%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL009-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:24:47 AM UTC 2026
% Result : Unsatisfiable 3.97s 1.56s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 37 ( 32 unt; 0 def)
% Number of atoms : 42 ( 41 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 11 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity_1,axiom,
! [VAR_0,VAR_1] : join(VAR_0,VAR_1) = join(VAR_1,VAR_0),
file('theBenchmark.p',maddux1_join_commutativity_1) ).
cnf(c_1,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity_1]) ).
fof(composition_distributivity_7,axiom,
! [VAR_0,VAR_1,VAR_2] : composition(join(VAR_0,VAR_1),VAR_2) = join(composition(VAR_0,VAR_2),composition(VAR_1,VAR_2)),
file('theBenchmark.p',composition_distributivity_7) ).
cnf(c_10,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity_7]) ).
fof(converse_idempotence_8,axiom,
! [VAR_0] : converse(converse(VAR_0)) = VAR_0,
file('theBenchmark.p',converse_idempotence_8) ).
cnf(c_11,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence_8]) ).
fof(converse_additivity_9,axiom,
! [VAR_0,VAR_1] : converse(join(VAR_0,VAR_1)) = join(converse(VAR_0),converse(VAR_1)),
file('theBenchmark.p',converse_additivity_9) ).
cnf(c_12,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity_9]) ).
fof(converse_multiplicativity_10,axiom,
! [VAR_0,VAR_1] : converse(composition(VAR_0,VAR_1)) = composition(converse(VAR_1),converse(VAR_0)),
file('theBenchmark.p',converse_multiplicativity_10) ).
cnf(c_13,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity_10]) ).
fof(goals_17,axiom,
join(sk1,sk2) = sk2,
file('theBenchmark.p',goals_17) ).
cnf(c_26,plain,
join(sk1,sk2) = sk2,
inference(clausify,[status(thm)],[goals_17]) ).
cnf(c_27,plain,
join(sk2,sk1) = sk2,
inference(paramod,[status(thm)],[c_1,c_26]) ).
fof(goals_18,axiom,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
file('theBenchmark.p',goals_18) ).
cnf(c_28,plain,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk1,sk3),composition(sk2,sk3)) != composition(sk2,sk3) ),
inference(clausify,[status(thm)],[goals_18]) ).
cnf(c_1724,plain,
( join(composition(sk3,sk1),composition(sk3,sk2)) != composition(sk3,sk2)
| join(composition(sk2,sk3),composition(sk1,sk3)) != composition(sk2,sk3) ),
inference(paramod,[status(thm)],[c_1,c_28]) ).
cnf(c_29,plain,
( join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2)
| join(composition(sk2,sk3),composition(sk1,sk3)) != composition(sk2,sk3) ),
inference(paramod,[status(thm)],[c_1,c_1724]) ).
cnf(c_1725,plain,
composition(sk2,A) = join(composition(sk2,A),composition(sk1,A)),
inference(paramod,[status(thm)],[c_27,c_10]) ).
cnf(c_87,plain,
join(composition(sk2,A),composition(sk1,A)) = composition(sk2,A),
inference(copy,[status(thm)],[c_1725]) ).
cnf(c_1726,plain,
converse(sk2) = join(converse(sk2),converse(sk1)),
inference(paramod,[status(thm)],[c_27,c_12]) ).
cnf(c_88,plain,
join(converse(sk2),converse(sk1)) = converse(sk2),
inference(copy,[status(thm)],[c_1726]) ).
cnf(c_1727,plain,
( join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2)
| composition(sk2,sk3) != composition(sk2,sk3) ),
inference(paramod,[status(thm)],[c_87,c_29]) ).
cnf(c_89,plain,
join(composition(sk3,sk2),composition(sk3,sk1)) != composition(sk3,sk2),
inference(copy,[status(thm)],[c_1727]) ).
cnf(c_1728,plain,
composition(converse(sk2),A) = join(composition(converse(sk2),A),composition(converse(sk1),A)),
inference(paramod,[status(thm)],[c_88,c_10]) ).
cnf(c_165,plain,
join(composition(converse(sk2),A),composition(converse(sk1),A)) = composition(converse(sk2),A),
inference(copy,[status(thm)],[c_1728]) ).
cnf(c_1729,plain,
converse(composition(converse(sk2),A)) = join(converse(composition(converse(sk2),A)),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_165,c_12]) ).
cnf(c_1730,plain,
composition(converse(A),converse(converse(sk2))) = join(converse(composition(converse(sk2),A)),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_13,c_1729]) ).
cnf(c_1731,plain,
composition(converse(A),sk2) = join(converse(composition(converse(sk2),A)),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_11,c_1730]) ).
cnf(c_1732,plain,
composition(converse(A),sk2) = join(composition(converse(A),converse(converse(sk2))),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_13,c_1731]) ).
cnf(c_1733,plain,
composition(converse(A),sk2) = join(composition(converse(A),sk2),converse(composition(converse(sk1),A))),
inference(paramod,[status(thm)],[c_11,c_1732]) ).
cnf(c_1734,plain,
composition(converse(A),sk2) = join(composition(converse(A),sk2),composition(converse(A),converse(converse(sk1)))),
inference(paramod,[status(thm)],[c_13,c_1733]) ).
cnf(c_1735,plain,
composition(converse(A),sk2) = join(composition(converse(A),sk2),composition(converse(A),sk1)),
inference(paramod,[status(thm)],[c_11,c_1734]) ).
cnf(c_1217,plain,
join(composition(converse(A),sk2),composition(converse(A),sk1)) = composition(converse(A),sk2),
inference(copy,[status(thm)],[c_1735]) ).
cnf(c_1736,plain,
join(composition(A,sk2),composition(converse(converse(A)),sk1)) = composition(converse(converse(A)),sk2),
inference(paramod,[status(thm)],[c_11,c_1217]) ).
cnf(c_1737,plain,
join(composition(A,sk2),composition(A,sk1)) = composition(converse(converse(A)),sk2),
inference(paramod,[status(thm)],[c_11,c_1736]) ).
cnf(c_1722,plain,
join(composition(A,sk2),composition(A,sk1)) = composition(A,sk2),
inference(paramod,[status(thm)],[c_11,c_1737]) ).
cnf(c_1723,plain,
$false,
inference(resolve,[status(thm)],[c_1722,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL009-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.40 % Computer : n026.cluster.edu
% 0.07/0.40 % Model : x86_64 x86_64
% 0.07/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.40 % Memory : 8046.5625MB
% 0.07/0.40 % OS : Linux 6.8.0-71-generic
% 0.07/0.40 % CPULimit : 300
% 0.07/0.40 % WCLimit : 300
% 0.07/0.40 % DateTime : Sat Sep 26 05:29:26 UTC 2026
% 0.07/0.40 % CPUTime :
% 0.07/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.40 % Process 179480 was started by sandbox on n026,
% 0.07/0.40 % Sat Sep 26 05:29:26 2026
% 0.07/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.41
% 0.07/0.41 % From the command line: assign(max_seconds, 300).
% 3.97/1.56
% 3.97/1.56 % SZS status Unsatisfiable for theBenchmark
% 3.97/1.56
% 3.97/1.56 % Proof 1 at 0.45 (+ 0.10) seconds.
% 3.97/1.56 % Length of proof is 16.
% 3.97/1.56 % Level of proof is 6.
% 3.97/1.56 % Maximum clause weight is 37.000.
% 3.97/1.56 % Given clauses 193.
% 3.97/1.56
% 3.97/1.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------