%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT018-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n018.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 12:07:31 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.52s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 20 unt; 3 def)
% Number of atoms : 70 ( 21 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 52 ( 26 ~; 23 |; 0 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 29 ( 29 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X] :
( there_exists(X)
| ~ there_exists(codomain(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
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(f8,axiom,
! [X,Y] :
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : compose(codomain(X),X) = X,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
there_exists(compose(a,b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
there_exists(compose(b,c)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,plain,
! [X0] :
( there_exists(X0)
| ~ there_exists(codomain(X0)) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f27,plain,
! [X] :
( there_exists(domain(X))
| ! [Y] : ~ there_exists(compose(X,Y)) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f28,plain,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
! [X0,X1] :
( there_exists(compose(X0,X1))
| domain(X0) != codomain(X1)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f31,plain,
! [X0,X1,X2] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f33,plain,
! [X0] : compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f42,plain,
there_exists(compose(a,b)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f43,plain,
there_exists(compose(b,c)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f44,plain,
~ there_exists(compose(a,compose(b,c))),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f60,plain,
! [X0,X1] : compose(codomain(X0),compose(X0,X1)) = compose(X0,X1),
inference(paramodulation,[status(thm)],[f33,f31]) ).
fof(f65,plain,
there_exists(domain(a)),
inference(resolution,[status(thm)],[f28,f42]) ).
fof(f70,plain,
domain(a) = codomain(b),
inference(resolution,[status(thm)],[f29,f42]) ).
fof(f101,plain,
! [X0] :
( there_exists(compose(a,X0))
| domain(a) != codomain(X0) ),
inference(resolution,[status(thm)],[f65,f30]) ).
fof(f143,plain,
! [X0,X1] :
( domain(codomain(X0)) = codomain(compose(X0,X1))
| ~ there_exists(compose(X0,X1)) ),
inference(paramodulation,[status(thm)],[f60,f29]) ).
fof(f181,plain,
( there_exists(b)
| ~ there_exists(domain(a)) ),
inference(paramodulation,[status(thm)],[f70,f26]) ).
fof(f182,plain,
compose(domain(a),b) = b,
inference(paramodulation,[status(thm)],[f70,f33]) ).
fof(f183,definition,
( sQ2_spl
<=> there_exists(domain(a)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f185,plain,
( sQ2_spl
| ~ there_exists(domain(a)) ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
( sQ3_spl
<=> there_exists(b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f189,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f181,f183,f186]) ).
fof(f190,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f185,f65]) ).
fof(f191,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f190]) ).
fof(f349,plain,
( domain(domain(a)) = codomain(b)
| ~ there_exists(b) ),
inference(paramodulation,[status(thm)],[f182,f29]) ).
fof(f360,definition,
( sQ9_spl
<=> domain(domain(a)) = codomain(b) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f361,plain,
( ~ sQ9_spl
| domain(domain(a)) = codomain(b) ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f363,plain,
( sQ9_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f349,f186,f360]) ).
fof(f368,plain,
( ~ sQ9_spl
| domain(domain(a)) = domain(a) ),
inference(forward_demodulation,[status(thm)],[f70,f361]) ).
fof(f915,plain,
domain(a) != codomain(compose(b,c)),
inference(resolution,[status(thm)],[f101,f44]) ).
fof(f1817,plain,
domain(codomain(b)) = codomain(compose(b,c)),
inference(resolution,[status(thm)],[f143,f43]) ).
fof(f1839,plain,
domain(domain(a)) = codomain(compose(b,c)),
inference(forward_demodulation,[status(thm)],[f70,f1817]) ).
fof(f1840,plain,
( ~ sQ9_spl
| domain(a) = codomain(compose(b,c)) ),
inference(forward_demodulation,[status(thm)],[f368,f1839]) ).
fof(f1841,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1840,f915]) ).
fof(f1842,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f1841]) ).
fof(f1843,plain,
$false,
inference(sat_refutation,[status(thm)],[f189,f191,f363,f1842]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n018.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 13:58:14 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.52 % Refutation found
% 0.12/0.52 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.54 % Elapsed time: 0.183828 seconds
% 0.19/0.54 % CPU time: 1.142329 seconds
% 0.19/0.54 % Total memory used: 124.890 MB
% 0.19/0.54 % Net memory used: 122.849 MB
%------------------------------------------------------------------------------