%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT014-1 : 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 : n003.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 06:55:58 AM UTC 2026
% Result : Unsatisfiable 0.22s 10.50s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 6
% Syntax : Number of formulae : 17 ( 11 unt; 0 def)
% Number of atoms : 27 ( 5 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 13 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 23 ( 1 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(codomain_is_an_identity_map,axiom,
! [VAR_0] : identity_map(codomain(VAR_0)),
file('theBenchmark.p',codomain_is_an_identity_map) ).
cnf(c_3,plain,
identity_map(codomain(A)),
inference(clausify,[status(thm)],[codomain_is_an_identity_map]) ).
fof(identity2,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,VAR_0)
| ~ identity_map(VAR_1)
| ~ defined(VAR_0,VAR_1) ),
file('theBenchmark.p',identity2) ).
cnf(c_5,plain,
( product(A,B,A)
| ~ identity_map(B)
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[identity2]) ).
cnf(c_7,plain,
( product(A,codomain(B),A)
| ~ defined(A,codomain(B)) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
fof(prove_codomain_is_idempotent,axiom,
codomain(codomain(a)) != codomain(a),
file('theBenchmark.p',prove_codomain_is_idempotent) ).
cnf(c_12,plain,
codomain(codomain(a)) != codomain(a),
inference(clausify,[status(thm)],[prove_codomain_is_idempotent]) ).
fof(composition_is_well_defined,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_2 = VAR_3
| ~ product(VAR_0,VAR_1,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',composition_is_well_defined) ).
cnf(c_13,plain,
( C = D
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[composition_is_well_defined]) ).
fof(product_on_codomain,axiom,
! [VAR_0] : product(codomain(VAR_0),VAR_0,VAR_0),
file('theBenchmark.p',product_on_codomain) ).
cnf(c_14,plain,
product(codomain(A),A,A),
inference(clausify,[status(thm)],[product_on_codomain]) ).
fof(mapping_from_codomain_of_x_to_x,axiom,
! [VAR_0] : defined(codomain(VAR_0),VAR_0),
file('theBenchmark.p',mapping_from_codomain_of_x_to_x) ).
cnf(c_16,plain,
defined(codomain(A),A),
inference(clausify,[status(thm)],[mapping_from_codomain_of_x_to_x]) ).
cnf(c_33,plain,
( B = A
| ~ product(codomain(A),A,B) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_26,plain,
~ product(codomain(codomain(a)),codomain(a),codomain(codomain(a))),
inference(resolve,[status(thm)],[c_33,c_12]) ).
cnf(c_31,plain,
product(codomain(codomain(A)),codomain(A),codomain(codomain(A))),
inference(resolve,[status(thm)],[c_7,c_16]) ).
cnf(c_32,plain,
$false,
inference(resolve,[status(thm)],[c_31,c_26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT014-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/10.47 % Computer : n003.cluster.edu
% 0.17/10.47 % Model : x86_64 x86_64
% 0.17/10.47 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.47 % Memory : 8046.5625MB
% 0.17/10.47 % OS : Linux 6.8.0-71-generic
% 0.17/10.47 % CPULimit : 300
% 0.17/10.47 % WCLimit : 300
% 0.17/10.47 % DateTime : Sat Sep 26 22:51:35 UTC 2026
% 0.17/10.48 % CPUTime :
% 0.17/10.48 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.48 % Process 3975548 was started by sandbox on n003,
% 0.17/10.48 % Sat Sep 26 22:51:35 2026
% 0.17/10.48 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/10.49
% 0.17/10.49 % From the command line: assign(max_seconds, 300).
% 0.22/10.50
% 0.22/10.50 % SZS status Unsatisfiable for theBenchmark
% 0.22/10.50
% 0.22/10.50 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.22/10.50 % Length of proof is 10.
% 0.22/10.50 % Level of proof is 3.
% 0.22/10.50 % Maximum clause weight is 11.000.
% 0.22/10.50 % Given clauses 11.
% 0.22/10.50
% 0.22/10.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------