%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT006-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 12:07:27 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of formulae : 37 ( 11 unt; 3 def)
% Number of atoms : 67 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 29 ~; 27 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : compose(codomain(X),X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] :
( there_exists(codomain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
there_exists(compose(d,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
! [X] :
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
codomain(a) != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,plain,
! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f30,plain,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f34,plain,
! [X0] : compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f38,plain,
! [X] :
( there_exists(codomain(X))
| ! [Y] : ~ there_exists(compose(X,Y)) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f39,plain,
! [X0,X1] :
( there_exists(codomain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f43,plain,
there_exists(compose(d,a)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f44,plain,
! [X0] :
( compose(X0,d) = X0
| ~ there_exists(compose(X0,d)) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f46,plain,
codomain(a) != d,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f50,plain,
there_exists(codomain(d)),
inference(resolution,[status(thm)],[f39,f43]) ).
fof(f52,plain,
domain(d) = codomain(a),
inference(resolution,[status(thm)],[f30,f43]) ).
fof(f53,plain,
! [X0] :
( domain(codomain(X0)) = codomain(X0)
| ~ there_exists(X0) ),
inference(paramodulation,[status(thm)],[f34,f30]) ).
fof(f54,plain,
there_exists(d),
inference(resolution,[status(thm)],[f50,f27]) ).
fof(f57,plain,
( compose(codomain(d),d) = codomain(d)
| ~ there_exists(d) ),
inference(paramodulation,[status(thm)],[f34,f44]) ).
fof(f58,definition,
( sQ0_spl
<=> there_exists(d) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f60,plain,
( sQ0_spl
| ~ there_exists(d) ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,definition,
( sQ1_spl
<=> compose(codomain(d),d) = codomain(d) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( ~ sQ1_spl
| compose(codomain(d),d) = codomain(d) ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f57,f58,f61]) ).
fof(f65,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f60,f54]) ).
fof(f66,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f65]) ).
fof(f67,plain,
( ~ sQ1_spl
| d = codomain(d) ),
inference(forward_demodulation,[status(thm)],[f34,f62]) ).
fof(f69,plain,
( ~ sQ1_spl
| domain(d) = codomain(d)
| ~ there_exists(d) ),
inference(paramodulation,[status(thm)],[f67,f53]) ).
fof(f74,definition,
( sQ2_spl
<=> domain(d) = codomain(d) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( ~ sQ2_spl
| domain(d) = codomain(d) ),
inference(component_clause,[status(thm)],[f74]) ).
fof(f77,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f69,f58,f74,f61]) ).
fof(f84,plain,
( ~ sQ2_spl
| codomain(a) = codomain(d) ),
inference(forward_demodulation,[status(thm)],[f52,f75]) ).
fof(f85,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| codomain(a) = d ),
inference(forward_demodulation,[status(thm)],[f67,f84]) ).
fof(f86,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f85,f46]) ).
fof(f87,plain,
( ~ sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f86]) ).
fof(f88,plain,
$false,
inference(sat_refutation,[status(thm)],[f64,f66,f77,f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT006-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n003.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 13:57:18 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.10/0.39 % Refutation found
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.10/0.41 % Elapsed time: 0.041396 seconds
% 0.10/0.41 % CPU time: 0.106168 seconds
% 0.10/0.41 % Total memory used: 63.534 MB
% 0.10/0.41 % Net memory used: 63.351 MB
%------------------------------------------------------------------------------