%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL024+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 : 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 08:24:53 AM UTC 2026
% Result : Theorem 7.34s 1.49s
% Output : CNFRefutation 7.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% 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 : 10 ( 10 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 151 ( 5 sgn 28 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('theBenchmark.p',maddux1_join_commutativity) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
file('theBenchmark.p',maddux2_join_associativity) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
file('theBenchmark.p',maddux3_a_kind_of_de_Morgan) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
file('theBenchmark.p',maddux4_definiton_of_meet) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
file('theBenchmark.p',converse_cancellativity) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)),
file('theBenchmark.p',def_top) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)),
file('theBenchmark.p',def_zero) ).
fof(goals,conjecture,
! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(meet(X0,converse(X1)),X2)) = composition(meet(X0,converse(X1)),X2),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] : join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(meet(X0,converse(X1)),X2)) = composition(meet(X0,converse(X1)),X2),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_18,plain,
join(A,B) = join(B,A),
inference(clausify,[status(thm)],[maddux1_join_commutativity]) ).
cnf(c_19,plain,
join(join(A,B),C) = join(A,join(B,C)),
inference(clausify,[status(thm)],[maddux2_join_associativity]) ).
cnf(c_20,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(A),B))) = A,
inference(clausify,[status(thm)],[maddux3_a_kind_of_de_Morgan]) ).
cnf(c_21,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = A,
inference(paramod,[status(thm)],[c_18,c_20]) ).
cnf(c_22,plain,
meet(A,B) = complement(join(complement(A),complement(B))),
inference(clausify,[status(thm)],[maddux4_definiton_of_meet]) ).
cnf(c_24,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_27,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_28,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_29,plain,
complement(A) = join(composition(converse(B),complement(composition(B,A))),complement(A)),
inference(clausify,[status(thm)],[converse_cancellativity]) ).
cnf(c_1631,plain,
complement(A) = join(complement(A),composition(converse(B),complement(composition(B,A)))),
inference(paramod,[status(thm)],[c_18,c_29]) ).
cnf(c_30,plain,
join(complement(A),composition(converse(B),complement(composition(B,A)))) = complement(A),
inference(copy,[status(thm)],[c_1631]) ).
cnf(c_31,plain,
join(A,complement(A)) = top,
inference(clausify,[status(thm)],[def_top]) ).
cnf(c_32,plain,
meet(A,complement(A)) = zero,
inference(clausify,[status(thm)],[def_zero]) ).
cnf(c_1632,plain,
complement(join(complement(A),complement(complement(A)))) = zero,
inference(paramod,[status(thm)],[c_22,c_32]) ).
cnf(c_33,plain,
complement(top) = zero,
inference(paramod,[status(thm)],[c_31,c_1632]) ).
fof(nnf_17,plain,
? [X0,X1,X2] : composition(meet(X0,converse(X1)),X2) != join(composition(meet(X0,converse(X1)),meet(X1,X2)),composition(meet(X0,converse(X1)),X2)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
composition(meet(sK0,converse(sK1)),sK2) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(meet(sK0,converse(sK1)),sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
composition(meet(sK0,converse(sK1)),sK2) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(meet(sK0,converse(sK1)),sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_1633,negated_conjecture,
composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2) != join(composition(meet(sK0,converse(sK1)),meet(sK1,sK2)),composition(meet(sK0,converse(sK1)),sK2)),
inference(paramod,[status(thm)],[c_22,c_40]) ).
cnf(c_1634,negated_conjecture,
composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),meet(sK1,sK2)),composition(meet(sK0,converse(sK1)),sK2)),
inference(paramod,[status(thm)],[c_22,c_1633]) ).
cnf(c_1635,negated_conjecture,
composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2)))),composition(meet(sK0,converse(sK1)),sK2)),
inference(paramod,[status(thm)],[c_22,c_1634]) ).
cnf(c_1636,negated_conjecture,
composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2)))),composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2)),
inference(paramod,[status(thm)],[c_22,c_1635]) ).
cnf(c_1637,negated_conjecture,
composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2) != join(composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2),composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2))))),
inference(paramod,[status(thm)],[c_18,c_1636]) ).
cnf(c_41,negated_conjecture,
join(composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2),composition(complement(join(complement(sK0),complement(converse(sK1)))),complement(join(complement(sK1),complement(sK2))))) != composition(complement(join(complement(sK0),complement(converse(sK1)))),sK2),
inference(copy,[status(thm)],[c_1637]) ).
cnf(c_44,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_45,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_1638,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_48,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_1638]) ).
cnf(c_1639,plain,
converse(join(composition(A,B),composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_25,c_28]) ).
cnf(c_1640,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_27,c_1639]) ).
cnf(c_1641,plain,
join(composition(converse(B),converse(A)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_28,c_1640]) ).
cnf(c_1642,plain,
join(composition(converse(B),converse(A)),composition(converse(B),converse(C))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_28,c_1641]) ).
cnf(c_1643,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_27,c_1642]) ).
cnf(c_49,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_1643]) ).
cnf(c_1644,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_55,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_1644]) ).
cnf(c_1645,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_1646,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_1645]) ).
cnf(c_56,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_1646]) ).
cnf(c_1647,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_48]) ).
cnf(c_74,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_1647]) ).
cnf(c_1648,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_74,c_24]) ).
cnf(c_76,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_1648]) ).
cnf(c_80,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_74,c_30]) ).
cnf(c_81,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_76,c_74]) ).
cnf(c_82,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_81,c_80]) ).
cnf(c_83,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_82,c_56]) ).
cnf(c_1649,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_45]) ).
cnf(c_1650,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_1649]) ).
cnf(c_1651,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_1650]) ).
cnf(c_86,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_1651]) ).
cnf(c_87,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_86,c_55]) ).
cnf(c_88,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_87,c_86]) ).
cnf(c_89,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_87,c_83]) ).
cnf(c_90,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_89,c_88]) ).
cnf(c_1652,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_87,c_44]) ).
cnf(c_107,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_87,c_1652]) ).
cnf(c_1653,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_90,c_87]) ).
cnf(c_1654,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_87,c_1653]) ).
cnf(c_113,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_1654]) ).
cnf(c_1655,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_26,c_49]) ).
cnf(c_1656,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(converse(converse(A)),converse(C))),
inference(paramod,[status(thm)],[c_26,c_1655]) ).
cnf(c_115,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_1656]) ).
cnf(c_1657,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_113,c_19]) ).
cnf(c_131,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_1657]) ).
cnf(c_1658,plain,
join(complement(join(A,B)),complement(B)) = join(complement(join(A,B)),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_107,c_131]) ).
cnf(c_1659,plain,
join(complement(B),complement(join(A,B))) = join(complement(join(A,B)),complement(join(B,complement(A)))),
inference(paramod,[status(thm)],[c_18,c_1658]) ).
cnf(c_255,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_107,c_1659]) ).
cnf(c_1660,plain,
join(A,complement(join(B,complement(A)))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_87,c_255]) ).
cnf(c_315,plain,
join(A,complement(join(B,complement(A)))) = A,
inference(paramod,[status(thm)],[c_87,c_1660]) ).
cnf(c_1661,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_115]) ).
cnf(c_327,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_1661]) ).
cnf(c_1662,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_26,c_327]) ).
cnf(c_1567,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_26,c_1662]) ).
cnf(c_1663,plain,
composition(A,B) = join(composition(A,B),composition(A,complement(join(C,complement(B))))),
inference(paramod,[status(thm)],[c_315,c_1567]) ).
cnf(c_1629,plain,
join(composition(A,B),composition(A,complement(join(C,complement(B))))) = composition(A,B),
inference(copy,[status(thm)],[c_1663]) ).
cnf(c_1630,plain,
$false,
inference(resolve,[status(thm)],[c_1629,c_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL024+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.38 % Computer : n001.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sat Sep 26 05:37:41 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.39 % Process 1006069 was started by sandbox on n001,
% 0.13/0.39 % Sat Sep 26 05:37:41 2026
% 0.13/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.39
% 0.13/0.39 % From the command line: assign(max_seconds, 300).
% 7.34/1.49
% 7.34/1.49 % SZS status Theorem for theBenchmark
% 7.34/1.49
% 7.34/1.49 % Proof 1 at 0.68 (+ 0.22) seconds.
% 7.34/1.49 % Length of proof is 57.
% 7.34/1.49 % Level of proof is 15.
% 7.34/1.49 % Maximum clause weight is 48.000.
% 7.34/1.49 % Given clauses 286.
% 7.34/1.49
% 7.34/1.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------