%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD023-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 12:21:55 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 41 ( 11 unt; 4 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 84 ( 43 ~; 37 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X] :
( ~ defined(X)
| equalish(add(X,additive_inverse(X)),additive_identity) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] :
( ~ defined(X)
| defined(additive_inverse(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(f24,axiom,
! [X,Z,Y] :
( ~ equalish(X,Y)
| ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
defined(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
equalish(a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ equalish(additive_identity,add(b,additive_inverse(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(f49,plain,
! [X0] :
( ~ defined(X0)
| defined(additive_inverse(X0)) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
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(f67,plain,
! [X,Y] :
( ~ equalish(X,Y)
| ! [Z] :
( ~ defined(Z)
| equalish(add(X,Z),add(Y,Z)) ) ),
inference(miniscoping,[status(thm)],[f24]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X2)
| ~ defined(X1)
| equalish(add(X0,X1),add(X2,X1)) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f74,plain,
defined(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f76,plain,
equalish(a,b),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
~ equalish(additive_identity,add(b,additive_inverse(a))),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f78,plain,
~ equalish(add(b,additive_inverse(a)),additive_identity),
inference(resolution,[status(thm)],[f64,f77]) ).
fof(f84,plain,
! [X0] :
( ~ equalish(X0,additive_identity)
| ~ equalish(add(b,additive_inverse(a)),X0) ),
inference(resolution,[status(thm)],[f78,f66]) ).
fof(f106,definition,
( sQ4_spl
<=> defined(additive_inverse(a)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f108,plain,
( sQ4_spl
| ~ defined(additive_inverse(a)) ),
inference(component_clause,[status(thm)],[f106]) ).
fof(f126,plain,
( sQ4_spl
| ~ defined(a) ),
inference(resolution,[status(thm)],[f108,f49]) ).
fof(f127,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f74]) ).
fof(f128,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f163,plain,
! [X0] :
( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(b,X0)
| ~ defined(additive_inverse(a)) ),
inference(resolution,[status(thm)],[f68,f84]) ).
fof(f164,definition,
! [X0] :
( sQ13_spl
<=> ( ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(b,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f165,plain,
! [X0] :
( ~ sQ13_spl
| ~ equalish(add(X0,additive_inverse(a)),additive_identity)
| ~ equalish(b,X0) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( sQ13_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f163,f106,f164]) ).
fof(f204,plain,
( ~ sQ13_spl
| ~ defined(a)
| ~ equalish(b,a) ),
inference(resolution,[status(thm)],[f165,f35]) ).
fof(f207,definition,
( sQ16_spl
<=> equalish(b,a) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f209,plain,
( sQ16_spl
| ~ equalish(b,a) ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,definition,
( sQ17_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f212,plain,
( sQ17_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,plain,
( ~ sQ13_spl
| ~ sQ17_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f204,f207,f210,f164]) ).
fof(f234,plain,
( sQ16_spl
| ~ equalish(a,b) ),
inference(resolution,[status(thm)],[f209,f64]) ).
fof(f235,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f76]) ).
fof(f236,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f235]) ).
fof(f237,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f212,f74]) ).
fof(f238,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f237]) ).
fof(f239,plain,
$false,
inference(sat_refutation,[status(thm)],[f128,f167,f213,f236,f238]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD023-1 : 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 : n016.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 15:43:08 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.030438 seconds
% 0.13/0.40 % CPU time: 0.065443 seconds
% 0.13/0.40 % Total memory used: 3.431 MB
% 0.13/0.40 % Net memory used: 3.395 MB
%------------------------------------------------------------------------------