%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : CAT018-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.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 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 37 ( 21 unt; 0 def)
% Number of atoms : 55 ( 20 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 39 ( 21 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 34 ( 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X] :
( there_exists(X)
| ~ there_exists(domain(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(f8,axiom,
! [X,Y] :
( there_exists(compose(X,Y))
| domain(X) != codomain(Y)
| ~ there_exists(domain(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X,Y,Z] : compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
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,b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
there_exists(compose(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,negated_conjecture,
~ there_exists(compose(a,compose(b,c))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0] :
( there_exists(X0)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X] :
( there_exists(domain(X))
| ! [Y] : ~ there_exists(compose(X,Y)) ),
inference(miniscoping,[status(thm)],[f6]) ).
fof(f22,plain,
! [X0,X1] :
( there_exists(domain(X0))
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( domain(X0) = codomain(X1)
| ~ there_exists(compose(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f24,plain,
! [X0,X1] :
( there_exists(compose(X0,X1))
| domain(X0) != codomain(X1)
| ~ there_exists(domain(X0)) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f25,plain,
! [X0,X1,X2] : compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f27,plain,
! [X0] : compose(codomain(X0),X0) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
there_exists(compose(a,b)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
there_exists(compose(b,c)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
~ there_exists(compose(a,compose(b,c))),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f35,plain,
! [X0,X1] :
( there_exists(X0)
| ~ there_exists(compose(X0,X1)) ),
inference(resolution,[status(thm)],[f22,f19]) ).
fof(f38,plain,
! [X0] :
( there_exists(codomain(X0))
| ~ there_exists(X0) ),
inference(paramodulation,[status(thm)],[f27,f35]) ).
fof(f45,plain,
! [X0] :
( domain(codomain(X0)) = codomain(X0)
| ~ there_exists(X0) ),
inference(paramodulation,[status(thm)],[f27,f23]) ).
fof(f50,plain,
! [X0,X1] : compose(codomain(X0),compose(X0,X1)) = compose(X0,X1),
inference(paramodulation,[status(thm)],[f27,f25]) ).
fof(f76,plain,
domain(a) = codomain(b),
inference(resolution,[status(thm)],[f28,f23]) ).
fof(f81,plain,
! [X0] : compose(domain(a),compose(b,X0)) = compose(b,X0),
inference(paramodulation,[status(thm)],[f76,f50]) ).
fof(f82,plain,
( there_exists(domain(a))
| ~ there_exists(b) ),
inference(paramodulation,[status(thm)],[f76,f38]) ).
fof(f87,plain,
there_exists(b),
inference(resolution,[status(thm)],[f29,f35]) ).
fof(f89,plain,
there_exists(domain(a)),
inference(backward_subsumption_resolution,[status(thm)],[f82,f87]) ).
fof(f91,plain,
! [X0] :
( there_exists(compose(a,X0))
| domain(a) != codomain(X0) ),
inference(resolution,[status(thm)],[f89,f24]) ).
fof(f103,plain,
domain(a) != codomain(compose(b,c)),
inference(resolution,[status(thm)],[f91,f30]) ).
fof(f119,plain,
! [X0] :
( domain(domain(a)) = codomain(compose(b,X0))
| ~ there_exists(compose(b,X0)) ),
inference(paramodulation,[status(thm)],[f81,f23]) ).
fof(f159,plain,
domain(codomain(b)) = codomain(b),
inference(resolution,[status(thm)],[f45,f87]) ).
fof(f174,plain,
domain(domain(a)) = codomain(b),
inference(forward_demodulation,[status(thm)],[f76,f159]) ).
fof(f176,plain,
! [X0] :
( domain(a) = codomain(compose(b,X0))
| ~ there_exists(compose(b,X0)) ),
inference(backward_demodulation,[status(thm)],[f177,f119]) ).
fof(f177,plain,
domain(domain(a)) = domain(a),
inference(forward_demodulation,[status(thm)],[f76,f174]) ).
fof(f359,plain,
domain(a) = codomain(compose(b,c)),
inference(resolution,[status(thm)],[f176,f29]) ).
fof(f363,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f359,f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT018-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.35 % Computer : n001.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % OS : Linux 6.8.0-71-generic
% 0.11/0.35 % CPULimit : 300
% 0.11/0.35 % WCLimit : 300
% 0.11/0.35 % DateTime : Mon Sep 21 14:02:15 UTC 2026
% 0.11/0.35 % CPUTime :
% 0.11/0.35 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.44 % Elapsed time: 0.073379 seconds
% 0.14/0.44 % CPU time: 0.349676 seconds
% 0.14/0.44 % Total memory used: 72.693 MB
% 0.14/0.44 % Net memory used: 72.144 MB
%------------------------------------------------------------------------------