%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : CAT002-1 : 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 : n026.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 0.14s 5.78s
% Output : CNFRefutation 0.14s
% 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(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(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_6,plain,
( product(A,domain(B),A)
| ~ defined(A,domain(B)) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
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(cg_equals_d,axiom,
product(c,g,d),
file('theBenchmark.p',cg_equals_d) ).
cnf(c_13,plain,
product(c,g,d),
inference(clausify,[status(thm)],[cg_equals_d]) ).
fof(ch_equals_d,axiom,
product(c,h,d),
file('theBenchmark.p',ch_equals_d) ).
cnf(c_14,plain,
product(c,h,d),
inference(clausify,[status(thm)],[ch_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(b,VAR_2,VAR_1)
| ~ product(b,VAR_0,VAR_1) ),
file('theBenchmark.p',cancellation_for_product2) ).
cnf(c_16,plain,
( A = C
| ~ product(b,C,B)
| ~ product(b,A,B) ),
inference(clausify,[status(thm)],[cancellation_for_product2]) ).
fof(cancellation_for_product1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| ~ product(a,VAR_2,VAR_1)
| ~ product(a,VAR_0,VAR_1) ),
file('theBenchmark.p',cancellation_for_product1) ).
cnf(c_17,plain,
( A = C
| ~ product(a,C,B)
| ~ product(a,A,B) ),
inference(clausify,[status(thm)],[cancellation_for_product1]) ).
fof(product_on_domain,axiom,
! [VAR_0] : product(VAR_0,domain(VAR_0),VAR_0),
file('theBenchmark.p',product_on_domain) ).
cnf(c_20,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_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_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_24,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_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(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_28,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_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(c,h),
inference(resolve,[status(thm)],[c_29,c_14]) ).
cnf(c_61,plain,
defined(c,g),
inference(resolve,[status(thm)],[c_29,c_13]) ).
cnf(c_573,plain,
( defined(b,A)
| ~ defined(c,A) ),
inference(resolve,[status(thm)],[c_28,c_15]) ).
cnf(c_75,plain,
defined(b,h),
inference(resolve,[status(thm)],[c_573,c_60]) ).
cnf(c_574,plain,
( defined(b,A)
| ~ defined(c,A) ),
inference(resolve,[status(thm)],[c_28,c_15]) ).
cnf(c_81,plain,
defined(b,g),
inference(resolve,[status(thm)],[c_574,c_61]) ).
cnf(c_575,plain,
( defined(C,domain(B))
| ~ defined(A,B)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_24,c_20]) ).
cnf(c_576,plain,
( defined(d,domain(g))
| ~ defined(c,g) ),
inference(resolve,[status(thm)],[c_575,c_13]) ).
cnf(c_83,plain,
defined(d,domain(g)),
inference(resolve,[status(thm)],[c_576,c_61]) ).
cnf(c_84,plain,
product(b,h,compose(b,h)),
inference(resolve,[status(thm)],[c_30,c_75]) ).
cnf(c_97,plain,
product(b,g,compose(b,g)),
inference(resolve,[status(thm)],[c_30,c_81]) ).
cnf(c_577,plain,
( defined(h,A)
| ~ defined(d,A) ),
inference(resolve,[status(thm)],[c_28,c_14]) ).
cnf(c_197,plain,
defined(h,domain(g)),
inference(resolve,[status(thm)],[c_577,c_83]) ).
cnf(c_226,plain,
product(h,domain(g),h),
inference(resolve,[status(thm)],[c_6,c_197]) ).
cnf(c_578,plain,
( product(a,C,B)
| ~ product(b,A,C)
| ~ product(c,A,B) ),
inference(resolve,[status(thm)],[c_26,c_15]) ).
cnf(c_579,plain,
( product(a,A,d)
| ~ product(b,h,A) ),
inference(resolve,[status(thm)],[c_578,c_14]) ).
cnf(c_405,plain,
product(a,compose(b,h),d),
inference(resolve,[status(thm)],[c_579,c_84]) ).
cnf(c_580,plain,
( product(a,C,B)
| ~ product(b,A,C)
| ~ product(c,A,B) ),
inference(resolve,[status(thm)],[c_26,c_15]) ).
cnf(c_581,plain,
( product(a,A,d)
| ~ product(b,g,A) ),
inference(resolve,[status(thm)],[c_580,c_13]) ).
cnf(c_429,plain,
product(a,compose(b,g),d),
inference(resolve,[status(thm)],[c_581,c_97]) ).
cnf(c_582,plain,
( product(D,domain(B),C)
| ~ product(A,B,D)
| ~ product(A,B,C) ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_583,plain,
( product(A,domain(g),compose(b,g))
| ~ product(b,g,A) ),
inference(resolve,[status(thm)],[c_582,c_97]) ).
cnf(c_434,plain,
product(compose(b,g),domain(g),compose(b,g)),
inference(resolve,[status(thm)],[c_583,c_97]) ).
cnf(c_584,plain,
( A = g
| ~ product(b,A,compose(b,g)) ),
inference(resolve,[status(thm)],[c_16,c_97]) ).
cnf(c_438,plain,
~ product(b,h,compose(b,g)),
inference(resolve,[status(thm)],[c_584,c_12]) ).
cnf(c_585,plain,
( product(b,C,B)
| ~ product(h,A,C)
| ~ product(compose(b,h),A,B) ),
inference(resolve,[status(thm)],[c_26,c_84]) ).
cnf(c_586,plain,
( product(b,h,A)
| ~ product(compose(b,h),domain(g),A) ),
inference(resolve,[status(thm)],[c_585,c_226]) ).
cnf(c_467,plain,
~ product(compose(b,h),domain(g),compose(b,g)),
inference(resolve,[status(thm)],[c_586,c_438]) ).
cnf(c_587,plain,
( compose(b,h) = A
| ~ product(a,A,d) ),
inference(resolve,[status(thm)],[c_17,c_405]) ).
cnf(c_561,plain,
compose(b,h) = compose(b,g),
inference(resolve,[status(thm)],[c_587,c_429]) ).
cnf(c_571,plain,
~ product(compose(b,g),domain(g),compose(b,g)),
inference(paramod,[status(thm)],[c_561,c_467]) ).
cnf(c_572,plain,
$false,
inference(resolve,[status(thm)],[c_571,c_434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT002-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.58 % Computer : n026.cluster.edu
% 0.10/5.58 % Model : x86_64 x86_64
% 0.10/5.58 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.58 % Memory : 8046.5625MB
% 0.10/5.58 % OS : Linux 6.8.0-71-generic
% 0.10/5.58 % CPULimit : 300
% 0.10/5.58 % WCLimit : 300
% 0.10/5.58 % DateTime : Sat Sep 26 22:49:47 UTC 2026
% 0.10/5.58 % CPUTime :
% 0.10/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.58 % Process 2132965 was started by sandbox2 on n026,
% 0.10/5.58 % Sat Sep 26 22:49:47 2026
% 0.10/5.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.59
% 0.10/5.59 % From the command line: assign(max_seconds, 300).
% 0.14/5.78
% 0.14/5.78 % SZS status Unsatisfiable for theBenchmark
% 0.14/5.78
% 0.14/5.78 % Proof 1 at 0.11 (+ 0.04) seconds.
% 0.14/5.78 % Length of proof is 33.
% 0.14/5.78 % Level of proof is 7.
% 0.14/5.78 % Maximum clause weight is 16.000.
% 0.14/5.78 % Given clauses 165.
% 0.14/5.78
% 0.14/5.78 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------