%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL024-1 : 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 : n006.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 08:24:53 AM UTC 2026
% Result : Unsatisfiable 3.33s 0.88s
% Output : CNFRefutation 3.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 93 ( 93 unt; 0 def)
% Number of atoms : 93 ( 92 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 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 : 149 ( 4 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_1983,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_1983]) ).
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_1984,plain,
zero = complement(join(complement(A),complement(complement(A)))),
inference(paramod,[status(thm)],[c_6,c_18]) ).
cnf(c_1985,plain,
zero = complement(top),
inference(paramod,[status(thm)],[c_17,c_1984]) ).
cnf(c_19,plain,
complement(top) = zero,
inference(copy,[status(thm)],[c_1985]) ).
fof(goals_14,axiom,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
file('theBenchmark.p',goals_14) ).
cnf(c_20,plain,
join(composition(meet(sk1,converse(sk2)),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
inference(clausify,[status(thm)],[goals_14]) ).
cnf(c_1986,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),meet(sk2,sk3)),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
inference(paramod,[status(thm)],[c_6,c_20]) ).
cnf(c_1987,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(meet(sk1,converse(sk2)),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
inference(paramod,[status(thm)],[c_6,c_1986]) ).
cnf(c_1988,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3)))),composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3)) != composition(meet(sk1,converse(sk2)),sk3),
inference(paramod,[status(thm)],[c_6,c_1987]) ).
cnf(c_1989,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3))))) != composition(meet(sk1,converse(sk2)),sk3),
inference(paramod,[status(thm)],[c_1,c_1988]) ).
cnf(c_21,plain,
join(composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),composition(complement(join(complement(sk1),complement(converse(sk2)))),complement(join(complement(sk2),complement(sk3))))) != composition(complement(join(complement(sk1),complement(converse(sk2)))),sk3),
inference(paramod,[status(thm)],[c_6,c_1989]) ).
cnf(c_24,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_25,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_1,c_5]) ).
cnf(c_1990,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_9,c_13]) ).
cnf(c_32,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1990]) ).
cnf(c_1991,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_1992,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_12,c_1991]) ).
cnf(c_1993,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_1992]) ).
cnf(c_1994,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_1993]) ).
cnf(c_1995,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_1994]) ).
cnf(c_33,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_1995]) ).
cnf(c_1996,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_17,c_5]) ).
cnf(c_44,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_19,c_1996]) ).
cnf(c_57,plain,
join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))) = B,
inference(paramod,[status(thm)],[c_1,c_24]) ).
cnf(c_1997,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_17,c_25]) ).
cnf(c_1998,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1997]) ).
cnf(c_1999,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_19,c_1998]) ).
cnf(c_75,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_1,c_1999]) ).
cnf(c_81,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_75,c_44]) ).
cnf(c_82,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_81,c_75]) ).
cnf(c_2000,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_11,c_32]) ).
cnf(c_90,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_11,c_2000]) ).
cnf(c_2001,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_90,c_9]) ).
cnf(c_92,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_2001]) ).
cnf(c_96,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_90,c_15]) ).
cnf(c_97,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_92,c_90]) ).
cnf(c_98,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_97,c_96]) ).
cnf(c_2002,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_98,c_5]) ).
cnf(c_2003,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_1,c_2002]) ).
cnf(c_2004,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_17,c_2003]) ).
cnf(c_2005,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_19,c_2004]) ).
cnf(c_157,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_81,c_2005]) ).
cnf(c_169,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_157,c_82]) ).
cnf(c_2006,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_169,c_5]) ).
cnf(c_2007,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_169,c_2006]) ).
cnf(c_2008,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_5,c_2007]) ).
cnf(c_199,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_2008]) ).
cnf(c_2009,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_33]) ).
cnf(c_2010,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_2009]) ).
cnf(c_211,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_2010]) ).
cnf(c_2011,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_199,c_3]) ).
cnf(c_230,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_2011]) ).
cnf(c_2012,plain,
join(complement(join(A,B)),complement(join(complement(A),complement(complement(B))))) = complement(B),
inference(paramod,[status(thm)],[c_81,c_57]) ).
cnf(c_496,plain,
join(complement(join(A,B)),complement(join(complement(A),B))) = complement(B),
inference(paramod,[status(thm)],[c_81,c_2012]) ).
cnf(c_2013,plain,
join(complement(join(A,complement(B))),B) = join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_57,c_230]) ).
cnf(c_2014,plain,
join(B,complement(join(A,complement(B)))) = join(complement(join(A,complement(B))),complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_1,c_2013]) ).
cnf(c_2015,plain,
join(B,complement(join(A,complement(B)))) = complement(complement(B)),
inference(paramod,[status(thm)],[c_496,c_2014]) ).
cnf(c_497,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_81,c_2015]) ).
cnf(c_2016,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_211]) ).
cnf(c_1640,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_11,c_2016]) ).
cnf(c_2017,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_11,c_1640]) ).
cnf(c_1900,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_11,c_2017]) ).
cnf(c_2018,plain,
composition(A,B) = join(composition(A,B),composition(A,complement(join(C,complement(B))))),
inference(paramod,[status(thm)],[c_497,c_1900]) ).
cnf(c_1981,plain,
join(composition(A,B),composition(A,complement(join(C,complement(B))))) = composition(A,B),
inference(copy,[status(thm)],[c_2018]) ).
cnf(c_1982,plain,
$false,
inference(resolve,[status(thm)],[c_1981,c_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL024-1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 05:31:40 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 463484 was started by sandbox2 on n006,
% 0.09/0.37 % Sat Sep 26 05:31:40 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 3.33/0.88
% 3.33/0.88 % SZS status Unsatisfiable for theBenchmark
% 3.33/0.88
% 3.33/0.88 % Proof 1 at 0.37 (+ 0.11) seconds.
% 3.33/0.88 % Length of proof is 44.
% 3.33/0.88 % Level of proof is 12.
% 3.33/0.88 % Maximum clause weight is 69.000.
% 3.33/0.88 % Given clauses 175.
% 3.33/0.88
% 3.33/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------