%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT009-1 : 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 : n026.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 06:55:56 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 60 ( 32 unt; 0 def)
% Number of atoms : 111 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 111 ( 60 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 103 ( 2 sgn 36 !; 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]) ).
cnf(c_6,plain,
( product(A,domain(B),A)
| ~ defined(A,domain(B)) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_8,plain,
( product(domain(A),B,B)
| ~ defined(domain(A),B) ),
inference(resolve,[status(thm)],[c_4,c_1]) ).
fof(prove_domain_of_ba_equals_domain_of_a,axiom,
domain(compose(b,a)) != domain(a),
file('theBenchmark.p',prove_domain_of_ba_equals_domain_of_a) ).
cnf(c_12,plain,
domain(compose(b,a)) != domain(a),
inference(clausify,[status(thm)],[prove_domain_of_ba_equals_domain_of_a]) ).
fof(ba_defined,axiom,
defined(b,a),
file('theBenchmark.p',ba_defined) ).
cnf(c_13,plain,
defined(b,a),
inference(clausify,[status(thm)],[ba_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_14,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_15,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_16,plain,
product(A,domain(A),A),
inference(clausify,[status(thm)],[product_on_domain]) ).
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_17,plain,
defined(codomain(A),A),
inference(clausify,[status(thm)],[mapping_from_codomain_of_x_to_x]) ).
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_18,plain,
defined(A,domain(A)),
inference(clausify,[status(thm)],[mapping_from_x_to_its_domain]) ).
fof(category_theory_axiom5,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( product(VAR_5,VAR_1,VAR_4)
| ~ product(VAR_3,VAR_0,VAR_5)
| ~ product(VAR_3,VAR_2,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',category_theory_axiom5) ).
cnf(c_19,plain,
( product(F,B,E)
| ~ product(D,A,F)
| ~ product(D,C,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[category_theory_axiom5]) ).
fof(category_theory_axiom4,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( defined(VAR_4,VAR_1)
| ~ defined(VAR_3,VAR_2)
| ~ product(VAR_3,VAR_0,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',category_theory_axiom4) ).
cnf(c_20,plain,
( defined(E,B)
| ~ defined(D,C)
| ~ product(D,A,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[category_theory_axiom4]) ).
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_22,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_24,plain,
( defined(B,D)
| ~ defined(C,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associative_property2]) ).
fof(closure_of_composition,axiom,
! [VAR_0,VAR_1] :
( product(VAR_0,VAR_1,compose(VAR_0,VAR_1))
| ~ defined(VAR_0,VAR_1) ),
file('theBenchmark.p',closure_of_composition) ).
cnf(c_26,plain,
( product(A,B,compose(A,B))
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[closure_of_composition]) ).
cnf(c_271,plain,
( B = A
| ~ product(codomain(A),A,B) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_272,plain,
domain(a) != domain(compose(b,a)),
inference(copy,[status(thm)],[c_12]) ).
cnf(c_28,plain,
~ product(codomain(domain(compose(b,a))),domain(compose(b,a)),domain(a)),
inference(resolve,[status(thm)],[c_271,c_272]) ).
cnf(c_33,plain,
product(codomain(domain(A)),domain(A),codomain(domain(A))),
inference(resolve,[status(thm)],[c_6,c_17]) ).
cnf(c_273,plain,
( defined(domain(A),B)
| ~ defined(A,B) ),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_44,plain,
defined(domain(A),domain(A)),
inference(resolve,[status(thm)],[c_273,c_18]) ).
cnf(c_49,plain,
product(b,a,compose(b,a)),
inference(resolve,[status(thm)],[c_26,c_13]) ).
cnf(c_70,plain,
product(domain(A),domain(A),domain(A)),
inference(resolve,[status(thm)],[c_8,c_44]) ).
cnf(c_274,plain,
( A = B
| ~ product(codomain(A),A,B) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_275,plain,
domain(A) = codomain(domain(A)),
inference(resolve,[status(thm)],[c_274,c_33]) ).
cnf(c_103,plain,
codomain(domain(A)) = domain(A),
inference(copy,[status(thm)],[c_275]) ).
cnf(c_276,plain,
( product(D,domain(B),C)
| ~ product(A,codomain(domain(B)),D)
| ~ product(A,codomain(domain(B)),C) ),
inference(resolve,[status(thm)],[c_19,c_33]) ).
cnf(c_277,plain,
( product(codomain(domain(A)),domain(A),B)
| ~ product(codomain(codomain(domain(A))),codomain(domain(A)),B) ),
inference(resolve,[status(thm)],[c_276,c_15]) ).
cnf(c_278,plain,
~ product(codomain(codomain(domain(compose(b,a)))),codomain(domain(compose(b,a))),domain(a)),
inference(resolve,[status(thm)],[c_277,c_28]) ).
cnf(c_279,plain,
~ product(codomain(domain(compose(b,a))),codomain(domain(compose(b,a))),domain(a)),
inference(paramod,[status(thm)],[c_103,c_278]) ).
cnf(c_280,plain,
~ product(domain(compose(b,a)),codomain(domain(compose(b,a))),domain(a)),
inference(paramod,[status(thm)],[c_103,c_279]) ).
cnf(c_104,plain,
~ product(domain(compose(b,a)),domain(compose(b,a)),domain(a)),
inference(paramod,[status(thm)],[c_103,c_280]) ).
cnf(c_281,plain,
( defined(C,domain(B))
| ~ defined(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_20,c_16]) ).
cnf(c_282,plain,
( defined(compose(b,a),domain(a))
| ~ defined(b,a) ),
inference(resolve,[status(thm)],[c_281,c_49]) ).
cnf(c_115,plain,
defined(compose(b,a),domain(a)),
inference(resolve,[status(thm)],[c_282,c_13]) ).
cnf(c_283,plain,
( defined(domain(A),B)
| ~ defined(A,B) ),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_121,plain,
defined(domain(compose(b,a)),domain(a)),
inference(resolve,[status(thm)],[c_283,c_115]) ).
cnf(c_234,plain,
product(domain(compose(b,a)),domain(a),domain(a)),
inference(resolve,[status(thm)],[c_8,c_121]) ).
cnf(c_235,plain,
product(domain(compose(b,a)),domain(a),domain(compose(b,a))),
inference(resolve,[status(thm)],[c_6,c_121]) ).
cnf(c_284,plain,
( product(domain(A),D,C)
| ~ product(domain(A),B,D)
| ~ product(domain(A),B,C) ),
inference(resolve,[status(thm)],[c_22,c_70]) ).
cnf(c_285,plain,
( product(domain(compose(b,a)),A,domain(a))
| ~ product(domain(compose(b,a)),domain(a),A) ),
inference(resolve,[status(thm)],[c_284,c_234]) ).
cnf(c_269,plain,
~ product(domain(compose(b,a)),domain(a),domain(compose(b,a))),
inference(resolve,[status(thm)],[c_285,c_104]) ).
cnf(c_270,plain,
$false,
inference(resolve,[status(thm)],[c_269,c_235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT009-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.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 22:51:40 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 2134305 was started by sandbox on n026,
% 0.10/0.37 % Sat Sep 26 22:51:40 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).
% 0.10/0.45
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45
% 0.10/0.45 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.10/0.45 % Length of proof is 30.
% 0.10/0.45 % Level of proof is 6.
% 0.10/0.45 % Maximum clause weight is 32.000.
% 0.10/0.45 % Given clauses 80.
% 0.10/0.45
% 0.10/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------