,
! [X0,X1,X2,X3] :
( ~ equalish(add(X1,X0),X3)
| less_or_equal(X3,add(X2,X0))
| ~ less_or_equal(X1,X2)
| ~ defined(X0) ),
inference(resolution,[status(thm)],[f60,f72]) ).
fof(f193,definition,
( sQ18_spl
<=> defined(additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ18_spl
| ~ defined(additive_identity) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f234,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f97,f74]) ).
fof(f235,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f234]) ).
fof(f321,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f48]) ).
fof(f322,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f321]) ).
fof(f419,plain,
( less_or_equal(b,b)
| less_or_equal(b,b) ),
inference(resolution,[status(thm)],[f106,f75]) ).
fof(f423,definition,
( sQ33_spl
<=> less_or_equal(b,b) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f426,plain,
sQ33_spl,
inference(split_clause,[status(thm)],[f419,f423]) ).
fof(f441,plain,
( less_or_equal(a,a)
| less_or_equal(a,a) ),
inference(resolution,[status(thm)],[f107,f74]) ).
fof(f445,definition,
( sQ36_spl
<=> less_or_equal(a,a) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f448,plain,
sQ36_spl,
inference(split_clause,[status(thm)],[f441,f445]) ).
fof(f492,plain,
( less_or_equal(additive_identity,additive_identity)
| less_or_equal(additive_identity,additive_identity) ),
inference(resolution,[status(thm)],[f108,f48]) ).
fof(f496,definition,
( sQ40_spl
<=> less_or_equal(additive_identity,additive_identity) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f499,plain,
sQ40_spl,
inference(split_clause,[status(thm)],[f492,f496]) ).
fof(f501,plain,
! [X0] :
( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ less_or_equal(X0,b)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[f171,f77]) ).
fof(f506,definition,
( sQ41_spl
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ41_spl
| ~ defined(additive_inverse(a)) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
! [X0] :
( sQ42_spl
<=> ( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ less_or_equal(X0,b) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f510,plain,
! [X0] :
( ~ sQ42_spl
| ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ less_or_equal(X0,b) ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( sQ42_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f501,f506,f509]) ).
fof(f517,plain,
( sQ41_spl
| ~ defined(a) ),
inference(resolution,[status(thm)],[f508,f49]) ).
fof(f518,plain,
( sQ41_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f517,f95,f506]) ).
fof(f568,plain,
( ~ sQ42_spl
| ~ defined(a)
| ~ less_or_equal(a,b) ),
inference(resolution,[status(thm)],[f510,f35]) ).
fof(f571,plain,
( ~ sQ42_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f568,f92,f95,f509]) ).
fof(f572,plain,
$false,
inference(sat_refutation,[status(thm)],[f98,f235,f322,f426,f448,f499,f512,f518,f571]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD067-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n018.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 15:46:15 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.052053 seconds
% 0.13/0.42 % CPU time: 0.182260 seconds
% 0.13/0.42 % Total memory used: 18.570 MB
% 0.13/0.42 % Net memory used: 18.267 MB
%------------------------------------------------------------------------------