%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT011-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 23 unt; 0 def)
% Number of atoms : 45 ( 21 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 : 6 ( 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_4,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_5,plain,
there_exists(domain(a)),
inference(clausify,[status(thm)],[assume_domain_exists]) ).
fof(compose_codomain,axiom,
! [VAR_0] : compose(codomain(VAR_0),VAR_0) = VAR_0,
file('theBenchmark.p',compose_codomain) ).
cnf(c_6,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_7,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_12,plain,
( domain(A) = codomain(B)
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[domain_codomain_composition1]) ).
cnf(c_13,plain,
( codomain(B) = domain(A)
| ~ there_exists(compose(A,B)) ),
inference(copy,[status(thm)],[c_12]) ).
fof(composition_implies_domain,axiom,
! [VAR_0,VAR_1] :
( there_exists(domain(VAR_0))
| ~ there_exists(compose(VAR_0,VAR_1)) ),
file('theBenchmark.p',composition_implies_domain) ).
cnf(c_14,plain,
( there_exists(domain(A))
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[composition_implies_domain]) ).
fof(domain_has_elements,axiom,
! [VAR_0] :
( there_exists(VAR_0)
| ~ there_exists(domain(VAR_0)) ),
file('theBenchmark.p',domain_has_elements) ).
cnf(c_16,plain,
( there_exists(A)
| ~ there_exists(domain(A)) ),
inference(clausify,[status(thm)],[domain_has_elements]) ).
cnf(c_102,plain,
( codomain(A) = domain(codomain(A))
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_6,c_13]) ).
cnf(c_20,plain,
( domain(codomain(A)) = codomain(A)
| ~ there_exists(A) ),
inference(copy,[status(thm)],[c_102]) ).
cnf(c_21,plain,
( codomain(domain(A)) = domain(A)
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_7,c_13]) ).
cnf(c_23,plain,
( there_exists(domain(codomain(A)))
| ~ there_exists(A) ),
inference(paramod,[status(thm)],[c_6,c_14]) ).
cnf(c_26,plain,
there_exists(a),
inference(resolve,[status(thm)],[c_16,c_5]) ).
cnf(c_41,plain,
there_exists(domain(codomain(domain(a)))),
inference(resolve,[status(thm)],[c_23,c_5]) ).
cnf(c_48,plain,
there_exists(codomain(domain(a))),
inference(resolve,[status(thm)],[c_16,c_41]) ).
cnf(c_53,plain,
there_exists(domain(codomain(codomain(domain(a))))),
inference(resolve,[status(thm)],[c_23,c_48]) ).
cnf(c_61,plain,
domain(codomain(codomain(domain(a)))) = codomain(codomain(domain(a))),
inference(resolve,[status(thm)],[c_20,c_48]) ).
cnf(c_72,plain,
there_exists(codomain(codomain(domain(a)))),
inference(paramod,[status(thm)],[c_61,c_53]) ).
cnf(c_79,plain,
domain(codomain(codomain(codomain(domain(a))))) = codomain(codomain(codomain(domain(a)))),
inference(resolve,[status(thm)],[c_20,c_72]) ).
cnf(c_97,plain,
codomain(domain(a)) = domain(a),
inference(resolve,[status(thm)],[c_21,c_26]) ).
cnf(c_103,plain,
domain(codomain(codomain(domain(a)))) = codomain(codomain(codomain(domain(a)))),
inference(paramod,[status(thm)],[c_97,c_79]) ).
cnf(c_104,plain,
domain(codomain(domain(a))) = codomain(codomain(codomain(domain(a)))),
inference(paramod,[status(thm)],[c_97,c_103]) ).
cnf(c_105,plain,
domain(domain(a)) = codomain(codomain(codomain(domain(a)))),
inference(paramod,[status(thm)],[c_97,c_104]) ).
cnf(c_106,plain,
domain(domain(a)) = codomain(codomain(domain(a))),
inference(paramod,[status(thm)],[c_97,c_105]) ).
cnf(c_107,plain,
domain(domain(a)) = codomain(domain(a)),
inference(paramod,[status(thm)],[c_97,c_106]) ).
cnf(c_100,plain,
domain(domain(a)) = domain(a),
inference(paramod,[status(thm)],[c_97,c_107]) ).
cnf(c_101,plain,
$false,
inference(resolve,[status(thm)],[c_100,c_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT011-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 22:49:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 1316989 was started by sandbox on n009,
% 0.10/0.37 % Sat Sep 26 22:49:30 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 21.
% 0.10/0.39 % Level of proof is 8.
% 0.10/0.39 % Maximum clause weight is 12.000.
% 0.10/0.39 % Given clauses 31.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------