%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT016-3 : 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 : n015.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 06:55:59 AM UTC 2026
% Result : Unsatisfiable 0.18s 0.46s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 18 ( 10 unt; 0 def)
% Number of atoms : 29 ( 8 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 27 ( 16 ~; 11 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 20 ( 5 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(existence_and_equality_implies_equivalence1,axiom,
! [VAR_0,VAR_1] :
( equivalent(VAR_0,VAR_1)
| VAR_0 != VAR_1
| ~ there_exists(VAR_0) ),
file('theBenchmark.p',existence_and_equality_implies_equivalence1) ).
cnf(c_1,plain,
( equivalent(A,B)
| A != B
| ~ there_exists(A) ),
inference(clausify,[status(thm)],[existence_and_equality_implies_equivalence1]) ).
fof(equivalence_implies_existence3,axiom,
! [VAR_0,VAR_1] :
( there_exists(VAR_1)
| ~ equivalent(VAR_0,VAR_1) ),
file('theBenchmark.p',equivalence_implies_existence3) ).
cnf(c_4,plain,
( there_exists(B)
| ~ equivalent(A,B) ),
inference(clausify,[status(thm)],[equivalence_implies_existence3]) ).
cnf(c_6,plain,
( B != A
| ~ there_exists(B)
| there_exists(A) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
fof(prove_domain_of_a_exists,axiom,
~ there_exists(domain(a)),
file('theBenchmark.p',prove_domain_of_a_exists) ).
cnf(c_7,plain,
~ there_exists(domain(a)),
inference(clausify,[status(thm)],[prove_domain_of_a_exists]) ).
fof(assume_a_exists,axiom,
there_exists(a),
file('theBenchmark.p',assume_a_exists) ).
cnf(c_8,plain,
there_exists(a),
inference(clausify,[status(thm)],[assume_a_exists]) ).
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(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_23,plain,
( there_exists(domain(A))
| ~ there_exists(compose(A,B)) ),
inference(clausify,[status(thm)],[composition_implies_domain]) ).
cnf(c_26,plain,
( a != A
| there_exists(A) ),
inference(resolve,[status(thm)],[c_8,c_6]) ).
cnf(c_41,plain,
~ there_exists(compose(a,A)),
inference(resolve,[status(thm)],[c_23,c_7]) ).
cnf(c_50,plain,
a != compose(a,A),
inference(resolve,[status(thm)],[c_26,c_41]) ).
cnf(c_48,plain,
compose(a,A) != a,
inference(copy,[status(thm)],[c_50]) ).
cnf(c_49,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT016-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n015.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Sat Sep 26 22:53:00 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 965129 was started by sandbox on n015,
% 0.18/0.44 % Sat Sep 26 22:53:00 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.46
% 0.18/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.46
% 0.18/0.46 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.18/0.46 % Length of proof is 11.
% 0.18/0.46 % Level of proof is 4.
% 0.18/0.46 % Maximum clause weight is 7.000.
% 0.18/0.46 % Given clauses 18.
% 0.18/0.46
% 0.18/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------