%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT003-1 : 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 : 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 06:55:54 AM UTC 2026
% Result : Unsatisfiable 1.49s 0.59s
% Output : CNFRefutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 49 ( 23 unt; 0 def)
% Number of atoms : 99 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 105 ( 55 ~; 50 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 86 ( 3 sgn 34 !; 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_h_equals_g,axiom,
h != g,
file('theBenchmark.p',prove_h_equals_g) ).
cnf(c_12,plain,
h != g,
inference(clausify,[status(thm)],[prove_h_equals_g]) ).
fof(ga_equals_d,axiom,
product(g,a,d),
file('theBenchmark.p',ga_equals_d) ).
cnf(c_13,plain,
product(g,a,d),
inference(clausify,[status(thm)],[ga_equals_d]) ).
fof(ha_equals_d,axiom,
product(h,a,d),
file('theBenchmark.p',ha_equals_d) ).
cnf(c_14,plain,
product(h,a,d),
inference(clausify,[status(thm)],[ha_equals_d]) ).
fof(cancellation_for_product,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| ~ product(VAR_2,c,VAR_1)
| ~ product(VAR_0,c,VAR_1) ),
file('theBenchmark.p',cancellation_for_product) ).
cnf(c_15,plain,
( A = C
| ~ product(C,c,B)
| ~ product(A,c,B) ),
inference(clausify,[status(thm)],[cancellation_for_product]) ).
fof(ab_equals_c,axiom,
product(a,b,c),
file('theBenchmark.p',ab_equals_c) ).
cnf(c_16,plain,
product(a,b,c),
inference(clausify,[status(thm)],[ab_equals_c]) ).
fof(product_on_codomain,axiom,
! [VAR_0] : product(codomain(VAR_0),VAR_0,VAR_0),
file('theBenchmark.p',product_on_codomain) ).
cnf(c_18,plain,
product(codomain(A),A,A),
inference(clausify,[status(thm)],[product_on_codomain]) ).
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_22,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_24,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_25,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_26,plain,
( defined(A,E)
| ~ defined(C,D)
| ~ product(B,D,E)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[category_theory_axiom1]) ).
fof(associative_property1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( defined(VAR_0,VAR_1)
| ~ product(VAR_0,VAR_1,VAR_2) ),
file('theBenchmark.p',associative_property1) ).
cnf(c_28,plain,
( defined(A,B)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associative_property1]) ).
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_29,plain,
( product(A,B,compose(A,B))
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[closure_of_composition]) ).
cnf(c_58,plain,
defined(a,b),
inference(resolve,[status(thm)],[c_28,c_16]) ).
cnf(c_59,plain,
defined(h,a),
inference(resolve,[status(thm)],[c_28,c_14]) ).
cnf(c_549,plain,
( defined(codomain(A),C)
| ~ defined(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_26,c_18]) ).
cnf(c_550,plain,
( defined(codomain(a),c)
| ~ defined(a,b) ),
inference(resolve,[status(thm)],[c_549,c_16]) ).
cnf(c_69,plain,
defined(codomain(a),c),
inference(resolve,[status(thm)],[c_550,c_58]) ).
cnf(c_551,plain,
( defined(A,codomain(B))
| ~ defined(A,B) ),
inference(resolve,[status(thm)],[c_24,c_18]) ).
cnf(c_75,plain,
defined(h,codomain(a)),
inference(resolve,[status(thm)],[c_551,c_59]) ).
cnf(c_552,plain,
( defined(h,A)
| ~ defined(codomain(a),A) ),
inference(resolve,[status(thm)],[c_10,c_75]) ).
cnf(c_157,plain,
defined(h,c),
inference(resolve,[status(thm)],[c_552,c_69]) ).
cnf(c_160,plain,
product(h,c,compose(h,c)),
inference(resolve,[status(thm)],[c_29,c_157]) ).
cnf(c_553,plain,
( product(C,b,B)
| ~ product(A,a,C)
| ~ product(A,c,B) ),
inference(resolve,[status(thm)],[c_22,c_16]) ).
cnf(c_554,plain,
( product(A,b,compose(h,c))
| ~ product(h,a,A) ),
inference(resolve,[status(thm)],[c_553,c_160]) ).
cnf(c_497,plain,
product(d,b,compose(h,c)),
inference(resolve,[status(thm)],[c_554,c_14]) ).
cnf(c_555,plain,
( A = h
| ~ product(A,c,compose(h,c)) ),
inference(resolve,[status(thm)],[c_15,c_160]) ).
cnf(c_556,plain,
g != h,
inference(copy,[status(thm)],[c_12]) ).
cnf(c_498,plain,
~ product(g,c,compose(h,c)),
inference(resolve,[status(thm)],[c_555,c_556]) ).
cnf(c_557,plain,
( product(g,C,B)
| ~ product(a,A,C)
| ~ product(d,A,B) ),
inference(resolve,[status(thm)],[c_25,c_13]) ).
cnf(c_558,plain,
( product(g,c,A)
| ~ product(d,b,A) ),
inference(resolve,[status(thm)],[c_557,c_16]) ).
cnf(c_547,plain,
~ product(d,b,compose(h,c)),
inference(resolve,[status(thm)],[c_558,c_498]) ).
cnf(c_548,plain,
$false,
inference(resolve,[status(thm)],[c_547,c_497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 22:49:54 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 1614573 was started by sandbox2 on n018,
% 0.09/0.37 % Sat Sep 26 22:49:54 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 1.49/0.59
% 1.49/0.59 % SZS status Unsatisfiable for theBenchmark
% 1.49/0.59
% 1.49/0.59 % Proof 1 at 0.15 (+ 0.05) seconds.
% 1.49/0.59 % Length of proof is 25.
% 1.49/0.59 % Level of proof is 7.
% 1.49/0.59 % Maximum clause weight is 16.000.
% 1.49/0.59 % Given clauses 139.
% 1.49/0.59
% 1.49/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------