%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL008-2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:24:46 AM UTC 2026
% Result : Unsatisfiable 3.55s 0.91s
% Output : CNFRefutation 3.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 13
% Syntax : Number of formulae : 94 ( 81 unt; 0 def)
% Number of atoms : 107 ( 106 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 40 ( 27 ~; 13 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 137 ( 0 sgn 22 !; 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(maddux2_join_associativity_2,axiom,
! [VAR_0,VAR_1,VAR_2] : join(VAR_0,join(VAR_1,VAR_2)) = join(join(VAR_0,VAR_1),VAR_2),
file('theBenchmark.p',maddux2_join_associativity_2) ).
cnf(c_2,plain,
join(A,join(B,C)) = join(join(A,B),C),
inference(clausify,[status(thm)],[maddux2_join_associativity_2]) ).
cnf(c_3,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(copy,[status(thm)],[c_2]) ).
fof(maddux3_a_kind_of_de_Morgan_3,axiom,
! [VAR_0,VAR_1] : VAR_0 = join(complement(join(complement(VAR_0),complement(VAR_1))),complement(join(complement(VAR_0),VAR_1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan_3) ).
cnf(c_4,plain,
A = join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))),
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan_3]) ).
cnf(c_1868,plain,
A = join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_1,c_4]) ).
cnf(c_5,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_1868]) ).
fof(maddux4_definiton_of_meet_4,axiom,
! [VAR_0,VAR_1] : meet(VAR_0,VAR_1) = complement(join(complement(VAR_0),complement(VAR_1))),
file('theBenchmark.p',maddux4_definiton_of_meet_4) ).
cnf(c_6,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet_4]) ).
fof(composition_identity_6,axiom,
! [VAR_0] : composition(VAR_0,one) = VAR_0,
file('theBenchmark.p',composition_identity_6) ).
cnf(c_9,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity_6]) ).
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(converse_cancellativity_11,axiom,
! [VAR_0,VAR_1] : join(composition(converse(VAR_0),complement(composition(VAR_0,VAR_1))),complement(VAR_1)) = complement(VAR_1),
file('theBenchmark.p',converse_cancellativity_11) ).
cnf(c_14,plain,
join(composition(converse(A),complement(composition(A,B))),complement(B)) = complement(B),
inference(clausify,[status(thm)],[converse_cancellativity_11]) ).
cnf(c_15,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_14]) ).
fof(def_top_12,axiom,
! [VAR_0] : top = join(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_top_12) ).
cnf(c_16,plain,
top = join(A,complement(A)),
inference(clausify,[status(thm)],[def_top_12]) ).
cnf(c_17,plain,
join(A,complement(A)) = top,
inference(copy,[status(thm)],[c_16]) ).
fof(def_zero_13,axiom,
! [VAR_0] : zero = meet(VAR_0,complement(VAR_0)),
file('theBenchmark.p',def_zero_13) ).
cnf(c_18,plain,
zero = meet(A,complement(A)),
inference(clausify,[status(thm)],[def_zero_13]) ).
cnf(c_1869,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_1870,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1869]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_1870]) ).
fof(goals_14,axiom,
( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3)) ),
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(join(composition(sk1,sk2),composition(sk1,sk3)),composition(sk1,join(sk2,sk3))) != composition(sk1,join(sk2,sk3)) ),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_1871,plain,
( join(join(composition(sk1,join(sk2,sk3)),composition(sk1,sk2)),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(paramod,[status(thm)],[c_3,c_20]) ).
cnf(c_1872,plain,
( join(join(composition(sk1,sk2),composition(sk1,join(sk2,sk3))),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(paramod,[status(thm)],[c_1,c_1871]) ).
cnf(c_21,plain,
( join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(paramod,[status(thm)],[c_1,c_1872]) ).
cnf(c_1873,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_1,c_3]) ).
cnf(c_23,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_3,c_1873]) ).
cnf(c_24,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(paramod,[status(thm)],[c_23,c_21]) ).
cnf(c_26,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1874,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_33,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1874]) ).
cnf(c_1875,plain,
converse(join(composition(A,B),composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_10,c_13]) ).
cnf(c_1876,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_12,c_1875]) ).
cnf(c_1877,plain,
join(composition(converse(B),converse(A)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_13,c_1876]) ).
cnf(c_1878,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_13,c_1877]) ).
cnf(c_1879,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),join(converse(A),converse(C))),
inference(paramod,[status(thm)],[c_12,c_1878]) ).
cnf(c_34,plain,
composition(converse(A),join(converse(B),converse(C))) = join(composition(converse(A),converse(B)),composition(converse(A),converse(C))),
inference(copy,[status(thm)],[c_1879]) ).
cnf(c_1880,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_45,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_1880]) ).
cnf(c_1881,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_1882,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_19,c_1881]) ).
cnf(c_46,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_1882]) ).
cnf(c_1883,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_33]) ).
cnf(c_75,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_1883]) ).
cnf(c_1884,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_75,c_9]) ).
cnf(c_77,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1884]) ).
cnf(c_81,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_75,c_15]) ).
cnf(c_82,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_77,c_75]) ).
cnf(c_83,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_82,c_81]) ).
cnf(c_84,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_83,c_46]) ).
cnf(c_1885,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_26]) ).
cnf(c_1886,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1885]) ).
cnf(c_1887,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_1886]) ).
cnf(c_95,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1887]) ).
cnf(c_101,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_95,c_45]) ).
cnf(c_102,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_101,c_95]) ).
cnf(c_103,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_101,c_84]) ).
cnf(c_105,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_103,c_102]) ).
cnf(c_1888,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_105,c_5]) ).
cnf(c_1889,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_105,c_1888]) ).
cnf(c_1890,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_1889]) ).
cnf(c_155,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1890]) ).
cnf(c_1891,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_155,c_3]) ).
cnf(c_156,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1891]) ).
cnf(c_1892,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_155,c_3]) ).
cnf(c_158,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_1,c_1892]) ).
cnf(c_1893,plain,
composition(A,join(converse(B),converse(C))) = join(composition(converse(converse(A)),converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_11,c_34]) ).
cnf(c_1894,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_11,c_1893]) ).
cnf(c_200,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_1894]) ).
cnf(c_1895,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_200]) ).
cnf(c_1658,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_1895]) ).
cnf(c_1896,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_11,c_1658]) ).
cnf(c_1823,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_11,c_1896]) ).
cnf(c_1897,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,sk3)))) != composition(sk1,join(sk2,sk3)) ),
inference(paramod,[status(thm)],[c_1823,c_24]) ).
cnf(c_1898,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),join(composition(sk1,sk2),composition(sk1,sk3))) != composition(sk1,join(sk2,sk3)) ),
inference(paramod,[status(thm)],[c_158,c_1897]) ).
cnf(c_1899,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),composition(sk1,sk3)) != composition(sk1,join(sk2,sk3)) ),
inference(paramod,[status(thm)],[c_156,c_1898]) ).
cnf(c_1900,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),composition(sk1,join(sk2,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(paramod,[status(thm)],[c_1823,c_1899]) ).
cnf(c_1901,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk3),join(composition(sk1,sk2),composition(sk1,sk3)))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(paramod,[status(thm)],[c_1823,c_1900]) ).
cnf(c_1902,plain,
( join(composition(sk1,sk2),join(composition(sk1,sk2),composition(sk1,sk3))) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(paramod,[status(thm)],[c_158,c_1901]) ).
cnf(c_1903,plain,
( join(composition(sk1,sk2),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3))
| join(composition(sk1,sk2),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)) ),
inference(paramod,[status(thm)],[c_156,c_1902]) ).
cnf(c_1904,plain,
join(composition(sk1,sk2),composition(sk1,sk3)) != join(composition(sk1,sk2),composition(sk1,sk3)),
inference(copy,[status(thm)],[c_1903]) ).
cnf(c_1867,plain,
$false,
inference(copy,[status(thm)],[c_1904]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL008-2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 26 05:25:51 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 899561 was started by sandbox2 on n004,
% 0.11/0.37 % Sat Sep 26 05:25:51 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.37
% 0.11/0.37 % From the command line: assign(max_seconds, 300).
% 3.55/0.91
% 3.55/0.91 % SZS status Unsatisfiable for theBenchmark
% 3.55/0.91
% 3.55/0.91 % Proof 1 at 0.36 (+ 0.14) seconds.
% 3.55/0.91 % Length of proof is 44.
% 3.55/0.91 % Level of proof is 11.
% 3.55/0.91 % Maximum clause weight is 75.000.
% 3.55/0.91 % Given clauses 171.
% 3.55/0.91
% 3.55/0.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------