%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT010-1 : 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 : n018.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 0.48s 0.46s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 57 ( 27 unt; 0 def)
% Number of atoms : 111 ( 8 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 116 ( 62 ~; 54 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 105 ( 2 sgn 34 !; 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(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_7,plain,
( product(A,codomain(B),A)
| ~ defined(A,codomain(B)) ),
inference(resolve,[status(thm)],[c_5,c_3]) ).
cnf(c_9,plain,
( product(codomain(A),B,B)
| ~ defined(codomain(A),B) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
fof(prove_codomain_of_ba_equals_codomain_of_b,axiom,
codomain(compose(b,a)) != codomain(b),
file('theBenchmark.p',prove_codomain_of_ba_equals_codomain_of_b) ).
cnf(c_12,plain,
codomain(compose(b,a)) != codomain(b),
inference(clausify,[status(thm)],[prove_codomain_of_ba_equals_codomain_of_b]) ).
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(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(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_axiom3,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( defined(VAR_3,VAR_0)
| ~ defined(VAR_3,VAR_2)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',category_theory_axiom3) ).
cnf(c_21,plain,
( defined(D,A)
| ~ defined(D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[category_theory_axiom3]) ).
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(category_theory_axiom1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( defined(VAR_0,VAR_4)
| ~ defined(VAR_2,VAR_3)
| ~ product(VAR_1,VAR_3,VAR_4)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',category_theory_axiom1) ).
cnf(c_23,plain,
( defined(A,E)
| ~ defined(C,D)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[category_theory_axiom1]) ).
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_306,plain,
( B = A
| ~ product(codomain(A),A,B) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_27,plain,
~ product(codomain(codomain(b)),codomain(b),codomain(compose(b,a))),
inference(resolve,[status(thm)],[c_306,c_12]) ).
cnf(c_32,plain,
product(codomain(codomain(A)),codomain(A),codomain(codomain(A))),
inference(resolve,[status(thm)],[c_7,c_17]) ).
cnf(c_307,plain,
( defined(A,codomain(B))
| ~ defined(A,B) ),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_41,plain,
defined(codomain(A),codomain(A)),
inference(resolve,[status(thm)],[c_307,c_17]) ).
cnf(c_49,plain,
product(b,a,compose(b,a)),
inference(resolve,[status(thm)],[c_26,c_13]) ).
cnf(c_308,plain,
( product(D,B,C)
| ~ product(A,codomain(B),D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_19,c_15]) ).
cnf(c_309,plain,
( product(codomain(A),A,B)
| ~ product(codomain(codomain(A)),A,B) ),
inference(resolve,[status(thm)],[c_308,c_15]) ).
cnf(c_50,plain,
~ product(codomain(codomain(codomain(b))),codomain(b),codomain(compose(b,a))),
inference(resolve,[status(thm)],[c_309,c_27]) ).
cnf(c_101,plain,
product(codomain(A),codomain(A),codomain(A)),
inference(resolve,[status(thm)],[c_9,c_41]) ).
cnf(c_310,plain,
( A = B
| ~ product(codomain(A),A,B) ),
inference(resolve,[status(thm)],[c_14,c_15]) ).
cnf(c_311,plain,
codomain(A) = codomain(codomain(A)),
inference(resolve,[status(thm)],[c_310,c_32]) ).
cnf(c_130,plain,
codomain(codomain(A)) = codomain(A),
inference(copy,[status(thm)],[c_311]) ).
cnf(c_312,plain,
( product(codomain(codomain(A)),D,C)
| ~ product(codomain(A),B,D)
| ~ product(codomain(codomain(A)),B,C) ),
inference(resolve,[status(thm)],[c_22,c_32]) ).
cnf(c_313,plain,
( product(codomain(codomain(A)),A,B)
| ~ product(codomain(codomain(A)),A,B) ),
inference(resolve,[status(thm)],[c_312,c_15]) ).
cnf(c_314,plain,
~ product(codomain(codomain(codomain(b))),codomain(b),codomain(compose(b,a))),
inference(resolve,[status(thm)],[c_313,c_50]) ).
cnf(c_315,plain,
~ product(codomain(codomain(b)),codomain(b),codomain(compose(b,a))),
inference(paramod,[status(thm)],[c_130,c_314]) ).
cnf(c_132,plain,
~ product(codomain(b),codomain(b),codomain(compose(b,a))),
inference(paramod,[status(thm)],[c_130,c_315]) ).
cnf(c_316,plain,
( defined(codomain(A),C)
| ~ defined(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_23,c_15]) ).
cnf(c_317,plain,
( defined(codomain(b),compose(b,a))
| ~ defined(b,a) ),
inference(resolve,[status(thm)],[c_316,c_49]) ).
cnf(c_185,plain,
defined(codomain(b),compose(b,a)),
inference(resolve,[status(thm)],[c_317,c_13]) ).
cnf(c_318,plain,
( defined(A,codomain(B))
| ~ defined(A,B) ),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_223,plain,
defined(codomain(b),codomain(compose(b,a))),
inference(resolve,[status(thm)],[c_318,c_185]) ).
cnf(c_283,plain,
product(codomain(b),codomain(compose(b,a)),codomain(compose(b,a))),
inference(resolve,[status(thm)],[c_9,c_223]) ).
cnf(c_284,plain,
product(codomain(b),codomain(compose(b,a)),codomain(b)),
inference(resolve,[status(thm)],[c_7,c_223]) ).
cnf(c_319,plain,
( product(codomain(A),D,C)
| ~ product(codomain(A),B,D)
| ~ product(codomain(A),B,C) ),
inference(resolve,[status(thm)],[c_22,c_101]) ).
cnf(c_320,plain,
( product(codomain(b),codomain(b),A)
| ~ product(codomain(b),codomain(compose(b,a)),A) ),
inference(resolve,[status(thm)],[c_319,c_284]) ).
cnf(c_304,plain,
~ product(codomain(b),codomain(compose(b,a)),codomain(compose(b,a))),
inference(resolve,[status(thm)],[c_320,c_132]) ).
cnf(c_305,plain,
$false,
inference(resolve,[status(thm)],[c_304,c_283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT010-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n018.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 22:51:24 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1618439 was started by sandbox on n018,
% 0.09/0.37 % Sat Sep 26 22:51:24 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.48/0.46
% 0.48/0.46 % SZS status Unsatisfiable for theBenchmark
% 0.48/0.46
% 0.48/0.46 % Proof 1 at 0.05 (+ 0.03) seconds.
% 0.48/0.46 % Length of proof is 29.
% 0.48/0.46 % Level of proof is 6.
% 0.48/0.46 % Maximum clause weight is 16.000.
% 0.48/0.46 % Given clauses 87.
% 0.48/0.46
% 0.48/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------