%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT018-1 : 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 : n014.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 06:56:00 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 28 ( 15 unt; 0 def)
% Number of atoms : 53 ( 0 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 29 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 42 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(category_theory_axiom6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( defined(VAR_0,VAR_2)
| ~ identity_map(VAR_1)
| ~ defined(VAR_1,VAR_2)
| ~ defined(VAR_0,VAR_1) ),
file('theBenchmark.p',category_theory_axiom6) ).
cnf(c_2,plain,
( defined(A,C)
| ~ identity_map(B)
| ~ defined(B,C)
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[category_theory_axiom6]) ).
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]) ).
cnf(c_10,plain,
( defined(A,C)
| ~ defined(codomain(B),C)
| ~ defined(A,codomain(B)) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
fof(prove_a_bc_exists,axiom,
~ defined(a,compose(b,c)),
file('theBenchmark.p',prove_a_bc_exists) ).
cnf(c_12,plain,
~ defined(a,compose(b,c)),
inference(clausify,[status(thm)],[prove_a_bc_exists]) ).
fof(assume_bc_exists,axiom,
defined(b,c),
file('theBenchmark.p',assume_bc_exists) ).
cnf(c_13,plain,
defined(b,c),
inference(clausify,[status(thm)],[assume_bc_exists]) ).
fof(assume_ab_exists,axiom,
defined(a,b),
file('theBenchmark.p',assume_ab_exists) ).
cnf(c_14,plain,
defined(a,b),
inference(clausify,[status(thm)],[assume_ab_exists]) ).
fof(product_on_codomain,axiom,
! [VAR_0] : product(codomain(VAR_0),VAR_0,VAR_0),
file('theBenchmark.p',product_on_codomain) ).
cnf(c_16,plain,
product(codomain(A),A,A),
inference(clausify,[status(thm)],[product_on_codomain]) ).
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_22,plain,
( defined(D,A)
| ~ defined(D,C)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[category_theory_axiom3]) ).
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_24,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_27,plain,
( product(A,B,compose(A,B))
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[closure_of_composition]) ).
cnf(c_186,plain,
( defined(A,codomain(B))
| ~ defined(A,B) ),
inference(resolve,[status(thm)],[c_22,c_16]) ).
cnf(c_46,plain,
defined(a,codomain(b)),
inference(resolve,[status(thm)],[c_186,c_14]) ).
cnf(c_65,plain,
product(b,c,compose(b,c)),
inference(resolve,[status(thm)],[c_27,c_13]) ).
cnf(c_187,plain,
( defined(a,A)
| ~ defined(codomain(b),A) ),
inference(resolve,[status(thm)],[c_10,c_46]) ).
cnf(c_119,plain,
~ defined(codomain(b),compose(b,c)),
inference(resolve,[status(thm)],[c_187,c_12]) ).
cnf(c_188,plain,
( defined(codomain(A),C)
| ~ defined(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_189,plain,
( defined(codomain(b),A)
| ~ product(b,c,A) ),
inference(resolve,[status(thm)],[c_188,c_13]) ).
cnf(c_190,plain,
~ product(b,c,compose(b,c)),
inference(resolve,[status(thm)],[c_189,c_119]) ).
cnf(c_185,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_190]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 22:50:03 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 104100 was started by sandbox on n014,
% 0.08/0.35 % Sat Sep 26 22:50:03 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 14.
% 0.13/0.37 % Level of proof is 3.
% 0.13/0.37 % Maximum clause weight is 21.000.
% 0.13/0.37 % Given clauses 37.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------