%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT011-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Sun Sep 27 06:55:57 AM UTC 2026
% Result : Unsatisfiable 0.18s 5.49s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 17 unt; 0 def)
% Number of atoms : 39 ( 18 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 13 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_domain_is_idempotent,axiom,
domain(domain(a)) != domain(a),
file('theBenchmark.p',prove_domain_is_idempotent) ).
cnf(c_7,plain,
domain(domain(a)) != domain(a),
inference(clausify,[status(thm)],[prove_domain_is_idempotent]) ).
fof(assume_domain_exists,axiom,
there_exists(domain(a)),
file('theBenchmark.p',assume_domain_exists) ).
cnf(c_8,plain,
there_exists(domain(a)),
inference(clausify,[status(thm)],[assume_domain_exists]) ).
fof(composition_implies_codomain,axiom,
! [VAR_0,VAR_1] :
( there_exists(codomain(VAR_0))
| ~ there_exists(compose(VAR_0,VAR_1)) ),
file('theBenchmark.p',composition_implies_codomain) ).
cnf(c_14,plain,
( there_exists(codomain(A))
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[composition_implies_codomain]) ).
fof(compose_codomain,axiom,
! [VAR_0] : compose(codomain(VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',compose_codomain) ).
cnf(c_15,plain,
compose(codomain(A),A) = A,
inference(clausify,[status(thm)],[compose_codomain]) ).
fof(compose_domain,axiom,
! [VAR_0] : compose(VAR_0,domain(VAR_0)) = VAR_0,
file('theBenchmark.p',compose_domain) ).
cnf(c_16,plain,
compose(A,domain(A)) = A,
inference(clausify,[status(thm)],[compose_domain]) ).
fof(domain_codomain_composition1,axiom,
! [VAR_0,VAR_1] :
( domain(VAR_0) = codomain(VAR_1)
| ~ there_exists(compose(VAR_0,VAR_1)) ),
file('theBenchmark.p',domain_codomain_composition1) ).
cnf(c_21,plain,
( domain(A) = codomain(B)
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[domain_codomain_composition1]) ).
cnf(c_22,plain,
( codomain(B) = domain(A)
| ~ there_exists(compose(A,B)) ),
inference(copy,[status(thm)],[c_21]) ).
fof(domain_has_elements,axiom,
! [VAR_0] :
( there_exists(VAR_0)
| ~ there_exists(domain(VAR_0)) ),
file('theBenchmark.p',domain_has_elements) ).
cnf(c_25,plain,
( there_exists(A)
| ~ there_exists(domain(A)) ),
inference(clausify,[status(thm)],[domain_has_elements]) ).
cnf(c_34,plain,
( there_exists(codomain(A))
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_16,c_14]) ).
cnf(c_170,plain,
( codomain(A) = domain(codomain(A))
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_15,c_22]) ).
cnf(c_40,plain,
( domain(codomain(A)) = codomain(A)
| ~ there_exists(A) ),
inference(copy,[status(thm)],[c_170]) ).
cnf(c_41,plain,
( codomain(domain(A)) = domain(A)
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_16,c_22]) ).
cnf(c_46,plain,
there_exists(a),
inference(resolve,[status(thm)],[c_25,c_8]) ).
cnf(c_56,plain,
there_exists(codomain(domain(a))),
inference(resolve,[status(thm)],[c_34,c_8]) ).
cnf(c_148,plain,
domain(codomain(codomain(domain(a)))) = codomain(codomain(domain(a))),
inference(resolve,[status(thm)],[c_40,c_56]) ).
cnf(c_164,plain,
codomain(domain(a)) = domain(a),
inference(resolve,[status(thm)],[c_41,c_46]) ).
cnf(c_171,plain,
domain(codomain(domain(a))) = codomain(codomain(domain(a))),
inference(paramod,[status(thm)],[c_164,c_148]) ).
cnf(c_172,plain,
domain(domain(a)) = codomain(codomain(domain(a))),
inference(paramod,[status(thm)],[c_164,c_171]) ).
cnf(c_173,plain,
domain(domain(a)) = codomain(domain(a)),
inference(paramod,[status(thm)],[c_164,c_172]) ).
cnf(c_174,plain,
domain(domain(a)) = domain(a),
inference(paramod,[status(thm)],[c_164,c_173]) ).
cnf(c_169,plain,
$false,
inference(resolve,[status(thm)],[c_7,c_174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT011-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/5.44 % Computer : n004.cluster.edu
% 0.18/5.44 % Model : x86_64 x86_64
% 0.18/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/5.44 % Memory : 8046.5625MB
% 0.18/5.44 % OS : Linux 6.8.0-71-generic
% 0.18/5.44 % CPULimit : 300
% 0.18/5.44 % WCLimit : 300
% 0.18/5.44 % DateTime : Sat Sep 26 22:49:30 UTC 2026
% 0.18/5.45 % CPUTime :
% 0.18/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/5.45 % Process 2811873 was started by sandbox2 on n004,
% 0.18/5.45 % Sat Sep 26 22:49:30 2026
% 0.18/5.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/5.46
% 0.18/5.46 % From the command line: assign(max_seconds, 300).
% 0.18/5.49
% 0.18/5.49 % SZS status Unsatisfiable for theBenchmark
% 0.18/5.49
% 0.18/5.49 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.18/5.49 % Length of proof is 16.
% 0.18/5.49 % Level of proof is 4.
% 0.18/5.49 % Maximum clause weight is 45.000.
% 0.18/5.49 % Given clauses 45.
% 0.18/5.49
% 0.18/5.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------