%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT004-1 : 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 : n001.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 06:55:55 AM UTC 2026
% Result : Unsatisfiable 0.12s 5.48s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 29 unt; 0 def)
% Number of atoms : 122 ( 9 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 123 ( 64 ~; 59 |; 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 : 99 ( 3 sgn 36 !; 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]) ).
cnf(c_9,plain,
( product(codomain(A),B,B)
| ~ defined(codomain(A),B) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
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(gc_equals_d,axiom,
product(g,c,d),
file('theBenchmark.p',gc_equals_d) ).
cnf(c_13,plain,
product(g,c,d),
inference(clausify,[status(thm)],[gc_equals_d]) ).
fof(hc_equals_d,axiom,
product(h,c,d),
file('theBenchmark.p',hc_equals_d) ).
cnf(c_14,plain,
product(h,c,d),
inference(clausify,[status(thm)],[hc_equals_d]) ).
fof(ab_equals_c,axiom,
product(a,b,c),
file('theBenchmark.p',ab_equals_c) ).
cnf(c_15,plain,
product(a,b,c),
inference(clausify,[status(thm)],[ab_equals_c]) ).
fof(cancellation_for_product2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| ~ product(VAR_2,b,VAR_1)
| ~ product(VAR_0,b,VAR_1) ),
file('theBenchmark.p',cancellation_for_product2) ).
cnf(c_16,plain,
( A = C
| ~ product(C,b,B)
| ~ product(A,b,B) ),
inference(clausify,[status(thm)],[cancellation_for_product2]) ).
fof(cancellation_for_product1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| ~ product(VAR_2,a,VAR_1)
| ~ product(VAR_0,a,VAR_1) ),
file('theBenchmark.p',cancellation_for_product1) ).
cnf(c_17,plain,
( A = C
| ~ product(C,a,B)
| ~ product(A,a,B) ),
inference(clausify,[status(thm)],[cancellation_for_product1]) ).
fof(product_on_codomain,axiom,
! [VAR_0] : product(codomain(VAR_0),VAR_0,VAR_0),
file('theBenchmark.p',product_on_codomain) ).
cnf(c_19,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_23,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_25,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_26,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_27,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_29,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_30,plain,
( product(A,B,compose(A,B))
| ~ defined(A,B) ),
inference(clausify,[status(thm)],[closure_of_composition]) ).
cnf(c_60,plain,
defined(h,c),
inference(resolve,[status(thm)],[c_29,c_14]) ).
cnf(c_61,plain,
defined(g,c),
inference(resolve,[status(thm)],[c_29,c_13]) ).
cnf(c_699,plain,
( defined(A,a)
| ~ defined(A,c) ),
inference(resolve,[status(thm)],[c_25,c_15]) ).
cnf(c_77,plain,
defined(h,a),
inference(resolve,[status(thm)],[c_699,c_60]) ).
cnf(c_700,plain,
( defined(codomain(A),C)
| ~ defined(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_27,c_19]) ).
cnf(c_701,plain,
( defined(codomain(g),d)
| ~ defined(g,c) ),
inference(resolve,[status(thm)],[c_700,c_13]) ).
cnf(c_81,plain,
defined(codomain(g),d),
inference(resolve,[status(thm)],[c_701,c_61]) ).
cnf(c_702,plain,
( defined(A,a)
| ~ defined(A,c) ),
inference(resolve,[status(thm)],[c_25,c_15]) ).
cnf(c_83,plain,
defined(g,a),
inference(resolve,[status(thm)],[c_702,c_61]) ).
cnf(c_84,plain,
product(h,a,compose(h,a)),
inference(resolve,[status(thm)],[c_30,c_77]) ).
cnf(c_87,plain,
product(g,a,compose(g,a)),
inference(resolve,[status(thm)],[c_30,c_83]) ).
cnf(c_703,plain,
( defined(A,h)
| ~ defined(A,d) ),
inference(resolve,[status(thm)],[c_25,c_14]) ).
cnf(c_187,plain,
defined(codomain(g),h),
inference(resolve,[status(thm)],[c_703,c_81]) ).
cnf(c_209,plain,
product(codomain(g),h,h),
inference(resolve,[status(thm)],[c_9,c_187]) ).
cnf(c_704,plain,
( product(C,b,B)
| ~ product(A,a,C)
| ~ product(A,c,B) ),
inference(resolve,[status(thm)],[c_23,c_15]) ).
cnf(c_705,plain,
( product(A,b,d)
| ~ product(h,a,A) ),
inference(resolve,[status(thm)],[c_704,c_14]) ).
cnf(c_333,plain,
product(compose(h,a),b,d),
inference(resolve,[status(thm)],[c_705,c_84]) ).
cnf(c_706,plain,
( product(codomain(A),D,C)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_26,c_19]) ).
cnf(c_707,plain,
( product(codomain(g),A,compose(g,a))
| ~ product(g,a,A) ),
inference(resolve,[status(thm)],[c_706,c_87]) ).
cnf(c_355,plain,
product(codomain(g),compose(g,a),compose(g,a)),
inference(resolve,[status(thm)],[c_707,c_87]) ).
cnf(c_708,plain,
( product(C,b,B)
| ~ product(A,a,C)
| ~ product(A,c,B) ),
inference(resolve,[status(thm)],[c_23,c_15]) ).
cnf(c_709,plain,
( product(A,b,d)
| ~ product(g,a,A) ),
inference(resolve,[status(thm)],[c_708,c_13]) ).
cnf(c_360,plain,
product(compose(g,a),b,d),
inference(resolve,[status(thm)],[c_709,c_87]) ).
cnf(c_710,plain,
( A = g
| ~ product(A,a,compose(g,a)) ),
inference(resolve,[status(thm)],[c_17,c_87]) ).
cnf(c_364,plain,
~ product(h,a,compose(g,a)),
inference(resolve,[status(thm)],[c_710,c_12]) ).
cnf(c_711,plain,
( product(C,a,B)
| ~ product(A,h,C)
| ~ product(A,compose(h,a),B) ),
inference(resolve,[status(thm)],[c_23,c_84]) ).
cnf(c_712,plain,
( product(h,a,A)
| ~ product(codomain(g),compose(h,a),A) ),
inference(resolve,[status(thm)],[c_711,c_209]) ).
cnf(c_497,plain,
~ product(codomain(g),compose(h,a),compose(g,a)),
inference(resolve,[status(thm)],[c_712,c_364]) ).
cnf(c_713,plain,
( compose(h,a) = A
| ~ product(A,b,d) ),
inference(resolve,[status(thm)],[c_16,c_333]) ).
cnf(c_694,plain,
compose(h,a) = compose(g,a),
inference(resolve,[status(thm)],[c_713,c_360]) ).
cnf(c_697,plain,
~ product(codomain(g),compose(g,a),compose(g,a)),
inference(paramod,[status(thm)],[c_694,c_497]) ).
cnf(c_698,plain,
$false,
inference(resolve,[status(thm)],[c_697,c_355]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT004-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.36 % Computer : n001.cluster.edu
% 0.09/5.36 % Model : x86_64 x86_64
% 0.09/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.36 % Memory : 8046.5625MB
% 0.09/5.36 % OS : Linux 6.8.0-71-generic
% 0.09/5.36 % CPULimit : 300
% 0.09/5.36 % WCLimit : 300
% 0.09/5.36 % DateTime : Sat Sep 26 22:54:04 UTC 2026
% 0.09/5.36 % CPUTime :
% 0.09/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.36 % Process 2867286 was started by sandbox2 on n001,
% 0.09/5.36 % Sat Sep 26 22:54:04 2026
% 0.09/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.37
% 0.09/5.37 % From the command line: assign(max_seconds, 300).
% 0.12/5.48
% 0.12/5.48 % SZS status Unsatisfiable for theBenchmark
% 0.12/5.48
% 0.12/5.48 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.12/5.48 % Length of proof is 33.
% 0.12/5.48 % Level of proof is 7.
% 0.12/5.48 % Maximum clause weight is 21.000.
% 0.12/5.48 % Given clauses 172.
% 0.12/5.48
% 0.12/5.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------