%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT005-1 : 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 : n005.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 06:55:55 AM UTC 2026
% Result : Unsatisfiable 0.15s 0.41s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 11
% Syntax : Number of formulae : 35 ( 19 unt; 0 def)
% Number of atoms : 64 ( 6 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 63 ( 34 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 54 ( 2 sgn 21 !; 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]) ).
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]) ).
fof(d_is_identity_map,axiom,
identity_map(d),
file('theBenchmark.p',d_is_identity_map) ).
cnf(c_6,plain,
identity_map(d),
inference(clausify,[status(thm)],[d_is_identity_map]) ).
cnf(c_9,plain,
( product(A,d,A)
| ~ defined(A,d) ),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_12,plain,
( product(domain(A),B,B)
| ~ defined(domain(A),B) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
fof(prove_domain_of_a_is_d,axiom,
domain(a) != d,
file('theBenchmark.p',prove_domain_of_a_is_d) ).
cnf(c_16,plain,
domain(a) != d,
inference(clausify,[status(thm)],[prove_domain_of_a_is_d]) ).
fof(ad_defined,axiom,
defined(a,d),
file('theBenchmark.p',ad_defined) ).
cnf(c_17,plain,
defined(a,d),
inference(clausify,[status(thm)],[ad_defined]) ).
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_18,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_19,plain,
product(codomain(A),A,A),
inference(clausify,[status(thm)],[product_on_codomain]) ).
fof(product_on_domain,axiom,
! [VAR_0] : product(VAR_0,domain(VAR_0),VAR_0),
file('theBenchmark.p',product_on_domain) ).
cnf(c_20,plain,
product(A,domain(A),A),
inference(clausify,[status(thm)],[product_on_domain]) ).
fof(category_theory_axiom2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_0,VAR_5,VAR_4)
| ~ product(VAR_1,VAR_3,VAR_5)
| ~ product(VAR_2,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',category_theory_axiom2) ).
cnf(c_26,plain,
( product(A,F,E)
| ~ product(B,D,F)
| ~ product(C,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[category_theory_axiom2]) ).
fof(associative_property2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( defined(VAR_1,VAR_3)
| ~ defined(VAR_2,VAR_3)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associative_property2) ).
cnf(c_28,plain,
( defined(B,D)
| ~ defined(C,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associative_property2]) ).
cnf(c_227,plain,
( B = A
| ~ product(codomain(A),A,B) ),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_228,plain,
d != domain(a),
inference(copy,[status(thm)],[c_16]) ).
cnf(c_41,plain,
~ product(codomain(domain(a)),domain(a),d),
inference(resolve,[status(thm)],[c_227,c_228]) ).
cnf(c_229,plain,
( defined(domain(A),B)
| ~ defined(A,B) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_63,plain,
defined(domain(a),d),
inference(resolve,[status(thm)],[c_229,c_17]) ).
cnf(c_91,plain,
product(domain(a),d,d),
inference(resolve,[status(thm)],[c_12,c_63]) ).
cnf(c_92,plain,
product(domain(a),d,domain(a)),
inference(resolve,[status(thm)],[c_9,c_63]) ).
cnf(c_230,plain,
( product(codomain(A),D,C)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_26,c_19]) ).
cnf(c_231,plain,
( product(codomain(domain(a)),A,d)
| ~ product(domain(a),d,A) ),
inference(resolve,[status(thm)],[c_230,c_91]) ).
cnf(c_232,plain,
~ product(domain(a),d,domain(a)),
inference(resolve,[status(thm)],[c_231,c_41]) ).
cnf(c_226,plain,
$false,
inference(resolve,[status(thm)],[c_92,c_232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT005-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 22:48:18 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 3289716 was started by sandbox on n005,
% 0.12/0.37 % Sat Sep 26 22:48:18 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.12/0.37
% 0.12/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.41
% 0.15/0.41 % SZS status Unsatisfiable for theBenchmark
% 0.15/0.41
% 0.15/0.41 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/0.41 % Length of proof is 18.
% 0.15/0.41 % Level of proof is 3.
% 0.15/0.41 % Maximum clause weight is 22.000.
% 0.15/0.41 % Given clauses 70.
% 0.15/0.41
% 0.15/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------