%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL040+3 : 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 : n015.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 08:25:03 AM UTC 2026
% Result : Theorem 52.59s 8.01s
% Output : CNFRefutation 52.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 15
% Syntax : Number of formulae : 214 ( 210 unt; 0 def)
% Number of atoms : 218 ( 217 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 20 ( 16 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 1 avg)
% Maximal term depth : 9 ( 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 : 349 ( 23 sgn 34 !; 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_associativity,axiom,
! [X0,X1,X2] : composition(X0,composition(X1,X2)) = composition(composition(X0,X1),X2),
file('theBenchmark.p',composition_associativity) ).
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(dedekind_law,axiom,
! [X0,X1,X2] : join(meet(composition(X0,X1),X2),composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2)))) = composition(meet(X0,composition(X2,converse(X1))),meet(X1,composition(converse(X0),X2))),
file('theBenchmark.p',dedekind_law) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( join(composition(converse(X0),X0),one) = one
=> composition(X0,meet(X1,X2)) = meet(composition(X0,X1),composition(X0,X2)) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(composition(converse(X0),X0),one) = one
=> composition(X0,meet(X1,X2)) = meet(composition(X0,X1),composition(X0,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_23,plain,
composition(composition(A,B),C) = composition(A,composition(B,C)),
inference(clausify,[status(thm)],[composition_associativity]) ).
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_3548,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_3548]) ).
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_3549,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_3549]) ).
cnf(c_34,plain,
composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(clausify,[status(thm)],[dedekind_law]) ).
cnf(c_3550,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),meet(C,composition(converse(A),B))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_34]) ).
cnf(c_3551,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(meet(composition(A,C),B),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_3550]) ).
cnf(c_3552,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(meet(A,composition(B,converse(C))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_3551]) ).
cnf(c_3553,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(C))))),meet(C,composition(converse(A),B)))),
inference(paramod,[status(thm)],[c_22,c_3552]) ).
cnf(c_3554,plain,
composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B))))) = join(complement(join(complement(composition(A,C)),complement(B))),composition(complement(join(complement(A),complement(composition(B,converse(C))))),complement(join(complement(C),complement(composition(converse(A),B)))))),
inference(paramod,[status(thm)],[c_22,c_3553]) ).
cnf(c_35,plain,
join(complement(join(complement(composition(A,B)),complement(C))),composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C)))))) = composition(complement(join(complement(A),complement(composition(C,converse(B))))),complement(join(complement(B),complement(composition(converse(A),C))))),
inference(copy,[status(thm)],[c_3554]) ).
fof(nnf_17,plain,
? [X0,X1,X2] :
( composition(X0,meet(X1,X2)) != meet(composition(X0,X1),composition(X0,X2))
& join(composition(converse(X0),X0),one) = one ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( composition(sK0,meet(sK1,sK2)) != meet(composition(sK0,sK1),composition(sK0,sK2))
& join(composition(converse(sK0),sK0),one) = one ),
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,
join(composition(converse(sK0),sK0),one) = one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,negated_conjecture,
join(one,composition(converse(sK0),sK0)) = one,
inference(paramod,[status(thm)],[c_18,c_40]) ).
cnf(c_42,negated_conjecture,
composition(sK0,meet(sK1,sK2)) != meet(composition(sK0,sK1),composition(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_3555,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != meet(composition(sK0,sK1),composition(sK0,sK2)),
inference(paramod,[status(thm)],[c_22,c_42]) ).
cnf(c_43,negated_conjecture,
composition(sK0,complement(join(complement(sK1),complement(sK2)))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_22,c_3555]) ).
cnf(c_3556,plain,
join(join(A,B),C) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_18,c_19]) ).
cnf(c_45,plain,
join(A,join(B,C)) = join(B,join(A,C)),
inference(paramod,[status(thm)],[c_19,c_3556]) ).
cnf(c_46,plain,
join(complement(join(A,complement(B))),complement(join(complement(B),complement(A)))) = B,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_47,plain,
join(complement(join(complement(A),B)),complement(join(complement(B),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_21]) ).
cnf(c_3557,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_50,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_3557]) ).
cnf(c_3558,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_3559,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_27,c_3558]) ).
cnf(c_3560,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_3559]) ).
cnf(c_3561,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_3560]) ).
cnf(c_3562,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_3561]) ).
cnf(c_51,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_3562]) ).
cnf(c_3563,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_57,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_3563]) ).
cnf(c_3564,plain,
join(complement(join(complement(A),complement(A))),complement(top)) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_3565,plain,
join(complement(join(complement(A),complement(A))),zero) = A,
inference(paramod,[status(thm)],[c_33,c_3564]) ).
cnf(c_58,plain,
join(zero,complement(join(complement(A),complement(A)))) = A,
inference(paramod,[status(thm)],[c_18,c_3565]) ).
cnf(c_3566,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_33,c_30]) ).
cnf(c_63,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_33,c_3566]) ).
cnf(c_3567,plain,
composition(one,A) = join(composition(one,A),composition(composition(converse(sK0),sK0),A)),
inference(paramod,[status(thm)],[c_41,c_25]) ).
cnf(c_3568,plain,
composition(one,A) = join(composition(one,A),composition(converse(sK0),composition(sK0,A))),
inference(paramod,[status(thm)],[c_23,c_3567]) ).
cnf(c_66,plain,
join(composition(one,A),composition(converse(sK0),composition(sK0,A))) = composition(one,A),
inference(copy,[status(thm)],[c_3568]) ).
cnf(c_3569,plain,
join(A,top) = join(B,join(A,complement(B))),
inference(paramod,[status(thm)],[c_31,c_45]) ).
cnf(c_68,plain,
join(A,join(B,complement(A))) = join(B,top),
inference(copy,[status(thm)],[c_3569]) ).
cnf(c_3570,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_50]) ).
cnf(c_80,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_3570]) ).
cnf(c_3571,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_80,c_24]) ).
cnf(c_82,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_3571]) ).
cnf(c_86,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_80,c_30]) ).
cnf(c_87,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_82,c_80]) ).
cnf(c_88,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_87,c_86]) ).
cnf(c_3572,plain,
join(A,composition(converse(sK0),composition(sK0,A))) = composition(one,A),
inference(paramod,[status(thm)],[c_87,c_66]) ).
cnf(c_89,plain,
join(A,composition(converse(sK0),composition(sK0,A))) = A,
inference(paramod,[status(thm)],[c_87,c_3572]) ).
cnf(c_90,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_88,c_58]) ).
cnf(c_3573,plain,
A = join(complement(join(complement(B),complement(A))),complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_47,c_18]) ).
cnf(c_91,plain,
join(complement(join(complement(A),complement(B))),complement(join(complement(B),A))) = B,
inference(copy,[status(thm)],[c_3573]) ).
cnf(c_3574,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_47]) ).
cnf(c_3575,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_3574]) ).
cnf(c_3576,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_3575]) ).
cnf(c_93,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_3576]) ).
cnf(c_94,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_93,c_57]) ).
cnf(c_95,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_94,c_93]) ).
cnf(c_96,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_94,c_90]) ).
cnf(c_97,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_96,c_95]) ).
cnf(c_99,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_96,c_63]) ).
cnf(c_3577,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_94,c_21]) ).
cnf(c_112,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_94,c_3577]) ).
cnf(c_3578,plain,
join(complement(join(A,B)),complement(join(complement(complement(B)),complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_94,c_46]) ).
cnf(c_114,plain,
join(complement(join(A,B)),complement(join(B,complement(A)))) = complement(B),
inference(paramod,[status(thm)],[c_94,c_3578]) ).
cnf(c_3579,plain,
join(complement(join(A,B)),complement(join(complement(B),complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_94,c_47]) ).
cnf(c_115,plain,
join(complement(join(A,B)),complement(join(complement(B),A))) = complement(A),
inference(paramod,[status(thm)],[c_94,c_3579]) ).
cnf(c_3580,plain,
join(join(A,A),complement(A)) = top,
inference(paramod,[status(thm)],[c_97,c_31]) ).
cnf(c_3581,plain,
join(A,join(A,complement(A))) = top,
inference(paramod,[status(thm)],[c_19,c_3580]) ).
cnf(c_119,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_3581]) ).
cnf(c_3582,plain,
complement(complement(A)) = join(A,A),
inference(paramod,[status(thm)],[c_97,c_94]) ).
cnf(c_3583,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_94,c_3582]) ).
cnf(c_120,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_3583]) ).
cnf(c_121,plain,
join(A,join(B,complement(A))) = top,
inference(paramod,[status(thm)],[c_119,c_68]) ).
cnf(c_3584,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_51]) ).
cnf(c_3585,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_3584]) ).
cnf(c_122,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_3585]) ).
cnf(c_3586,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_119,c_18]) ).
cnf(c_134,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_3586]) ).
cnf(c_3587,plain,
converse(top) = join(converse(A),converse(top)),
inference(paramod,[status(thm)],[c_119,c_27]) ).
cnf(c_136,plain,
join(converse(A),converse(top)) = converse(top),
inference(copy,[status(thm)],[c_3587]) ).
cnf(c_3588,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_120,c_19]) ).
cnf(c_138,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_3588]) ).
cnf(c_3589,plain,
join(join(A,B),B) = join(A,B),
inference(paramod,[status(thm)],[c_120,c_19]) ).
cnf(c_140,plain,
join(A,join(B,A)) = join(B,A),
inference(paramod,[status(thm)],[c_18,c_3589]) ).
cnf(c_160,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_136]) ).
cnf(c_163,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_160,c_134]) ).
cnf(c_196,plain,
composition(top,complement(composition(top,top))) = zero,
inference(paramod,[status(thm)],[c_163,c_99]) ).
cnf(c_3590,plain,
composition(join(top,A),complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_196,c_25]) ).
cnf(c_3591,plain,
composition(top,complement(composition(top,top))) = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_134,c_3590]) ).
cnf(c_3592,plain,
zero = join(zero,composition(A,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_196,c_3591]) ).
cnf(c_3593,plain,
zero = composition(A,complement(composition(top,top))),
inference(paramod,[status(thm)],[c_96,c_3592]) ).
cnf(c_203,plain,
composition(A,complement(composition(top,top))) = zero,
inference(copy,[status(thm)],[c_3593]) ).
cnf(c_3594,plain,
zero = composition(A,composition(B,complement(composition(top,top)))),
inference(paramod,[status(thm)],[c_203,c_23]) ).
cnf(c_3595,plain,
zero = composition(A,zero),
inference(paramod,[status(thm)],[c_203,c_3594]) ).
cnf(c_205,plain,
composition(A,zero) = zero,
inference(copy,[status(thm)],[c_3595]) ).
cnf(c_251,plain,
join(complement(A),join(B,A)) = top,
inference(paramod,[status(thm)],[c_94,c_121]) ).
cnf(c_3596,plain,
join(complement(join(complement(A),B)),complement(join(complement(complement(B)),A))) = complement(B),
inference(paramod,[status(thm)],[c_94,c_91]) ).
cnf(c_253,plain,
join(complement(join(complement(A),B)),complement(join(B,A))) = complement(B),
inference(paramod,[status(thm)],[c_94,c_3596]) ).
cnf(c_3597,plain,
join(complement(join(complement(A),B)),A) = join(complement(join(complement(B),complement(A))),complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_91,c_140]) ).
cnf(c_3598,plain,
join(A,complement(join(complement(A),B))) = join(complement(join(complement(B),complement(A))),complement(join(complement(A),B))),
inference(paramod,[status(thm)],[c_18,c_3597]) ).
cnf(c_3599,plain,
join(A,complement(join(complement(A),B))) = complement(complement(A)),
inference(paramod,[status(thm)],[c_253,c_3598]) ).
cnf(c_257,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_94,c_3599]) ).
cnf(c_3600,plain,
join(complement(composition(converse(sK0),composition(sK0,A))),A) = top,
inference(paramod,[status(thm)],[c_89,c_251]) ).
cnf(c_275,plain,
join(A,complement(composition(converse(sK0),composition(sK0,A)))) = top,
inference(paramod,[status(thm)],[c_18,c_3600]) ).
cnf(c_3601,plain,
join(complement(join(A,B)),complement(A)) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_112,c_138]) ).
cnf(c_3602,plain,
join(complement(A),complement(join(A,B))) = join(complement(join(A,B)),complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_3601]) ).
cnf(c_298,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_112,c_3602]) ).
cnf(c_3603,plain,
join(complement(complement(A)),complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_114,c_112]) ).
cnf(c_3604,plain,
join(A,complement(join(complement(join(B,A)),complement(complement(join(A,complement(B))))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_94,c_3603]) ).
cnf(c_3605,plain,
join(A,complement(join(complement(join(B,A)),join(A,complement(B))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_94,c_3604]) ).
cnf(c_3606,plain,
join(A,complement(join(join(A,complement(B)),complement(join(B,A))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_18,c_3605]) ).
cnf(c_3607,plain,
join(A,complement(join(A,join(complement(B),complement(join(B,A)))))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_19,c_3606]) ).
cnf(c_3608,plain,
join(A,complement(join(A,complement(B)))) = complement(complement(join(B,A))),
inference(paramod,[status(thm)],[c_298,c_3607]) ).
cnf(c_345,plain,
join(A,complement(join(A,complement(B)))) = join(B,A),
inference(paramod,[status(thm)],[c_94,c_3608]) ).
cnf(c_3609,plain,
join(complement(complement(A)),complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_114,c_114]) ).
cnf(c_3610,plain,
join(A,complement(join(complement(join(A,complement(B))),complement(complement(join(B,A)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_94,c_3609]) ).
cnf(c_3611,plain,
join(A,complement(join(complement(join(A,complement(B))),join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_94,c_3610]) ).
cnf(c_3612,plain,
join(A,complement(join(join(B,A),complement(join(A,complement(B)))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_3611]) ).
cnf(c_3613,plain,
join(A,complement(join(B,join(A,complement(join(A,complement(B))))))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_19,c_3612]) ).
cnf(c_3614,plain,
join(A,complement(join(B,join(B,A)))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_345,c_3613]) ).
cnf(c_3615,plain,
join(A,complement(join(B,A))) = complement(complement(join(A,complement(B)))),
inference(paramod,[status(thm)],[c_138,c_3614]) ).
cnf(c_348,plain,
join(A,complement(join(B,A))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_94,c_3615]) ).
cnf(c_3616,plain,
join(complement(complement(A)),complement(join(complement(join(complement(B),A)),complement(complement(join(A,B)))))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_115,c_114]) ).
cnf(c_3617,plain,
join(A,complement(join(complement(join(complement(B),A)),complement(complement(join(A,B)))))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_94,c_3616]) ).
cnf(c_3618,plain,
join(A,complement(join(complement(join(complement(B),A)),join(A,B)))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_94,c_3617]) ).
cnf(c_3619,plain,
join(A,complement(join(join(A,B),complement(join(complement(B),A))))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_18,c_3618]) ).
cnf(c_3620,plain,
join(A,complement(join(A,join(B,complement(join(complement(B),A)))))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_19,c_3619]) ).
cnf(c_3621,plain,
join(A,complement(join(A,B))) = complement(complement(join(complement(B),A))),
inference(paramod,[status(thm)],[c_257,c_3620]) ).
cnf(c_351,plain,
join(A,complement(join(A,B))) = join(complement(B),A),
inference(paramod,[status(thm)],[c_94,c_3621]) ).
cnf(c_3622,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_122]) ).
cnf(c_383,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_3622]) ).
cnf(c_3623,plain,
composition(A,join(top,converse(B))) = join(composition(A,converse(top)),composition(A,converse(B))),
inference(paramod,[status(thm)],[c_163,c_122]) ).
cnf(c_3624,plain,
composition(A,top) = join(composition(A,converse(top)),composition(A,converse(B))),
inference(paramod,[status(thm)],[c_134,c_3623]) ).
cnf(c_3625,plain,
composition(A,top) = join(composition(A,top),composition(A,converse(B))),
inference(paramod,[status(thm)],[c_163,c_3624]) ).
cnf(c_385,plain,
join(composition(A,top),composition(A,converse(B))) = composition(A,top),
inference(copy,[status(thm)],[c_3625]) ).
cnf(c_402,plain,
join(A,complement(join(B,join(C,A)))) = join(A,complement(join(B,C))),
inference(paramod,[status(thm)],[c_19,c_348]) ).
cnf(c_3626,plain,
join(join(A,B),complement(join(A,join(C,B)))) = join(join(A,B),complement(C)),
inference(paramod,[status(thm)],[c_45,c_348]) ).
cnf(c_3627,plain,
join(A,join(B,complement(join(A,join(C,B))))) = join(join(A,B),complement(C)),
inference(paramod,[status(thm)],[c_19,c_3626]) ).
cnf(c_3628,plain,
join(A,join(B,complement(join(A,C)))) = join(join(A,B),complement(C)),
inference(paramod,[status(thm)],[c_402,c_3627]) ).
cnf(c_406,plain,
join(A,join(B,complement(join(A,C)))) = join(A,join(B,complement(C))),
inference(paramod,[status(thm)],[c_19,c_3628]) ).
cnf(c_3629,plain,
join(join(complement(A),B),C) = join(B,join(complement(join(B,A)),C)),
inference(paramod,[status(thm)],[c_351,c_19]) ).
cnf(c_3630,plain,
join(complement(A),join(B,C)) = join(B,join(complement(join(B,A)),C)),
inference(paramod,[status(thm)],[c_19,c_3629]) ).
cnf(c_444,plain,
join(A,join(complement(join(A,B)),C)) = join(complement(B),join(A,C)),
inference(copy,[status(thm)],[c_3630]) ).
cnf(c_571,plain,
join(composition(A,top),composition(A,B)) = composition(A,top),
inference(paramod,[status(thm)],[c_26,c_385]) ).
cnf(c_3631,plain,
join(complement(composition(A,top)),complement(join(composition(A,B),complement(composition(A,top))))) = complement(composition(A,B)),
inference(paramod,[status(thm)],[c_571,c_114]) ).
cnf(c_580,plain,
join(complement(composition(A,top)),complement(composition(A,B))) = complement(composition(A,B)),
inference(paramod,[status(thm)],[c_348,c_3631]) ).
cnf(c_3632,plain,
join(complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))),composition(complement(join(complement(sK0),complement(composition(composition(sK0,complement(A)),converse(A))))),complement(top))) = composition(complement(join(complement(sK0),complement(composition(composition(sK0,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sK0),composition(sK0,complement(A))))))),
inference(paramod,[status(thm)],[c_275,c_35]) ).
cnf(c_3633,plain,
join(complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))),composition(complement(join(complement(sK0),complement(composition(sK0,composition(complement(A),converse(A)))))),complement(top))) = composition(complement(join(complement(sK0),complement(composition(composition(sK0,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sK0),composition(sK0,complement(A))))))),
inference(paramod,[status(thm)],[c_23,c_3632]) ).
cnf(c_3634,plain,
join(complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))),composition(complement(join(complement(sK0),complement(composition(sK0,composition(complement(A),converse(A)))))),zero)) = composition(complement(join(complement(sK0),complement(composition(composition(sK0,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sK0),composition(sK0,complement(A))))))),
inference(paramod,[status(thm)],[c_33,c_3633]) ).
cnf(c_3635,plain,
join(complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))),zero) = composition(complement(join(complement(sK0),complement(composition(composition(sK0,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sK0),composition(sK0,complement(A))))))),
inference(paramod,[status(thm)],[c_205,c_3634]) ).
cnf(c_3636,plain,
join(zero,complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A)))))) = composition(complement(join(complement(sK0),complement(composition(composition(sK0,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sK0),composition(sK0,complement(A))))))),
inference(paramod,[status(thm)],[c_18,c_3635]) ).
cnf(c_3637,plain,
complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))) = composition(complement(join(complement(sK0),complement(composition(composition(sK0,complement(A)),converse(A))))),complement(join(complement(A),complement(composition(converse(sK0),composition(sK0,complement(A))))))),
inference(paramod,[status(thm)],[c_96,c_3636]) ).
cnf(c_3638,plain,
complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))) = composition(complement(join(complement(sK0),complement(composition(sK0,composition(complement(A),converse(A)))))),complement(join(complement(A),complement(composition(converse(sK0),composition(sK0,complement(A))))))),
inference(paramod,[status(thm)],[c_23,c_3637]) ).
cnf(c_3639,plain,
complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))) = composition(complement(join(complement(sK0),complement(composition(sK0,composition(complement(A),converse(A)))))),complement(top)),
inference(paramod,[status(thm)],[c_275,c_3638]) ).
cnf(c_3640,plain,
complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))) = composition(complement(join(complement(sK0),complement(composition(sK0,composition(complement(A),converse(A)))))),zero),
inference(paramod,[status(thm)],[c_33,c_3639]) ).
cnf(c_1155,plain,
complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))) = zero,
inference(paramod,[status(thm)],[c_205,c_3640]) ).
cnf(c_3641,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_26,c_383]) ).
cnf(c_1838,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_26,c_3641]) ).
cnf(c_3642,plain,
composition(A,top) = join(composition(A,B),composition(A,complement(B))),
inference(paramod,[status(thm)],[c_31,c_1838]) ).
cnf(c_1885,plain,
join(composition(A,B),composition(A,complement(B))) = composition(A,top),
inference(copy,[status(thm)],[c_3642]) ).
cnf(c_3643,plain,
join(composition(A,B),complement(composition(A,top))) = join(complement(composition(A,complement(B))),composition(A,B)),
inference(paramod,[status(thm)],[c_1885,c_351]) ).
cnf(c_3644,plain,
join(composition(A,B),complement(composition(A,top))) = join(composition(A,B),complement(composition(A,complement(B)))),
inference(paramod,[status(thm)],[c_18,c_3643]) ).
cnf(c_1954,plain,
join(composition(A,B),complement(composition(A,complement(B)))) = join(composition(A,B),complement(composition(A,top))),
inference(copy,[status(thm)],[c_3644]) ).
cnf(c_3645,plain,
join(zero,complement(join(complement(composition(sK0,complement(A))),complement(complement(composition(sK0,A)))))) = complement(complement(composition(sK0,complement(A)))),
inference(paramod,[status(thm)],[c_1155,c_114]) ).
cnf(c_3646,plain,
join(zero,complement(join(complement(composition(sK0,complement(A))),composition(sK0,A)))) = complement(complement(composition(sK0,complement(A)))),
inference(paramod,[status(thm)],[c_94,c_3645]) ).
cnf(c_3647,plain,
join(zero,complement(join(composition(sK0,A),complement(composition(sK0,complement(A)))))) = complement(complement(composition(sK0,complement(A)))),
inference(paramod,[status(thm)],[c_18,c_3646]) ).
cnf(c_3648,plain,
join(zero,complement(join(composition(sK0,A),complement(composition(sK0,top))))) = complement(complement(composition(sK0,complement(A)))),
inference(paramod,[status(thm)],[c_1954,c_3647]) ).
cnf(c_3649,plain,
complement(join(composition(sK0,A),complement(composition(sK0,top)))) = complement(complement(composition(sK0,complement(A)))),
inference(paramod,[status(thm)],[c_96,c_3648]) ).
cnf(c_3650,plain,
complement(join(composition(sK0,A),complement(composition(sK0,top)))) = composition(sK0,complement(A)),
inference(paramod,[status(thm)],[c_94,c_3649]) ).
cnf(c_3544,plain,
composition(sK0,complement(A)) = complement(join(composition(sK0,A),complement(composition(sK0,top)))),
inference(copy,[status(thm)],[c_3650]) ).
cnf(c_3651,negated_conjecture,
complement(join(composition(sK0,join(complement(sK1),complement(sK2))),complement(composition(sK0,top)))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_3544,c_43]) ).
cnf(c_3652,negated_conjecture,
complement(join(join(composition(sK0,complement(sK1)),composition(sK0,complement(sK2))),complement(composition(sK0,top)))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_1838,c_3651]) ).
cnf(c_3653,negated_conjecture,
complement(join(join(complement(join(composition(sK0,sK1),complement(composition(sK0,top)))),composition(sK0,complement(sK2))),complement(composition(sK0,top)))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_3544,c_3652]) ).
cnf(c_3654,negated_conjecture,
complement(join(join(complement(join(complement(composition(sK0,top)),composition(sK0,sK1))),composition(sK0,complement(sK2))),complement(composition(sK0,top)))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_18,c_3653]) ).
cnf(c_3655,negated_conjecture,
complement(join(join(complement(join(complement(composition(sK0,top)),composition(sK0,sK1))),complement(join(composition(sK0,sK2),complement(composition(sK0,top))))),complement(composition(sK0,top)))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_3544,c_3654]) ).
cnf(c_3656,negated_conjecture,
complement(join(join(complement(join(complement(composition(sK0,top)),composition(sK0,sK1))),complement(join(complement(composition(sK0,top)),composition(sK0,sK2)))),complement(composition(sK0,top)))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_18,c_3655]) ).
cnf(c_3657,negated_conjecture,
complement(join(complement(composition(sK0,top)),join(complement(join(complement(composition(sK0,top)),composition(sK0,sK1))),complement(join(complement(composition(sK0,top)),composition(sK0,sK2)))))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_18,c_3656]) ).
cnf(c_3658,negated_conjecture,
complement(join(complement(composition(sK0,top)),join(complement(join(complement(composition(sK0,top)),composition(sK0,sK1))),complement(composition(sK0,sK2))))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_406,c_3657]) ).
cnf(c_3659,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),join(complement(composition(sK0,top)),complement(composition(sK0,sK2))))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_444,c_3658]) ).
cnf(c_3660,negated_conjecture,
complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))) != complement(join(complement(composition(sK0,sK1)),complement(composition(sK0,sK2)))),
inference(paramod,[status(thm)],[c_580,c_3659]) ).
cnf(c_3547,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_3660]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL040+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n015.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 05:42:44 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 3253455 was started by sandbox on n015,
% 0.09/0.36 % Sat Sep 26 05:42:44 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 52.59/8.01
% 52.59/8.01 % given #500 (T,wt=24): 1277 join(composition(complement(one),A),join(B,A)) = join(composition(top,A),B). [back_rewrite(1257),rewrite([1261(9)])].
% 52.59/8.01
% 52.59/8.01 % SZS status Theorem for theBenchmark
% 52.59/8.01
% 52.59/8.01 % Proof 1 at 5.74 (+ 1.82) seconds.
% 52.59/8.01 % Length of proof is 98.
% 52.59/8.01 % Level of proof is 19.
% 52.59/8.01 % Maximum clause weight is 64.000.
% 52.59/8.01 % Given clauses 655.
% 52.59/8.01
% 52.59/8.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------