TSTP Solution File: REL001+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : REL001+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 19:42:56 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 56
% Syntax : Number of formulae : 234 ( 138 unt; 0 def)
% Number of atoms : 372 ( 371 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 282 ( 144 ~; 138 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 287 ( 0 sgn 54 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(maddux1_join_commutativity,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0) ).
fof(maddux2_join_associativity,axiom,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2) ).
fof(maddux3_a_kind_of_de_Morgan,axiom,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) ).
fof(maddux4_definiton_of_meet,axiom,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))) ).
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0 ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0 ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)) ).
fof(converse_cancellativity,axiom,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1) ).
fof(def_top,axiom,
! [X0] : top = join(X0,complement(X0)) ).
fof(def_zero,axiom,
! [X0] : zero = meet(X0,complement(X0)) ).
fof(goals,conjecture,
! [X0] : join(zero,X0) = X0 ).
fof(subgoal_0,plain,
! [X0] : join(zero,X0) = X0,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : join(zero,X0) = X0,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : join(zero,X0) != X0,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
join(zero,skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0,
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[maddux1_join_commutativity]) ).
fof(normalize_0_3,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[maddux2_join_associativity]) ).
fof(normalize_0_5,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[converse_cancellativity]) ).
fof(normalize_0_7,plain,
! [X0,X1] : join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[converse_multiplicativity]) ).
fof(normalize_0_9,plain,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0] : converse(converse(X0)) = X0,
inference(canonicalize,[],[converse_idempotence]) ).
fof(normalize_0_11,plain,
! [X0] : converse(converse(X0)) = X0,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0] : composition(X0,one) = X0,
inference(canonicalize,[],[composition_identity]) ).
fof(normalize_0_13,plain,
! [X0] : composition(X0,one) = X0,
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(canonicalize,[],[def_zero]) ).
fof(normalize_0_15,plain,
! [X0] : zero = meet(X0,complement(X0)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[maddux4_definiton_of_meet]) ).
fof(normalize_0_17,plain,
! [X0,X1] : meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X0] : top = join(X0,complement(X0)),
inference(canonicalize,[],[def_top]) ).
fof(normalize_0_19,plain,
! [X0] : top = join(X0,complement(X0)),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[maddux3_a_kind_of_de_Morgan]) ).
fof(normalize_0_21,plain,
! [X0,X1] : X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(specialize,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
join(zero,skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
join(X0,X1) = join(X1,X0),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( join(X0,X1) != join(X1,X0)
| join(X1,X0) = join(X0,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X0,X1))),bind(Y,$fot(join(X1,X0)))]]) ).
cnf(refute_0_6,plain,
join(X1,X0) = join(X0,X1),
inference(resolve,[$cnf( $equal(join(X0,X1),join(X1,X0)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
join(zero,skolemFOFtoCNF_X0) = join(skolemFOFtoCNF_X0,zero),
inference(subst,[],[refute_0_6:[bind(X0,$fot(skolemFOFtoCNF_X0)),bind(X1,$fot(zero))]]) ).
cnf(refute_0_8,plain,
( join(skolemFOFtoCNF_X0,zero) != skolemFOFtoCNF_X0
| join(zero,skolemFOFtoCNF_X0) != join(skolemFOFtoCNF_X0,zero)
| join(zero,skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,skolemFOFtoCNF_X0),join(skolemFOFtoCNF_X0,zero)) ),[1],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_9,plain,
( join(skolemFOFtoCNF_X0,zero) != skolemFOFtoCNF_X0
| join(zero,skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0 ),
inference(resolve,[$cnf( $equal(join(zero,skolemFOFtoCNF_X0),join(skolemFOFtoCNF_X0,zero)) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
join(skolemFOFtoCNF_X0,zero) != skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(join(zero,skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
join(join(zero,X_40),zero) = join(zero,join(zero,X_40)),
inference(subst,[],[refute_0_1:[bind(X0,$fot(join(zero,X_40))),bind(X1,$fot(zero))]]) ).
cnf(refute_0_12,plain,
join(X0,join(X1,X2)) = join(join(X0,X1),X2),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_13,plain,
join(zero,join(zero,X2)) = join(join(zero,zero),X2),
inference(subst,[],[refute_0_12:[bind(X0,$fot(zero)),bind(X1,$fot(zero))]]) ).
cnf(refute_0_14,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = complement(X1),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_15,plain,
join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) = join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(X1))),bind(X1,$fot(composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_0_16,plain,
( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != complement(X1)
| join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))
| join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1) ),
introduced(tautology,[equality,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) ),[0],$fot(join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))))]]) ).
cnf(refute_0_17,plain,
( join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)) != complement(X1)
| join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1) ),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),join(complement(X1),composition(converse(X0),complement(composition(X0,X1))))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
join(complement(X1),composition(converse(X0),complement(composition(X0,X1)))) = complement(X1),
inference(resolve,[$cnf( $equal(join(composition(converse(X0),complement(composition(X0,X1))),complement(X1)),complement(X1)) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
join(complement(X_18),composition(converse(one),complement(composition(one,X_18)))) = complement(X_18),
inference(subst,[],[refute_0_18:[bind(X0,$fot(one)),bind(X1,$fot(X_18))]]) ).
cnf(refute_0_20,plain,
converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_21,plain,
converse(composition(converse(X0),X_7)) = composition(converse(X_7),converse(converse(X0))),
inference(subst,[],[refute_0_20:[bind(X0,$fot(converse(X0))),bind(X1,$fot(X_7))]]) ).
cnf(refute_0_22,plain,
converse(converse(X0)) = X0,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_23,plain,
( converse(composition(converse(X0),X_7)) != composition(converse(X_7),converse(converse(X0)))
| converse(converse(X0)) != X0
| converse(composition(converse(X0),X_7)) = composition(converse(X_7),X0) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X0),X_7)),composition(converse(X_7),converse(converse(X0)))) ),[1,1],$fot(X0)]]) ).
cnf(refute_0_24,plain,
( converse(composition(converse(X0),X_7)) != composition(converse(X_7),converse(converse(X0)))
| converse(composition(converse(X0),X_7)) = composition(converse(X_7),X0) ),
inference(resolve,[$cnf( $equal(converse(converse(X0)),X0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
converse(composition(converse(X0),X_7)) = composition(converse(X_7),X0),
inference(resolve,[$cnf( $equal(converse(composition(converse(X0),X_7)),composition(converse(X_7),converse(converse(X0)))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
converse(composition(converse(X_11),one)) = composition(converse(one),X_11),
inference(subst,[],[refute_0_25:[bind(X0,$fot(X_11)),bind(X_7,$fot(one))]]) ).
cnf(refute_0_27,plain,
composition(X0,one) = X0,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_28,plain,
composition(converse(X_11),one) = converse(X_11),
inference(subst,[],[refute_0_27:[bind(X0,$fot(converse(X_11)))]]) ).
cnf(refute_0_29,plain,
( composition(converse(X_11),one) != converse(X_11)
| converse(composition(converse(X_11),one)) != composition(converse(one),X_11)
| converse(converse(X_11)) = composition(converse(one),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(converse(composition(converse(X_11),one)),composition(converse(one),X_11)) ),[0,0],$fot(converse(X_11))]]) ).
cnf(refute_0_30,plain,
( converse(composition(converse(X_11),one)) != composition(converse(one),X_11)
| converse(converse(X_11)) = composition(converse(one),X_11) ),
inference(resolve,[$cnf( $equal(composition(converse(X_11),one),converse(X_11)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
converse(converse(X_11)) = composition(converse(one),X_11),
inference(resolve,[$cnf( $equal(converse(composition(converse(X_11),one)),composition(converse(one),X_11)) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
converse(converse(X_11)) = X_11,
inference(subst,[],[refute_0_22:[bind(X0,$fot(X_11))]]) ).
cnf(refute_0_33,plain,
( converse(converse(X_11)) != X_11
| converse(converse(X_11)) != composition(converse(one),X_11)
| X_11 = composition(converse(one),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(converse(converse(X_11)),composition(converse(one),X_11)) ),[0],$fot(X_11)]]) ).
cnf(refute_0_34,plain,
( converse(converse(X_11)) != composition(converse(one),X_11)
| X_11 = composition(converse(one),X_11) ),
inference(resolve,[$cnf( $equal(converse(converse(X_11)),X_11) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
X_11 = composition(converse(one),X_11),
inference(resolve,[$cnf( $equal(converse(converse(X_11)),composition(converse(one),X_11)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
composition(converse(one),one) = converse(one),
inference(subst,[],[refute_0_27:[bind(X0,$fot(converse(one)))]]) ).
cnf(refute_0_37,plain,
one = composition(converse(one),one),
inference(subst,[],[refute_0_35:[bind(X_11,$fot(one))]]) ).
cnf(refute_0_38,plain,
( one != composition(converse(one),one)
| composition(converse(one),one) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(composition(converse(one),one)))]]) ).
cnf(refute_0_39,plain,
composition(converse(one),one) = one,
inference(resolve,[$cnf( $equal(one,composition(converse(one),one)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( composition(converse(one),one) != converse(one)
| composition(converse(one),one) != one
| one = converse(one) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),one),converse(one)) ),[0],$fot(one)]]) ).
cnf(refute_0_41,plain,
( composition(converse(one),one) != converse(one)
| one = converse(one) ),
inference(resolve,[$cnf( $equal(composition(converse(one),one),one) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
one = converse(one),
inference(resolve,[$cnf( $equal(composition(converse(one),one),converse(one)) )],[refute_0_36,refute_0_41]) ).
cnf(refute_0_43,plain,
( one != converse(one)
| converse(one) = one ),
inference(subst,[],[refute_0_4:[bind(X,$fot(one)),bind(Y,$fot(converse(one)))]]) ).
cnf(refute_0_44,plain,
converse(one) = one,
inference(resolve,[$cnf( $equal(one,converse(one)) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
composition(converse(one),X_11) = composition(converse(one),X_11),
introduced(tautology,[refl,[$fot(composition(converse(one),X_11))]]) ).
cnf(refute_0_46,plain,
( composition(converse(one),X_11) != composition(converse(one),X_11)
| converse(one) != one
| composition(converse(one),X_11) = composition(one,X_11) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),X_11),composition(converse(one),X_11)) ),[1,0],$fot(one)]]) ).
cnf(refute_0_47,plain,
( converse(one) != one
| composition(converse(one),X_11) = composition(one,X_11) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_11),composition(converse(one),X_11)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
composition(converse(one),X_11) = composition(one,X_11),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( X_11 != composition(converse(one),X_11)
| composition(converse(one),X_11) != composition(one,X_11)
| X_11 = composition(one,X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_11,composition(one,X_11)) ),[0],$fot(composition(converse(one),X_11))]]) ).
cnf(refute_0_50,plain,
( X_11 != composition(converse(one),X_11)
| X_11 = composition(one,X_11) ),
inference(resolve,[$cnf( $equal(composition(converse(one),X_11),composition(one,X_11)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
X_11 = composition(one,X_11),
inference(resolve,[$cnf( $equal(X_11,composition(converse(one),X_11)) )],[refute_0_35,refute_0_50]) ).
cnf(refute_0_52,plain,
X_18 = composition(one,X_18),
inference(subst,[],[refute_0_51:[bind(X_11,$fot(X_18))]]) ).
cnf(refute_0_53,plain,
( X_18 != composition(one,X_18)
| composition(one,X_18) = X_18 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_18)),bind(Y,$fot(composition(one,X_18)))]]) ).
cnf(refute_0_54,plain,
composition(one,X_18) = X_18,
inference(resolve,[$cnf( $equal(X_18,composition(one,X_18)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( composition(one,X_18) != X_18
| join(complement(X_18),composition(converse(one),complement(composition(one,X_18)))) != complement(X_18)
| join(complement(X_18),composition(converse(one),complement(X_18))) = complement(X_18) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_18),composition(converse(one),complement(composition(one,X_18)))),complement(X_18)) ),[0,1,1,0],$fot(X_18)]]) ).
cnf(refute_0_56,plain,
( join(complement(X_18),composition(converse(one),complement(composition(one,X_18)))) != complement(X_18)
| join(complement(X_18),composition(converse(one),complement(X_18))) = complement(X_18) ),
inference(resolve,[$cnf( $equal(composition(one,X_18),X_18) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
join(complement(X_18),composition(converse(one),complement(X_18))) = complement(X_18),
inference(resolve,[$cnf( $equal(join(complement(X_18),composition(converse(one),complement(composition(one,X_18)))),complement(X_18)) )],[refute_0_19,refute_0_56]) ).
cnf(refute_0_58,plain,
( X_11 != composition(one,X_11)
| composition(one,X_11) = X_11 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_11)),bind(Y,$fot(composition(one,X_11)))]]) ).
cnf(refute_0_59,plain,
composition(one,X_11) = X_11,
inference(resolve,[$cnf( $equal(X_11,composition(one,X_11)) )],[refute_0_51,refute_0_58]) ).
cnf(refute_0_60,plain,
composition(one,complement(X_18)) = complement(X_18),
inference(subst,[],[refute_0_59:[bind(X_11,$fot(complement(X_18)))]]) ).
cnf(refute_0_61,plain,
composition(converse(one),complement(X_18)) = composition(converse(one),complement(X_18)),
introduced(tautology,[refl,[$fot(composition(converse(one),complement(X_18)))]]) ).
cnf(refute_0_62,plain,
( composition(converse(one),complement(X_18)) != composition(converse(one),complement(X_18))
| converse(one) != one
| composition(converse(one),complement(X_18)) = composition(one,complement(X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(composition(converse(one),complement(X_18)),composition(converse(one),complement(X_18))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_63,plain,
( converse(one) != one
| composition(converse(one),complement(X_18)) = composition(one,complement(X_18)) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_18)),composition(converse(one),complement(X_18))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
composition(converse(one),complement(X_18)) = composition(one,complement(X_18)),
inference(resolve,[$cnf( $equal(converse(one),one) )],[refute_0_44,refute_0_63]) ).
cnf(refute_0_65,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_66,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_65]) ).
cnf(refute_0_67,plain,
( composition(converse(one),complement(X_18)) != composition(one,complement(X_18))
| composition(one,complement(X_18)) != complement(X_18)
| composition(converse(one),complement(X_18)) = complement(X_18) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(composition(converse(one),complement(X_18)))),bind(Y,$fot(composition(one,complement(X_18)))),bind(Z,$fot(complement(X_18)))]]) ).
cnf(refute_0_68,plain,
( composition(one,complement(X_18)) != complement(X_18)
| composition(converse(one),complement(X_18)) = complement(X_18) ),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_18)),composition(one,complement(X_18))) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
composition(converse(one),complement(X_18)) = complement(X_18),
inference(resolve,[$cnf( $equal(composition(one,complement(X_18)),complement(X_18)) )],[refute_0_60,refute_0_68]) ).
cnf(refute_0_70,plain,
join(complement(X_18),composition(converse(one),complement(X_18))) = join(complement(X_18),composition(converse(one),complement(X_18))),
introduced(tautology,[refl,[$fot(join(complement(X_18),composition(converse(one),complement(X_18))))]]) ).
cnf(refute_0_71,plain,
( composition(converse(one),complement(X_18)) != complement(X_18)
| join(complement(X_18),composition(converse(one),complement(X_18))) != join(complement(X_18),composition(converse(one),complement(X_18)))
| join(complement(X_18),composition(converse(one),complement(X_18))) = join(complement(X_18),complement(X_18)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_18),composition(converse(one),complement(X_18))),join(complement(X_18),composition(converse(one),complement(X_18)))) ),[1,1],$fot(complement(X_18))]]) ).
cnf(refute_0_72,plain,
( composition(converse(one),complement(X_18)) != complement(X_18)
| join(complement(X_18),composition(converse(one),complement(X_18))) = join(complement(X_18),complement(X_18)) ),
inference(resolve,[$cnf( $equal(join(complement(X_18),composition(converse(one),complement(X_18))),join(complement(X_18),composition(converse(one),complement(X_18)))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
join(complement(X_18),composition(converse(one),complement(X_18))) = join(complement(X_18),complement(X_18)),
inference(resolve,[$cnf( $equal(composition(converse(one),complement(X_18)),complement(X_18)) )],[refute_0_69,refute_0_72]) ).
cnf(refute_0_74,plain,
( join(complement(X_18),composition(converse(one),complement(X_18))) != complement(X_18)
| join(complement(X_18),composition(converse(one),complement(X_18))) != join(complement(X_18),complement(X_18))
| join(complement(X_18),complement(X_18)) = complement(X_18) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(X_18),composition(converse(one),complement(X_18))),complement(X_18)) ),[0],$fot(join(complement(X_18),complement(X_18)))]]) ).
cnf(refute_0_75,plain,
( join(complement(X_18),composition(converse(one),complement(X_18))) != complement(X_18)
| join(complement(X_18),complement(X_18)) = complement(X_18) ),
inference(resolve,[$cnf( $equal(join(complement(X_18),composition(converse(one),complement(X_18))),join(complement(X_18),complement(X_18))) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
join(complement(X_18),complement(X_18)) = complement(X_18),
inference(resolve,[$cnf( $equal(join(complement(X_18),composition(converse(one),complement(X_18))),complement(X_18)) )],[refute_0_57,refute_0_75]) ).
cnf(refute_0_77,plain,
join(complement(top),complement(top)) = complement(top),
inference(subst,[],[refute_0_76:[bind(X_18,$fot(top))]]) ).
cnf(refute_0_78,plain,
zero = meet(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_79,plain,
zero = meet(join(complement(X_35),complement(X_36)),complement(join(complement(X_35),complement(X_36)))),
inference(subst,[],[refute_0_78:[bind(X0,$fot(join(complement(X_35),complement(X_36))))]]) ).
cnf(refute_0_80,plain,
meet(X0,X1) = complement(join(complement(X0),complement(X1))),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_81,plain,
meet(X_35,X_36) = complement(join(complement(X_35),complement(X_36))),
inference(subst,[],[refute_0_80:[bind(X0,$fot(X_35)),bind(X1,$fot(X_36))]]) ).
cnf(refute_0_82,plain,
( meet(X_35,X_36) != complement(join(complement(X_35),complement(X_36)))
| complement(join(complement(X_35),complement(X_36))) = meet(X_35,X_36) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X_35,X_36))),bind(Y,$fot(complement(join(complement(X_35),complement(X_36)))))]]) ).
cnf(refute_0_83,plain,
complement(join(complement(X_35),complement(X_36))) = meet(X_35,X_36),
inference(resolve,[$cnf( $equal(meet(X_35,X_36),complement(join(complement(X_35),complement(X_36)))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( complement(join(complement(X_35),complement(X_36))) != meet(X_35,X_36)
| zero != meet(join(complement(X_35),complement(X_36)),complement(join(complement(X_35),complement(X_36))))
| zero = meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_35),complement(X_36)),complement(join(complement(X_35),complement(X_36))))) ),[1,1],$fot(meet(X_35,X_36))]]) ).
cnf(refute_0_85,plain,
( zero != meet(join(complement(X_35),complement(X_36)),complement(join(complement(X_35),complement(X_36))))
| zero = meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_35),complement(X_36))),meet(X_35,X_36)) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
zero = meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_35),complement(X_36)),complement(join(complement(X_35),complement(X_36))))) )],[refute_0_79,refute_0_85]) ).
cnf(refute_0_87,plain,
top = join(X0,complement(X0)),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_88,plain,
( top != join(X0,complement(X0))
| join(X0,complement(X0)) = top ),
inference(subst,[],[refute_0_4:[bind(X,$fot(top)),bind(Y,$fot(join(X0,complement(X0))))]]) ).
cnf(refute_0_89,plain,
join(X0,complement(X0)) = top,
inference(resolve,[$cnf( $equal(top,join(X0,complement(X0))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
join(meet(X_35,X_36),complement(meet(X_35,X_36))) = top,
inference(subst,[],[refute_0_89:[bind(X0,$fot(meet(X_35,X_36)))]]) ).
cnf(refute_0_91,plain,
complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))) = complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))),
introduced(tautology,[refl,[$fot(complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))))]]) ).
cnf(refute_0_92,plain,
( complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))) != complement(join(meet(X_35,X_36),complement(meet(X_35,X_36))))
| join(meet(X_35,X_36),complement(meet(X_35,X_36))) != top
| complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))),complement(join(meet(X_35,X_36),complement(meet(X_35,X_36))))) ),[1,0],$fot(top)]]) ).
cnf(refute_0_93,plain,
( join(meet(X_35,X_36),complement(meet(X_35,X_36))) != top
| complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))),complement(join(meet(X_35,X_36),complement(meet(X_35,X_36))))) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))) = complement(top),
inference(resolve,[$cnf( $equal(join(meet(X_35,X_36),complement(meet(X_35,X_36))),top) )],[refute_0_90,refute_0_93]) ).
cnf(refute_0_95,plain,
meet(join(complement(X_35),complement(X_36)),X1) = complement(join(complement(join(complement(X_35),complement(X_36))),complement(X1))),
inference(subst,[],[refute_0_80:[bind(X0,$fot(join(complement(X_35),complement(X_36))))]]) ).
cnf(refute_0_96,plain,
( complement(join(complement(X_35),complement(X_36))) != meet(X_35,X_36)
| meet(join(complement(X_35),complement(X_36)),X1) != complement(join(complement(join(complement(X_35),complement(X_36))),complement(X1)))
| meet(join(complement(X_35),complement(X_36)),X1) = complement(join(meet(X_35,X_36),complement(X1))) ),
introduced(tautology,[equality,[$cnf( $equal(meet(join(complement(X_35),complement(X_36)),X1),complement(join(complement(join(complement(X_35),complement(X_36))),complement(X1)))) ),[1,0,0],$fot(meet(X_35,X_36))]]) ).
cnf(refute_0_97,plain,
( meet(join(complement(X_35),complement(X_36)),X1) != complement(join(complement(join(complement(X_35),complement(X_36))),complement(X1)))
| meet(join(complement(X_35),complement(X_36)),X1) = complement(join(meet(X_35,X_36),complement(X1))) ),
inference(resolve,[$cnf( $equal(complement(join(complement(X_35),complement(X_36))),meet(X_35,X_36)) )],[refute_0_83,refute_0_96]) ).
cnf(refute_0_98,plain,
meet(join(complement(X_35),complement(X_36)),X1) = complement(join(meet(X_35,X_36),complement(X1))),
inference(resolve,[$cnf( $equal(meet(join(complement(X_35),complement(X_36)),X1),complement(join(complement(join(complement(X_35),complement(X_36))),complement(X1)))) )],[refute_0_95,refute_0_97]) ).
cnf(refute_0_99,plain,
meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)) = complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))),
inference(subst,[],[refute_0_98:[bind(X1,$fot(meet(X_35,X_36)))]]) ).
cnf(refute_0_100,plain,
( complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))) != complement(top)
| meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)) != complement(join(meet(X_35,X_36),complement(meet(X_35,X_36))))
| meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)) = complement(top) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)))),bind(Y,$fot(complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))))),bind(Z,$fot(complement(top)))]]) ).
cnf(refute_0_101,plain,
( complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))) != complement(top)
| meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)) = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)),complement(join(meet(X_35,X_36),complement(meet(X_35,X_36))))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)) = complement(top),
inference(resolve,[$cnf( $equal(complement(join(meet(X_35,X_36),complement(meet(X_35,X_36)))),complement(top)) )],[refute_0_94,refute_0_101]) ).
cnf(refute_0_103,plain,
( meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)) != complement(top)
| zero != meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36))
| zero = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(zero,meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36))) ),[1],$fot(complement(top))]]) ).
cnf(refute_0_104,plain,
( zero != meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36))
| zero = complement(top) ),
inference(resolve,[$cnf( $equal(meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36)),complement(top)) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
zero = complement(top),
inference(resolve,[$cnf( $equal(zero,meet(join(complement(X_35),complement(X_36)),meet(X_35,X_36))) )],[refute_0_86,refute_0_104]) ).
cnf(refute_0_106,plain,
( zero != complement(top)
| complement(top) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(complement(top)))]]) ).
cnf(refute_0_107,plain,
complement(top) = zero,
inference(resolve,[$cnf( $equal(zero,complement(top)) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
( complement(top) != zero
| join(complement(top),complement(top)) != complement(top)
| join(zero,complement(top)) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_109,plain,
( join(complement(top),complement(top)) != complement(top)
| join(zero,complement(top)) = complement(top) ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
join(zero,complement(top)) = complement(top),
inference(resolve,[$cnf( $equal(join(complement(top),complement(top)),complement(top)) )],[refute_0_77,refute_0_109]) ).
cnf(refute_0_111,plain,
join(zero,complement(top)) = join(zero,complement(top)),
introduced(tautology,[refl,[$fot(join(zero,complement(top)))]]) ).
cnf(refute_0_112,plain,
( complement(top) != zero
| join(zero,complement(top)) != join(zero,complement(top))
| join(zero,complement(top)) = join(zero,zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_113,plain,
( complement(top) != zero
| join(zero,complement(top)) = join(zero,zero) ),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,complement(top))) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
join(zero,complement(top)) = join(zero,zero),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_107,refute_0_113]) ).
cnf(refute_0_115,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,complement(top)) != join(zero,zero)
| join(zero,zero) = complement(top) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,complement(top)),complement(top)) ),[0],$fot(join(zero,zero))]]) ).
cnf(refute_0_116,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,zero) = complement(top) ),
inference(resolve,[$cnf( $equal(join(zero,complement(top)),join(zero,zero)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( complement(top) != zero
| join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,zero),complement(top)) ),[1],$fot(zero)]]) ).
cnf(refute_0_118,plain,
( join(zero,zero) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(complement(top),zero) )],[refute_0_107,refute_0_117]) ).
cnf(refute_0_119,plain,
( join(zero,complement(top)) != complement(top)
| join(zero,zero) = zero ),
inference(resolve,[$cnf( $equal(join(zero,zero),complement(top)) )],[refute_0_116,refute_0_118]) ).
cnf(refute_0_120,plain,
join(zero,zero) = zero,
inference(resolve,[$cnf( $equal(join(zero,complement(top)),complement(top)) )],[refute_0_110,refute_0_119]) ).
cnf(refute_0_121,plain,
( join(zero,join(zero,X2)) != join(join(zero,zero),X2)
| join(zero,zero) != zero
| join(zero,join(zero,X2)) = join(zero,X2) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,X2)),join(join(zero,zero),X2)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_122,plain,
( join(zero,join(zero,X2)) != join(join(zero,zero),X2)
| join(zero,join(zero,X2)) = join(zero,X2) ),
inference(resolve,[$cnf( $equal(join(zero,zero),zero) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
join(zero,join(zero,X2)) = join(zero,X2),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X2)),join(join(zero,zero),X2)) )],[refute_0_13,refute_0_122]) ).
cnf(refute_0_124,plain,
join(zero,join(zero,X_40)) = join(zero,X_40),
inference(subst,[],[refute_0_123:[bind(X2,$fot(X_40))]]) ).
cnf(refute_0_125,plain,
( join(join(zero,X_40),zero) != join(zero,join(zero,X_40))
| join(zero,join(zero,X_40)) != join(zero,X_40)
| join(join(zero,X_40),zero) = join(zero,X_40) ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(join(zero,X_40),zero),join(zero,X_40)) ),[0],$fot(join(zero,join(zero,X_40)))]]) ).
cnf(refute_0_126,plain,
( join(join(zero,X_40),zero) != join(zero,join(zero,X_40))
| join(join(zero,X_40),zero) = join(zero,X_40) ),
inference(resolve,[$cnf( $equal(join(zero,join(zero,X_40)),join(zero,X_40)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
join(join(zero,X_40),zero) = join(zero,X_40),
inference(resolve,[$cnf( $equal(join(join(zero,X_40),zero),join(zero,join(zero,X_40))) )],[refute_0_11,refute_0_126]) ).
cnf(refute_0_128,plain,
( join(X0,join(X1,X2)) != join(join(X0,X1),X2)
| join(join(X0,X1),X2) = join(X0,join(X1,X2)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(join(X0,join(X1,X2)))),bind(Y,$fot(join(join(X0,X1),X2)))]]) ).
cnf(refute_0_129,plain,
join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(resolve,[$cnf( $equal(join(X0,join(X1,X2)),join(join(X0,X1),X2)) )],[refute_0_12,refute_0_128]) ).
cnf(refute_0_130,plain,
join(join(zero,X_40),zero) = join(zero,join(X_40,zero)),
inference(subst,[],[refute_0_129:[bind(X0,$fot(zero)),bind(X1,$fot(X_40)),bind(X2,$fot(zero))]]) ).
cnf(refute_0_131,plain,
( join(join(zero,X_40),zero) != join(zero,X_40)
| join(join(zero,X_40),zero) != join(zero,join(X_40,zero))
| join(zero,join(X_40,zero)) = join(zero,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(join(join(zero,X_40),zero),join(zero,X_40)) ),[0],$fot(join(zero,join(X_40,zero)))]]) ).
cnf(refute_0_132,plain,
( join(join(zero,X_40),zero) != join(zero,X_40)
| join(zero,join(X_40,zero)) = join(zero,X_40) ),
inference(resolve,[$cnf( $equal(join(join(zero,X_40),zero),join(zero,join(X_40,zero))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
join(zero,join(X_40,zero)) = join(zero,X_40),
inference(resolve,[$cnf( $equal(join(join(zero,X_40),zero),join(zero,X_40)) )],[refute_0_127,refute_0_132]) ).
cnf(refute_0_134,plain,
join(zero,join(zero,complement(complement(X_46)))) = join(zero,complement(complement(X_46))),
inference(subst,[],[refute_0_123:[bind(X2,$fot(complement(complement(X_46))))]]) ).
cnf(refute_0_135,plain,
X0 = join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_136,plain,
join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(join(complement(X0),X1)))),bind(X1,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_137,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[0],$fot(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_138,plain,
( X0 != join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))
| X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
X0 = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),complement(X1))),complement(join(complement(X0),X1)))) )],[refute_0_135,refute_0_138]) ).
cnf(refute_0_140,plain,
join(complement(join(complement(X0),X1)),meet(X0,X1)) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(meet(X0,X1))),bind(X1,$fot(complement(join(complement(X0),X1))))]]) ).
cnf(refute_0_141,plain,
( meet(X0,X1) != complement(join(complement(X0),complement(X1)))
| complement(join(complement(X0),complement(X1))) = meet(X0,X1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(meet(X0,X1))),bind(Y,$fot(complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_142,plain,
complement(join(complement(X0),complement(X1))) = meet(X0,X1),
inference(resolve,[$cnf( $equal(meet(X0,X1),complement(join(complement(X0),complement(X1)))) )],[refute_0_80,refute_0_141]) ).
cnf(refute_0_143,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),
introduced(tautology,[refl,[$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_144,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) ),[1,1],$fot(meet(X0,X1))]]) ).
cnf(refute_0_145,plain,
( complement(join(complement(X0),complement(X1))) != meet(X0,X1)
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(complement(join(complement(X0),X1)),meet(X0,X1)),
inference(resolve,[$cnf( $equal(complement(join(complement(X0),complement(X1))),meet(X0,X1)) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(complement(join(complement(X0),X1)),meet(X0,X1))
| join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))),bind(Y,$fot(join(complement(join(complement(X0),X1)),meet(X0,X1)))),bind(Z,$fot(join(meet(X0,X1),complement(join(complement(X0),X1)))))]]) ).
cnf(refute_0_148,plain,
( join(complement(join(complement(X0),X1)),meet(X0,X1)) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(complement(join(complement(X0),X1)),meet(X0,X1))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),meet(X0,X1)),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_140,refute_0_148]) ).
cnf(refute_0_150,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))) != join(meet(X0,X1),complement(join(complement(X0),X1)))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X0,join(meet(X0,X1),complement(join(complement(X0),X1)))) ),[0],$fot(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))))]]) ).
cnf(refute_0_151,plain,
( X0 != join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))
| X0 = join(meet(X0,X1),complement(join(complement(X0),X1))) ),
inference(resolve,[$cnf( $equal(join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1)))),join(meet(X0,X1),complement(join(complement(X0),X1)))) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
X0 = join(meet(X0,X1),complement(join(complement(X0),X1))),
inference(resolve,[$cnf( $equal(X0,join(complement(join(complement(X0),X1)),complement(join(complement(X0),complement(X1))))) )],[refute_0_139,refute_0_151]) ).
cnf(refute_0_153,plain,
X_44 = join(meet(X_44,complement(X_44)),complement(join(complement(X_44),complement(X_44)))),
inference(subst,[],[refute_0_152:[bind(X0,$fot(X_44)),bind(X1,$fot(complement(X_44)))]]) ).
cnf(refute_0_154,plain,
join(complement(X_44),complement(X_44)) = complement(X_44),
inference(subst,[],[refute_0_76:[bind(X_18,$fot(X_44))]]) ).
cnf(refute_0_155,plain,
( X_44 != join(meet(X_44,complement(X_44)),complement(join(complement(X_44),complement(X_44))))
| join(complement(X_44),complement(X_44)) != complement(X_44)
| X_44 = join(meet(X_44,complement(X_44)),complement(complement(X_44))) ),
introduced(tautology,[equality,[$cnf( $equal(X_44,join(meet(X_44,complement(X_44)),complement(join(complement(X_44),complement(X_44))))) ),[1,1,0],$fot(complement(X_44))]]) ).
cnf(refute_0_156,plain,
( X_44 != join(meet(X_44,complement(X_44)),complement(join(complement(X_44),complement(X_44))))
| X_44 = join(meet(X_44,complement(X_44)),complement(complement(X_44))) ),
inference(resolve,[$cnf( $equal(join(complement(X_44),complement(X_44)),complement(X_44)) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
X_44 = join(meet(X_44,complement(X_44)),complement(complement(X_44))),
inference(resolve,[$cnf( $equal(X_44,join(meet(X_44,complement(X_44)),complement(join(complement(X_44),complement(X_44))))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
join(complement(complement(X_44)),zero) = join(zero,complement(complement(X_44))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(zero)),bind(X1,$fot(complement(complement(X_44))))]]) ).
cnf(refute_0_159,plain,
( zero != meet(X0,complement(X0))
| meet(X0,complement(X0)) = zero ),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero)),bind(Y,$fot(meet(X0,complement(X0))))]]) ).
cnf(refute_0_160,plain,
meet(X0,complement(X0)) = zero,
inference(resolve,[$cnf( $equal(zero,meet(X0,complement(X0))) )],[refute_0_78,refute_0_159]) ).
cnf(refute_0_161,plain,
meet(X_44,complement(X_44)) = zero,
inference(subst,[],[refute_0_160:[bind(X0,$fot(X_44))]]) ).
cnf(refute_0_162,plain,
join(complement(complement(X_44)),meet(X_44,complement(X_44))) = join(complement(complement(X_44)),meet(X_44,complement(X_44))),
introduced(tautology,[refl,[$fot(join(complement(complement(X_44)),meet(X_44,complement(X_44))))]]) ).
cnf(refute_0_163,plain,
( join(complement(complement(X_44)),meet(X_44,complement(X_44))) != join(complement(complement(X_44)),meet(X_44,complement(X_44)))
| meet(X_44,complement(X_44)) != zero
| join(complement(complement(X_44)),meet(X_44,complement(X_44))) = join(complement(complement(X_44)),zero) ),
introduced(tautology,[equality,[$cnf( $equal(join(complement(complement(X_44)),meet(X_44,complement(X_44))),join(complement(complement(X_44)),meet(X_44,complement(X_44)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_164,plain,
( meet(X_44,complement(X_44)) != zero
| join(complement(complement(X_44)),meet(X_44,complement(X_44))) = join(complement(complement(X_44)),zero) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_44)),meet(X_44,complement(X_44))),join(complement(complement(X_44)),meet(X_44,complement(X_44)))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
join(complement(complement(X_44)),meet(X_44,complement(X_44))) = join(complement(complement(X_44)),zero),
inference(resolve,[$cnf( $equal(meet(X_44,complement(X_44)),zero) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( join(complement(complement(X_44)),meet(X_44,complement(X_44))) != join(complement(complement(X_44)),zero)
| join(complement(complement(X_44)),zero) != join(zero,complement(complement(X_44)))
| join(complement(complement(X_44)),meet(X_44,complement(X_44))) = join(zero,complement(complement(X_44))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(join(complement(complement(X_44)),meet(X_44,complement(X_44))))),bind(Y,$fot(join(complement(complement(X_44)),zero))),bind(Z,$fot(join(zero,complement(complement(X_44)))))]]) ).
cnf(refute_0_167,plain,
( join(complement(complement(X_44)),zero) != join(zero,complement(complement(X_44)))
| join(complement(complement(X_44)),meet(X_44,complement(X_44))) = join(zero,complement(complement(X_44))) ),
inference(resolve,[$cnf( $equal(join(complement(complement(X_44)),meet(X_44,complement(X_44))),join(complement(complement(X_44)),zero)) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
join(complement(complement(X_44)),meet(X_44,complement(X_44))) = join(zero,complement(complement(X_44))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_44)),zero),join(zero,complement(complement(X_44)))) )],[refute_0_158,refute_0_167]) ).
cnf(refute_0_169,plain,
join(meet(X_44,complement(X_44)),complement(complement(X_44))) = join(complement(complement(X_44)),meet(X_44,complement(X_44))),
inference(subst,[],[refute_0_6:[bind(X0,$fot(complement(complement(X_44)))),bind(X1,$fot(meet(X_44,complement(X_44))))]]) ).
cnf(refute_0_170,plain,
( join(complement(complement(X_44)),meet(X_44,complement(X_44))) != join(zero,complement(complement(X_44)))
| join(meet(X_44,complement(X_44)),complement(complement(X_44))) != join(complement(complement(X_44)),meet(X_44,complement(X_44)))
| join(meet(X_44,complement(X_44)),complement(complement(X_44))) = join(zero,complement(complement(X_44))) ),
inference(subst,[],[refute_0_66:[bind(X,$fot(join(meet(X_44,complement(X_44)),complement(complement(X_44))))),bind(Y,$fot(join(complement(complement(X_44)),meet(X_44,complement(X_44))))),bind(Z,$fot(join(zero,complement(complement(X_44)))))]]) ).
cnf(refute_0_171,plain,
( join(complement(complement(X_44)),meet(X_44,complement(X_44))) != join(zero,complement(complement(X_44)))
| join(meet(X_44,complement(X_44)),complement(complement(X_44))) = join(zero,complement(complement(X_44))) ),
inference(resolve,[$cnf( $equal(join(meet(X_44,complement(X_44)),complement(complement(X_44))),join(complement(complement(X_44)),meet(X_44,complement(X_44)))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
join(meet(X_44,complement(X_44)),complement(complement(X_44))) = join(zero,complement(complement(X_44))),
inference(resolve,[$cnf( $equal(join(complement(complement(X_44)),meet(X_44,complement(X_44))),join(zero,complement(complement(X_44)))) )],[refute_0_168,refute_0_171]) ).
cnf(refute_0_173,plain,
( X_44 != join(meet(X_44,complement(X_44)),complement(complement(X_44)))
| join(meet(X_44,complement(X_44)),complement(complement(X_44))) != join(zero,complement(complement(X_44)))
| X_44 = join(zero,complement(complement(X_44))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_44,join(zero,complement(complement(X_44)))) ),[0],$fot(join(meet(X_44,complement(X_44)),complement(complement(X_44))))]]) ).
cnf(refute_0_174,plain,
( X_44 != join(meet(X_44,complement(X_44)),complement(complement(X_44)))
| X_44 = join(zero,complement(complement(X_44))) ),
inference(resolve,[$cnf( $equal(join(meet(X_44,complement(X_44)),complement(complement(X_44))),join(zero,complement(complement(X_44)))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
X_44 = join(zero,complement(complement(X_44))),
inference(resolve,[$cnf( $equal(X_44,join(meet(X_44,complement(X_44)),complement(complement(X_44)))) )],[refute_0_157,refute_0_174]) ).
cnf(refute_0_176,plain,
X_46 = join(zero,complement(complement(X_46))),
inference(subst,[],[refute_0_175:[bind(X_44,$fot(X_46))]]) ).
cnf(refute_0_177,plain,
( X_46 != join(zero,complement(complement(X_46)))
| join(zero,complement(complement(X_46))) = X_46 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_46)),bind(Y,$fot(join(zero,complement(complement(X_46)))))]]) ).
cnf(refute_0_178,plain,
join(zero,complement(complement(X_46))) = X_46,
inference(resolve,[$cnf( $equal(X_46,join(zero,complement(complement(X_46)))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
( join(zero,complement(complement(X_46))) != X_46
| join(zero,join(zero,complement(complement(X_46)))) != join(zero,complement(complement(X_46)))
| join(zero,X_46) = join(zero,complement(complement(X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(zero,complement(complement(X_46)))),join(zero,complement(complement(X_46)))) ),[0,1],$fot(X_46)]]) ).
cnf(refute_0_180,plain,
( join(zero,join(zero,complement(complement(X_46)))) != join(zero,complement(complement(X_46)))
| join(zero,X_46) = join(zero,complement(complement(X_46))) ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_46))),X_46) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
join(zero,X_46) = join(zero,complement(complement(X_46))),
inference(resolve,[$cnf( $equal(join(zero,join(zero,complement(complement(X_46)))),join(zero,complement(complement(X_46)))) )],[refute_0_134,refute_0_180]) ).
cnf(refute_0_182,plain,
( join(zero,X_46) != join(zero,complement(complement(X_46)))
| join(zero,complement(complement(X_46))) != X_46
| join(zero,X_46) = X_46 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(zero,X_46),X_46) ),[0],$fot(join(zero,complement(complement(X_46))))]]) ).
cnf(refute_0_183,plain,
( join(zero,X_46) != join(zero,complement(complement(X_46)))
| join(zero,X_46) = X_46 ),
inference(resolve,[$cnf( $equal(join(zero,complement(complement(X_46))),X_46) )],[refute_0_178,refute_0_182]) ).
cnf(refute_0_184,plain,
join(zero,X_46) = X_46,
inference(resolve,[$cnf( $equal(join(zero,X_46),join(zero,complement(complement(X_46)))) )],[refute_0_181,refute_0_183]) ).
cnf(refute_0_185,plain,
join(zero,join(X_40,zero)) = join(X_40,zero),
inference(subst,[],[refute_0_184:[bind(X_46,$fot(join(X_40,zero)))]]) ).
cnf(refute_0_186,plain,
( join(zero,join(X_40,zero)) != join(X_40,zero)
| join(zero,join(X_40,zero)) != join(zero,X_40)
| join(X_40,zero) = join(zero,X_40) ),
introduced(tautology,[equality,[$cnf( $equal(join(zero,join(X_40,zero)),join(zero,X_40)) ),[0],$fot(join(X_40,zero))]]) ).
cnf(refute_0_187,plain,
( join(zero,join(X_40,zero)) != join(zero,X_40)
| join(X_40,zero) = join(zero,X_40) ),
inference(resolve,[$cnf( $equal(join(zero,join(X_40,zero)),join(X_40,zero)) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
join(zero,X_40) = X_40,
inference(subst,[],[refute_0_184:[bind(X_46,$fot(X_40))]]) ).
cnf(refute_0_189,plain,
( join(X_40,zero) != join(zero,X_40)
| join(zero,X_40) != X_40
| join(X_40,zero) = X_40 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(X_40,zero),X_40) ),[0],$fot(join(zero,X_40))]]) ).
cnf(refute_0_190,plain,
( join(X_40,zero) != join(zero,X_40)
| join(X_40,zero) = X_40 ),
inference(resolve,[$cnf( $equal(join(zero,X_40),X_40) )],[refute_0_188,refute_0_189]) ).
cnf(refute_0_191,plain,
( join(zero,join(X_40,zero)) != join(zero,X_40)
| join(X_40,zero) = X_40 ),
inference(resolve,[$cnf( $equal(join(X_40,zero),join(zero,X_40)) )],[refute_0_187,refute_0_190]) ).
cnf(refute_0_192,plain,
join(X_40,zero) = X_40,
inference(resolve,[$cnf( $equal(join(zero,join(X_40,zero)),join(zero,X_40)) )],[refute_0_133,refute_0_191]) ).
cnf(refute_0_193,plain,
join(skolemFOFtoCNF_X0,zero) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_192:[bind(X_40,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_194,plain,
( join(skolemFOFtoCNF_X0,zero) != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0
| join(skolemFOFtoCNF_X0,zero) = skolemFOFtoCNF_X0 ),
introduced(tautology,[equality,[$cnf( ~ $equal(join(skolemFOFtoCNF_X0,zero),skolemFOFtoCNF_X0) ),[0],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_195,plain,
( skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0
| join(skolemFOFtoCNF_X0,zero) = skolemFOFtoCNF_X0 ),
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,zero),skolemFOFtoCNF_X0) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(join(skolemFOFtoCNF_X0,zero),skolemFOFtoCNF_X0) )],[refute_0_195,refute_0_10]) ).
cnf(refute_0_197,plain,
skolemFOFtoCNF_X0 = skolemFOFtoCNF_X0,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_198,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0) )],[refute_0_197,refute_0_196]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL001+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jul 8 11:26:23 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.52
%------------------------------------------------------------------------------