%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : FLD034-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 12:21:58 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 9
% Syntax : Number of formulae : 30 ( 9 unt; 3 def)
% Number of atoms : 62 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 67 ( 35 ~; 29 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [X] :
( ~ defined(X)
| equalish(multiply(multiplicative_identity,X),X) ),
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(f30,negated_conjecture,
equalish(m,multiplicative_identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,negated_conjecture,
~ equalish(multiply(m,a),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [X0] :
( ~ defined(X0)
| equalish(multiply(multiplicative_identity,X0),X0) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
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(f76,plain,
equalish(m,multiplicative_identity),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
~ equalish(multiply(m,a),a),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f85,plain,
! [X0] :
( ~ equalish(X0,a)
| ~ equalish(multiply(m,a),X0) ),
inference(resolution,[status(thm)],[f66,f77]) ).
fof(f92,definition,
( sQ1_spl
<=> defined(a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f94,plain,
( sQ1_spl
| ~ defined(a) ),
inference(component_clause,[status(thm)],[f92]) ).
fof(f114,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f94,f74]) ).
fof(f115,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f159,plain,
! [X0] :
( ~ equalish(multiply(X0,a),a)
| ~ equalish(m,X0)
| ~ defined(a) ),
inference(resolution,[status(thm)],[f70,f85]) ).
fof(f164,definition,
! [X0] :
( sQ13_spl
<=> ( ~ equalish(multiply(X0,a),a)
| ~ equalish(m,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f165,plain,
! [X0] :
( ~ sQ13_spl
| ~ equalish(multiply(X0,a),a)
| ~ equalish(m,X0) ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( sQ13_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f159,f92,f164]) ).
fof(f241,plain,
( ~ sQ13_spl
| ~ defined(a)
| ~ equalish(m,multiplicative_identity) ),
inference(resolution,[status(thm)],[f165,f40]) ).
fof(f244,definition,
( sQ22_spl
<=> equalish(m,multiplicative_identity) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f246,plain,
( sQ22_spl
| ~ equalish(m,multiplicative_identity) ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( ~ sQ13_spl
| ~ sQ1_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f241,f244,f92,f164]) ).
fof(f248,plain,
( sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f246,f76]) ).
fof(f249,plain,
sQ22_spl,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f250,plain,
$false,
inference(sat_refutation,[status(thm)],[f115,f167,f247,f249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : FLD034-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n005.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 15:39:18 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.043842 seconds
% 0.13/0.41 % CPU time: 0.144547 seconds
% 0.13/0.41 % Total memory used: 17.718 MB
% 0.13/0.41 % Net memory used: 17.490 MB
%------------------------------------------------------------------------------