%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT011-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 12:07:29 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 39 ( 13 unt; 2 def)
% Number of atoms : 65 ( 17 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 57 ( 31 ~; 24 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 25 ( 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X] :
( there_exists(X)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
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(f10,axiom,
! [X] : compose(X,domain(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : compose(codomain(X),X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
there_exists(domain(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
domain(domain(a)) != domain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X] :
( there_exists(domain(X))
| ! [Y] : ~ there_exists(compose(X,Y)) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f31,plain,
! [X0] : compose(X0,domain(X0)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f32,plain,
! [X0] : compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f41,plain,
there_exists(domain(a)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f42,plain,
domain(domain(a)) != domain(a),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f51,plain,
! [X0] :
( domain(codomain(X0)) = codomain(X0)
| ~ there_exists(X0) ),
inference(paramodulation,[status(thm)],[f32,f28]) ).
fof(f52,plain,
! [X0] :
( domain(X0) = codomain(domain(X0))
| ~ there_exists(X0) ),
inference(paramodulation,[status(thm)],[f31,f28]) ).
fof(f55,plain,
domain(codomain(domain(a))) = codomain(domain(a)),
inference(resolution,[status(thm)],[f51,f41]) ).
fof(f60,plain,
! [X0] :
( ~ there_exists(domain(X0))
| domain(codomain(X0)) = codomain(X0) ),
inference(resolution,[status(thm)],[f51,f24]) ).
fof(f65,plain,
! [X0] :
( ~ there_exists(codomain(X0))
| domain(X0) = codomain(domain(X0)) ),
inference(resolution,[status(thm)],[f52,f25]) ).
fof(f113,plain,
domain(codomain(a)) = codomain(a),
inference(resolution,[status(thm)],[f60,f41]) ).
fof(f122,plain,
! [X0] :
( there_exists(codomain(a))
| ~ there_exists(compose(codomain(a),X0)) ),
inference(paramodulation,[status(thm)],[f113,f27]) ).
fof(f127,definition,
( sQ1_spl
<=> there_exists(codomain(a)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f128,plain,
( ~ sQ1_spl
| there_exists(codomain(a)) ),
inference(component_clause,[status(thm)],[f127]) ).
fof(f131,definition,
! [X0] :
( sQ2_spl
<=> ~ there_exists(compose(codomain(a),X0)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f132,plain,
! [X0] :
( ~ sQ2_spl
| ~ there_exists(compose(codomain(a),X0)) ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f122,f131,f127]) ).
fof(f141,plain,
( ~ sQ2_spl
| ~ there_exists(a) ),
inference(paramodulation,[status(thm)],[f32,f132]) ).
fof(f155,plain,
( ~ sQ2_spl
| ~ there_exists(domain(a)) ),
inference(resolution,[status(thm)],[f141,f24]) ).
fof(f156,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f155,f41]) ).
fof(f157,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f156]) ).
fof(f206,plain,
( ~ sQ1_spl
| domain(a) = codomain(domain(a)) ),
inference(resolution,[status(thm)],[f65,f128]) ).
fof(f290,plain,
( ~ sQ1_spl
| domain(domain(a)) = codomain(domain(a)) ),
inference(forward_demodulation,[status(thm)],[f206,f55]) ).
fof(f291,plain,
( ~ sQ1_spl
| domain(domain(a)) = domain(a) ),
inference(forward_demodulation,[status(thm)],[f206,f290]) ).
fof(f292,plain,
( ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f42]) ).
fof(f293,plain,
~ sQ1_spl,
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f294,plain,
$false,
inference(sat_refutation,[status(thm)],[f134,f157,f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT011-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n011.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 13:55:55 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.42 % Elapsed time: 0.061818 seconds
% 0.14/0.42 % CPU time: 0.171720 seconds
% 0.14/0.42 % Total memory used: 102.195 MB
% 0.14/0.42 % Net memory used: 101.805 MB
%------------------------------------------------------------------------------