%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 10
% Syntax : Number of formulae : 33 ( 11 unt; 3 def)
% Number of atoms : 55 ( 14 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 43 ( 21 ~; 19 |; 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 : 16 ( 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y] :
( domain(X) = codomain(Y)
| ~ there_exists(compose(X,Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : compose(codomain(X),X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
there_exists(compose(a,d)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
! [X] :
( compose(X,d) = X
| ~ there_exists(compose(X,d)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,negated_conjecture,
domain(a) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X] :
( there_exists(domain(X))
| ! [Y] : ~ there_exists(compose(X,Y)) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0] : compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f29,plain,
there_exists(compose(a,d)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f30,plain,
! [X0] :
( compose(X0,d) = X0
| ~ there_exists(compose(X0,d)) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
domain(a) != d,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f35,plain,
there_exists(domain(a)),
inference(resolution,[status(thm)],[f23,f29]) ).
fof(f40,plain,
domain(a) = codomain(d),
inference(resolution,[status(thm)],[f24,f29]) ).
fof(f61,plain,
( compose(codomain(d),d) = codomain(d)
| ~ there_exists(d) ),
inference(paramodulation,[status(thm)],[f28,f30]) ).
fof(f66,definition,
( sQ0_spl
<=> there_exists(d) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f69,definition,
( sQ1_spl
<=> compose(codomain(d),d) = codomain(d) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f70,plain,
( ~ sQ1_spl
| compose(codomain(d),d) = codomain(d) ),
inference(component_clause,[status(thm)],[f69]) ).
fof(f72,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f61,f66,f69]) ).
fof(f79,plain,
( there_exists(d)
| ~ there_exists(domain(a)) ),
inference(paramodulation,[status(thm)],[f40,f21]) ).
fof(f81,definition,
( sQ3_spl
<=> there_exists(domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( sQ3_spl
| ~ there_exists(domain(a)) ),
inference(component_clause,[status(thm)],[f81]) ).
fof(f84,plain,
( sQ0_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f79,f81,f66]) ).
fof(f85,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f35]) ).
fof(f86,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( ~ sQ1_spl
| domain(a) = d ),
inference(backward_demodulation,[status(thm)],[f88,f40]) ).
fof(f88,plain,
( ~ sQ1_spl
| d = codomain(d) ),
inference(forward_demodulation,[status(thm)],[f28,f70]) ).
fof(f90,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f32]) ).
fof(f91,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f90]) ).
fof(f92,plain,
$false,
inference(sat_refutation,[status(thm)],[f72,f84,f86,f91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT005-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n026.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 13:58:23 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.42 % Elapsed time: 0.043414 seconds
% 0.11/0.42 % CPU time: 0.123674 seconds
% 0.11/0.42 % Total memory used: 43.863 MB
% 0.11/0.42 % Net memory used: 43.590 MB
%------------------------------------------------------------------------------