%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : LAT395-1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 : Thu Sep 24 01:03:58 PM UTC 2026
% Result : Satisfiable 0.13s 10.76s
% Output : Saturation 0.13s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : meet(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : join(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] : meet(X,join(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : join(X,meet(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : meet(X,Y) = meet(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y] : join(X,Y) = join(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] : meet(meet(X,Y),Z) = meet(X,meet(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [X,Y,Z] : join(join(X,Y),Z) = join(X,join(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : meet(X,n0) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X] : join(X,n0) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X] : meet(X,n1) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X] : join(X,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Z,Y] :
( meet(Z,join(X,Y)) = join(X,meet(Y,Z))
| meet(X,Z) != X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X,Y] :
( meet(X,Y) = n0
| ~ complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X,Y] :
( join(X,Y) = n1
| ~ complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X,Y] :
( complement(X,Y)
| join(X,Y) != n1
| meet(X,Y) != n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [X,Y] :
( complement(X,Y)
| ~ unique_complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [X,Y,Z] :
( Z = Y
| ~ complement(X,Z)
| ~ unique_complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [X,Y] :
( complement(X,f(X,Y))
| ~ complement(X,Y)
| unique_complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [X,Y] :
( f(X,Y) != Y
| ~ complement(X,Y)
| unique_complement(X,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,plain,
! [X0] : meet(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f22,plain,
! [X0] : join(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f23,plain,
! [X0,X1] : meet(X0,join(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f24,plain,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f25,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f26,plain,
! [X0,X1] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f27,plain,
! [X0,X1,X2] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f29,plain,
! [X0] : meet(X0,n0) = n0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f30,plain,
! [X0] : join(X0,n0) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f31,plain,
! [X0] : meet(X0,n1) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f32,plain,
! [X0] : join(X0,n1) = n1,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f33,plain,
! [X,Z] :
( ! [Y] : meet(Z,join(X,Y)) = join(X,meet(Y,Z))
| meet(X,Z) != X ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f34,plain,
! [X0,X1,X2] :
( meet(X1,join(X0,X2)) = join(X0,meet(X2,X1))
| meet(X0,X1) != X0 ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0,X1] :
( meet(X0,X1) = n0
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f36,plain,
! [X0,X1] :
( join(X0,X1) = n1
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f37,plain,
! [X0,X1] :
( complement(X0,X1)
| join(X0,X1) != n1
| meet(X0,X1) != n0 ),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f38,plain,
! [X0,X1] :
( complement(X0,X1)
| ~ unique_complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f39,plain,
! [Y,Z] :
( Z = Y
| ! [X] :
( ~ complement(X,Z)
| ~ unique_complement(X,Y) ) ),
inference(miniscoping,[status(thm)],[f18]) ).
fof(f40,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ complement(X0,X2)
| ~ unique_complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( complement(X0,f(X0,X1))
| ~ complement(X0,X1)
| unique_complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f42,plain,
! [X0,X1] :
( f(X0,X1) != X1
| ~ complement(X0,X1)
| unique_complement(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f56,plain,
! [X0] : n0 = meet(n0,X0),
inference(paramodulation,[status(thm)],[f29,f25]) ).
fof(f57,plain,
! [X0] : X0 = meet(n1,X0),
inference(paramodulation,[status(thm)],[f31,f25]) ).
fof(f66,plain,
! [X0,X1] : join(X0,meet(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f25,f24]) ).
fof(f70,plain,
! [X0] : X0 = join(n0,X0),
inference(paramodulation,[status(thm)],[f30,f26]) ).
fof(f77,plain,
! [X0,X1] : meet(X0,join(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f26,f23]) ).
fof(f80,plain,
! [X0] : join(n1,X0) = n1,
inference(paramodulation,[status(thm)],[f23,f57]) ).
fof(f93,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X0,meet(X1,join(meet(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f96,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X1,meet(X2,X0)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f101,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X0,meet(join(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f104,plain,
! [X0,X1,X2] : meet(meet(X0,X1),X2) = meet(X1,meet(X0,X2)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f106,plain,
! [X0,X1] : meet(X0,X1) = meet(X0,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f112,plain,
! [X0,X1,X2] : join(meet(X0,X1),meet(X0,meet(X1,X2))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f27,f24]) ).
fof(f169,plain,
! [X0,X1,X2] : join(X0,X1) = join(X0,join(X1,meet(join(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f24,f28]) ).
fof(f171,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X2,X0)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f178,plain,
! [X0,X1,X2] : join(X0,X1) = join(X0,join(meet(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f24,f28]) ).
fof(f180,plain,
! [X0,X1,X2] : join(join(X0,X1),X2) = join(X1,join(X0,X2)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f182,plain,
! [X0,X1] : join(X0,X1) = join(X0,join(X0,X1)),
inference(paramodulation,[status(thm)],[f22,f28]) ).
fof(f188,plain,
! [X0,X1,X2] : meet(join(X0,X1),join(X0,join(X1,X2))) = join(X0,X1),
inference(paramodulation,[status(thm)],[f28,f23]) ).
fof(f197,plain,
! [X0,X1,X2] : meet(join(X0,X1),join(X0,X2)) = join(X0,meet(X2,join(X0,X1))),
inference(resolution,[status(thm)],[f34,f23]) ).
fof(f203,plain,
! [X0,X1] :
( meet(X0,join(n0,X1)) = join(n0,meet(X1,X0))
| n0 != n0 ),
inference(paramodulation,[status(thm)],[f56,f34]) ).
fof(f204,plain,
! [X0,X1,X2,X3] :
( meet(X2,join(meet(X0,X1),X3)) = join(meet(X0,X1),meet(X3,X2))
| meet(X0,meet(X1,X2)) != meet(X0,X1) ),
inference(paramodulation,[status(thm)],[f27,f34]) ).
fof(f209,plain,
! [X0,X1,X2] :
( meet(X0,join(X1,X2)) = join(X1,meet(X2,X0))
| meet(X0,X1) != X1 ),
inference(paramodulation,[status(thm)],[f25,f34]) ).
fof(f220,definition,
( sQ0_spl
<=> n0 = n0 ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( sQ0_spl
| n0 != n0 ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
! [X0,X1] :
( sQ1_spl
<=> meet(X0,join(n0,X1)) = join(n0,meet(X1,X0)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f226,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f203,f220,f223]) ).
fof(f233,plain,
( sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f222]) ).
fof(f234,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f233]) ).
fof(f237,plain,
! [X0] :
( complement(n1,X0)
| meet(n1,X0) != n0 ),
inference(resolution,[status(thm)],[f37,f80]) ).
fof(f238,plain,
! [X0] :
( complement(X0,n1)
| meet(X0,n1) != n0 ),
inference(resolution,[status(thm)],[f37,f32]) ).
fof(f240,plain,
( complement(n1,n0)
| meet(n1,n0) != n0 ),
inference(resolution,[status(thm)],[f37,f30]) ).
fof(f241,plain,
( complement(n1,n1)
| meet(n1,n1) != n0 ),
inference(resolution,[status(thm)],[f37,f22]) ).
fof(f242,plain,
( complement(n0,n1)
| meet(n0,n1) != n0 ),
inference(resolution,[status(thm)],[f37,f70]) ).
fof(f243,plain,
! [X0,X1,X2] :
( complement(join(X0,X1),X2)
| join(X0,join(X1,X2)) != n1
| meet(join(X0,X1),X2) != n0 ),
inference(paramodulation,[status(thm)],[f28,f37]) ).
fof(f244,plain,
! [X0] :
( complement(n1,X0)
| n1 != n1
| meet(n1,X0) != n0 ),
inference(paramodulation,[status(thm)],[f80,f37]) ).
fof(f245,plain,
! [X0] :
( complement(n0,X0)
| X0 != n1
| meet(n0,X0) != n0 ),
inference(paramodulation,[status(thm)],[f70,f37]) ).
fof(f246,plain,
! [X0] :
( complement(X0,n1)
| n1 != n1
| meet(X0,n1) != n0 ),
inference(paramodulation,[status(thm)],[f32,f37]) ).
fof(f247,plain,
! [X0,X1] :
( complement(X0,meet(X0,X1))
| X0 != n1
| meet(X0,meet(X0,X1)) != n0 ),
inference(paramodulation,[status(thm)],[f24,f37]) ).
fof(f248,plain,
! [X0] :
( complement(X0,n0)
| X0 != n1
| meet(X0,n0) != n0 ),
inference(paramodulation,[status(thm)],[f30,f37]) ).
fof(f249,plain,
! [X0,X1] :
( complement(X0,X1)
| join(X1,X0) != n1
| meet(X0,X1) != n0 ),
inference(paramodulation,[status(thm)],[f26,f37]) ).
fof(f251,plain,
! [X0] :
( complement(X0,X0)
| X0 != n1
| meet(X0,X0) != n0 ),
inference(paramodulation,[status(thm)],[f22,f37]) ).
fof(f252,plain,
! [X0] :
( complement(n1,X0)
| X0 != n0 ),
inference(forward_demodulation,[status(thm)],[f57,f237]) ).
fof(f253,plain,
! [X0] :
( complement(X0,n1)
| X0 != n0 ),
inference(forward_demodulation,[status(thm)],[f31,f238]) ).
fof(f257,definition,
( sQ2_spl
<=> meet(n1,n0) = n0 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f259,plain,
( sQ2_spl
| meet(n1,n0) != n0 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,definition,
( sQ3_spl
<=> complement(n1,n0) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f261,plain,
( ~ sQ3_spl
| complement(n1,n0) ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f240,f257,f260]) ).
fof(f264,definition,
( sQ4_spl
<=> meet(n1,n1) = n0 ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( ~ sQ4_spl
| meet(n1,n1) = n0 ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f266,plain,
( sQ4_spl
| meet(n1,n1) != n0 ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,definition,
( sQ5_spl
<=> complement(n1,n1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ5_spl
| complement(n1,n1) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f269,plain,
( sQ5_spl
| ~ complement(n1,n1) ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f241,f264,f267]) ).
fof(f271,definition,
( sQ6_spl
<=> meet(n0,n1) = n0 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ6_spl
| meet(n0,n1) != n0 ),
inference(component_clause,[status(thm)],[f271]) ).
fof(f274,definition,
( sQ7_spl
<=> complement(n0,n1) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ7_spl
| complement(n0,n1) ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,plain,
( sQ7_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f242,f271,f274]) ).
fof(f278,definition,
! [X0] :
( sQ8_spl
<=> ( complement(n1,X0)
| meet(n1,X0) != n0 ) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f281,definition,
( sQ9_spl
<=> n1 = n1 ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( sQ9_spl
| n1 != n1 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f244,f278,f281]) ).
fof(f285,plain,
! [X0] :
( complement(n0,X0)
| X0 != n1
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f56,f245]) ).
fof(f286,plain,
! [X0] :
( complement(n0,X0)
| X0 != n1 ),
inference(trivial_equality_resolution,[status(thm)],[f285]) ).
fof(f287,definition,
! [X0] :
( sQ10_spl
<=> ( complement(X0,n1)
| meet(X0,n1) != n0 ) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f290,plain,
( ~ sQ9_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f246,f287,f281]) ).
fof(f291,plain,
! [X0,X1] :
( complement(X0,meet(X0,X1))
| X0 != n1
| meet(X0,X1) != n0 ),
inference(forward_demodulation,[status(thm)],[f106,f247]) ).
fof(f292,plain,
! [X0] :
( complement(X0,n0)
| X0 != n1
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f29,f248]) ).
fof(f293,plain,
! [X0] :
( complement(X0,n0)
| X0 != n1 ),
inference(trivial_equality_resolution,[status(thm)],[f292]) ).
fof(f294,plain,
! [X0] :
( complement(X0,X0)
| X0 != n1
| X0 != n0 ),
inference(forward_demodulation,[status(thm)],[f21,f251]) ).
fof(f295,plain,
( sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f283]) ).
fof(f296,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f297,plain,
( sQ6_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f56,f273]) ).
fof(f298,plain,
( sQ6_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f297]) ).
fof(f299,plain,
sQ6_spl,
inference(contradiction_clause,[status(thm)],[f298]) ).
fof(f300,plain,
( sQ4_spl
| n1 != n0 ),
inference(forward_demodulation,[status(thm)],[f57,f266]) ).
fof(f301,plain,
( sQ2_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f57,f259]) ).
fof(f302,plain,
( sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f301]) ).
fof(f303,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f302]) ).
fof(f308,plain,
( ~ sQ7_spl
| complement(n0,f(n0,n1))
| unique_complement(n0,n1) ),
inference(resolution,[status(thm)],[f275,f41]) ).
fof(f309,definition,
( sQ11_spl
<=> unique_complement(n0,n1) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( ~ sQ11_spl
| unique_complement(n0,n1) ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,definition,
( sQ12_spl
<=> complement(n0,f(n0,n1)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f315,plain,
( ~ sQ7_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f308,f309,f312,f274]) ).
fof(f318,plain,
( ~ sQ3_spl
| complement(n1,f(n1,n0))
| unique_complement(n1,n0) ),
inference(resolution,[status(thm)],[f261,f41]) ).
fof(f319,definition,
( sQ13_spl
<=> unique_complement(n1,n0) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f320,plain,
( ~ sQ13_spl
| unique_complement(n1,n0) ),
inference(component_clause,[status(thm)],[f319]) ).
fof(f322,definition,
( sQ14_spl
<=> complement(n1,f(n1,n0)) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f323,plain,
( ~ sQ14_spl
| complement(n1,f(n1,n0)) ),
inference(component_clause,[status(thm)],[f322]) ).
fof(f325,plain,
( ~ sQ3_spl
| sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f318,f319,f322,f260]) ).
fof(f326,plain,
( ~ sQ11_spl
| complement(n0,n1) ),
inference(resolution,[status(thm)],[f310,f38]) ).
fof(f327,plain,
! [X0] :
( ~ sQ11_spl
| X0 = n1
| ~ complement(n0,X0) ),
inference(resolution,[status(thm)],[f40,f310]) ).
fof(f329,plain,
! [X0,X1,X2] : join(X0,join(X1,meet(X2,join(X0,X1)))) = join(X0,X1),
inference(paramodulation,[status(thm)],[f28,f66]) ).
fof(f334,plain,
! [X0,X1,X2] : join(X0,meet(X1,meet(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f27,f66]) ).
fof(f336,plain,
! [X0,X1] : join(join(X0,X1),X0) = join(X0,X1),
inference(paramodulation,[status(thm)],[f23,f66]) ).
fof(f346,plain,
! [X0,X1] :
( complement(X0,meet(X1,X0))
| X0 != n1
| meet(X0,meet(X1,X0)) != n0 ),
inference(paramodulation,[status(thm)],[f66,f37]) ).
fof(f347,plain,
! [X0,X1,X2] : join(X0,X1) = join(X0,join(meet(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f66,f28]) ).
fof(f353,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X0,X1),
inference(forward_demodulation,[status(thm)],[f28,f336]) ).
fof(f354,plain,
! [X0,X1,X2] : meet(join(X0,X1),join(X1,X2)) = join(X1,meet(X2,join(X0,X1))),
inference(resolution,[status(thm)],[f77,f34]) ).
fof(f356,plain,
! [X0,X1,X2] : meet(X0,meet(X1,join(X2,meet(X0,X1)))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f27,f77]) ).
fof(f359,plain,
! [X0,X1,X2] : meet(X0,join(X1,join(X2,X0))) = X0,
inference(paramodulation,[status(thm)],[f28,f77]) ).
fof(f364,plain,
! [X0,X1] : meet(meet(X0,X1),X0) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f24,f77]) ).
fof(f375,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X0,meet(join(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f77,f27]) ).
fof(f377,plain,
! [X0,X1,X2] : join(X0,meet(join(X0,X1),join(X1,X2))) = join(X0,X1),
inference(backward_demodulation,[status(thm)],[f354,f329]) ).
fof(f379,plain,
! [X0,X1] :
( complement(X0,meet(X1,X0))
| X0 != n1
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f381,f346]) ).
fof(f381,plain,
! [X0,X1] : meet(X0,meet(X1,X0)) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f27,f364]) ).
fof(f383,plain,
! [X0] :
( ~ sQ13_spl
| X0 = n0
| ~ complement(n1,X0) ),
inference(resolution,[status(thm)],[f320,f40]) ).
fof(f384,plain,
( ~ sQ13_spl
| complement(n1,n0) ),
inference(resolution,[status(thm)],[f320,f38]) ).
fof(f386,plain,
! [X0,X1,X2,X3] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,meet(X2,join(meet(meet(X0,X1),X2),X3)))),
inference(paramodulation,[status(thm)],[f27,f93]) ).
fof(f407,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X0,meet(X1,join(meet(X1,X0),X2))),
inference(paramodulation,[status(thm)],[f25,f93]) ).
fof(f414,plain,
! [X0,X1,X2,X3] :
( meet(meet(X1,join(meet(X0,X1),X2)),join(X0,X3)) = join(X0,meet(X3,meet(X1,join(meet(X0,X1),X2))))
| meet(X0,X1) != X0 ),
inference(paramodulation,[status(thm)],[f93,f34]) ).
fof(f415,plain,
! [X0,X1,X2,X3] : meet(meet(X0,X1),X2) = meet(X0,meet(meet(X1,join(meet(X0,X1),X3)),X2)),
inference(paramodulation,[status(thm)],[f93,f27]) ).
fof(f417,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X2,join(meet(meet(X0,X1),X2),X3)))),
inference(forward_demodulation,[status(thm)],[f27,f386]) ).
fof(f418,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X2,join(meet(X0,meet(X1,X2)),X3)))),
inference(forward_demodulation,[status(thm)],[f27,f417]) ).
fof(f452,plain,
! [X0,X1,X2,X3] :
( meet(X1,meet(join(meet(X0,X1),X2),join(X0,X3))) = join(X0,meet(X3,meet(X1,join(meet(X0,X1),X2))))
| meet(X0,X1) != X0 ),
inference(forward_demodulation,[status(thm)],[f27,f414]) ).
fof(f453,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(meet(X1,join(meet(X0,X1),X3)),X2)),
inference(forward_demodulation,[status(thm)],[f27,f415]) ).
fof(f455,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(join(meet(X0,X1),X3),X2))),
inference(forward_demodulation,[status(thm)],[f27,f453]) ).
fof(f456,plain,
! [X0] : complement(n1,join(n0,meet(X0,n0))),
inference(resolution,[status(thm)],[f252,f66]) ).
fof(f457,plain,
! [X0] : complement(n1,join(n0,meet(n0,X0))),
inference(resolution,[status(thm)],[f252,f24]) ).
fof(f458,plain,
complement(n1,join(n0,n0)),
inference(resolution,[status(thm)],[f252,f30]) ).
fof(f459,plain,
complement(n1,join(n0,n0)),
inference(resolution,[status(thm)],[f252,f22]) ).
fof(f460,plain,
! [X0] : complement(n1,meet(n0,join(X0,n0))),
inference(resolution,[status(thm)],[f252,f77]) ).
fof(f461,plain,
! [X0] : complement(n1,meet(n0,join(n0,X0))),
inference(resolution,[status(thm)],[f252,f23]) ).
fof(f462,plain,
! [X0] : complement(n1,meet(X0,n0)),
inference(resolution,[status(thm)],[f252,f29]) ).
fof(f463,plain,
complement(n1,meet(n0,n1)),
inference(resolution,[status(thm)],[f252,f31]) ).
fof(f464,plain,
complement(n1,meet(n0,n0)),
inference(resolution,[status(thm)],[f252,f21]) ).
fof(f465,plain,
! [X0] : complement(n1,meet(n0,X0)),
inference(resolution,[status(thm)],[f252,f56]) ).
fof(f466,plain,
complement(n1,join(n0,n0)),
inference(resolution,[status(thm)],[f252,f70]) ).
fof(f467,plain,
complement(n1,meet(n1,n0)),
inference(resolution,[status(thm)],[f252,f57]) ).
fof(f468,plain,
complement(n1,n0),
inference(equality_resolution,[status(thm)],[f252]) ).
fof(f469,plain,
! [X0] : complement(n1,meet(X0,n0)),
inference(forward_demodulation,[status(thm)],[f70,f456]) ).
fof(f470,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f29,f469]) ).
fof(f471,plain,
! [X0] : complement(n1,meet(n0,X0)),
inference(forward_demodulation,[status(thm)],[f70,f457]) ).
fof(f472,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f56,f471]) ).
fof(f473,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f70,f458]) ).
fof(f474,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f70,f459]) ).
fof(f475,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f56,f460]) ).
fof(f476,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f56,f461]) ).
fof(f477,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f29,f462]) ).
fof(f478,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f56,f463]) ).
fof(f479,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f56,f464]) ).
fof(f480,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f56,f465]) ).
fof(f481,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f70,f466]) ).
fof(f482,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f57,f467]) ).
fof(f483,plain,
! [X0] : complement(join(n0,meet(X0,n0)),n1),
inference(resolution,[status(thm)],[f253,f66]) ).
fof(f484,plain,
! [X0] : complement(join(n0,meet(n0,X0)),n1),
inference(resolution,[status(thm)],[f253,f24]) ).
fof(f485,plain,
complement(join(n0,n0),n1),
inference(resolution,[status(thm)],[f253,f30]) ).
fof(f486,plain,
complement(join(n0,n0),n1),
inference(resolution,[status(thm)],[f253,f22]) ).
fof(f487,plain,
! [X0] : complement(meet(n0,join(X0,n0)),n1),
inference(resolution,[status(thm)],[f253,f77]) ).
fof(f488,plain,
! [X0] : complement(meet(n0,join(n0,X0)),n1),
inference(resolution,[status(thm)],[f253,f23]) ).
fof(f489,plain,
! [X0] : complement(meet(X0,n0),n1),
inference(resolution,[status(thm)],[f253,f29]) ).
fof(f490,plain,
complement(meet(n0,n1),n1),
inference(resolution,[status(thm)],[f253,f31]) ).
fof(f491,plain,
complement(meet(n0,n0),n1),
inference(resolution,[status(thm)],[f253,f21]) ).
fof(f492,plain,
! [X0] : complement(meet(n0,X0),n1),
inference(resolution,[status(thm)],[f253,f56]) ).
fof(f493,plain,
complement(join(n0,n0),n1),
inference(resolution,[status(thm)],[f253,f70]) ).
fof(f494,plain,
complement(meet(n1,n0),n1),
inference(resolution,[status(thm)],[f253,f57]) ).
fof(f495,plain,
complement(n0,n1),
inference(equality_resolution,[status(thm)],[f253]) ).
fof(f496,plain,
! [X0] : complement(meet(X0,n0),n1),
inference(forward_demodulation,[status(thm)],[f70,f483]) ).
fof(f497,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f29,f496]) ).
fof(f498,plain,
! [X0] : complement(meet(n0,X0),n1),
inference(forward_demodulation,[status(thm)],[f70,f484]) ).
fof(f499,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f56,f498]) ).
fof(f500,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f70,f485]) ).
fof(f501,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f70,f486]) ).
fof(f502,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f56,f487]) ).
fof(f503,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f56,f488]) ).
fof(f504,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f29,f489]) ).
fof(f505,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f56,f490]) ).
fof(f506,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f56,f491]) ).
fof(f507,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f56,f492]) ).
fof(f508,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f70,f493]) ).
fof(f509,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f57,f494]) ).
fof(f510,plain,
! [X0] : complement(n0,join(n1,X0)),
inference(resolution,[status(thm)],[f286,f80]) ).
fof(f511,plain,
! [X0] : complement(n0,join(X0,n1)),
inference(resolution,[status(thm)],[f286,f32]) ).
fof(f512,plain,
! [X0] : complement(n0,join(n1,meet(X0,n1))),
inference(resolution,[status(thm)],[f286,f66]) ).
fof(f513,plain,
! [X0] : complement(n0,join(n1,meet(n1,X0))),
inference(resolution,[status(thm)],[f286,f24]) ).
fof(f514,plain,
complement(n0,join(n1,n0)),
inference(resolution,[status(thm)],[f286,f30]) ).
fof(f515,plain,
complement(n0,join(n1,n1)),
inference(resolution,[status(thm)],[f286,f22]) ).
fof(f516,plain,
! [X0] : complement(n0,meet(n1,join(X0,n1))),
inference(resolution,[status(thm)],[f286,f77]) ).
fof(f517,plain,
! [X0] : complement(n0,meet(n1,join(n1,X0))),
inference(resolution,[status(thm)],[f286,f23]) ).
fof(f518,plain,
complement(n0,meet(n1,n1)),
inference(resolution,[status(thm)],[f286,f31]) ).
fof(f519,plain,
complement(n0,meet(n1,n1)),
inference(resolution,[status(thm)],[f286,f21]) ).
fof(f520,plain,
complement(n0,join(n0,n1)),
inference(resolution,[status(thm)],[f286,f70]) ).
fof(f521,plain,
complement(n0,meet(n1,n1)),
inference(resolution,[status(thm)],[f286,f57]) ).
fof(f522,plain,
complement(n0,n1),
inference(equality_resolution,[status(thm)],[f286]) ).
fof(f523,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f80,f510]) ).
fof(f524,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f32,f511]) ).
fof(f525,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f80,f512]) ).
fof(f526,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f80,f513]) ).
fof(f527,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f80,f514]) ).
fof(f528,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f80,f515]) ).
fof(f529,plain,
! [X0] : complement(n0,join(X0,n1)),
inference(forward_demodulation,[status(thm)],[f57,f516]) ).
fof(f530,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f32,f529]) ).
fof(f531,plain,
! [X0] : complement(n0,join(n1,X0)),
inference(forward_demodulation,[status(thm)],[f57,f517]) ).
fof(f532,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f80,f531]) ).
fof(f533,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f57,f518]) ).
fof(f534,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f57,f519]) ).
fof(f535,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f70,f520]) ).
fof(f536,plain,
complement(n0,n1),
inference(forward_demodulation,[status(thm)],[f57,f521]) ).
fof(f537,plain,
! [X0] : complement(join(n1,X0),n0),
inference(resolution,[status(thm)],[f293,f80]) ).
fof(f538,plain,
! [X0] : complement(join(X0,n1),n0),
inference(resolution,[status(thm)],[f293,f32]) ).
fof(f539,plain,
! [X0] : complement(join(n1,meet(X0,n1)),n0),
inference(resolution,[status(thm)],[f293,f66]) ).
fof(f540,plain,
! [X0] : complement(join(n1,meet(n1,X0)),n0),
inference(resolution,[status(thm)],[f293,f24]) ).
fof(f541,plain,
complement(join(n1,n0),n0),
inference(resolution,[status(thm)],[f293,f30]) ).
fof(f542,plain,
complement(join(n1,n1),n0),
inference(resolution,[status(thm)],[f293,f22]) ).
fof(f543,plain,
! [X0] : complement(meet(n1,join(X0,n1)),n0),
inference(resolution,[status(thm)],[f293,f77]) ).
fof(f544,plain,
! [X0] : complement(meet(n1,join(n1,X0)),n0),
inference(resolution,[status(thm)],[f293,f23]) ).
fof(f545,plain,
complement(meet(n1,n1),n0),
inference(resolution,[status(thm)],[f293,f31]) ).
fof(f546,plain,
complement(meet(n1,n1),n0),
inference(resolution,[status(thm)],[f293,f21]) ).
fof(f547,plain,
complement(join(n0,n1),n0),
inference(resolution,[status(thm)],[f293,f70]) ).
fof(f548,plain,
complement(meet(n1,n1),n0),
inference(resolution,[status(thm)],[f293,f57]) ).
fof(f549,plain,
complement(n1,n0),
inference(equality_resolution,[status(thm)],[f293]) ).
fof(f550,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f80,f537]) ).
fof(f551,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f32,f538]) ).
fof(f552,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f80,f539]) ).
fof(f553,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f80,f540]) ).
fof(f554,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f80,f541]) ).
fof(f555,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f80,f542]) ).
fof(f556,plain,
! [X0] : complement(join(X0,n1),n0),
inference(forward_demodulation,[status(thm)],[f57,f543]) ).
fof(f557,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f32,f556]) ).
fof(f558,plain,
! [X0] : complement(join(n1,X0),n0),
inference(forward_demodulation,[status(thm)],[f57,f544]) ).
fof(f559,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f80,f558]) ).
fof(f560,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f57,f545]) ).
fof(f561,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f57,f546]) ).
fof(f562,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f70,f547]) ).
fof(f563,plain,
complement(n1,n0),
inference(forward_demodulation,[status(thm)],[f57,f548]) ).
fof(f565,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X2,meet(X3,meet(X0,X1))),
inference(paramodulation,[status(thm)],[f27,f96]) ).
fof(f567,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X1,meet(join(meet(X0,X1),X2),X0)),
inference(paramodulation,[status(thm)],[f93,f96]) ).
fof(f574,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(meet(X1,X2),meet(X3,X0)),
inference(paramodulation,[status(thm)],[f27,f96]) ).
fof(f576,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X1,meet(meet(X2,join(meet(X1,X2),X3)),X0)),
inference(paramodulation,[status(thm)],[f93,f96]) ).
fof(f577,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X2,meet(meet(X3,X1),X0)),
inference(paramodulation,[status(thm)],[f96,f96]) ).
fof(f578,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X3,meet(meet(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f96,f96]) ).
fof(f579,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X1,meet(join(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f77,f96]) ).
fof(f580,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X1,meet(join(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f23,f96]) ).
fof(f583,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X2,meet(X1,X0)),
inference(paramodulation,[status(thm)],[f25,f96]) ).
fof(f585,plain,
! [X0,X1] : meet(X0,X1) = meet(X1,meet(X1,X0)),
inference(paramodulation,[status(thm)],[f21,f96]) ).
fof(f591,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(meet(X2,X0),X1),
inference(paramodulation,[status(thm)],[f25,f96]) ).
fof(f593,plain,
! [X0,X1] : meet(X0,meet(meet(X1,X0),X1)) = meet(X1,X0),
inference(paramodulation,[status(thm)],[f21,f96]) ).
fof(f597,plain,
! [X0,X1,X2,X3] : meet(meet(X0,join(meet(X1,X0),X2)),meet(X3,X1)) = meet(X3,meet(X1,X0)),
inference(paramodulation,[status(thm)],[f93,f96]) ).
fof(f598,plain,
! [X0,X1,X2,X3] : meet(meet(X0,X1),meet(X2,X3)) = meet(X2,meet(X1,meet(X3,X0))),
inference(paramodulation,[status(thm)],[f96,f96]) ).
fof(f599,plain,
! [X0,X1,X2,X3] : meet(meet(X0,X1),meet(X2,X3)) = meet(X2,meet(X0,meet(X1,X3))),
inference(paramodulation,[status(thm)],[f96,f96]) ).
fof(f604,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X1,meet(X0,X2)),
inference(paramodulation,[status(thm)],[f25,f96]) ).
fof(f611,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(meet(X1,X2),join(meet(X1,meet(X2,X0)),X3))),
inference(paramodulation,[status(thm)],[f96,f93]) ).
fof(f613,plain,
! [X0,X1,X2,X3] :
( meet(meet(X0,X1),join(X2,X3)) = join(X2,meet(X3,meet(X0,X1)))
| meet(X0,meet(X1,X2)) != X2 ),
inference(paramodulation,[status(thm)],[f96,f34]) ).
fof(f622,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(meet(X1,X2),join(meet(X2,meet(X0,X1)),X3))),
inference(paramodulation,[status(thm)],[f96,f93]) ).
fof(f623,plain,
! [X0,X1,X2] : join(meet(X0,X1),meet(X1,meet(X2,X0))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f96,f66]) ).
fof(f624,plain,
! [X0,X1,X2,X3] :
( meet(meet(X2,X0),join(X1,X3)) = join(X1,meet(X3,meet(X2,X0)))
| meet(X0,meet(X1,X2)) != X1 ),
inference(paramodulation,[status(thm)],[f96,f34]) ).
fof(f628,plain,
! [X0,X1,X2] : join(X0,meet(X1,meet(X0,X2))) = X0,
inference(paramodulation,[status(thm)],[f96,f24]) ).
fof(f631,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X1,meet(X0,join(meet(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f25,f567]) ).
fof(f634,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X1,meet(X2,meet(X3,X0))),
inference(forward_demodulation,[status(thm)],[f27,f574]) ).
fof(f636,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X1,meet(X2,meet(join(meet(X1,X2),X3),X0))),
inference(forward_demodulation,[status(thm)],[f27,f576]) ).
fof(f637,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X2,meet(X3,meet(X1,X0))),
inference(forward_demodulation,[status(thm)],[f27,f577]) ).
fof(f638,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X3,meet(X1,meet(X2,X0))),
inference(forward_demodulation,[status(thm)],[f27,f578]) ).
fof(f645,plain,
! [X0,X1] : meet(X0,meet(X1,meet(X0,X1))) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f27,f593]) ).
fof(f646,plain,
! [X0,X1] : meet(X0,meet(X1,X0)) = meet(X1,X0),
inference(forward_demodulation,[status(thm)],[f381,f645]) ).
fof(f650,plain,
! [X0,X1,X2,X3] : meet(X0,meet(join(meet(X1,X0),X2),meet(X3,X1))) = meet(X3,meet(X1,X0)),
inference(forward_demodulation,[status(thm)],[f27,f597]) ).
fof(f651,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(join(meet(X1,X0),X2),X3))) = meet(X3,meet(X1,X0)),
inference(forward_demodulation,[status(thm)],[f96,f650]) ).
fof(f652,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X2,meet(X1,meet(X3,X0))),
inference(forward_demodulation,[status(thm)],[f27,f598]) ).
fof(f653,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X2,meet(X0,meet(X1,X3))),
inference(forward_demodulation,[status(thm)],[f27,f599]) ).
fof(f659,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X2,join(meet(X1,meet(X2,X0)),X3)))),
inference(forward_demodulation,[status(thm)],[f27,f611]) ).
fof(f660,plain,
! [X0,X1,X2,X3] :
( meet(X0,meet(X1,join(X2,X3))) = join(X2,meet(X3,meet(X0,X1)))
| meet(X0,meet(X1,X2)) != X2 ),
inference(forward_demodulation,[status(thm)],[f27,f613]) ).
fof(f668,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X2,join(meet(X2,meet(X0,X1)),X3)))),
inference(forward_demodulation,[status(thm)],[f27,f622]) ).
fof(f669,plain,
! [X0,X1,X2,X3] :
( meet(X2,meet(X0,join(X1,X3))) = join(X1,meet(X3,meet(X2,X0)))
| meet(X0,meet(X1,X2)) != X1 ),
inference(forward_demodulation,[status(thm)],[f27,f624]) ).
fof(f681,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,join(meet(join(X0,X2),X1),X3))) = meet(X0,meet(join(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f93,f101]) ).
fof(f682,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X2,meet(join(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f96,f101]) ).
fof(f683,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X2,join(X0,X3)))),
inference(paramodulation,[status(thm)],[f96,f101]) ).
fof(f684,plain,
! [X0,X1,X2] : meet(X0,join(X1,join(X0,X2))) = meet(X0,join(X0,X2)),
inference(paramodulation,[status(thm)],[f77,f101]) ).
fof(f688,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X0,meet(X1,join(X0,X2))),
inference(paramodulation,[status(thm)],[f25,f101]) ).
fof(f691,plain,
! [X0,X1,X2,X3] : meet(join(X0,X1),X2) = meet(join(X0,X1),meet(join(X0,join(X1,X3)),X2)),
inference(paramodulation,[status(thm)],[f28,f101]) ).
fof(f706,plain,
! [X0,X1,X2,X3] : meet(meet(join(X0,X1),X2),meet(X3,X0)) = meet(X3,meet(X0,X2)),
inference(paramodulation,[status(thm)],[f101,f96]) ).
fof(f709,plain,
! [X0,X1,X2] : join(meet(join(X0,X1),X2),meet(X0,X2)) = meet(join(X0,X1),X2),
inference(paramodulation,[status(thm)],[f101,f66]) ).
fof(f710,plain,
! [X0,X1,X2,X3] :
( meet(meet(join(X0,X2),X1),join(X0,X3)) = join(X0,meet(X3,meet(join(X0,X2),X1)))
| meet(X0,X1) != X0 ),
inference(paramodulation,[status(thm)],[f101,f34]) ).
fof(f721,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,join(meet(join(X0,X2),X1),X3))) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f101,f681]) ).
fof(f722,plain,
! [X0,X1,X2] : meet(X0,join(X1,join(X0,X2))) = X0,
inference(forward_demodulation,[status(thm)],[f23,f684]) ).
fof(f733,plain,
! [X0,X1,X2,X3] : meet(join(X0,X1),meet(X2,meet(X3,X0))) = meet(X3,meet(X0,X2)),
inference(forward_demodulation,[status(thm)],[f27,f706]) ).
fof(f734,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(join(X0,X2),X3))) = meet(X3,meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f652,f733]) ).
fof(f740,plain,
! [X0,X1,X2] : join(meet(X0,X1),meet(join(X0,X2),X1)) = meet(join(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f26,f709]) ).
fof(f741,plain,
! [X0,X1,X2,X3] :
( meet(join(X0,X2),meet(X1,join(X0,X3))) = join(X0,meet(X3,meet(join(X0,X2),X1)))
| meet(X0,X1) != X0 ),
inference(forward_demodulation,[status(thm)],[f27,f710]) ).
fof(f745,plain,
! [X0,X1,X2,X3] : meet(meet(X0,X1),X2) = meet(X1,meet(X0,meet(join(meet(X0,X1),X3),X2))),
inference(paramodulation,[status(thm)],[f101,f104]) ).
fof(f749,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X1,meet(X0,join(X2,meet(X0,X1)))),
inference(paramodulation,[status(thm)],[f77,f104]) ).
fof(f757,plain,
! [X0,X1,X2,X3] : meet(meet(X0,meet(X1,X2)),X3) = meet(X2,meet(meet(X1,X0),X3)),
inference(paramodulation,[status(thm)],[f104,f104]) ).
fof(f761,plain,
! [X0,X1,X2,X3] : meet(meet(X0,X1),X2) = meet(meet(X1,join(meet(X0,X1),X3)),meet(X0,X2)),
inference(paramodulation,[status(thm)],[f93,f104]) ).
fof(f764,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(join(X2,X0),meet(X0,X1)),
inference(paramodulation,[status(thm)],[f77,f104]) ).
fof(f776,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X2,meet(X1,join(meet(X0,meet(X1,X2)),X3)))),
inference(paramodulation,[status(thm)],[f104,f93]) ).
fof(f781,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X1,meet(X3,meet(X2,X0))),
inference(paramodulation,[status(thm)],[f104,f96]) ).
fof(f785,plain,
! [X0,X1,X2,X3] :
( meet(X2,join(meet(X1,X0),X3)) = join(meet(X1,X0),meet(X3,X2))
| meet(X0,meet(X1,X2)) != meet(X1,X0) ),
inference(paramodulation,[status(thm)],[f104,f34]) ).
fof(f786,plain,
! [X0,X1,X2,X3] : meet(meet(X0,meet(X1,X2)),X3) = meet(meet(X1,X0),meet(X2,X3)),
inference(paramodulation,[status(thm)],[f104,f27]) ).
fof(f789,plain,
! [X0,X1,X2] : join(meet(X0,X1),meet(X1,meet(X0,X2))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f104,f24]) ).
fof(f791,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(join(meet(X1,X0),X3),X2))),
inference(forward_demodulation,[status(thm)],[f104,f745]) ).
fof(f800,plain,
! [X0,X1,X2,X3] : meet(meet(X0,X1),meet(X2,X3)) = meet(X1,meet(meet(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f104,f757]) ).
fof(f801,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X0,meet(meet(X1,X2),X3)),
inference(forward_demodulation,[status(thm)],[f104,f800]) ).
fof(f802,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X0,meet(X2,meet(X1,X3))),
inference(forward_demodulation,[status(thm)],[f104,f801]) ).
fof(f808,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(meet(X0,join(meet(X1,X0),X3)),meet(X1,X2)),
inference(forward_demodulation,[status(thm)],[f104,f761]) ).
fof(f809,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(join(meet(X1,X0),X3),meet(X0,meet(X1,X2))),
inference(forward_demodulation,[status(thm)],[f104,f808]) ).
fof(f810,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(meet(X1,X2),join(meet(X1,X0),X3))),
inference(forward_demodulation,[status(thm)],[f96,f809]) ).
fof(f811,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,X2)) = meet(X0,meet(X2,meet(X1,join(meet(X1,X0),X3)))),
inference(forward_demodulation,[status(thm)],[f104,f810]) ).
fof(f818,plain,
! [X0,X1,X2] : meet(X0,X1) = meet(X0,meet(X1,join(X2,X0))),
inference(forward_demodulation,[status(thm)],[f96,f764]) ).
fof(f830,plain,
! [X0,X1,X2,X3] : meet(meet(X0,X1),meet(X2,X3)) = meet(meet(X0,X2),meet(X1,X3)),
inference(forward_demodulation,[status(thm)],[f104,f786]) ).
fof(f831,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(meet(X1,X2),meet(X0,X3)),
inference(forward_demodulation,[status(thm)],[f104,f830]) ).
fof(f832,plain,
! [X0,X1,X2,X3] : meet(X0,meet(X1,meet(X2,X3))) = meet(X2,meet(X1,meet(X0,X3))),
inference(forward_demodulation,[status(thm)],[f104,f831]) ).
fof(f836,plain,
! [X0,X1,X2] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,meet(meet(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f27,f106]) ).
fof(f843,plain,
! [X0,X1,X2] : meet(meet(X0,X1),X2) = meet(meet(X0,X1),meet(X0,meet(X1,X2))),
inference(paramodulation,[status(thm)],[f27,f106]) ).
fof(f848,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(X2,meet(X0,X1))),
inference(paramodulation,[status(thm)],[f96,f106]) ).
fof(f849,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X2,X0))),
inference(paramodulation,[status(thm)],[f96,f106]) ).
fof(f859,plain,
! [X0,X1,X2] : meet(meet(X0,X1),X2) = meet(X1,meet(X0,meet(meet(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f106,f104]) ).
fof(f867,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X1,meet(meet(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f106,f96]) ).
fof(f870,plain,
! [X0,X1,X2] :
( meet(meet(X0,X1),join(X0,X2)) = join(X0,meet(X2,meet(X0,X1)))
| meet(X0,X1) != X0 ),
inference(paramodulation,[status(thm)],[f106,f34]) ).
fof(f875,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X1,meet(X0,meet(meet(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f104,f836]) ).
fof(f876,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X1,meet(X0,meet(X0,meet(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f104,f875]) ).
fof(f878,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X1,meet(X0,meet(X1,X2))),
inference(forward_demodulation,[status(thm)],[f106,f876]) ).
fof(f886,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(meet(X1,X0),meet(X1,meet(X0,X2))),
inference(forward_demodulation,[status(thm)],[f104,f843]) ).
fof(f887,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X1,meet(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f104,f886]) ).
fof(f888,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X0,X2))),
inference(forward_demodulation,[status(thm)],[f106,f887]) ).
fof(f894,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(meet(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f104,f859]) ).
fof(f895,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(X1,meet(X0,meet(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f104,f894]) ).
fof(f896,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(meet(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f848,f895]) ).
fof(f897,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(X2,meet(X1,X1))),
inference(forward_demodulation,[status(thm)],[f104,f896]) ).
fof(f898,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X0,meet(X2,X1)),
inference(forward_demodulation,[status(thm)],[f21,f897]) ).
fof(f909,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(X1,meet(X2,meet(X1,X0))),
inference(forward_demodulation,[status(thm)],[f104,f867]) ).
fof(f915,plain,
! [X0,X1,X2] :
( meet(X1,meet(X0,join(X0,X2))) = join(X0,meet(X2,meet(X0,X1)))
| meet(X0,X1) != X0 ),
inference(forward_demodulation,[status(thm)],[f104,f870]) ).
fof(f916,plain,
! [X0,X1,X2] :
( meet(X1,X0) = join(X0,meet(X2,meet(X0,X1)))
| meet(X0,X1) != X0 ),
inference(forward_demodulation,[status(thm)],[f23,f915]) ).
fof(f917,plain,
! [X0,X1] :
( meet(X1,X0) = X0
| meet(X0,X1) != X0 ),
inference(forward_demodulation,[status(thm)],[f628,f916]) ).
fof(f923,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(meet(X1,X0),meet(X2,X3))) = meet(meet(X1,X0),X2),
inference(paramodulation,[status(thm)],[f104,f112]) ).
fof(f924,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(meet(X0,X1),meet(X2,X3))) = meet(meet(X0,X1),X2),
inference(paramodulation,[status(thm)],[f27,f112]) ).
fof(f929,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X1,meet(meet(X2,X0),X3))) = meet(X1,meet(X2,X0)),
inference(paramodulation,[status(thm)],[f96,f112]) ).
fof(f930,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X2,meet(meet(X0,X1),X3))) = meet(X2,meet(X0,X1)),
inference(paramodulation,[status(thm)],[f96,f112]) ).
fof(f935,plain,
! [X0,X1,X2] : join(meet(X0,X1),meet(X1,meet(X0,X2))) = meet(X1,X0),
inference(paramodulation,[status(thm)],[f25,f112]) ).
fof(f940,plain,
! [X0,X1,X2,X3] : join(meet(meet(X0,X1),X2),meet(X0,meet(X1,meet(X2,X3)))) = meet(meet(X0,X1),X2),
inference(paramodulation,[status(thm)],[f27,f112]) ).
fof(f947,plain,
! [X0,X1,X2] : join(meet(X0,X1),meet(meet(X1,X2),X0)) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f25,f112]) ).
fof(f951,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X0,meet(X2,meet(X1,X3)))) = meet(X0,meet(X1,X2)),
inference(paramodulation,[status(thm)],[f104,f112]) ).
fof(f957,plain,
! [X0,X1,X2,X3] : join(meet(X0,X1),meet(X0,meet(X2,meet(X1,X3)))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f96,f112]) ).
fof(f958,plain,
! [X0,X1,X2,X3] : join(meet(X0,X1),meet(X0,meet(X2,meet(X3,X1)))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f96,f112]) ).
fof(f963,plain,
! [X0,X1,X2] : join(meet(X0,X1),meet(X0,meet(X2,X1))) = meet(X0,X1),
inference(paramodulation,[status(thm)],[f25,f112]) ).
fof(f970,plain,
! [X0,X1,X2] :
( complement(meet(X0,X1),meet(X0,meet(X1,X2)))
| meet(X0,X1) != n1
| meet(meet(X0,X1),meet(X0,meet(X1,X2))) != n0 ),
inference(paramodulation,[status(thm)],[f112,f37]) ).
fof(f971,plain,
! [X0,X1,X2,X3] : join(meet(X0,X1),X2) = join(meet(X0,X1),join(meet(X0,meet(X1,X3)),X2)),
inference(paramodulation,[status(thm)],[f112,f28]) ).
fof(f975,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X0,meet(X1,meet(X2,X3)))) = meet(meet(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f104,f923]) ).
fof(f976,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X0,meet(X1,meet(X2,X3)))) = meet(X0,meet(X1,X2)),
inference(forward_demodulation,[status(thm)],[f104,f975]) ).
fof(f977,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X1,meet(X0,meet(X2,X3)))) = meet(meet(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f104,f924]) ).
fof(f978,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X1,meet(X0,meet(X2,X3)))) = meet(X1,meet(X0,X2)),
inference(forward_demodulation,[status(thm)],[f104,f977]) ).
fof(f986,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X1,meet(X0,meet(X2,X3)))) = meet(X1,meet(X2,X0)),
inference(forward_demodulation,[status(thm)],[f104,f929]) ).
fof(f987,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X2,meet(X1,meet(X0,X3)))) = meet(X2,meet(X0,X1)),
inference(forward_demodulation,[status(thm)],[f104,f930]) ).
fof(f995,plain,
! [X0,X1,X2,X3] : join(meet(X0,meet(X1,X2)),meet(X1,meet(X0,meet(X2,X3)))) = meet(meet(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f104,f940]) ).
fof(f996,plain,
! [X0,X1,X2] : meet(X0,meet(X1,X2)) = meet(meet(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f986,f995]) ).
fof(f1003,plain,
! [X0,X1,X2] : join(meet(X0,X1),meet(X2,meet(X1,X0))) = meet(X0,X1),
inference(forward_demodulation,[status(thm)],[f104,f947]) ).
fof(f1023,plain,
! [X0,X1,X2] :
( complement(meet(X1,X0),meet(X1,meet(X0,X2)))
| meet(X1,X0) != n1
| meet(X0,meet(X1,meet(X1,meet(X0,X2)))) != n0 ),
inference(forward_demodulation,[status(thm)],[f104,f970]) ).
fof(f1024,plain,
! [X0,X1,X2] :
( complement(meet(X1,X0),meet(X1,meet(X0,X2)))
| meet(X1,X0) != n1
| meet(X0,meet(X1,meet(X0,X2))) != n0 ),
inference(forward_demodulation,[status(thm)],[f106,f1023]) ).
fof(f1025,plain,
! [X0,X1,X2] :
( complement(meet(X2,X1),meet(X2,meet(X1,X0)))
| meet(X2,X1) != n1
| meet(X0,meet(X1,X2)) != n0 ),
inference(forward_demodulation,[status(thm)],[f909,f1024]) ).
fof(f1034,plain,
( complement(join(n1,n0),join(n1,n0))
| join(n1,n0) != n0 ),
inference(resolution,[status(thm)],[f294,f30]) ).
fof(f1035,plain,
( complement(join(n1,n1),join(n1,n1))
| join(n1,n1) != n0 ),
inference(resolution,[status(thm)],[f294,f22]) ).
fof(f1038,plain,
( complement(meet(n1,n1),meet(n1,n1))
| meet(n1,n1) != n0 ),
inference(resolution,[status(thm)],[f294,f31]) ).
fof(f1040,plain,
( complement(join(n0,n1),join(n0,n1))
| join(n0,n1) != n0 ),
inference(resolution,[status(thm)],[f294,f70]) ).
fof(f1042,plain,
( complement(n1,n1)
| n1 != n0 ),
inference(equality_resolution,[status(thm)],[f294]) ).
fof(f1055,definition,
( sQ15_spl
<=> join(n1,n0) = n0 ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( ~ sQ15_spl
| join(n1,n0) = n0 ),
inference(component_clause,[status(thm)],[f1055]) ).
fof(f1057,plain,
( sQ15_spl
| join(n1,n0) != n0 ),
inference(component_clause,[status(thm)],[f1055]) ).
fof(f1058,definition,
( sQ16_spl
<=> complement(join(n1,n0),join(n1,n0)) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f1059,plain,
( ~ sQ16_spl
| complement(join(n1,n0),join(n1,n0)) ),
inference(component_clause,[status(thm)],[f1058]) ).
fof(f1060,plain,
( sQ16_spl
| ~ complement(join(n1,n0),join(n1,n0)) ),
inference(component_clause,[status(thm)],[f1058]) ).
fof(f1061,plain,
( sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1034,f1055,f1058]) ).
fof(f1062,definition,
( sQ17_spl
<=> join(n1,n1) = n0 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f1063,plain,
( ~ sQ17_spl
| join(n1,n1) = n0 ),
inference(component_clause,[status(thm)],[f1062]) ).
fof(f1064,plain,
( sQ17_spl
| join(n1,n1) != n0 ),
inference(component_clause,[status(thm)],[f1062]) ).
fof(f1065,definition,
( sQ18_spl
<=> complement(join(n1,n1),join(n1,n1)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f1066,plain,
( ~ sQ18_spl
| complement(join(n1,n1),join(n1,n1)) ),
inference(component_clause,[status(thm)],[f1065]) ).
fof(f1068,plain,
( sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1035,f1062,f1065]) ).
fof(f1081,definition,
( sQ19_spl
<=> complement(meet(n1,n1),meet(n1,n1)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f1082,plain,
( ~ sQ19_spl
| complement(meet(n1,n1),meet(n1,n1)) ),
inference(component_clause,[status(thm)],[f1081]) ).
fof(f1083,plain,
( sQ19_spl
| ~ complement(meet(n1,n1),meet(n1,n1)) ),
inference(component_clause,[status(thm)],[f1081]) ).
fof(f1084,plain,
( sQ19_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1038,f264,f1081]) ).
fof(f1086,definition,
( sQ20_spl
<=> join(n0,n1) = n0 ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f1087,plain,
( ~ sQ20_spl
| join(n0,n1) = n0 ),
inference(component_clause,[status(thm)],[f1086]) ).
fof(f1088,plain,
( sQ20_spl
| join(n0,n1) != n0 ),
inference(component_clause,[status(thm)],[f1086]) ).
fof(f1089,definition,
( sQ21_spl
<=> complement(join(n0,n1),join(n0,n1)) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f1090,plain,
( ~ sQ21_spl
| complement(join(n0,n1),join(n0,n1)) ),
inference(component_clause,[status(thm)],[f1089]) ).
fof(f1092,plain,
( sQ21_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1040,f1086,f1089]) ).
fof(f1094,definition,
( sQ22_spl
<=> n1 = n0 ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f1095,plain,
( ~ sQ22_spl
| n1 = n0 ),
inference(component_clause,[status(thm)],[f1094]) ).
fof(f1096,plain,
( sQ22_spl
| n1 != n0 ),
inference(component_clause,[status(thm)],[f1094]) ).
fof(f1097,plain,
( sQ5_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1042,f1094,f267]) ).
fof(f1098,plain,
( sQ20_spl
| n1 != n0 ),
inference(forward_demodulation,[status(thm)],[f70,f1088]) ).
fof(f1099,plain,
( sQ17_spl
| n1 != n0 ),
inference(forward_demodulation,[status(thm)],[f80,f1064]) ).
fof(f1100,plain,
( sQ15_spl
| n1 != n0 ),
inference(forward_demodulation,[status(thm)],[f80,f1057]) ).
fof(f1101,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| n1 = n0 ),
inference(resolution,[status(thm)],[f268,f383]) ).
fof(f1103,plain,
( ~ sQ5_spl
| meet(n1,n1) = n0 ),
inference(resolution,[status(thm)],[f268,f35]) ).
fof(f1104,plain,
( ~ sQ5_spl
| complement(n1,f(n1,n1))
| unique_complement(n1,n1) ),
inference(resolution,[status(thm)],[f268,f41]) ).
fof(f1105,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1101,f300]) ).
fof(f1106,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1105]) ).
fof(f1107,plain,
! [X0,X1,X2,X3] : join(join(X0,X1),X2) = join(X0,join(X1,join(X2,meet(join(join(X0,X1),X2),X3)))),
inference(paramodulation,[status(thm)],[f28,f169]) ).
fof(f1117,plain,
! [X0,X1,X2,X3] : join(X0,X1) = join(X0,join(X1,meet(X2,meet(join(X0,X1),X3)))),
inference(paramodulation,[status(thm)],[f96,f169]) ).
fof(f1118,plain,
! [X0,X1,X2,X3] : join(X0,X1) = join(X0,join(X1,meet(X2,meet(X3,join(X0,X1))))),
inference(paramodulation,[status(thm)],[f96,f169]) ).
fof(f1135,plain,
! [X0,X1,X2] : join(X0,X1) = join(X0,join(X1,meet(join(X1,X0),X2))),
inference(paramodulation,[status(thm)],[f26,f169]) ).
fof(f1143,plain,
! [X0,X1,X2] : meet(join(X0,meet(join(X1,X0),X2)),join(X1,X0)) = join(X0,meet(join(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f169,f77]) ).
fof(f1144,plain,
! [X0,X1,X2] :
( complement(X0,join(X1,meet(join(X0,X1),X2)))
| join(X0,X1) != n1
| meet(X0,join(X1,meet(join(X0,X1),X2))) != n0 ),
inference(paramodulation,[status(thm)],[f169,f37]) ).
fof(f1145,plain,
! [X0,X1,X2,X3] : join(join(X0,X1),X2) = join(X0,join(join(X1,meet(join(X0,X1),X3)),X2)),
inference(paramodulation,[status(thm)],[f169,f28]) ).
fof(f1147,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X2,meet(join(join(X0,X1),X2),X3)))),
inference(forward_demodulation,[status(thm)],[f28,f1107]) ).
fof(f1148,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X2,meet(join(X0,join(X1,X2)),X3)))),
inference(forward_demodulation,[status(thm)],[f28,f1147]) ).
fof(f1182,plain,
! [X0,X1,X2] : meet(join(X0,X1),join(X1,meet(join(X0,X1),X2))) = join(X1,meet(join(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f25,f1143]) ).
fof(f1183,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(join(X1,meet(join(X0,X1),X3)),X2)),
inference(forward_demodulation,[status(thm)],[f28,f1145]) ).
fof(f1185,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X1,join(meet(join(X0,X1),X3),X2))),
inference(forward_demodulation,[status(thm)],[f28,f1183]) ).
fof(f1186,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X2,join(X3,join(X0,X1))),
inference(paramodulation,[status(thm)],[f28,f171]) ).
fof(f1189,plain,
! [X0,X1,X2] : join(X0,X1) = join(X1,join(meet(join(X0,X1),X2),X0)),
inference(paramodulation,[status(thm)],[f169,f171]) ).
fof(f1195,plain,
! [X0,X1,X2,X3] : join(X0,meet(X1,X2)) = join(meet(X1,X2),join(meet(X1,meet(X2,X3)),X0)),
inference(paramodulation,[status(thm)],[f112,f171]) ).
fof(f1196,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(join(X1,X2),join(X3,X0)),
inference(paramodulation,[status(thm)],[f28,f171]) ).
fof(f1199,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X1,join(join(X2,meet(join(X1,X2),X3)),X0)),
inference(paramodulation,[status(thm)],[f169,f171]) ).
fof(f1200,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X2,join(join(X3,X1),X0)),
inference(paramodulation,[status(thm)],[f171,f171]) ).
fof(f1201,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X3,join(join(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f171,f171]) ).
fof(f1203,plain,
! [X0,X1,X2] : join(X0,X1) = join(X1,join(meet(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f66,f171]) ).
fof(f1204,plain,
! [X0,X1,X2] : join(X0,X1) = join(X1,join(meet(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f24,f171]) ).
fof(f1206,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X2,join(X1,X0)),
inference(paramodulation,[status(thm)],[f26,f171]) ).
fof(f1208,plain,
! [X0,X1] : join(X0,X1) = join(X1,join(X1,X0)),
inference(paramodulation,[status(thm)],[f22,f171]) ).
fof(f1214,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X2,X0),X1),
inference(paramodulation,[status(thm)],[f26,f171]) ).
fof(f1216,plain,
! [X0,X1] : join(X0,join(join(X1,X0),X1)) = join(X1,X0),
inference(paramodulation,[status(thm)],[f22,f171]) ).
fof(f1221,plain,
! [X0,X1,X2,X3] : join(join(X0,meet(join(X1,X0),X2)),join(X3,X1)) = join(X3,join(X1,X0)),
inference(paramodulation,[status(thm)],[f169,f171]) ).
fof(f1222,plain,
! [X0,X1,X2,X3] : join(join(X0,X1),join(X2,X3)) = join(X2,join(X1,join(X3,X0))),
inference(paramodulation,[status(thm)],[f171,f171]) ).
fof(f1223,plain,
! [X0,X1,X2,X3] : join(join(X0,X1),join(X2,X3)) = join(X2,join(X0,join(X1,X3))),
inference(paramodulation,[status(thm)],[f171,f171]) ).
fof(f1228,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(paramodulation,[status(thm)],[f26,f171]) ).
fof(f1231,plain,
! [X0,X1,X2,X3] : meet(X0,X1) = meet(X0,meet(X1,join(X2,join(X3,meet(X0,X1))))),
inference(paramodulation,[status(thm)],[f171,f93]) ).
fof(f1236,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(join(X1,X2),meet(join(X1,join(X2,X0)),X3))),
inference(paramodulation,[status(thm)],[f171,f169]) ).
fof(f1237,plain,
! [X0,X1,X2,X3] : meet(X0,X1) = meet(X0,meet(join(X2,join(X3,X0)),X1)),
inference(paramodulation,[status(thm)],[f171,f101]) ).
fof(f1239,plain,
! [X0,X1,X2] :
( complement(X0,join(X1,X2))
| join(X1,join(X2,X0)) != n1
| meet(X0,join(X1,X2)) != n0 ),
inference(paramodulation,[status(thm)],[f171,f37]) ).
fof(f1245,plain,
! [X0,X1,X2,X3] : meet(X0,X1) = meet(X0,meet(X1,join(X2,join(meet(X0,X1),X3)))),
inference(paramodulation,[status(thm)],[f171,f93]) ).
fof(f1249,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(join(X1,X2),meet(join(X2,join(X0,X1)),X3))),
inference(paramodulation,[status(thm)],[f171,f169]) ).
fof(f1250,plain,
! [X0,X1,X2,X3] : meet(X0,X1) = meet(X0,meet(join(X2,join(X0,X3)),X1)),
inference(paramodulation,[status(thm)],[f171,f101]) ).
fof(f1251,plain,
! [X0,X1,X2] : meet(join(X0,X1),join(X1,join(X2,X0))) = join(X0,X1),
inference(paramodulation,[status(thm)],[f171,f77]) ).
fof(f1252,plain,
! [X0,X1,X2] :
( complement(X0,join(X1,X2))
| join(X2,join(X0,X1)) != n1
| meet(X0,join(X1,X2)) != n0 ),
inference(paramodulation,[status(thm)],[f171,f37]) ).
fof(f1259,plain,
! [X0,X1,X2] : join(X0,X1) = join(X1,join(X0,meet(join(X0,X1),X2))),
inference(forward_demodulation,[status(thm)],[f26,f1189]) ).
fof(f1261,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X1,join(X2,join(X3,X0))),
inference(forward_demodulation,[status(thm)],[f28,f1196]) ).
fof(f1264,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X1,join(X2,join(meet(join(X1,X2),X3),X0))),
inference(forward_demodulation,[status(thm)],[f28,f1199]) ).
fof(f1265,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X2,join(X3,join(X1,X0))),
inference(forward_demodulation,[status(thm)],[f28,f1200]) ).
fof(f1266,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X3,join(X1,join(X2,X0))),
inference(forward_demodulation,[status(thm)],[f28,f1201]) ).
fof(f1273,plain,
! [X0,X1] : join(X0,join(X1,join(X0,X1))) = join(X1,X0),
inference(forward_demodulation,[status(thm)],[f28,f1216]) ).
fof(f1274,plain,
! [X0,X1] : join(X0,join(X1,X0)) = join(X1,X0),
inference(forward_demodulation,[status(thm)],[f353,f1273]) ).
fof(f1279,plain,
! [X0,X1,X2,X3] : join(X0,join(meet(join(X1,X0),X2),join(X3,X1))) = join(X3,join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f28,f1221]) ).
fof(f1280,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(meet(join(X1,X0),X2),X3))) = join(X3,join(X1,X0)),
inference(forward_demodulation,[status(thm)],[f171,f1279]) ).
fof(f1281,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X2,join(X1,join(X3,X0))),
inference(forward_demodulation,[status(thm)],[f28,f1222]) ).
fof(f1282,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X2,join(X0,join(X1,X3))),
inference(forward_demodulation,[status(thm)],[f28,f1223]) ).
fof(f1288,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X2,meet(join(X1,join(X2,X0)),X3)))),
inference(forward_demodulation,[status(thm)],[f28,f1236]) ).
fof(f1296,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X2,meet(join(X2,join(X0,X1)),X3)))),
inference(forward_demodulation,[status(thm)],[f28,f1249]) ).
fof(f1308,plain,
! [X0,X1,X2,X3] : join(X0,join(meet(meet(X0,X1),X2),X3)) = join(X0,join(meet(X0,X1),X3)),
inference(paramodulation,[status(thm)],[f178,f178]) ).
fof(f1309,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,meet(join(meet(X0,X2),X1),X3))) = join(X0,join(meet(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f169,f178]) ).
fof(f1310,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X2,join(meet(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f171,f178]) ).
fof(f1311,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X2,meet(X0,X3)))),
inference(paramodulation,[status(thm)],[f171,f178]) ).
fof(f1316,plain,
! [X0,X1,X2] : join(X0,X1) = join(X0,join(X1,meet(X0,X2))),
inference(paramodulation,[status(thm)],[f26,f178]) ).
fof(f1320,plain,
! [X0,X1,X2,X3] : join(meet(X0,X1),X2) = join(meet(X0,X1),join(meet(X1,meet(X0,X3)),X2)),
inference(paramodulation,[status(thm)],[f104,f178]) ).
fof(f1327,plain,
! [X0,X1,X2,X3] : join(X0,X1) = join(X0,join(meet(X2,meet(X3,X0)),X1)),
inference(paramodulation,[status(thm)],[f96,f178]) ).
fof(f1341,plain,
! [X0,X1,X2,X3] : join(join(meet(X0,X1),X2),join(X3,X0)) = join(X3,join(X0,X2)),
inference(paramodulation,[status(thm)],[f178,f171]) ).
fof(f1345,plain,
! [X0,X1,X2] : meet(join(meet(X0,X1),X2),join(X0,X2)) = join(meet(X0,X1),X2),
inference(paramodulation,[status(thm)],[f178,f77]) ).
fof(f1346,plain,
! [X0,X1,X2] :
( complement(X0,join(meet(X0,X1),X2))
| join(X0,X2) != n1
| meet(X0,join(meet(X0,X1),X2)) != n0 ),
inference(paramodulation,[status(thm)],[f178,f37]) ).
fof(f1356,plain,
! [X0,X1,X2,X3] : join(X0,join(meet(X1,meet(X0,X2)),X3)) = join(X0,join(meet(X0,X1),X3)),
inference(forward_demodulation,[status(thm)],[f104,f1308]) ).
fof(f1357,plain,
! [X0,X1,X2,X3] : join(X0,join(meet(X1,meet(X0,X2)),X3)) = join(X0,X3),
inference(forward_demodulation,[status(thm)],[f178,f1356]) ).
fof(f1358,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,meet(join(meet(X0,X2),X1),X3))) = join(X0,X1),
inference(forward_demodulation,[status(thm)],[f178,f1309]) ).
fof(f1370,plain,
! [X0,X1,X2,X3] : join(meet(X0,X1),join(X2,join(X3,X0))) = join(X3,join(X0,X2)),
inference(forward_demodulation,[status(thm)],[f28,f1341]) ).
fof(f1371,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(meet(X0,X2),X3))) = join(X3,join(X0,X1)),
inference(forward_demodulation,[status(thm)],[f1281,f1370]) ).
fof(f1377,plain,
! [X0,X1,X2] : meet(join(X0,X1),join(meet(X0,X2),X1)) = join(meet(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f25,f1345]) ).
fof(f1381,plain,
! [X0,X1,X2,X3] : join(join(X0,X1),X2) = join(X1,join(X0,join(meet(join(X0,X1),X3),X2))),
inference(paramodulation,[status(thm)],[f178,f180]) ).
fof(f1386,plain,
! [X0,X1,X2] : join(X0,X1) = join(X1,join(X0,meet(X2,join(X0,X1)))),
inference(paramodulation,[status(thm)],[f66,f180]) ).
fof(f1392,plain,
! [X0,X1,X2,X3] : join(meet(X0,X1),X2) = join(meet(X0,meet(X1,X3)),join(meet(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f112,f180]) ).
fof(f1393,plain,
! [X0,X1,X2,X3] : join(join(X0,join(X1,X2)),X3) = join(X2,join(join(X1,X0),X3)),
inference(paramodulation,[status(thm)],[f180,f180]) ).
fof(f1398,plain,
! [X0,X1,X2,X3] : join(join(X0,X1),X2) = join(join(X1,meet(join(X0,X1),X3)),join(X0,X2)),
inference(paramodulation,[status(thm)],[f169,f180]) ).
fof(f1402,plain,
! [X0,X1,X2] : join(X0,X1) = join(meet(X2,X0),join(X0,X1)),
inference(paramodulation,[status(thm)],[f66,f180]) ).
fof(f1414,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X2,join(X1,meet(join(X0,join(X1,X2)),X3)))),
inference(paramodulation,[status(thm)],[f180,f169]) ).
fof(f1418,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X1,join(X3,join(X2,X0))),
inference(paramodulation,[status(thm)],[f180,f171]) ).
fof(f1421,plain,
! [X0,X1,X2,X3] : meet(join(X0,X1),X2) = meet(join(X0,X1),meet(join(X1,join(X0,X3)),X2)),
inference(paramodulation,[status(thm)],[f180,f101]) ).
fof(f1423,plain,
! [X0,X1,X2] :
( complement(join(X0,X1),X2)
| join(X1,join(X0,X2)) != n1
| meet(join(X0,X1),X2) != n0 ),
inference(paramodulation,[status(thm)],[f180,f37]) ).
fof(f1424,plain,
! [X0,X1,X2,X3] : join(join(X0,join(X1,X2)),X3) = join(join(X1,X0),join(X2,X3)),
inference(paramodulation,[status(thm)],[f180,f28]) ).
fof(f1427,plain,
! [X0,X1,X2] : meet(join(X0,X1),join(X1,join(X0,X2))) = join(X0,X1),
inference(paramodulation,[status(thm)],[f180,f23]) ).
fof(f1429,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X1,join(meet(join(X1,X0),X3),X2))),
inference(forward_demodulation,[status(thm)],[f180,f1381]) ).
fof(f1434,plain,
! [X0,X1,X2] : join(X0,X1) = join(X1,meet(join(X0,X1),join(X0,X2))),
inference(forward_demodulation,[status(thm)],[f197,f1386]) ).
fof(f1437,plain,
! [X0,X1,X2,X3] : join(meet(X0,X1),X2) = join(meet(X0,X1),join(X2,meet(X0,meet(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f171,f1392]) ).
fof(f1438,plain,
! [X0,X1,X2,X3] : join(join(X0,X1),join(X2,X3)) = join(X1,join(join(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f180,f1393]) ).
fof(f1439,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X0,join(join(X1,X2),X3)),
inference(forward_demodulation,[status(thm)],[f180,f1438]) ).
fof(f1440,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X0,join(X2,join(X1,X3))),
inference(forward_demodulation,[status(thm)],[f180,f1439]) ).
fof(f1448,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(join(X0,meet(join(X1,X0),X3)),join(X1,X2)),
inference(forward_demodulation,[status(thm)],[f180,f1398]) ).
fof(f1449,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(meet(join(X1,X0),X3),join(X0,join(X1,X2))),
inference(forward_demodulation,[status(thm)],[f180,f1448]) ).
fof(f1450,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(join(X1,X2),meet(join(X1,X0),X3))),
inference(forward_demodulation,[status(thm)],[f171,f1449]) ).
fof(f1451,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,X2)) = join(X0,join(X2,join(X1,meet(join(X1,X0),X3)))),
inference(forward_demodulation,[status(thm)],[f180,f1450]) ).
fof(f1459,plain,
! [X0,X1,X2] : join(X0,X1) = join(X0,join(X1,meet(X2,X0))),
inference(forward_demodulation,[status(thm)],[f171,f1402]) ).
fof(f1471,plain,
! [X0,X1,X2,X3] : join(join(X0,X1),join(X2,X3)) = join(join(X0,X2),join(X1,X3)),
inference(forward_demodulation,[status(thm)],[f180,f1424]) ).
fof(f1472,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(join(X1,X2),join(X0,X3)),
inference(forward_demodulation,[status(thm)],[f180,f1471]) ).
fof(f1473,plain,
! [X0,X1,X2,X3] : join(X0,join(X1,join(X2,X3))) = join(X2,join(X1,join(X0,X3))),
inference(forward_demodulation,[status(thm)],[f180,f1472]) ).
fof(f1482,plain,
! [X0] :
( meet(X0,n0) = n0
| n0 != n0 ),
inference(paramodulation,[status(thm)],[f56,f917]) ).
fof(f1483,plain,
! [X0,X1,X2] :
( meet(X2,meet(X1,X0)) = meet(X1,X0)
| meet(X0,meet(X1,X2)) != meet(X1,X0) ),
inference(paramodulation,[status(thm)],[f104,f917]) ).
fof(f1484,plain,
! [X0,X1,X2] :
( meet(X2,meet(X0,X1)) = meet(X0,X1)
| meet(X0,meet(X1,X2)) != meet(X0,X1) ),
inference(paramodulation,[status(thm)],[f27,f917]) ).
fof(f1489,plain,
! [X0,X1,X2] :
( meet(meet(X2,X0),X1) = X1
| meet(X0,meet(X1,X2)) != X1 ),
inference(paramodulation,[status(thm)],[f96,f917]) ).
fof(f1490,plain,
! [X0,X1,X2] :
( meet(meet(X0,X1),X2) = X2
| meet(X0,meet(X1,X2)) != X2 ),
inference(paramodulation,[status(thm)],[f96,f917]) ).
fof(f1500,definition,
! [X0] :
( sQ23_spl
<=> meet(X0,n0) = n0 ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f1503,plain,
( sQ23_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f1482,f220,f1500]) ).
fof(f1512,plain,
! [X0,X1,X2] :
( meet(X0,meet(X2,X1)) = X1
| meet(X0,meet(X1,X2)) != X1 ),
inference(forward_demodulation,[status(thm)],[f104,f1489]) ).
fof(f1513,plain,
! [X0,X1,X2] :
( meet(X1,meet(X0,X2)) = X2
| meet(X0,meet(X1,X2)) != X2 ),
inference(forward_demodulation,[status(thm)],[f104,f1490]) ).
fof(f1517,plain,
! [X0,X1,X2] : join(join(X0,X1),X2) = join(X0,join(X1,join(join(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f28,f182]) ).
fof(f1525,plain,
! [X0,X1,X2] : join(join(X0,X1),X2) = join(join(X0,X1),join(X0,join(X1,X2))),
inference(paramodulation,[status(thm)],[f28,f182]) ).
fof(f1531,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X2,join(X0,X1))),
inference(paramodulation,[status(thm)],[f171,f182]) ).
fof(f1532,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X2,X0))),
inference(paramodulation,[status(thm)],[f171,f182]) ).
fof(f1542,plain,
! [X0,X1,X2] : join(join(X0,X1),X2) = join(X1,join(X0,join(join(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f182,f180]) ).
fof(f1551,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(join(X1,X2),X0)),
inference(paramodulation,[status(thm)],[f182,f171]) ).
fof(f1555,plain,
! [X0,X1] :
( complement(X0,join(X0,X1))
| join(X0,X1) != n1
| meet(X0,join(X0,X1)) != n0 ),
inference(paramodulation,[status(thm)],[f182,f37]) ).
fof(f1560,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,join(join(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f180,f1517]) ).
fof(f1561,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,join(X0,join(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f180,f1560]) ).
fof(f1563,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X0,join(X1,X2))),
inference(forward_demodulation,[status(thm)],[f182,f1561]) ).
fof(f1571,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(join(X1,X0),join(X1,join(X0,X2))),
inference(forward_demodulation,[status(thm)],[f180,f1525]) ).
fof(f1572,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X1,join(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f180,f1571]) ).
fof(f1573,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X0,X2))),
inference(forward_demodulation,[status(thm)],[f182,f1572]) ).
fof(f1580,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X1,join(join(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f180,f1542]) ).
fof(f1581,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X1,join(X0,join(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f180,f1580]) ).
fof(f1582,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(join(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f1531,f1581]) ).
fof(f1583,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X2,join(X1,X1))),
inference(forward_demodulation,[status(thm)],[f180,f1582]) ).
fof(f1584,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X0,join(X2,X1)),
inference(forward_demodulation,[status(thm)],[f22,f1583]) ).
fof(f1595,plain,
! [X0,X1,X2] : join(X0,join(X1,X2)) = join(X1,join(X2,join(X1,X0))),
inference(forward_demodulation,[status(thm)],[f180,f1551]) ).
fof(f1601,plain,
! [X0,X1] :
( complement(X0,join(X0,X1))
| join(X0,X1) != n1
| X0 != n0 ),
inference(forward_demodulation,[status(thm)],[f23,f1555]) ).
fof(f1605,plain,
( ~ sQ14_spl
| meet(n1,f(n1,n0)) = n0 ),
inference(resolution,[status(thm)],[f323,f35]) ).
fof(f1606,plain,
( ~ sQ14_spl
| complement(n1,f(n1,f(n1,n0)))
| unique_complement(n1,f(n1,n0)) ),
inference(resolution,[status(thm)],[f323,f41]) ).
fof(f1607,plain,
( ~ sQ14_spl
| complement(n1,n0) ),
inference(backward_demodulation,[status(thm)],[f1608,f323]) ).
fof(f1608,plain,
( ~ sQ14_spl
| f(n1,n0) = n0 ),
inference(forward_demodulation,[status(thm)],[f57,f1605]) ).
fof(f1609,definition,
( sQ24_spl
<=> unique_complement(n1,f(n1,n0)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f1612,definition,
( sQ25_spl
<=> complement(n1,f(n1,f(n1,n0))) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f1613,plain,
( ~ sQ25_spl
| complement(n1,f(n1,f(n1,n0))) ),
inference(component_clause,[status(thm)],[f1612]) ).
fof(f1615,plain,
( ~ sQ14_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f1606,f1609,f1612,f322]) ).
fof(f1616,plain,
( ~ sQ19_spl
| complement(n1,meet(n1,n1)) ),
inference(forward_demodulation,[status(thm)],[f57,f1082]) ).
fof(f1617,plain,
( ~ sQ19_spl
| complement(n1,n1) ),
inference(forward_demodulation,[status(thm)],[f57,f1616]) ).
fof(f1624,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ5_spl
| unique_complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1101,f310]) ).
fof(f1625,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1101,f261]) ).
fof(f1626,plain,
( ~ sQ7_spl
| ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1101,f275]) ).
fof(f1627,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(X0,X1)
| join(X0,X1) != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1101,f37]) ).
fof(f1630,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| join(X0,n1) = n0 ),
inference(backward_demodulation,[status(thm)],[f1101,f32]) ).
fof(f1634,plain,
( ~ sQ19_spl
| ~ sQ13_spl
| ~ sQ5_spl
| complement(n1,n0) ),
inference(backward_demodulation,[status(thm)],[f1101,f1617]) ).
fof(f1645,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(join(X0,X1),X2)
| join(X0,join(X1,X2)) != n0
| meet(join(X0,X1),X2) != n0 ),
inference(backward_demodulation,[status(thm)],[f1101,f243]) ).
fof(f1646,plain,
( sQ15_spl
| ~ sQ13_spl
| ~ sQ5_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f1101,f1100]) ).
fof(f1647,plain,
( sQ15_spl
| ~ sQ13_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1646]) ).
fof(f1648,plain,
( sQ15_spl
| ~ sQ13_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1647]) ).
fof(f1649,plain,
( sQ17_spl
| ~ sQ13_spl
| ~ sQ5_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f1101,f1099]) ).
fof(f1650,plain,
( sQ17_spl
| ~ sQ13_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1649]) ).
fof(f1651,plain,
( sQ17_spl
| ~ sQ13_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1650]) ).
fof(f1652,plain,
( sQ20_spl
| ~ sQ13_spl
| ~ sQ5_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f1101,f1098]) ).
fof(f1653,plain,
( sQ20_spl
| ~ sQ13_spl
| ~ sQ5_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1652]) ).
fof(f1654,plain,
( sQ20_spl
| ~ sQ13_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1653]) ).
fof(f1661,plain,
( ~ sQ16_spl
| complement(n1,join(n1,n0)) ),
inference(forward_demodulation,[status(thm)],[f30,f1059]) ).
fof(f1662,plain,
( ~ sQ16_spl
| complement(n1,n1) ),
inference(forward_demodulation,[status(thm)],[f30,f1661]) ).
fof(f1663,plain,
( ~ sQ18_spl
| complement(n1,join(n1,n1)) ),
inference(forward_demodulation,[status(thm)],[f22,f1066]) ).
fof(f1664,plain,
( ~ sQ18_spl
| complement(n1,n1) ),
inference(forward_demodulation,[status(thm)],[f22,f1663]) ).
fof(f1665,plain,
( ~ sQ21_spl
| complement(n1,join(n0,n1)) ),
inference(forward_demodulation,[status(thm)],[f70,f1090]) ).
fof(f1666,plain,
( ~ sQ21_spl
| complement(n1,n1) ),
inference(forward_demodulation,[status(thm)],[f70,f1665]) ).
fof(f1667,plain,
( ~ sQ19_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1617,f267,f1081]) ).
fof(f1668,plain,
( sQ5_spl
| ~ sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f269,f1662]) ).
fof(f1669,plain,
( sQ5_spl
| ~ sQ16_spl ),
inference(contradiction_clause,[status(thm)],[f1668]) ).
fof(f1670,plain,
( ~ sQ4_spl
| n1 = n0 ),
inference(forward_demodulation,[status(thm)],[f21,f265]) ).
fof(f1671,plain,
( ~ sQ4_spl
| sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1670,f1096]) ).
fof(f1672,plain,
( ~ sQ4_spl
| sQ22_spl ),
inference(contradiction_clause,[status(thm)],[f1671]) ).
fof(f1673,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| complement(join(X0,X1),X2)
| join(X0,join(X1,X2)) != n0
| meet(join(X0,X1),X2) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f243]) ).
fof(f1674,plain,
! [X0,X1] :
( ~ sQ5_spl
| complement(X0,meet(X0,X1))
| X0 != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f291]) ).
fof(f1675,plain,
! [X0,X1] :
( ~ sQ5_spl
| complement(X0,X1)
| join(X1,X0) != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f249]) ).
fof(f1676,plain,
! [X0,X1] :
( ~ sQ5_spl
| complement(X0,meet(X1,X0))
| X0 != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f379]) ).
fof(f1677,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| complement(meet(X2,X1),meet(X2,meet(X1,X0)))
| meet(X2,X1) != n0
| meet(X0,meet(X1,X2)) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f1025]) ).
fof(f1678,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| complement(X0,join(X1,meet(join(X0,X1),X2)))
| join(X0,X1) != n0
| meet(X0,join(X1,meet(join(X0,X1),X2))) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f1144]) ).
fof(f1679,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| complement(X0,join(X1,X2))
| join(X1,join(X2,X0)) != n0
| meet(X0,join(X1,X2)) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f1239]) ).
fof(f1680,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| complement(X0,join(X1,X2))
| join(X2,join(X0,X1)) != n0
| meet(X0,join(X1,X2)) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f1252]) ).
fof(f1681,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| complement(X0,join(meet(X0,X1),X2))
| join(X0,X2) != n0
| meet(X0,join(meet(X0,X1),X2)) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f1346]) ).
fof(f1682,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| complement(join(X0,X1),X2)
| join(X1,join(X0,X2)) != n0
| meet(join(X0,X1),X2) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f1423]) ).
fof(f1683,plain,
! [X0,X1] :
( ~ sQ5_spl
| complement(X0,join(X0,X1))
| join(X0,X1) != n0
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f1601]) ).
fof(f1684,plain,
( ~ sQ25_spl
| ~ sQ5_spl
| complement(n1,f(n1,f(n0,n0))) ),
inference(backward_demodulation,[status(thm)],[f1703,f1613]) ).
fof(f1685,plain,
! [X0] :
( ~ sQ5_spl
| meet(X0,n0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1703,f31]) ).
fof(f1686,plain,
! [X0] :
( ~ sQ5_spl
| X0 = meet(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f1703,f57]) ).
fof(f1687,plain,
! [X0] :
( ~ sQ5_spl
| join(X0,n1) = n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f32]) ).
fof(f1688,plain,
! [X0] :
( ~ sQ5_spl
| join(n1,X0) = n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f80]) ).
fof(f1689,plain,
! [X0,X1] :
( ~ sQ5_spl
| join(X0,X1) = n0
| ~ complement(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f1703,f36]) ).
fof(f1690,plain,
! [X0,X1] :
( ~ sQ5_spl
| complement(X0,X1)
| join(X0,X1) != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f37]) ).
fof(f1691,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1703,f275]) ).
fof(f1692,plain,
( ~ sQ3_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1703,f261]) ).
fof(f1693,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| unique_complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1703,f310]) ).
fof(f1694,plain,
! [X0] :
( ~ sQ5_spl
| complement(n0,X0)
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f252]) ).
fof(f1695,plain,
! [X0] :
( ~ sQ5_spl
| complement(X0,n0)
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f253]) ).
fof(f1696,plain,
! [X0] :
( ~ sQ5_spl
| complement(n0,X0)
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f286]) ).
fof(f1697,plain,
! [X0] :
( ~ sQ5_spl
| complement(X0,n0)
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f293]) ).
fof(f1698,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ5_spl
| X0 = n0
| ~ complement(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f1703,f327]) ).
fof(f1699,plain,
! [X0] :
( ~ sQ5_spl
| complement(X0,X0)
| X0 != n0
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1703,f294]) ).
fof(f1700,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| complement(n1,n0) ),
inference(backward_demodulation,[status(thm)],[f1703,f1662]) ).
fof(f1701,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| X0 = n0
| ~ complement(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f1703,f383]) ).
fof(f1702,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| unique_complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1703,f320]) ).
fof(f1703,plain,
( ~ sQ5_spl
| n1 = n0 ),
inference(forward_demodulation,[status(thm)],[f21,f1103]) ).
fof(f1704,definition,
( sQ26_spl
<=> unique_complement(n1,n1) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1705,plain,
( ~ sQ26_spl
| unique_complement(n1,n1) ),
inference(component_clause,[status(thm)],[f1704]) ).
fof(f1707,definition,
( sQ27_spl
<=> complement(n1,f(n1,n1)) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1708,plain,
( ~ sQ27_spl
| complement(n1,f(n1,n1)) ),
inference(component_clause,[status(thm)],[f1707]) ).
fof(f1710,plain,
( ~ sQ5_spl
| sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1104,f1704,f1707,f267]) ).
fof(f1713,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| join(X0,n0) = n0 ),
inference(forward_demodulation,[status(thm)],[f1703,f1630]) ).
fof(f1716,plain,
( ~ sQ19_spl
| ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1703,f1634]) ).
fof(f1717,plain,
( ~ sQ15_spl
| n1 = n0 ),
inference(forward_demodulation,[status(thm)],[f30,f1056]) ).
fof(f1718,plain,
( ~ sQ17_spl
| n1 = n0 ),
inference(forward_demodulation,[status(thm)],[f22,f1063]) ).
fof(f1719,plain,
( ~ sQ20_spl
| n1 = n0 ),
inference(forward_demodulation,[status(thm)],[f70,f1087]) ).
fof(f1720,plain,
( ~ sQ25_spl
| ~ sQ5_spl
| complement(n0,f(n1,f(n0,n0))) ),
inference(forward_demodulation,[status(thm)],[f1703,f1684]) ).
fof(f1721,plain,
( ~ sQ25_spl
| ~ sQ5_spl
| complement(n0,f(n0,f(n0,n0))) ),
inference(forward_demodulation,[status(thm)],[f1703,f1720]) ).
fof(f1722,plain,
! [X0] :
( ~ sQ5_spl
| join(X0,n0) = n0 ),
inference(forward_demodulation,[status(thm)],[f1703,f1687]) ).
fof(f1723,plain,
! [X0] :
( ~ sQ5_spl
| join(n0,X0) = n0 ),
inference(forward_demodulation,[status(thm)],[f1703,f1688]) ).
fof(f1724,plain,
! [X0] :
( ~ sQ5_spl
| complement(X0,X0)
| X0 != n0 ),
inference(duplicate_literals_removal,[status(thm)],[f1699]) ).
fof(f1725,plain,
( ~ sQ16_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1703,f1700]) ).
fof(f1726,plain,
( ~ sQ26_spl
| ~ sQ5_spl
| unique_complement(n0,n1) ),
inference(forward_demodulation,[status(thm)],[f1703,f1705]) ).
fof(f1727,plain,
( ~ sQ26_spl
| ~ sQ5_spl
| unique_complement(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1703,f1726]) ).
fof(f1728,plain,
( ~ sQ27_spl
| ~ sQ5_spl
| complement(n0,f(n1,n1)) ),
inference(forward_demodulation,[status(thm)],[f1703,f1708]) ).
fof(f1729,plain,
( ~ sQ27_spl
| ~ sQ5_spl
| complement(n0,f(n0,n1)) ),
inference(forward_demodulation,[status(thm)],[f1703,f1728]) ).
fof(f1730,plain,
( ~ sQ27_spl
| ~ sQ5_spl
| complement(n0,f(n0,n0)) ),
inference(forward_demodulation,[status(thm)],[f1703,f1729]) ).
fof(f1732,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(resolution,[status(thm)],[f1624,f38]) ).
fof(f1734,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,f(n0,n0))
| unique_complement(n0,n0) ),
inference(resolution,[status(thm)],[f1625,f41]) ).
fof(f1735,definition,
( sQ28_spl
<=> unique_complement(n0,n0) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1736,plain,
( ~ sQ28_spl
| unique_complement(n0,n0) ),
inference(component_clause,[status(thm)],[f1735]) ).
fof(f1738,definition,
( sQ29_spl
<=> complement(n0,f(n0,n0)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1739,plain,
( ~ sQ29_spl
| complement(n0,f(n0,n0)) ),
inference(component_clause,[status(thm)],[f1738]) ).
fof(f1741,plain,
( ~ sQ3_spl
| ~ sQ13_spl
| ~ sQ5_spl
| sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f1734,f1735,f1738,f267,f319,f260]) ).
fof(f1742,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,meet(X0,n0))
| meet(n0,meet(X0,n0)) != n0 ),
inference(resolution,[status(thm)],[f1627,f66]) ).
fof(f1743,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,meet(n0,X0))
| meet(n0,meet(n0,X0)) != n0 ),
inference(resolution,[status(thm)],[f1627,f24]) ).
fof(f1744,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0)
| meet(n0,n0) != n0 ),
inference(resolution,[status(thm)],[f1627,f30]) ).
fof(f1762,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,meet(X0,n0))
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f56,f1742]) ).
fof(f1763,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f29,f1762]) ).
fof(f1764,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(trivial_equality_resolution,[status(thm)],[f1763]) ).
fof(f1765,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,meet(n0,X0))
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f56,f1743]) ).
fof(f1766,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0)
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f56,f1765]) ).
fof(f1767,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| complement(n0,n0) ),
inference(trivial_equality_resolution,[status(thm)],[f1766]) ).
fof(f1768,definition,
( sQ30_spl
<=> meet(n0,n0) = n0 ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1770,plain,
( sQ30_spl
| meet(n0,n0) != n0 ),
inference(component_clause,[status(thm)],[f1768]) ).
fof(f1771,definition,
( sQ31_spl
<=> complement(n0,n0) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1772,plain,
( ~ sQ31_spl
| complement(n0,n0) ),
inference(component_clause,[status(thm)],[f1771]) ).
fof(f1774,plain,
( ~ sQ13_spl
| ~ sQ5_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1744,f1768,f1771,f267,f319]) ).
fof(f1789,plain,
( sQ30_spl
| n0 != n0 ),
inference(forward_demodulation,[status(thm)],[f56,f1770]) ).
fof(f1790,plain,
( sQ30_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1789]) ).
fof(f1791,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1790]) ).
fof(f1792,plain,
( sQ19_spl
| ~ complement(n1,meet(n1,n1)) ),
inference(forward_demodulation,[status(thm)],[f21,f1083]) ).
fof(f1793,plain,
( sQ19_spl
| ~ complement(n1,n1) ),
inference(forward_demodulation,[status(thm)],[f21,f1792]) ).
fof(f1794,plain,
( ~ sQ21_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1666,f267,f1089]) ).
fof(f1795,plain,
( ~ sQ18_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1664,f267,f1065]) ).
fof(f1796,plain,
( sQ16_spl
| ~ complement(n1,join(n1,n0)) ),
inference(forward_demodulation,[status(thm)],[f30,f1060]) ).
fof(f1797,plain,
( sQ16_spl
| ~ complement(n1,n1) ),
inference(forward_demodulation,[status(thm)],[f30,f1796]) ).
fof(f1798,plain,
( ~ sQ13_spl
| ~ sQ4_spl
| unique_complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1670,f320]) ).
fof(f1799,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ4_spl
| X0 = n0
| ~ complement(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f1670,f383]) ).
fof(f1800,plain,
! [X0] :
( ~ sQ4_spl
| complement(X0,X0)
| X0 != n0
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f294]) ).
fof(f1801,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ4_spl
| X0 = n0
| ~ complement(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f1670,f327]) ).
fof(f1802,plain,
! [X0] :
( ~ sQ4_spl
| complement(X0,n0)
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f293]) ).
fof(f1803,plain,
! [X0] :
( ~ sQ4_spl
| complement(n0,X0)
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f286]) ).
fof(f1804,plain,
! [X0] :
( ~ sQ4_spl
| complement(X0,n0)
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f253]) ).
fof(f1805,plain,
! [X0] :
( ~ sQ4_spl
| complement(n0,X0)
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f252]) ).
fof(f1806,plain,
( ~ sQ11_spl
| ~ sQ4_spl
| unique_complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1670,f310]) ).
fof(f1807,plain,
( ~ sQ3_spl
| ~ sQ4_spl
| complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1670,f261]) ).
fof(f1808,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| complement(n0,n0) ),
inference(backward_demodulation,[status(thm)],[f1670,f275]) ).
fof(f1809,plain,
! [X0,X1] :
( ~ sQ4_spl
| complement(X0,X1)
| join(X0,X1) != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f37]) ).
fof(f1810,plain,
! [X0,X1] :
( ~ sQ4_spl
| join(X0,X1) = n0
| ~ complement(X0,X1) ),
inference(backward_demodulation,[status(thm)],[f1670,f36]) ).
fof(f1811,plain,
! [X0] :
( ~ sQ4_spl
| join(n1,X0) = n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f80]) ).
fof(f1812,plain,
! [X0] :
( ~ sQ4_spl
| join(X0,n1) = n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f32]) ).
fof(f1813,plain,
! [X0] :
( ~ sQ4_spl
| X0 = meet(n0,X0) ),
inference(backward_demodulation,[status(thm)],[f1670,f57]) ).
fof(f1814,plain,
! [X0] :
( ~ sQ4_spl
| meet(X0,n0) = X0 ),
inference(backward_demodulation,[status(thm)],[f1670,f31]) ).
fof(f1815,plain,
( ~ sQ25_spl
| ~ sQ4_spl
| complement(n1,f(n1,f(n0,n0))) ),
inference(backward_demodulation,[status(thm)],[f1670,f1613]) ).
fof(f1816,plain,
! [X0,X1] :
( ~ sQ4_spl
| complement(X0,join(X0,X1))
| join(X0,X1) != n0
| X0 != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f1601]) ).
fof(f1817,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| complement(join(X0,X1),X2)
| join(X1,join(X0,X2)) != n0
| meet(join(X0,X1),X2) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f1423]) ).
fof(f1818,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| complement(X0,join(meet(X0,X1),X2))
| join(X0,X2) != n0
| meet(X0,join(meet(X0,X1),X2)) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f1346]) ).
fof(f1819,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| complement(X0,join(X1,X2))
| join(X2,join(X0,X1)) != n0
| meet(X0,join(X1,X2)) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f1252]) ).
fof(f1820,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| complement(X0,join(X1,X2))
| join(X1,join(X2,X0)) != n0
| meet(X0,join(X1,X2)) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f1239]) ).
fof(f1821,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| complement(X0,join(X1,meet(join(X0,X1),X2)))
| join(X0,X1) != n0
| meet(X0,join(X1,meet(join(X0,X1),X2))) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f1144]) ).
fof(f1822,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| complement(meet(X2,X1),meet(X2,meet(X1,X0)))
| meet(X2,X1) != n0
| meet(X0,meet(X1,X2)) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f1025]) ).
fof(f1823,plain,
! [X0,X1] :
( ~ sQ4_spl
| complement(X0,meet(X1,X0))
| X0 != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f379]) ).
fof(f1824,plain,
! [X0,X1] :
( ~ sQ4_spl
| complement(X0,X1)
| join(X1,X0) != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f249]) ).
fof(f1825,plain,
! [X0,X1] :
( ~ sQ4_spl
| complement(X0,meet(X0,X1))
| X0 != n0
| meet(X0,X1) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f291]) ).
fof(f1826,plain,
! [X0,X1,X2] :
( ~ sQ4_spl
| complement(join(X0,X1),X2)
| join(X0,join(X1,X2)) != n0
| meet(join(X0,X1),X2) != n0 ),
inference(backward_demodulation,[status(thm)],[f1670,f243]) ).
fof(f1827,plain,
( ~ sQ26_spl
| ~ sQ4_spl
| unique_complement(n1,n0) ),
inference(backward_demodulation,[status(thm)],[f1670,f1705]) ).
fof(f1828,plain,
( ~ sQ27_spl
| ~ sQ4_spl
| complement(n1,f(n1,n0)) ),
inference(backward_demodulation,[status(thm)],[f1670,f1708]) ).
fof(f1829,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| complement(n0,n1) ),
inference(forward_demodulation,[status(thm)],[f1670,f268]) ).
fof(f1830,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| complement(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1670,f1829]) ).
fof(f1831,plain,
( ~ sQ16_spl
| ~ sQ4_spl
| complement(n0,n1) ),
inference(forward_demodulation,[status(thm)],[f1670,f1662]) ).
fof(f1832,plain,
( ~ sQ16_spl
| ~ sQ4_spl
| complement(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1670,f1831]) ).
fof(f1833,plain,
! [X0] :
( ~ sQ4_spl
| complement(X0,X0)
| X0 != n0 ),
inference(duplicate_literals_removal,[status(thm)],[f1800]) ).
fof(f1834,plain,
! [X0] :
( ~ sQ4_spl
| join(n0,X0) = n0 ),
inference(forward_demodulation,[status(thm)],[f1670,f1811]) ).
fof(f1835,plain,
! [X0] :
( ~ sQ4_spl
| join(X0,n0) = n0 ),
inference(forward_demodulation,[status(thm)],[f1670,f1812]) ).
fof(f1836,plain,
( ~ sQ25_spl
| ~ sQ4_spl
| complement(n0,f(n1,f(n0,n0))) ),
inference(forward_demodulation,[status(thm)],[f1670,f1815]) ).
fof(f1837,plain,
( ~ sQ25_spl
| ~ sQ4_spl
| complement(n0,f(n0,f(n0,n0))) ),
inference(forward_demodulation,[status(thm)],[f1670,f1836]) ).
fof(f1838,plain,
( ~ sQ26_spl
| ~ sQ4_spl
| unique_complement(n0,n0) ),
inference(forward_demodulation,[status(thm)],[f1670,f1827]) ).
fof(f1839,plain,
( ~ sQ27_spl
| ~ sQ4_spl
| complement(n0,f(n1,n0)) ),
inference(forward_demodulation,[status(thm)],[f1670,f1828]) ).
fof(f1840,plain,
( ~ sQ27_spl
| ~ sQ4_spl
| complement(n0,f(n0,n0)) ),
inference(forward_demodulation,[status(thm)],[f1670,f1839]) ).
fof(f1844,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ5_spl
| X0 = n0 ),
inference(paramodulation,[status(thm)],[f30,f1713]) ).
fof(f1855,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| join(n0,X0) = join(n0,join(X1,X0)) ),
inference(paramodulation,[status(thm)],[f1713,f180]) ).
fof(f1868,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(join(X0,X1),X2)
| meet(join(X0,X1),X2) != n0 ),
inference(backward_subsumption_resolution,[status(thm)],[f1645,f1844]) ).
fof(f1888,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| X0 = join(n0,join(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f70,f1855]) ).
fof(f1897,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ5_spl
| join(X0,join(X1,X2)) = join(X2,X0) ),
inference(backward_demodulation,[status(thm)],[f2017,f171]) ).
fof(f1907,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ5_spl
| join(X0,join(X1,X2)) = X1 ),
inference(backward_demodulation,[status(thm)],[f2017,f1214]) ).
fof(f2017,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| X0 = join(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f70,f1888]) ).
fof(f2032,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(join(X2,X0),X1)
| meet(X0,X1) != n0 ),
inference(forward_demodulation,[status(thm)],[f2017,f1868]) ).
fof(f2033,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(X0,X1)
| meet(X0,X1) != n0 ),
inference(forward_demodulation,[status(thm)],[f2017,f2032]) ).
fof(f2034,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| f(X0,X1) != X1
| unique_complement(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f42,f2036]) ).
fof(f2036,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| complement(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2033,f1844]) ).
fof(f2091,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ5_spl
| join(X0,X1) = join(X1,X2) ),
inference(forward_demodulation,[status(thm)],[f2017,f1897]) ).
fof(f2092,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| X0 = join(X0,X1) ),
inference(forward_demodulation,[status(thm)],[f2017,f2091]) ).
fof(f2098,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| X0 = X1 ),
inference(forward_demodulation,[status(thm)],[f2092,f1907]) ).
fof(f2335,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ5_spl
| unique_complement(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f2034,f2098]) ).
fof(model,axiom,
( sQ0_spl
| sQ1_spl
| sQ2_spl
| sQ3_spl
| sQ4_spl
| sQ5_spl
| sQ6_spl
| sQ7_spl
| sQ8_spl
| sQ9_spl
| sQ10_spl
| sQ11_spl
| sQ13_spl
| sQ15_spl
| sQ16_spl
| sQ17_spl
| sQ18_spl
| sQ19_spl
| sQ20_spl
| sQ21_spl
| sQ22_spl
| sQ23_spl
| sQ25_spl
| sQ26_spl
| sQ27_spl
| sQ28_spl
| sQ29_spl
| sQ30_spl
| sQ31_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LAT395-1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.03 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/10.37 % Computer : n011.cluster.edu
% 0.08/10.37 % Model : x86_64 x86_64
% 0.08/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/10.37 % Memory : 8046.5625MB
% 0.08/10.37 % OS : Linux 6.8.0-71-generic
% 0.08/10.37 % CPULimit : 300
% 0.08/10.37 % WCLimit : 300
% 0.08/10.37 % DateTime : Sun Sep 20 23:58:35 UTC 2026
% 0.08/10.37 % CPUTime :
% 0.08/10.37 % Drodi V4.1.1
% 0.13/10.76 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 0.13/10.76 % SZS output start Saturation for theBenchmark
% See solution above
% 0.13/10.78 % Elapsed time: 0.404611 seconds
% 0.13/10.78 % CPU time: 3.069592 seconds
% 0.13/10.78 % Total memory used: 44.649 MB
% 0.13/10.78 % Net memory used: 41.185 MB
%------------------------------------------------------------------------------