%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT001-1 : 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 : n008.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 06:55:53 AM UTC 2026
% Result : Unsatisfiable 0.13s 0.44s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% 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(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(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]) ).
cnf(c_11,plain,
( defined(A,C)
| ~ defined(domain(B),C)
| ~ defined(A,domain(B)) ),
inference(resolve,[status(thm)],[c_1,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(bg_equals_d,axiom,
product(b,g,d),
file('theBenchmark.p',bg_equals_d) ).
cnf(c_13,plain,
product(b,g,d),
inference(clausify,[status(thm)],[bg_equals_d]) ).
fof(bh_equals_d,axiom,
product(b,h,d),
file('theBenchmark.p',bh_equals_d) ).
cnf(c_14,plain,
product(b,h,d),
inference(clausify,[status(thm)],[bh_equals_d]) ).
fof(cancellation_for_product,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| ~ product(c,VAR_2,VAR_1)
| ~ product(c,VAR_0,VAR_1) ),
file('theBenchmark.p',cancellation_for_product) ).
cnf(c_15,plain,
( A = C
| ~ product(c,C,B)
| ~ product(c,A,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_domain,axiom,
! [VAR_0] : product(VAR_0,domain(VAR_0),VAR_0),
file('theBenchmark.p',product_on_domain) ).
cnf(c_19,plain,
product(A,domain(A),A),
inference(clausify,[status(thm)],[product_on_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_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_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_23,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_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(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_27,plain,
( defined(B,D)
| ~ defined(C,D)
| ~ product(A,B,C) ),
inference(clausify,[status(thm)],[associative_property2]) ).
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(b,h),
inference(resolve,[status(thm)],[c_28,c_14]) ).
cnf(c_560,plain,
( defined(C,domain(B))
| ~ defined(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_23,c_19]) ).
cnf(c_561,plain,
( defined(c,domain(b))
| ~ defined(a,b) ),
inference(resolve,[status(thm)],[c_560,c_16]) ).
cnf(c_71,plain,
defined(c,domain(b)),
inference(resolve,[status(thm)],[c_561,c_58]) ).
cnf(c_562,plain,
( defined(domain(A),B)
| ~ defined(A,B) ),
inference(resolve,[status(thm)],[c_27,c_19]) ).
cnf(c_73,plain,
defined(domain(b),h),
inference(resolve,[status(thm)],[c_562,c_59]) ).
cnf(c_563,plain,
( defined(c,A)
| ~ defined(domain(b),A) ),
inference(resolve,[status(thm)],[c_11,c_71]) ).
cnf(c_150,plain,
defined(c,h),
inference(resolve,[status(thm)],[c_563,c_73]) ).
cnf(c_152,plain,
product(c,h,compose(c,h)),
inference(resolve,[status(thm)],[c_29,c_150]) ).
cnf(c_564,plain,
( product(a,C,B)
| ~ product(b,A,C)
| ~ product(c,A,B) ),
inference(resolve,[status(thm)],[c_25,c_16]) ).
cnf(c_565,plain,
( product(a,A,compose(c,h))
| ~ product(b,h,A) ),
inference(resolve,[status(thm)],[c_564,c_152]) ).
cnf(c_499,plain,
product(a,d,compose(c,h)),
inference(resolve,[status(thm)],[c_565,c_14]) ).
cnf(c_566,plain,
( A = h
| ~ product(c,A,compose(c,h)) ),
inference(resolve,[status(thm)],[c_15,c_152]) ).
cnf(c_567,plain,
g != h,
inference(copy,[status(thm)],[c_12]) ).
cnf(c_507,plain,
~ product(c,g,compose(c,h)),
inference(resolve,[status(thm)],[c_566,c_567]) ).
cnf(c_568,plain,
( product(C,g,B)
| ~ product(A,b,C)
| ~ product(A,d,B) ),
inference(resolve,[status(thm)],[c_22,c_13]) ).
cnf(c_569,plain,
( product(c,g,A)
| ~ product(a,d,A) ),
inference(resolve,[status(thm)],[c_568,c_16]) ).
cnf(c_558,plain,
~ product(a,d,compose(c,h)),
inference(resolve,[status(thm)],[c_569,c_507]) ).
cnf(c_559,plain,
$false,
inference(resolve,[status(thm)],[c_558,c_499]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : CAT001-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.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 22:48:25 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 552775 was started by sandbox2 on n008,
% 0.08/0.35 % Sat Sep 26 22:48:25 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.44
% 0.13/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.13/0.44
% 0.13/0.44 % Proof 1 at 0.05 (+ 0.02) seconds.
% 0.13/0.44 % Length of proof is 25.
% 0.13/0.44 % Level of proof is 7.
% 0.13/0.44 % Maximum clause weight is 16.000.
% 0.13/0.44 % Given clauses 141.
% 0.13/0.44
% 0.13/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------