%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL042+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 : n008.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 08:25:05 AM UTC 2026
% Result : Theorem 5.42s 6.16s
% Output : CNFRefutation 5.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 45
% Number of leaves : 13
% Syntax : Number of formulae : 172 ( 168 unt; 0 def)
% Number of atoms : 176 ( 175 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 9 ( 5 ~; 0 |; 2 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 250 ( 13 sgn 28 !; 1 ?)
% 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] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero
=> join(composition(converse(X0),X0),one) = one ),
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_3578,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_3578]) ).
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_3579,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_3579]) ).
fof(nnf_17,plain,
? [X0] :
( join(composition(converse(X0),X0),one) != one
& ! [X1] : meet(composition(X0,X1),composition(X0,complement(X1))) = zero ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( join(composition(converse(sK0),sK0),one) != one
& ! [X1] : meet(composition(sK0,X1),composition(sK0,complement(X1))) = zero ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
meet(composition(sK0,A),composition(sK0,complement(A))) = zero,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_41,negated_conjecture,
complement(join(complement(composition(sK0,A)),complement(composition(sK0,complement(A))))) = zero,
inference(paramod,[status(thm)],[c_22,c_40]) ).
cnf(c_42,negated_conjecture,
join(composition(converse(sK0),sK0),one) != one,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_43,negated_conjecture,
join(one,composition(converse(sK0),sK0)) != one,
inference(paramod,[status(thm)],[c_18,c_42]) ).
cnf(c_3580,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_3580]) ).
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_3581,plain,
join(A,B) = join(complement(join(complement(A),C)),join(complement(join(complement(A),complement(C))),B)),
inference(paramod,[status(thm)],[c_21,c_19]) ).
cnf(c_48,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),C)) = join(A,C),
inference(copy,[status(thm)],[c_3581]) ).
cnf(c_3582,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_24,c_28]) ).
cnf(c_54,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_3582]) ).
cnf(c_3583,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_3584,plain,
join(converse(composition(A,B)),converse(composition(C,B))) = composition(converse(B),converse(join(A,C))),
inference(paramod,[status(thm)],[c_27,c_3583]) ).
cnf(c_3585,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_3584]) ).
cnf(c_3586,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_3585]) ).
cnf(c_3587,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_3586]) ).
cnf(c_55,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_3587]) ).
cnf(c_3588,plain,
join(complement(A),B) = join(complement(A),join(composition(converse(C),complement(composition(C,A))),B)),
inference(paramod,[status(thm)],[c_30,c_19]) ).
cnf(c_56,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),C)) = join(complement(A),C),
inference(copy,[status(thm)],[c_3588]) ).
cnf(c_59,plain,
join(complement(one),composition(converse(A),complement(A))) = complement(one),
inference(paramod,[status(thm)],[c_24,c_30]) ).
cnf(c_3589,plain,
join(complement(top),complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_31,c_21]) ).
cnf(c_66,plain,
join(zero,complement(join(complement(A),complement(complement(complement(A)))))) = A,
inference(paramod,[status(thm)],[c_33,c_3589]) ).
cnf(c_3590,plain,
composition(top,A) = join(composition(B,A),composition(complement(B),A)),
inference(paramod,[status(thm)],[c_31,c_25]) ).
cnf(c_68,plain,
join(composition(A,B),composition(complement(A),B)) = composition(top,B),
inference(copy,[status(thm)],[c_3590]) ).
cnf(c_3591,plain,
converse(top) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_31,c_27]) ).
cnf(c_69,plain,
join(converse(A),converse(complement(A))) = converse(top),
inference(copy,[status(thm)],[c_3591]) ).
cnf(c_3592,plain,
join(complement(join(zero,A)),complement(join(complement(top),complement(A)))) = top,
inference(paramod,[status(thm)],[c_33,c_21]) ).
cnf(c_70,plain,
join(complement(join(zero,A)),complement(join(zero,complement(A)))) = top,
inference(paramod,[status(thm)],[c_33,c_3592]) ).
cnf(c_3593,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = complement(top),
inference(paramod,[status(thm)],[c_33,c_30]) ).
cnf(c_72,plain,
join(zero,composition(converse(A),complement(composition(A,top)))) = zero,
inference(paramod,[status(thm)],[c_33,c_3593]) ).
cnf(c_3594,plain,
join(complement(join(zero,A)),complement(join(complement(join(complement(composition(sK0,B)),complement(composition(sK0,complement(B))))),complement(A)))) = join(complement(composition(sK0,B)),complement(composition(sK0,complement(B)))),
inference(paramod,[status(thm)],[c_41,c_21]) ).
cnf(c_3595,plain,
join(complement(join(zero,A)),complement(join(zero,complement(A)))) = join(complement(composition(sK0,B)),complement(composition(sK0,complement(B)))),
inference(paramod,[status(thm)],[c_41,c_3594]) ).
cnf(c_3596,plain,
top = join(complement(composition(sK0,B)),complement(composition(sK0,complement(B)))),
inference(paramod,[status(thm)],[c_70,c_3595]) ).
cnf(c_99,plain,
join(complement(composition(sK0,A)),complement(composition(sK0,complement(A)))) = top,
inference(copy,[status(thm)],[c_3596]) ).
cnf(c_3597,plain,
join(complement(join(complement(composition(sK0,A)),composition(sK0,complement(A)))),zero) = composition(sK0,A),
inference(paramod,[status(thm)],[c_41,c_21]) ).
cnf(c_101,plain,
join(zero,complement(join(complement(composition(sK0,A)),composition(sK0,complement(A))))) = composition(sK0,A),
inference(paramod,[status(thm)],[c_18,c_3597]) ).
cnf(c_3598,plain,
join(A,B) = join(complement(join(C,complement(B))),join(A,complement(join(complement(B),complement(C))))),
inference(paramod,[status(thm)],[c_46,c_45]) ).
cnf(c_118,plain,
join(complement(join(A,complement(B))),join(C,complement(join(complement(B),complement(A))))) = join(C,B),
inference(copy,[status(thm)],[c_3598]) ).
cnf(c_3599,plain,
join(complement(join(complement(complement(A)),A)),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_31,c_47]) ).
cnf(c_3600,plain,
join(complement(join(A,complement(complement(A)))),complement(top)) = complement(A),
inference(paramod,[status(thm)],[c_18,c_3599]) ).
cnf(c_3601,plain,
join(complement(join(A,complement(complement(A)))),zero) = complement(A),
inference(paramod,[status(thm)],[c_33,c_3600]) ).
cnf(c_127,plain,
join(zero,complement(join(A,complement(complement(A))))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_3601]) ).
cnf(c_133,plain,
complement(complement(A)) = A,
inference(paramod,[status(thm)],[c_127,c_66]) ).
cnf(c_134,plain,
join(zero,complement(join(A,A))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_127]) ).
cnf(c_3602,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_26,c_54]) ).
cnf(c_143,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_26,c_3602]) ).
cnf(c_3603,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_143,c_24]) ).
cnf(c_152,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_3603]) ).
cnf(c_156,plain,
join(complement(A),complement(composition(one,A))) = complement(A),
inference(paramod,[status(thm)],[c_143,c_30]) ).
cnf(c_171,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_152,c_143]) ).
cnf(c_176,plain,
join(complement(A),complement(A)) = complement(A),
inference(paramod,[status(thm)],[c_171,c_156]) ).
cnf(c_180,plain,
join(complement(join(A,B)),complement(join(complement(join(complement(A),C)),complement(join(complement(join(complement(A),complement(C))),B))))) = join(complement(A),C),
inference(paramod,[status(thm)],[c_48,c_21]) ).
cnf(c_3604,plain,
join(complement(join(complement(A),A)),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_176,c_21]) ).
cnf(c_3605,plain,
join(complement(join(A,complement(A))),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_18,c_3604]) ).
cnf(c_3606,plain,
join(complement(top),complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_31,c_3605]) ).
cnf(c_3607,plain,
join(zero,complement(complement(A))) = A,
inference(paramod,[status(thm)],[c_33,c_3606]) ).
cnf(c_239,plain,
join(zero,A) = A,
inference(paramod,[status(thm)],[c_133,c_3607]) ).
cnf(c_3608,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_176,c_48]) ).
cnf(c_3609,plain,
A = join(A,complement(join(complement(A),complement(B)))),
inference(paramod,[status(thm)],[c_21,c_3608]) ).
cnf(c_242,plain,
join(A,complement(join(complement(A),complement(B)))) = A,
inference(copy,[status(thm)],[c_3609]) ).
cnf(c_251,plain,
complement(join(A,A)) = complement(A),
inference(paramod,[status(thm)],[c_239,c_134]) ).
cnf(c_252,plain,
complement(join(complement(composition(sK0,A)),composition(sK0,complement(A)))) = composition(sK0,A),
inference(paramod,[status(thm)],[c_239,c_101]) ).
cnf(c_260,plain,
composition(converse(A),complement(composition(A,top))) = zero,
inference(paramod,[status(thm)],[c_239,c_72]) ).
cnf(c_3610,plain,
join(complement(join(complement(A),B)),complement(join(complement(join(A,A)),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_251,c_21]) ).
cnf(c_3611,plain,
join(complement(join(complement(A),B)),complement(join(complement(A),complement(B)))) = join(A,A),
inference(paramod,[status(thm)],[c_251,c_3610]) ).
cnf(c_3612,plain,
A = join(A,A),
inference(paramod,[status(thm)],[c_21,c_3611]) ).
cnf(c_296,plain,
join(A,A) = A,
inference(copy,[status(thm)],[c_3612]) ).
cnf(c_3613,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_55]) ).
cnf(c_3614,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_3613]) ).
cnf(c_310,plain,
composition(A,join(converse(B),converse(C))) = join(composition(A,converse(B)),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_3614]) ).
cnf(c_3615,plain,
join(A,B) = join(A,join(A,B)),
inference(paramod,[status(thm)],[c_296,c_19]) ).
cnf(c_329,plain,
join(A,join(A,B)) = join(A,B),
inference(copy,[status(thm)],[c_3615]) ).
cnf(c_3616,plain,
join(complement(join(complement(A),B)),join(complement(join(complement(A),complement(B))),A)) = A,
inference(paramod,[status(thm)],[c_296,c_48]) ).
cnf(c_3617,plain,
join(complement(join(complement(A),B)),join(A,complement(join(complement(A),complement(B))))) = A,
inference(paramod,[status(thm)],[c_18,c_3616]) ).
cnf(c_3618,plain,
join(complement(join(complement(A),B)),A) = A,
inference(paramod,[status(thm)],[c_242,c_3617]) ).
cnf(c_332,plain,
join(A,complement(join(complement(A),B))) = A,
inference(paramod,[status(thm)],[c_18,c_3618]) ).
cnf(c_3619,plain,
join(complement(join(A,B)),complement(join(complement(complement(A)),complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_21]) ).
cnf(c_354,plain,
join(complement(join(A,B)),complement(join(A,complement(B)))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_3619]) ).
cnf(c_394,plain,
join(complement(one),composition(converse(complement(A)),A)) = complement(one),
inference(paramod,[status(thm)],[c_133,c_59]) ).
cnf(c_3620,plain,
join(A,top) = join(A,complement(A)),
inference(paramod,[status(thm)],[c_31,c_329]) ).
cnf(c_474,plain,
join(A,top) = top,
inference(paramod,[status(thm)],[c_31,c_3620]) ).
cnf(c_3621,plain,
join(converse(A),converse(top)) = join(converse(A),converse(complement(A))),
inference(paramod,[status(thm)],[c_69,c_329]) ).
cnf(c_475,plain,
join(converse(A),converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_69,c_3621]) ).
cnf(c_3622,plain,
top = join(top,A),
inference(paramod,[status(thm)],[c_474,c_18]) ).
cnf(c_478,plain,
join(top,A) = top,
inference(copy,[status(thm)],[c_3622]) ).
cnf(c_504,plain,
join(A,composition(complement(one),A)) = composition(top,A),
inference(paramod,[status(thm)],[c_171,c_68]) ).
cnf(c_524,plain,
join(A,converse(top)) = converse(top),
inference(paramod,[status(thm)],[c_26,c_475]) ).
cnf(c_529,plain,
converse(top) = top,
inference(paramod,[status(thm)],[c_524,c_478]) ).
cnf(c_3623,plain,
converse(composition(top,A)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_504,c_27]) ).
cnf(c_3624,plain,
composition(converse(A),converse(top)) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_28,c_3623]) ).
cnf(c_3625,plain,
composition(converse(A),top) = join(converse(A),converse(composition(complement(one),A))),
inference(paramod,[status(thm)],[c_529,c_3624]) ).
cnf(c_3626,plain,
composition(converse(A),top) = join(converse(A),composition(converse(A),converse(complement(one)))),
inference(paramod,[status(thm)],[c_28,c_3625]) ).
cnf(c_673,plain,
join(converse(A),composition(converse(A),converse(complement(one)))) = composition(converse(A),top),
inference(copy,[status(thm)],[c_3626]) ).
cnf(c_3627,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(complement(complement(A)),C)))) = complement(A),
inference(paramod,[status(thm)],[c_332,c_56]) ).
cnf(c_3628,plain,
join(complement(A),join(composition(converse(B),complement(composition(B,A))),complement(join(A,C)))) = complement(A),
inference(paramod,[status(thm)],[c_133,c_3627]) ).
cnf(c_898,plain,
join(complement(A),complement(join(A,B))) = complement(A),
inference(paramod,[status(thm)],[c_56,c_3628]) ).
cnf(c_918,plain,
join(complement(A),complement(join(B,A))) = complement(A),
inference(paramod,[status(thm)],[c_18,c_898]) ).
cnf(c_3629,plain,
join(complement(join(A,complement(B))),complement(complement(A))) = join(complement(complement(A)),B),
inference(paramod,[status(thm)],[c_918,c_118]) ).
cnf(c_3630,plain,
join(complement(join(A,complement(B))),A) = join(complement(complement(A)),B),
inference(paramod,[status(thm)],[c_133,c_3629]) ).
cnf(c_3631,plain,
join(A,complement(join(A,complement(B)))) = join(complement(complement(A)),B),
inference(paramod,[status(thm)],[c_18,c_3630]) ).
cnf(c_1208,plain,
join(A,complement(join(A,complement(B)))) = join(A,B),
inference(paramod,[status(thm)],[c_133,c_3631]) ).
cnf(c_3632,plain,
join(complement(join(composition(sK0,A),B)),complement(join(complement(join(complement(composition(sK0,A)),composition(sK0,complement(A)))),complement(join(complement(top),B))))) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_99,c_180]) ).
cnf(c_3633,plain,
join(complement(join(composition(sK0,A),B)),complement(join(composition(sK0,A),complement(join(complement(top),B))))) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_252,c_3632]) ).
cnf(c_3634,plain,
join(complement(join(composition(sK0,A),B)),complement(join(composition(sK0,A),complement(join(zero,B))))) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_33,c_3633]) ).
cnf(c_3635,plain,
join(complement(join(composition(sK0,A),B)),complement(join(composition(sK0,A),complement(B)))) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_239,c_3634]) ).
cnf(c_3636,plain,
complement(composition(sK0,A)) = join(complement(composition(sK0,A)),composition(sK0,complement(A))),
inference(paramod,[status(thm)],[c_354,c_3635]) ).
cnf(c_1717,plain,
join(complement(composition(sK0,A)),composition(sK0,complement(A))) = complement(composition(sK0,A)),
inference(copy,[status(thm)],[c_3636]) ).
cnf(c_3637,plain,
join(complement(sK0),composition(sK0,complement(one))) = complement(composition(sK0,one)),
inference(paramod,[status(thm)],[c_24,c_1717]) ).
cnf(c_1767,plain,
join(complement(sK0),composition(sK0,complement(one))) = complement(sK0),
inference(paramod,[status(thm)],[c_24,c_3637]) ).
cnf(c_3638,plain,
join(complement(composition(sK0,complement(one))),complement(complement(sK0))) = complement(composition(sK0,complement(one))),
inference(paramod,[status(thm)],[c_1767,c_918]) ).
cnf(c_3639,plain,
join(complement(composition(sK0,complement(one))),sK0) = complement(composition(sK0,complement(one))),
inference(paramod,[status(thm)],[c_133,c_3638]) ).
cnf(c_1779,plain,
join(sK0,complement(composition(sK0,complement(one)))) = complement(composition(sK0,complement(one))),
inference(paramod,[status(thm)],[c_18,c_3639]) ).
cnf(c_2381,plain,
join(complement(one),converse(complement(one))) = complement(one),
inference(paramod,[status(thm)],[c_24,c_394]) ).
cnf(c_3640,plain,
converse(complement(one)) = join(converse(complement(one)),converse(converse(complement(one)))),
inference(paramod,[status(thm)],[c_2381,c_27]) ).
cnf(c_3641,plain,
converse(complement(one)) = join(converse(complement(one)),complement(one)),
inference(paramod,[status(thm)],[c_26,c_3640]) ).
cnf(c_3642,plain,
converse(complement(one)) = join(complement(one),converse(complement(one))),
inference(paramod,[status(thm)],[c_18,c_3641]) ).
cnf(c_2394,plain,
converse(complement(one)) = complement(one),
inference(paramod,[status(thm)],[c_2381,c_3642]) ).
cnf(c_2402,plain,
join(converse(A),composition(converse(A),complement(one))) = composition(converse(A),top),
inference(paramod,[status(thm)],[c_2394,c_673]) ).
cnf(c_3643,plain,
join(A,composition(converse(converse(A)),complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_26,c_2402]) ).
cnf(c_3644,plain,
join(A,composition(A,complement(one))) = composition(converse(converse(A)),top),
inference(paramod,[status(thm)],[c_26,c_3643]) ).
cnf(c_2589,plain,
join(A,composition(A,complement(one))) = composition(A,top),
inference(paramod,[status(thm)],[c_26,c_3644]) ).
cnf(c_2824,plain,
join(A,complement(join(A,B))) = join(A,complement(B)),
inference(paramod,[status(thm)],[c_133,c_1208]) ).
cnf(c_3645,plain,
join(A,complement(composition(A,top))) = join(A,complement(composition(A,complement(one)))),
inference(paramod,[status(thm)],[c_2589,c_2824]) ).
cnf(c_2872,plain,
join(A,complement(composition(A,complement(one)))) = join(A,complement(composition(A,top))),
inference(copy,[status(thm)],[c_3645]) ).
cnf(c_3646,plain,
join(sK0,complement(composition(sK0,top))) = complement(composition(sK0,complement(one))),
inference(paramod,[status(thm)],[c_2872,c_1779]) ).
cnf(c_2883,plain,
complement(composition(sK0,complement(one))) = join(sK0,complement(composition(sK0,top))),
inference(copy,[status(thm)],[c_3646]) ).
cnf(c_3647,plain,
join(complement(complement(one)),composition(converse(sK0),join(sK0,complement(composition(sK0,top))))) = complement(complement(one)),
inference(paramod,[status(thm)],[c_2883,c_30]) ).
cnf(c_3648,plain,
join(one,composition(converse(sK0),join(sK0,complement(composition(sK0,top))))) = complement(complement(one)),
inference(paramod,[status(thm)],[c_133,c_3647]) ).
cnf(c_3186,plain,
join(one,composition(converse(sK0),join(sK0,complement(composition(sK0,top))))) = one,
inference(paramod,[status(thm)],[c_133,c_3648]) ).
cnf(c_3649,plain,
composition(A,join(B,converse(C))) = join(composition(A,converse(converse(B))),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_310]) ).
cnf(c_3250,plain,
composition(A,join(B,converse(C))) = join(composition(A,B),composition(A,converse(C))),
inference(paramod,[status(thm)],[c_26,c_3649]) ).
cnf(c_3650,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,converse(converse(C)))),
inference(paramod,[status(thm)],[c_26,c_3250]) ).
cnf(c_3492,plain,
composition(A,join(B,C)) = join(composition(A,B),composition(A,C)),
inference(paramod,[status(thm)],[c_26,c_3650]) ).
cnf(c_3651,plain,
join(one,join(composition(converse(sK0),sK0),composition(converse(sK0),complement(composition(sK0,top))))) = one,
inference(paramod,[status(thm)],[c_3492,c_3186]) ).
cnf(c_3652,plain,
join(one,join(composition(converse(sK0),sK0),zero)) = one,
inference(paramod,[status(thm)],[c_260,c_3651]) ).
cnf(c_3653,plain,
join(one,join(zero,composition(converse(sK0),sK0))) = one,
inference(paramod,[status(thm)],[c_18,c_3652]) ).
cnf(c_3576,plain,
join(one,composition(converse(sK0),sK0)) = one,
inference(paramod,[status(thm)],[c_239,c_3653]) ).
cnf(c_3577,plain,
$false,
inference(resolve,[status(thm)],[c_3576,c_43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL042+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n008.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % OS : Linux 6.8.0-71-generic
% 0.10/5.36 % CPULimit : 300
% 0.10/5.36 % WCLimit : 300
% 0.10/5.36 % DateTime : Sat Sep 26 05:41:17 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 2900046 was started by sandbox on n008,
% 0.10/5.37 % Sat Sep 26 05:41:17 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/5.37
% 0.10/5.37 % From the command line: assign(max_seconds, 300).
% 5.42/6.16
% 5.42/6.16 % SZS status Theorem for theBenchmark
% 5.42/6.16
% 5.42/6.16 % Proof 1 at 0.63 (+ 0.14) seconds.
% 5.42/6.16 % Length of proof is 93.
% 5.42/6.16 % Level of proof is 21.
% 5.42/6.16 % Maximum clause weight is 71.000.
% 5.42/6.16 % Given clauses 252.
% 5.42/6.16
% 5.42/6.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------