%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT011-1 : 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 : n002.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 0.16s 5.46s
% Output : CNFRefutation 0.16s
% 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(domain_is_an_identity_map,axiom,
! [VAR_0] : identity_map(domain(VAR_0)),
file('theBenchmark.p',domain_is_an_identity_map) ).
cnf(c_1,plain,
identity_map(domain(A)),
inference(clausify,[status(thm)],[domain_is_an_identity_map]) ).
fof(identity1,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,VAR_1)
| ~ identity_map(VAR_0)
| ~ defined(VAR_0,VAR_1) ),
file('theBenchmark.p',identity1) ).
cnf(c_4,plain,
( product(A,B,B)
| ~ identity_map(A)
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[identity1]) ).
cnf(c_8,plain,
( product(domain(A),B,B)
| ~ defined(domain(A),B) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
fof(prove_domain_is_idempotent,axiom,
domain(domain(a)) != domain(a),
file('theBenchmark.p',prove_domain_is_idempotent) ).
cnf(c_12,plain,
domain(domain(a)) != domain(a),
inference(clausify,[status(thm)],[prove_domain_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_domain,axiom,
! [VAR_0] : product(VAR_0,domain(VAR_0),VAR_0),
file('theBenchmark.p',product_on_domain) ).
cnf(c_15,plain,
product(A,domain(A),A),
inference(clausify,[status(thm)],[product_on_domain]) ).
fof(mapping_from_x_to_its_domain,axiom,
! [VAR_0] : defined(VAR_0,domain(VAR_0)),
file('theBenchmark.p',mapping_from_x_to_its_domain) ).
cnf(c_17,plain,
defined(A,domain(A)),
inference(clausify,[status(thm)],[mapping_from_x_to_its_domain]) ).
cnf(c_39,plain,
( B = A
| ~ product(A,domain(A),B) ),
inference(resolve,[status(thm)],[c_13,c_15]) ).
cnf(c_28,plain,
~ product(domain(a),domain(domain(a)),domain(domain(a))),
inference(resolve,[status(thm)],[c_39,c_12]) ).
cnf(c_37,plain,
product(domain(A),domain(domain(A)),domain(domain(A))),
inference(resolve,[status(thm)],[c_8,c_17]) ).
cnf(c_38,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : CAT011-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n002.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 22:51:58 UTC 2026
% 0.16/5.44 % CPUTime :
% 0.16/5.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.44 % Process 2885840 was started by sandbox2 on n002,
% 0.16/5.44 % Sat Sep 26 22:51:58 2026
% 0.16/5.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/5.45
% 0.16/5.45 % From the command line: assign(max_seconds, 300).
% 0.16/5.46
% 0.16/5.46 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.46
% 0.16/5.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.46 % Length of proof is 10.
% 0.16/5.46 % Level of proof is 3.
% 0.16/5.46 % Maximum clause weight is 11.000.
% 0.16/5.46 % Given clauses 12.
% 0.16/5.46
% 0.16/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------