%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 12:32:18 PM UTC 2026
% Result : Unsatisfiable 12.83s 2.05s
% Output : CNFRefutation 12.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 110
% Syntax : Number of formulae : 769 ( 85 unt; 70 def)
% Number of atoms : 2257 ( 301 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2966 (1478 ~;1418 |; 0 &)
% ( 70 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 74 ( 72 usr; 71 prp; 0-4 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-3 aty)
% Number of variables : 197 ( 197 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Xg] : group_member(identity_for(Xg),Xg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Xg,X] : product(Xg,identity_for(Xg),X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Xg,X] : product(Xg,X,identity_for(Xg),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Xg,X] : product(Xg,X,inverse(Xg,X),identity_for(Xg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Xg,Y] :
( product(Xg,X,Y,multiply(Xg,X,Y))
| ~ group_member(Y,Xg)
| ~ group_member(X,Xg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Xg,X,Y,Z,W] :
( W = Z
| ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Xg,X,Y,Xy,Z,Yz,Xyz] :
( product(Xg,X,Yz,Xyz)
| ~ product(Xg,Xy,Z,Xyz)
| ~ product(Xg,Y,Z,Yz)
| ~ product(Xg,X,Y,Xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Xg,X,Y,Xy,Z,Yz,Xyz] :
( product(Xg,Xy,Z,Xyz)
| ~ product(Xg,X,Yz,Xyz)
| ~ product(Xg,Y,Z,Yz)
| ~ product(Xg,X,Y,Xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
group_member(a,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
group_member(b,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
group_member(c,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
group_member(f,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
group_member(g,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
group_member(h,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
! [X] :
( X = c
| X = b
| X = a
| ~ group_member(X,g1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
! [X] :
( X = h
| X = g
| X = f
| ~ group_member(X,g2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
product(g1,a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
product(g1,a,b,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
product(g1,a,c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
product(g1,b,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
product(g1,b,c,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
product(g1,c,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
product(g1,c,c,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
product(g2,f,f,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
product(g2,f,g,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
product(g2,g,f,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
product(g2,f,h,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
product(g2,h,f,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
product(g2,g,g,h),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,hypothesis,
product(g2,g,h,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
product(g2,h,g,f),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
product(g2,h,h,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
an_isomorphism(a) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
an_isomorphism(b) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
an_isomorphism(c) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
group_member(d1,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
group_member(d2,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
group_member(d3,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,plain,
! [X0] : group_member(identity_for(X0),X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f47,plain,
! [X0,X1] : product(X0,identity_for(X0),X1,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f48,plain,
! [X0,X1] : product(X0,X1,identity_for(X0),X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f51,plain,
! [X0,X1] : product(X0,X1,inverse(X0,X1),identity_for(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f52,plain,
! [X0,X1,X2] :
( product(X1,X0,X2,multiply(X1,X0,X2))
| ~ group_member(X2,X1)
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f54,plain,
! [Z,W] :
( W = Z
| ! [Xg,X,Y] :
( ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( X4 = X3
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f56,plain,
! [Xg,X,Yz,Xyz] :
( product(Xg,X,Yz,Xyz)
| ! [Xy,Z] :
( ~ product(Xg,Xy,Z,Xyz)
| ! [Y] :
( ~ product(Xg,Y,Z,Yz)
| ~ product(Xg,X,Y,Xy) ) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f57,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X0,X1,X5,X6)
| ~ product(X0,X3,X4,X6)
| ~ product(X0,X2,X4,X5)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [Xg,Xy,Z,Xyz] :
( product(Xg,Xy,Z,Xyz)
| ! [X,Yz] :
( ~ product(Xg,X,Yz,Xyz)
| ! [Y] :
( ~ product(Xg,Y,Z,Yz)
| ~ product(Xg,X,Y,Xy) ) ) ),
inference(miniscoping,[status(thm)],[f11]) ).
fof(f59,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( product(X0,X3,X4,X6)
| ~ product(X0,X1,X5,X6)
| ~ product(X0,X2,X4,X5)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f60,plain,
group_member(a,g1),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f61,plain,
group_member(b,g1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f62,plain,
group_member(c,g1),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f63,plain,
group_member(f,g2),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f64,plain,
group_member(g,g2),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f65,plain,
group_member(h,g2),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f66,plain,
! [X0] :
( X0 = c
| X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f67,plain,
! [X0] :
( X0 = h
| X0 = g
| X0 = f
| ~ group_member(X0,g2) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f68,plain,
product(g1,a,a,a),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f69,plain,
product(g1,a,b,b),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f71,plain,
product(g1,a,c,c),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f73,plain,
product(g1,b,b,c),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f74,plain,
product(g1,b,c,a),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f75,plain,
product(g1,c,b,a),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f76,plain,
product(g1,c,c,b),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f77,plain,
product(g2,f,f,f),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f78,plain,
product(g2,f,g,g),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f79,plain,
product(g2,g,f,g),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f80,plain,
product(g2,f,h,h),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f81,plain,
product(g2,h,f,h),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f82,plain,
product(g2,g,g,h),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f83,plain,
product(g2,g,h,f),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f84,plain,
product(g2,h,g,f),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f85,plain,
product(g2,h,h,g),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f86,plain,
an_isomorphism(a) = f,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f87,plain,
an_isomorphism(b) = g,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f88,plain,
an_isomorphism(c) = h,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f89,plain,
group_member(d1,g1),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f90,plain,
group_member(d2,g1),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f91,plain,
group_member(d3,g1),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f92,plain,
product(g1,d1,d2,d3),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f93,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f98,plain,
! [X0,X1,X2] :
( product(X0,X1,X2,X2)
| ~ product(X0,X1,identity_for(X0),identity_for(X0)) ),
inference(resolution,[status(thm)],[f47,f57]) ).
fof(f102,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(resolution,[status(thm)],[f47,f55]) ).
fof(f111,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ product(X0,X1,identity_for(X0),X2) ),
inference(resolution,[status(thm)],[f48,f55]) ).
fof(f118,plain,
! [X0] :
( d3 = X0
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f92,f55]) ).
fof(f132,plain,
! [X0,X1,X2] :
( product(X0,X1,identity_for(X0),identity_for(X0))
| ~ product(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f51,f57]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( product(X1,X3,multiply(X1,X0,X2),multiply(X1,X0,X2))
| ~ product(X1,X3,X0,X0)
| ~ group_member(X2,X1)
| ~ group_member(X0,X1) ),
inference(resolution,[status(thm)],[f52,f57]) ).
fof(f150,plain,
! [X0,X1] :
( ~ group_member(X0,X1)
| ~ group_member(identity_for(X1),X1)
| X0 = multiply(X1,identity_for(X1),X0) ),
inference(resolution,[status(thm)],[f102,f52]) ).
fof(f151,plain,
! [X0,X1] :
( ~ group_member(X0,X1)
| X0 = multiply(X1,identity_for(X1),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f150,f46]) ).
fof(f163,plain,
! [X0,X1] :
( ~ group_member(identity_for(X1),X1)
| ~ group_member(X0,X1)
| X0 = multiply(X1,X0,identity_for(X1)) ),
inference(resolution,[status(thm)],[f111,f52]) ).
fof(f164,plain,
! [X0,X1] :
( ~ group_member(X0,X1)
| X0 = multiply(X1,X0,identity_for(X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f163,f46]) ).
fof(f170,plain,
! [X0] :
( product(g1,X0,a,a)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f68,f59]) ).
fof(f171,plain,
! [X0,X1,X2] :
( product(g1,X1,X2,a)
| ~ product(g1,X0,X2,a)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f68,f59]) ).
fof(f173,plain,
! [X0,X1,X2] :
( product(g1,X1,a,X2)
| ~ product(g1,X0,a,X2)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f68,f59]) ).
fof(f175,plain,
! [X0,X1,X2] :
( product(g1,X0,X2,a)
| ~ product(g1,X1,a,X2)
| ~ product(g1,X0,X1,a) ),
inference(resolution,[status(thm)],[f68,f57]) ).
fof(f177,plain,
! [X0,X1,X2] :
( product(g1,X0,a,X2)
| ~ product(g1,X1,a,X2)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f68,f57]) ).
fof(f189,plain,
( c = c
| c = b
| c = a ),
inference(resolution,[status(thm)],[f66,f62]) ).
fof(f190,plain,
( d3 = c
| d3 = b
| d3 = a ),
inference(resolution,[status(thm)],[f66,f91]) ).
fof(f191,plain,
( d2 = c
| d2 = b
| d2 = a ),
inference(resolution,[status(thm)],[f66,f90]) ).
fof(f192,plain,
( d1 = c
| d1 = b
| d1 = a ),
inference(resolution,[status(thm)],[f66,f89]) ).
fof(f194,plain,
( b = c
| b = b
| b = a ),
inference(resolution,[status(thm)],[f66,f61]) ).
fof(f195,plain,
( a = c
| a = b
| a = a ),
inference(resolution,[status(thm)],[f66,f60]) ).
fof(f196,plain,
( identity_for(g1) = c
| identity_for(g1) = b
| identity_for(g1) = a ),
inference(resolution,[status(thm)],[f66,f46]) ).
fof(f197,definition,
( sQ0_spl
<=> c = a ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( ~ sQ0_spl
| c = a ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f199,plain,
( sQ0_spl
| c != a ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,definition,
( sQ1_spl
<=> c = b ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( ~ sQ1_spl
| c = b ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f202,plain,
( sQ1_spl
| c != b ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,definition,
( sQ2_spl
<=> c = c ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f206,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f189,f197,f200,f203]) ).
fof(f207,definition,
( sQ3_spl
<=> d3 = a ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f208,plain,
( ~ sQ3_spl
| d3 = a ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f209,plain,
( sQ3_spl
| d3 != a ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,definition,
( sQ4_spl
<=> d3 = b ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f211,plain,
( ~ sQ4_spl
| d3 = b ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f212,plain,
( sQ4_spl
| d3 != b ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f213,definition,
( sQ5_spl
<=> d3 = c ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f214,plain,
( ~ sQ5_spl
| d3 = c ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f215,plain,
( sQ5_spl
| d3 != c ),
inference(component_clause,[status(thm)],[f213]) ).
fof(f216,plain,
( sQ5_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f190,f207,f210,f213]) ).
fof(f217,definition,
( sQ6_spl
<=> d2 = a ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f218,plain,
( ~ sQ6_spl
| d2 = a ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f219,plain,
( sQ6_spl
| d2 != a ),
inference(component_clause,[status(thm)],[f217]) ).
fof(f220,definition,
( sQ7_spl
<=> d2 = b ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f221,plain,
( ~ sQ7_spl
| d2 = b ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f222,plain,
( sQ7_spl
| d2 != b ),
inference(component_clause,[status(thm)],[f220]) ).
fof(f223,definition,
( sQ8_spl
<=> d2 = c ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( ~ sQ8_spl
| d2 = c ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f191,f217,f220,f223]) ).
fof(f227,definition,
( sQ9_spl
<=> d1 = a ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f228,plain,
( ~ sQ9_spl
| d1 = a ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f229,plain,
( sQ9_spl
| d1 != a ),
inference(component_clause,[status(thm)],[f227]) ).
fof(f230,definition,
( sQ10_spl
<=> d1 = b ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f231,plain,
( ~ sQ10_spl
| d1 = b ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f232,plain,
( sQ10_spl
| d1 != b ),
inference(component_clause,[status(thm)],[f230]) ).
fof(f233,definition,
( sQ11_spl
<=> d1 = c ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f234,plain,
( ~ sQ11_spl
| d1 = c ),
inference(component_clause,[status(thm)],[f233]) ).
fof(f236,plain,
( sQ11_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f192,f227,f230,f233]) ).
fof(f237,definition,
( sQ12_spl
<=> b = a ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( ~ sQ12_spl
| b = a ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f239,plain,
( sQ12_spl
| b != a ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,definition,
( sQ13_spl
<=> b = b ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( sQ1_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f194,f237,f240,f200]) ).
fof(f244,definition,
( sQ14_spl
<=> a = a ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f247,plain,
( sQ0_spl
| sQ12_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f195,f244,f237,f197]) ).
fof(f248,definition,
( sQ15_spl
<=> identity_for(g1) = a ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f249,plain,
( ~ sQ15_spl
| identity_for(g1) = a ),
inference(component_clause,[status(thm)],[f248]) ).
fof(f251,definition,
( sQ16_spl
<=> identity_for(g1) = b ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f252,plain,
( ~ sQ16_spl
| identity_for(g1) = b ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f253,plain,
( sQ16_spl
| identity_for(g1) != b ),
inference(component_clause,[status(thm)],[f251]) ).
fof(f254,definition,
( sQ17_spl
<=> identity_for(g1) = c ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f255,plain,
( ~ sQ17_spl
| identity_for(g1) = c ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( sQ17_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f196,f248,f251,f254]) ).
fof(f259,plain,
( h = h
| h = g
| h = f ),
inference(resolution,[status(thm)],[f67,f65]) ).
fof(f260,plain,
( g = h
| g = g
| g = f ),
inference(resolution,[status(thm)],[f67,f64]) ).
fof(f261,plain,
( f = h
| f = g
| f = f ),
inference(resolution,[status(thm)],[f67,f63]) ).
fof(f263,plain,
( identity_for(g2) = h
| identity_for(g2) = g
| identity_for(g2) = f ),
inference(resolution,[status(thm)],[f67,f46]) ).
fof(f264,definition,
( sQ18_spl
<=> h = f ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f265,plain,
( ~ sQ18_spl
| h = f ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f266,plain,
( sQ18_spl
| h != f ),
inference(component_clause,[status(thm)],[f264]) ).
fof(f267,definition,
( sQ19_spl
<=> h = g ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f268,plain,
( ~ sQ19_spl
| h = g ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f269,plain,
( sQ19_spl
| h != g ),
inference(component_clause,[status(thm)],[f267]) ).
fof(f270,definition,
( sQ20_spl
<=> h = h ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( sQ20_spl
| sQ19_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f259,f264,f267,f270]) ).
fof(f274,definition,
( sQ21_spl
<=> g = f ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f275,plain,
( ~ sQ21_spl
| g = f ),
inference(component_clause,[status(thm)],[f274]) ).
fof(f277,definition,
( sQ22_spl
<=> g = g ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f280,plain,
( sQ19_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f260,f274,f277,f267]) ).
fof(f281,definition,
( sQ23_spl
<=> f = f ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f284,plain,
( sQ18_spl
| sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f261,f281,f274,f264]) ).
fof(f285,definition,
( sQ24_spl
<=> identity_for(g2) = f ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ24_spl
| identity_for(g2) = f ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f287,plain,
( sQ24_spl
| identity_for(g2) != f ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,definition,
( sQ25_spl
<=> identity_for(g2) = g ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f289,plain,
( ~ sQ25_spl
| identity_for(g2) = g ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f290,plain,
( sQ25_spl
| identity_for(g2) != g ),
inference(component_clause,[status(thm)],[f288]) ).
fof(f291,definition,
( sQ26_spl
<=> identity_for(g2) = h ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( ~ sQ26_spl
| identity_for(g2) = h ),
inference(component_clause,[status(thm)],[f291]) ).
fof(f294,plain,
( sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f263,f285,f288,f291]) ).
fof(f315,plain,
( ~ sQ0_spl
| an_isomorphism(a) = h ),
inference(backward_demodulation,[status(thm)],[f198,f88]) ).
fof(f317,plain,
( ~ sQ0_spl
| f = h ),
inference(forward_demodulation,[status(thm)],[f86,f315]) ).
fof(f320,plain,
( ~ sQ12_spl
| an_isomorphism(a) = g ),
inference(backward_demodulation,[status(thm)],[f238,f87]) ).
fof(f322,plain,
( ~ sQ12_spl
| f = g ),
inference(forward_demodulation,[status(thm)],[f86,f320]) ).
fof(f349,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| d3 = a ),
inference(forward_demodulation,[status(thm)],[f198,f214]) ).
fof(f399,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| d3 = a ),
inference(forward_demodulation,[status(thm)],[f238,f211]) ).
fof(f400,plain,
( sQ5_spl
| ~ sQ0_spl
| d3 != a ),
inference(forward_demodulation,[status(thm)],[f198,f215]) ).
fof(f403,plain,
( ~ sQ21_spl
| product(g2,f,f,g) ),
inference(forward_demodulation,[status(thm)],[f275,f78]) ).
fof(f404,plain,
( ~ sQ21_spl
| product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f275,f403]) ).
fof(f425,plain,
( sQ5_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ12_spl
| a != a ),
inference(forward_demodulation,[status(thm)],[f399,f400]) ).
fof(f426,plain,
( sQ5_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ12_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f425]) ).
fof(f427,plain,
( sQ5_spl
| ~ sQ0_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f426]) ).
fof(f429,plain,
( ~ sQ9_spl
| product(g1,a,d2,d3) ),
inference(forward_demodulation,[status(thm)],[f228,f92]) ).
fof(f431,plain,
( ~ sQ9_spl
| ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f228,f93]) ).
fof(f432,plain,
( ~ sQ9_spl
| ~ product(g2,f,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f86,f431]) ).
fof(f440,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ product(g2,f,an_isomorphism(a),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f218,f432]) ).
fof(f441,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ product(g2,f,f,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f86,f440]) ).
fof(f443,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ product(g2,f,f,an_isomorphism(a)) ),
inference(backward_demodulation,[status(thm)],[f349,f441]) ).
fof(f444,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f86,f443]) ).
fof(f445,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f404]) ).
fof(f446,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( ~ sQ19_spl
| an_isomorphism(c) = g ),
inference(backward_demodulation,[status(thm)],[f268,f88]) ).
fof(f449,plain,
( ~ sQ19_spl
| ~ sQ18_spl
| f = g ),
inference(backward_demodulation,[status(thm)],[f265,f268]) ).
fof(f476,plain,
( ~ sQ3_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(a)) ),
inference(forward_demodulation,[status(thm)],[f208,f93]) ).
fof(f477,plain,
( ~ sQ3_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f86,f476]) ).
fof(f478,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(b),f) ),
inference(backward_demodulation,[status(thm)],[f221,f477]) ).
fof(f479,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),g,f) ),
inference(forward_demodulation,[status(thm)],[f87,f478]) ).
fof(f491,plain,
( sQ0_spl
| ~ sQ1_spl
| b != a ),
inference(forward_demodulation,[status(thm)],[f201,f199]) ).
fof(f501,plain,
! [X0,X1] :
( ~ sQ15_spl
| X0 = X1
| ~ product(g1,X0,a,X1) ),
inference(paramodulation,[status(thm)],[f249,f111]) ).
fof(f504,plain,
! [X0,X1] :
( ~ sQ15_spl
| X0 = X1
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f249,f102]) ).
fof(f517,plain,
( ~ sQ18_spl
| product(g2,f,h,g) ),
inference(forward_demodulation,[status(thm)],[f265,f85]) ).
fof(f518,plain,
( ~ sQ18_spl
| product(g2,f,f,g) ),
inference(forward_demodulation,[status(thm)],[f265,f517]) ).
fof(f519,plain,
( ~ sQ18_spl
| ~ sQ19_spl
| product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f449,f518]) ).
fof(f539,plain,
( ~ sQ12_spl
| sQ0_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f238,f491]) ).
fof(f540,plain,
( ~ sQ12_spl
| sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f539]) ).
fof(f541,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ product(g2,an_isomorphism(d1),f,f) ),
inference(forward_demodulation,[status(thm)],[f449,f479]) ).
fof(f542,plain,
( ~ sQ7_spl
| product(g1,d1,b,d3) ),
inference(forward_demodulation,[status(thm)],[f221,f92]) ).
fof(f553,plain,
( ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(b),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f221,f93]) ).
fof(f554,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f399,f207,f237,f210]) ).
fof(f555,plain,
( sQ4_spl
| ~ sQ5_spl
| c != b ),
inference(forward_demodulation,[status(thm)],[f214,f212]) ).
fof(f564,plain,
! [X0] :
( b = X0
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f76,f55]) ).
fof(f571,plain,
! [X0] :
( a = X0
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f75,f55]) ).
fof(f572,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ9_spl
| ~ product(g2,an_isomorphism(a),f,f) ),
inference(forward_demodulation,[status(thm)],[f228,f541]) ).
fof(f573,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ9_spl
| ~ product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f86,f572]) ).
fof(f574,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f573,f519]) ).
fof(f575,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f574]) ).
fof(f576,plain,
( sQ3_spl
| ~ sQ5_spl
| c != a ),
inference(forward_demodulation,[status(thm)],[f214,f209]) ).
fof(f577,plain,
( ~ sQ5_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(c)) ),
inference(forward_demodulation,[status(thm)],[f214,f93]) ).
fof(f578,plain,
( ~ sQ5_spl
| product(g1,d1,d2,c) ),
inference(forward_demodulation,[status(thm)],[f214,f92]) ).
fof(f580,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f211,f214]) ).
fof(f610,plain,
( sQ9_spl
| ~ sQ10_spl
| b != a ),
inference(backward_demodulation,[status(thm)],[f231,f229]) ).
fof(f648,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| g = h ),
inference(backward_demodulation,[status(thm)],[f289,f292]) ).
fof(f653,plain,
! [X0,X1] :
( ~ sQ25_spl
| X0 = X1
| ~ product(g2,X0,g,X1) ),
inference(paramodulation,[status(thm)],[f289,f111]) ).
fof(f661,plain,
! [X0] :
( ~ sQ25_spl
| product(g2,X0,g,X0) ),
inference(paramodulation,[status(thm)],[f289,f48]) ).
fof(f693,plain,
( sQ9_spl
| ~ sQ10_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f610,f237,f230,f227]) ).
fof(f694,plain,
( sQ3_spl
| ~ sQ5_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f576,f197,f213,f207]) ).
fof(f697,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ product(g2,an_isomorphism(b),an_isomorphism(b),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f231,f553]) ).
fof(f722,plain,
( sQ10_spl
| ~ sQ9_spl
| a != b ),
inference(backward_demodulation,[status(thm)],[f228,f232]) ).
fof(f727,plain,
( ~ sQ25_spl
| ~ sQ24_spl
| f = g ),
inference(backward_demodulation,[status(thm)],[f286,f289]) ).
fof(f732,plain,
! [X0,X1] :
( ~ sQ24_spl
| X0 = X1
| ~ product(g2,X0,f,X1) ),
inference(paramodulation,[status(thm)],[f286,f111]) ).
fof(f735,plain,
! [X0,X1] :
( ~ sQ24_spl
| X0 = X1
| ~ product(g2,f,X0,X1) ),
inference(paramodulation,[status(thm)],[f286,f102]) ).
fof(f740,plain,
! [X0] :
( ~ sQ24_spl
| product(g2,X0,f,X0) ),
inference(paramodulation,[status(thm)],[f286,f48]) ).
fof(f754,plain,
! [X0] :
( a = X0
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f74,f55]) ).
fof(f761,plain,
! [X0] :
( c = X0
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f73,f55]) ).
fof(f769,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ product(g2,f,an_isomorphism(a),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f218,f432]) ).
fof(f770,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ product(g2,f,f,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f86,f769]) ).
fof(f771,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ product(g2,f,f,an_isomorphism(c)) ),
inference(forward_demodulation,[status(thm)],[f214,f770]) ).
fof(f783,definition,
( sQ27_spl
<=> group_member(a,g1) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( sQ27_spl
| ~ group_member(a,g1) ),
inference(component_clause,[status(thm)],[f783]) ).
fof(f803,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl
| f = h ),
inference(backward_demodulation,[status(thm)],[f727,f648]) ).
fof(f824,plain,
( sQ18_spl
| ~ sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl
| f != f ),
inference(forward_demodulation,[status(thm)],[f803,f266]) ).
fof(f825,plain,
( sQ18_spl
| ~ sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f824]) ).
fof(f826,plain,
( sQ18_spl
| ~ sQ26_spl
| ~ sQ25_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f825]) ).
fof(f827,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ product(g2,an_isomorphism(a),an_isomorphism(d2),an_isomorphism(c)) ),
inference(forward_demodulation,[status(thm)],[f228,f577]) ).
fof(f828,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ product(g2,f,an_isomorphism(d2),an_isomorphism(c)) ),
inference(forward_demodulation,[status(thm)],[f86,f827]) ).
fof(f863,plain,
( ~ sQ1_spl
| sQ4_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f555]) ).
fof(f864,plain,
( ~ sQ1_spl
| sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f863]) ).
fof(f865,plain,
( sQ6_spl
| ~ sQ7_spl
| b != a ),
inference(backward_demodulation,[status(thm)],[f221,f219]) ).
fof(f892,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ21_spl
| ~ product(g2,an_isomorphism(b),f,an_isomorphism(d3)) ),
inference(backward_demodulation,[status(thm)],[f893,f697]) ).
fof(f893,plain,
( ~ sQ21_spl
| an_isomorphism(b) = f ),
inference(forward_demodulation,[status(thm)],[f275,f87]) ).
fof(f894,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ21_spl
| ~ product(g2,f,f,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f893,f892]) ).
fof(f896,plain,
( ~ sQ18_spl
| an_isomorphism(c) = f ),
inference(forward_demodulation,[status(thm)],[f265,f88]) ).
fof(f925,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ21_spl
| ~ sQ4_spl
| ~ product(g2,f,f,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f211,f894]) ).
fof(f926,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ21_spl
| ~ sQ4_spl
| ~ product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f893,f925]) ).
fof(f927,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ21_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f926,f77]) ).
fof(f928,plain,
( ~ sQ7_spl
| ~ sQ10_spl
| ~ sQ21_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f927]) ).
fof(f932,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ18_spl
| ~ product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f896,f771]) ).
fof(f933,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f932,f77]) ).
fof(f934,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f933]) ).
fof(f945,plain,
( ~ sQ6_spl
| product(g1,d1,a,d3) ),
inference(backward_demodulation,[status(thm)],[f218,f92]) ).
fof(f974,plain,
( sQ6_spl
| ~ sQ7_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f865,f237,f220,f217]) ).
fof(f975,plain,
( sQ10_spl
| ~ sQ9_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f722,f237,f227,f230]) ).
fof(f979,plain,
( ~ sQ12_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f322,f274,f237]) ).
fof(f980,plain,
( sQ19_spl
| ~ sQ18_spl
| f != g ),
inference(forward_demodulation,[status(thm)],[f265,f269]) ).
fof(f1003,plain,
( sQ5_spl
| ~ sQ4_spl
| b != c ),
inference(backward_demodulation,[status(thm)],[f211,f215]) ).
fof(f1004,plain,
( ~ sQ4_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(b)) ),
inference(backward_demodulation,[status(thm)],[f211,f93]) ).
fof(f1030,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ product(g2,f,f,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f211,f770]) ).
fof(f1031,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ product(g2,f,an_isomorphism(d2),an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f211,f432]) ).
fof(f1037,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ product(g2,f,f,g) ),
inference(backward_demodulation,[status(thm)],[f87,f1030]) ).
fof(f1041,plain,
! [X0] :
( ~ sQ19_spl
| X0 = g
| X0 = g
| X0 = f
| ~ group_member(X0,g2) ),
inference(forward_demodulation,[status(thm)],[f268,f67]) ).
fof(f1042,plain,
! [X0] :
( ~ sQ19_spl
| X0 = g
| X0 = f
| ~ group_member(X0,g2) ),
inference(duplicate_literals_removal,[status(thm)],[f1041]) ).
fof(f1043,plain,
( ~ sQ19_spl
| g = g
| g = f ),
inference(resolution,[status(thm)],[f1042,f64]) ).
fof(f1045,plain,
( ~ sQ19_spl
| f = g
| f = f ),
inference(resolution,[status(thm)],[f1042,f63]) ).
fof(f1047,plain,
( ~ sQ19_spl
| identity_for(g2) = g
| identity_for(g2) = f ),
inference(resolution,[status(thm)],[f1042,f46]) ).
fof(f1048,plain,
( ~ sQ19_spl
| sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1043,f274,f277,f267]) ).
fof(f1049,plain,
( ~ sQ19_spl
| sQ21_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f1045,f281,f274,f267]) ).
fof(f1050,plain,
( ~ sQ19_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f1047,f285,f288,f267]) ).
fof(f1068,plain,
( ~ sQ25_spl
| ~ sQ24_spl
| sQ19_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f727,f980]) ).
fof(f1069,plain,
( ~ sQ25_spl
| ~ sQ24_spl
| sQ19_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f1068]) ).
fof(f1090,plain,
( ~ sQ21_spl
| f = g ),
inference(backward_demodulation,[status(thm)],[f893,f87]) ).
fof(f1094,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ21_spl
| ~ product(g2,f,f,f) ),
inference(backward_demodulation,[status(thm)],[f1090,f1037]) ).
fof(f1099,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1094,f77]) ).
fof(f1100,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ4_spl
| ~ sQ21_spl ),
inference(contradiction_clause,[status(thm)],[f1099]) ).
fof(f1111,plain,
( ~ sQ5_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),h) ),
inference(forward_demodulation,[status(thm)],[f88,f577]) ).
fof(f1160,plain,
( ~ sQ4_spl
| product(g1,d1,d2,b) ),
inference(backward_demodulation,[status(thm)],[f211,f92]) ).
fof(f1162,plain,
( ~ sQ4_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(b)) ),
inference(backward_demodulation,[status(thm)],[f211,f93]) ).
fof(f1205,definition,
( sQ28_spl
<=> group_member(g,g2) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1207,plain,
( sQ28_spl
| ~ group_member(g,g2) ),
inference(component_clause,[status(thm)],[f1205]) ).
fof(f1216,plain,
! [X0,X1] :
( ~ sQ17_spl
| X0 = X1
| ~ product(g1,X0,c,X1) ),
inference(paramodulation,[status(thm)],[f255,f111]) ).
fof(f1238,plain,
! [X0,X1] :
( ~ sQ16_spl
| X0 = X1
| ~ product(g1,X0,b,X1) ),
inference(paramodulation,[status(thm)],[f252,f111]) ).
fof(f1255,plain,
( ~ sQ1_spl
| sQ5_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f201,f1003]) ).
fof(f1256,plain,
( ~ sQ1_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1255]) ).
fof(f1294,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| product(g1,d1,a,c) ),
inference(backward_demodulation,[status(thm)],[f214,f945]) ).
fof(f1376,definition,
( sQ29_spl
<=> group_member(c,g1) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1378,plain,
( sQ29_spl
| ~ group_member(c,g1) ),
inference(component_clause,[status(thm)],[f1376]) ).
fof(f1438,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f231,f1162]) ).
fof(f1439,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ product(g2,g,an_isomorphism(d2),an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f87,f1438]) ).
fof(f1440,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ product(g2,g,an_isomorphism(a),an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f218,f1439]) ).
fof(f1441,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ product(g2,g,f,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f86,f1440]) ).
fof(f1442,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ6_spl
| ~ product(g2,g,f,g) ),
inference(forward_demodulation,[status(thm)],[f87,f1441]) ).
fof(f1443,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1442,f79]) ).
fof(f1444,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1443]) ).
fof(f1445,plain,
( ~ sQ4_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),g) ),
inference(forward_demodulation,[status(thm)],[f87,f1004]) ).
fof(f1446,plain,
( ~ sQ5_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(c)) ),
inference(forward_demodulation,[status(thm)],[f214,f93]) ).
fof(f1447,plain,
( ~ sQ5_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),h) ),
inference(forward_demodulation,[status(thm)],[f88,f1446]) ).
fof(f1449,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ product(g2,f,an_isomorphism(d2),g) ),
inference(forward_demodulation,[status(thm)],[f87,f1031]) ).
fof(f1453,plain,
( ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),g,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f87,f553]) ).
fof(f1454,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ product(g2,an_isomorphism(d1),g,an_isomorphism(c)) ),
inference(forward_demodulation,[status(thm)],[f214,f1453]) ).
fof(f1455,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ product(g2,an_isomorphism(d1),g,h) ),
inference(forward_demodulation,[status(thm)],[f88,f1454]) ).
fof(f1470,plain,
( ~ sQ4_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),g) ),
inference(forward_demodulation,[status(thm)],[f87,f1162]) ).
fof(f1475,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ product(g2,f,an_isomorphism(d2),h) ),
inference(forward_demodulation,[status(thm)],[f88,f828]) ).
fof(f1491,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| an_isomorphism(b) = h ),
inference(backward_demodulation,[status(thm)],[f580,f88]) ).
fof(f1501,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| g = h ),
inference(forward_demodulation,[status(thm)],[f87,f1491]) ).
fof(f1502,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1501,f269]) ).
fof(f1503,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f1502]) ).
fof(f1527,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(b),h) ),
inference(backward_demodulation,[status(thm)],[f221,f1111]) ).
fof(f1528,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(b),g) ),
inference(backward_demodulation,[status(thm)],[f221,f1445]) ).
fof(f1530,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),g,h) ),
inference(forward_demodulation,[status(thm)],[f87,f1527]) ).
fof(f1531,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),g,g) ),
inference(forward_demodulation,[status(thm)],[f87,f1528]) ).
fof(f1543,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(b),h) ),
inference(forward_demodulation,[status(thm)],[f221,f1447]) ).
fof(f1544,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ product(g2,an_isomorphism(d1),g,h) ),
inference(forward_demodulation,[status(thm)],[f87,f1543]) ).
fof(f1547,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ product(g2,f,an_isomorphism(b),g) ),
inference(forward_demodulation,[status(thm)],[f221,f1449]) ).
fof(f1548,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| ~ product(g2,f,g,g) ),
inference(forward_demodulation,[status(thm)],[f87,f1547]) ).
fof(f1549,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1548,f78]) ).
fof(f1550,plain,
( ~ sQ9_spl
| ~ sQ4_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f1549]) ).
fof(f1610,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ product(g2,an_isomorphism(b),an_isomorphism(d2),g) ),
inference(forward_demodulation,[status(thm)],[f231,f1470]) ).
fof(f1611,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ product(g2,g,an_isomorphism(d2),g) ),
inference(forward_demodulation,[status(thm)],[f87,f1610]) ).
fof(f1646,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ product(g2,an_isomorphism(b),g,h) ),
inference(forward_demodulation,[status(thm)],[f231,f1530]) ).
fof(f1647,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ10_spl
| ~ product(g2,g,g,h) ),
inference(forward_demodulation,[status(thm)],[f87,f1646]) ).
fof(f1654,definition,
( sQ30_spl
<=> group_member(b,g1) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1656,plain,
( sQ30_spl
| ~ group_member(b,g1) ),
inference(component_clause,[status(thm)],[f1654]) ).
fof(f1661,definition,
( sQ31_spl
<=> group_member(f,g2) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1663,plain,
( sQ31_spl
| ~ group_member(f,g2) ),
inference(component_clause,[status(thm)],[f1661]) ).
fof(f1672,plain,
! [X0,X1] :
( ~ sQ24_spl
| X0 = X1
| ~ product(g2,X0,f,X1) ),
inference(paramodulation,[status(thm)],[f286,f111]) ).
fof(f1688,plain,
( sQ25_spl
| ~ sQ24_spl
| f != g ),
inference(forward_demodulation,[status(thm)],[f286,f290]) ).
fof(f1712,plain,
( ~ sQ16_spl
| a = b ),
inference(resolution,[status(thm)],[f1238,f69]) ).
fof(f1716,plain,
! [X0] :
( ~ sQ16_spl
| ~ group_member(b,g1)
| ~ group_member(X0,g1)
| X0 = multiply(g1,X0,b) ),
inference(resolution,[status(thm)],[f1238,f52]) ).
fof(f1718,plain,
( ~ sQ16_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f1712,f237,f251]) ).
fof(f1720,definition,
! [X0] :
( sQ32_spl
<=> ( ~ group_member(X0,g1)
| X0 = multiply(g1,X0,b) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1723,plain,
( ~ sQ16_spl
| ~ sQ30_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1716,f1720,f1654,f251]) ).
fof(f1724,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1656,f61]) ).
fof(f1725,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f1724]) ).
fof(f1758,plain,
( ~ sQ0_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f317,f264,f197]) ).
fof(f1760,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ product(g2,an_isomorphism(b),an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f231,f477]) ).
fof(f1761,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ product(g2,g,an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f87,f1760]) ).
fof(f1806,plain,
( sQ1_spl
| ~ sQ0_spl
| a != b ),
inference(forward_demodulation,[status(thm)],[f198,f202]) ).
fof(f1814,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f1647]) ).
fof(f1815,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f1814]) ).
fof(f1902,plain,
( sQ16_spl
| ~ sQ15_spl
| a != b ),
inference(backward_demodulation,[status(thm)],[f249,f253]) ).
fof(f2021,plain,
! [X0] :
( ~ sQ0_spl
| X0 = a
| X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f198,f66]) ).
fof(f2022,plain,
! [X0] :
( ~ sQ0_spl
| X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(duplicate_literals_removal,[status(thm)],[f2021]) ).
fof(f2027,plain,
( ~ sQ0_spl
| identity_for(g1) = b
| identity_for(g1) = a ),
inference(resolution,[status(thm)],[f2022,f46]) ).
fof(f2030,plain,
( ~ sQ0_spl
| sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f2027,f248,f251,f197]) ).
fof(f2039,plain,
( ~ sQ0_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f198,f74]) ).
fof(f2059,plain,
( ~ sQ25_spl
| g = identity_for(g2) ),
inference(resolution,[status(thm)],[f661,f102]) ).
fof(f2084,plain,
! [X0] :
( ~ sQ24_spl
| product(g2,f,X0,X0) ),
inference(paramodulation,[status(thm)],[f286,f47]) ).
fof(f2093,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ product(g2,an_isomorphism(a),g,h) ),
inference(forward_demodulation,[status(thm)],[f228,f1455]) ).
fof(f2094,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ product(g2,f,g,h) ),
inference(forward_demodulation,[status(thm)],[f86,f2093]) ).
fof(f2129,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f208,f211]) ).
fof(f2130,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2129,f239]) ).
fof(f2131,plain,
( ~ sQ4_spl
| ~ sQ3_spl
| sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f2130]) ).
fof(f2160,plain,
( sQ16_spl
| ~ sQ15_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1902,f237,f248,f251]) ).
fof(f2161,plain,
( sQ1_spl
| ~ sQ0_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1806,f237,f197,f200]) ).
fof(f2269,plain,
( ~ sQ0_spl
| d1 = b
| d1 = a ),
inference(resolution,[status(thm)],[f89,f2022]) ).
fof(f2270,plain,
( ~ sQ0_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f2269,f227,f230,f197]) ).
fof(f2438,plain,
( ~ sQ6_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(a),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f218,f93]) ).
fof(f2439,plain,
( ~ sQ6_spl
| ~ product(g2,an_isomorphism(d1),f,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f86,f2438]) ).
fof(f2555,plain,
( sQ24_spl
| ~ sQ25_spl
| g != f ),
inference(forward_demodulation,[status(thm)],[f2059,f287]) ).
fof(f2579,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| b = a ),
inference(resolution,[status(thm)],[f501,f2039]) ).
fof(f2585,plain,
! [X0] :
( ~ sQ15_spl
| ~ group_member(a,g1)
| ~ group_member(X0,g1)
| X0 = multiply(g1,X0,a) ),
inference(resolution,[status(thm)],[f501,f52]) ).
fof(f2586,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f2579,f237,f248,f197]) ).
fof(f2589,definition,
! [X0] :
( sQ33_spl
<=> ( ~ group_member(X0,g1)
| X0 = multiply(g1,X0,a) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f2592,plain,
( ~ sQ15_spl
| ~ sQ27_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f2585,f2589,f783,f248]) ).
fof(f2593,plain,
( sQ27_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f785,f60]) ).
fof(f2594,plain,
sQ27_spl,
inference(contradiction_clause,[status(thm)],[f2593]) ).
fof(f2604,plain,
( ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ10_spl
| product(g1,b,a,c) ),
inference(forward_demodulation,[status(thm)],[f231,f1294]) ).
fof(f2634,plain,
( sQ25_spl
| ~ sQ24_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f1688,f274,f285,f288]) ).
fof(f2637,plain,
( ~ sQ10_spl
| ~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f231,f93]) ).
fof(f2638,plain,
( ~ sQ10_spl
| ~ product(g2,g,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f87,f2637]) ).
fof(f2657,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ10_spl
| b = c ),
inference(resolution,[status(thm)],[f2604,f501]) ).
fof(f2665,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ5_spl
| ~ sQ10_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f2657,f200,f230,f213,f217,f248]) ).
fof(f2715,plain,
( ~ sQ6_spl
| product(g1,d1,a,d3) ),
inference(forward_demodulation,[status(thm)],[f218,f92]) ).
fof(f2716,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| d1 = d3 ),
inference(resolution,[status(thm)],[f2715,f501]) ).
fof(f2752,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ product(g2,f,f,an_isomorphism(a)) ),
inference(backward_demodulation,[status(thm)],[f208,f441]) ).
fof(f2753,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ3_spl
| ~ product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f86,f2752]) ).
fof(f2754,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2753,f77]) ).
fof(f2755,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f2754]) ).
fof(f2756,plain,
( ~ sQ3_spl
| product(g1,d1,d2,a) ),
inference(forward_demodulation,[status(thm)],[f208,f92]) ).
fof(f2757,plain,
( ~ sQ3_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(a)) ),
inference(forward_demodulation,[status(thm)],[f208,f93]) ).
fof(f2758,plain,
( ~ sQ3_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f86,f2757]) ).
fof(f2781,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ product(g2,g,an_isomorphism(d2),an_isomorphism(a)) ),
inference(forward_demodulation,[status(thm)],[f208,f2638]) ).
fof(f2782,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ product(g2,g,an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f86,f2781]) ).
fof(f2788,plain,
! [X0] :
( ~ sQ1_spl
| X0 = b
| X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(backward_demodulation,[status(thm)],[f201,f66]) ).
fof(f2792,plain,
( ~ sQ1_spl
| an_isomorphism(b) = h ),
inference(backward_demodulation,[status(thm)],[f201,f88]) ).
fof(f2794,plain,
! [X0] :
( ~ sQ1_spl
| X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(duplicate_literals_removal,[status(thm)],[f2788]) ).
fof(f2795,plain,
( ~ sQ1_spl
| g = h ),
inference(forward_demodulation,[status(thm)],[f87,f2792]) ).
fof(f2796,plain,
( ~ sQ1_spl
| sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2795,f269]) ).
fof(f2797,plain,
( ~ sQ1_spl
| sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f2796]) ).
fof(f2839,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| product(g1,a,d2,c) ),
inference(forward_demodulation,[status(thm)],[f228,f578]) ).
fof(f2840,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ7_spl
| product(g1,a,b,c) ),
inference(forward_demodulation,[status(thm)],[f221,f2839]) ).
fof(f2950,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| product(g1,a,b,d3) ),
inference(forward_demodulation,[status(thm)],[f228,f542]) ).
fof(f2952,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ15_spl
| b = c ),
inference(resolution,[status(thm)],[f504,f2840]) ).
fof(f2957,plain,
! [X0] :
( ~ sQ15_spl
| ~ group_member(X0,g1)
| ~ group_member(a,g1)
| X0 = multiply(g1,a,X0) ),
inference(resolution,[status(thm)],[f504,f52]) ).
fof(f2958,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ7_spl
| ~ sQ15_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f2952,f200,f248,f220,f227,f213]) ).
fof(f2960,definition,
! [X0] :
( sQ34_spl
<=> ( ~ group_member(X0,g1)
| X0 = multiply(g1,a,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f2963,plain,
( ~ sQ15_spl
| ~ sQ27_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f2957,f2960,f783,f248]) ).
fof(f3026,plain,
( ~ sQ1_spl
| product(g2,g,g,f) ),
inference(backward_demodulation,[status(thm)],[f2795,f83]) ).
fof(f3083,plain,
( ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ3_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f208,f2950]) ).
fof(f3084,plain,
( ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ3_spl
| b = a ),
inference(resolution,[status(thm)],[f3083,f504]) ).
fof(f3092,plain,
( ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ9_spl
| ~ sQ3_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f3084,f237,f207,f227,f220,f248]) ).
fof(f3099,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ product(g2,g,an_isomorphism(b),f) ),
inference(forward_demodulation,[status(thm)],[f221,f2782]) ).
fof(f3100,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f87,f3099]) ).
fof(f3149,plain,
( ~ sQ1_spl
| b = b
| b = a ),
inference(resolution,[status(thm)],[f2794,f61]) ).
fof(f3154,plain,
( ~ sQ1_spl
| sQ13_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f3149,f237,f240,f200]) ).
fof(f3214,plain,
( ~ sQ10_spl
| ~ product(g2,an_isomorphism(b),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f231,f93]) ).
fof(f3215,plain,
( ~ sQ10_spl
| ~ product(g2,g,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f87,f3214]) ).
fof(f3236,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3026,f3100]) ).
fof(f3237,plain,
( ~ sQ1_spl
| ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f3236]) ).
fof(f3239,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ product(g2,g,an_isomorphism(d2),an_isomorphism(a)) ),
inference(forward_demodulation,[status(thm)],[f208,f3215]) ).
fof(f3240,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ product(g2,g,an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f86,f3239]) ).
fof(f3249,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ product(g2,g,an_isomorphism(d2),an_isomorphism(a)) ),
inference(forward_demodulation,[status(thm)],[f208,f2638]) ).
fof(f3250,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ product(g2,g,an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f86,f3249]) ).
fof(f3251,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| product(g1,b,d2,a) ),
inference(forward_demodulation,[status(thm)],[f231,f2756]) ).
fof(f3254,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| d2 = b ),
inference(forward_demodulation,[status(thm)],[f201,f224]) ).
fof(f3271,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3254,f222]) ).
fof(f3272,plain,
( ~ sQ8_spl
| ~ sQ1_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f3271]) ).
fof(f3273,plain,
( ~ sQ3_spl
| product(g1,d1,d2,a) ),
inference(forward_demodulation,[status(thm)],[f208,f92]) ).
fof(f3279,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| d1 = b ),
inference(forward_demodulation,[status(thm)],[f201,f234]) ).
fof(f3306,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3279,f232]) ).
fof(f3307,plain,
( ~ sQ11_spl
| ~ sQ1_spl
| sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f3306]) ).
fof(f3363,plain,
( ~ sQ1_spl
| d2 = b
| d2 = a ),
inference(resolution,[status(thm)],[f90,f2794]) ).
fof(f3364,plain,
( ~ sQ1_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f3363,f217,f220,f200]) ).
fof(f3366,plain,
( sQ7_spl
| ~ sQ6_spl
| a != b ),
inference(backward_demodulation,[status(thm)],[f218,f222]) ).
fof(f3429,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ9_spl
| a = d3 ),
inference(forward_demodulation,[status(thm)],[f228,f2716]) ).
fof(f3430,plain,
( sQ3_spl
| ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ9_spl
| a != a ),
inference(forward_demodulation,[status(thm)],[f3429,f209]) ).
fof(f3431,plain,
( sQ3_spl
| ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ9_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3430]) ).
fof(f3432,plain,
( sQ3_spl
| ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ9_spl ),
inference(contradiction_clause,[status(thm)],[f3431]) ).
fof(f3433,plain,
( sQ24_spl
| ~ sQ25_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2555,f274,f288,f285]) ).
fof(f3434,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| d2 = d3 ),
inference(resolution,[status(thm)],[f429,f504]) ).
fof(f3492,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ product(g2,f,an_isomorphism(c),h) ),
inference(backward_demodulation,[status(thm)],[f224,f1475]) ).
fof(f3493,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ product(g2,f,h,h) ),
inference(forward_demodulation,[status(thm)],[f88,f3492]) ).
fof(f3494,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| c = d3 ),
inference(forward_demodulation,[status(thm)],[f224,f3434]) ).
fof(f3587,plain,
! [X0] :
( ~ sQ24_spl
| product(g2,f,X0,X0) ),
inference(resolution,[status(thm)],[f2084,f98]) ).
fof(f3590,plain,
( ~ sQ24_spl
| f = identity_for(g2) ),
inference(resolution,[status(thm)],[f2084,f111]) ).
fof(f3610,plain,
! [X0] :
( ~ sQ18_spl
| X0 = f
| X0 = g
| X0 = f
| ~ group_member(X0,g2) ),
inference(backward_demodulation,[status(thm)],[f265,f67]) ).
fof(f3617,plain,
! [X0] :
( ~ sQ18_spl
| X0 = g
| X0 = f
| ~ group_member(X0,g2) ),
inference(duplicate_literals_removal,[status(thm)],[f3610]) ).
fof(f3655,plain,
! [X0] :
( ~ sQ25_spl
| product(g2,X0,g,X0) ),
inference(paramodulation,[status(thm)],[f2059,f48]) ).
fof(f3663,plain,
( ~ sQ19_spl
| g = h ),
inference(backward_demodulation,[status(thm)],[f448,f88]) ).
fof(f3853,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f80,f3493]) ).
fof(f3854,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f3853]) ).
fof(f3857,plain,
( ~ sQ5_spl
| product(g1,d1,d2,c) ),
inference(forward_demodulation,[status(thm)],[f214,f92]) ).
fof(f3860,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ product(g2,an_isomorphism(d1),g,an_isomorphism(c)) ),
inference(forward_demodulation,[status(thm)],[f214,f1453]) ).
fof(f3861,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ product(g2,an_isomorphism(d1),g,h) ),
inference(forward_demodulation,[status(thm)],[f88,f3860]) ).
fof(f3910,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),g,h) ),
inference(backward_demodulation,[status(thm)],[f234,f3861]) ).
fof(f3911,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ product(g2,h,g,h) ),
inference(forward_demodulation,[status(thm)],[f88,f3910]) ).
fof(f3912,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3911,f3655]) ).
fof(f3913,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f3912]) ).
fof(f3954,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),f,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f234,f2439]) ).
fof(f3955,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ product(g2,h,f,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f88,f3954]) ).
fof(f3956,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ product(g2,h,f,an_isomorphism(c)) ),
inference(forward_demodulation,[status(thm)],[f214,f3955]) ).
fof(f3957,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ5_spl
| ~ product(g2,h,f,h) ),
inference(forward_demodulation,[status(thm)],[f88,f3956]) ).
fof(f3958,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3957,f81]) ).
fof(f3959,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f3958]) ).
fof(f4193,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),g,h) ),
inference(forward_demodulation,[status(thm)],[f234,f1544]) ).
fof(f4213,plain,
! [X0] :
( ~ sQ24_spl
| ~ group_member(f,g2)
| ~ group_member(X0,g2)
| X0 = multiply(g2,X0,f) ),
inference(resolution,[status(thm)],[f732,f52]) ).
fof(f4215,definition,
! [X0] :
( sQ38_spl
<=> ( ~ group_member(X0,g2)
| X0 = multiply(g2,X0,f) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f4218,plain,
( ~ sQ24_spl
| ~ sQ31_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f4213,f4215,f1661,f285]) ).
fof(f4224,plain,
! [X0] :
( ~ sQ24_spl
| ~ group_member(X0,g2)
| ~ group_member(f,g2)
| X0 = multiply(g2,f,X0) ),
inference(resolution,[status(thm)],[f735,f52]) ).
fof(f4227,definition,
! [X0] :
( sQ39_spl
<=> ( ~ group_member(X0,g2)
| X0 = multiply(g2,f,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f4230,plain,
( ~ sQ24_spl
| ~ sQ31_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f4224,f4227,f1661,f285]) ).
fof(f4231,plain,
( sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1663,f63]) ).
fof(f4232,plain,
sQ31_spl,
inference(contradiction_clause,[status(thm)],[f4231]) ).
fof(f4398,plain,
( ~ sQ18_spl
| identity_for(g2) = g
| identity_for(g2) = f ),
inference(resolution,[status(thm)],[f3617,f46]) ).
fof(f4401,plain,
( ~ sQ18_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f4398,f285,f288,f264]) ).
fof(f4417,plain,
! [X0] :
( ~ sQ25_spl
| ~ group_member(g,g2)
| ~ group_member(X0,g2)
| X0 = multiply(g2,X0,g) ),
inference(resolution,[status(thm)],[f653,f52]) ).
fof(f4420,definition,
! [X0] :
( sQ40_spl
<=> ( ~ group_member(X0,g2)
| X0 = multiply(g2,X0,g) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f4423,plain,
( ~ sQ25_spl
| ~ sQ28_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f4417,f4420,f1205,f288]) ).
fof(f4436,plain,
( ~ sQ25_spl
| f = g ),
inference(resolution,[status(thm)],[f78,f653]) ).
fof(f4446,plain,
( ~ sQ25_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f4436,f274,f288]) ).
fof(f4575,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ product(g2,g,an_isomorphism(b),f) ),
inference(forward_demodulation,[status(thm)],[f221,f3250]) ).
fof(f4576,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f87,f4575]) ).
fof(f4577,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ product(g2,g,an_isomorphism(b),f) ),
inference(forward_demodulation,[status(thm)],[f221,f1761]) ).
fof(f4578,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f87,f4577]) ).
fof(f4606,plain,
( ~ sQ18_spl
| product(g2,f,h,g) ),
inference(forward_demodulation,[status(thm)],[f265,f85]) ).
fof(f4607,plain,
( ~ sQ18_spl
| product(g2,f,f,g) ),
inference(forward_demodulation,[status(thm)],[f265,f4606]) ).
fof(f4615,plain,
( ~ sQ18_spl
| product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f265,f82]) ).
fof(f4623,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4576,f4615]) ).
fof(f4624,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ7_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f4623]) ).
fof(f4657,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ product(g2,g,an_isomorphism(c),f) ),
inference(backward_demodulation,[status(thm)],[f224,f3240]) ).
fof(f4662,plain,
( sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1207,f64]) ).
fof(f4663,plain,
sQ28_spl,
inference(contradiction_clause,[status(thm)],[f4662]) ).
fof(f4667,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ3_spl
| d1 = a ),
inference(forward_demodulation,[status(thm)],[f208,f2716]) ).
fof(f4711,plain,
( ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f234,f93]) ).
fof(f4712,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ product(g2,f,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f896,f4711]) ).
fof(f4713,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ7_spl
| ~ product(g2,f,an_isomorphism(b),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f221,f4712]) ).
fof(f4714,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ7_spl
| ~ product(g2,f,g,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f87,f4713]) ).
fof(f4752,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ3_spl
| ~ product(g2,f,an_isomorphism(d2),an_isomorphism(a)) ),
inference(forward_demodulation,[status(thm)],[f208,f4712]) ).
fof(f4753,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ3_spl
| ~ product(g2,f,an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f86,f4752]) ).
fof(f4754,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f234,f2758]) ).
fof(f4761,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ product(g2,f,an_isomorphism(c),f) ),
inference(backward_demodulation,[status(thm)],[f224,f4753]) ).
fof(f4762,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f896,f4761]) ).
fof(f4763,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ3_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4762,f77]) ).
fof(f4764,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ3_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f4763]) ).
fof(f4782,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f3494,f213,f223,f227,f248]) ).
fof(f4783,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| c = d3 ),
inference(forward_demodulation,[status(thm)],[f224,f3434]) ).
fof(f4784,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ3_spl
| c = a ),
inference(forward_demodulation,[status(thm)],[f208,f4783]) ).
fof(f4785,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4784,f199]) ).
fof(f4786,plain,
( ~ sQ15_spl
| ~ sQ9_spl
| ~ sQ8_spl
| ~ sQ3_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f4785]) ).
fof(f4883,plain,
( ~ sQ18_spl
| ~ sQ24_spl
| f = g ),
inference(resolution,[status(thm)],[f1672,f4607]) ).
fof(f4890,plain,
( ~ sQ18_spl
| ~ sQ24_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f4883,f274,f285,f264]) ).
fof(f4967,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ product(g2,g,an_isomorphism(c),g) ),
inference(backward_demodulation,[status(thm)],[f224,f1611]) ).
fof(f4970,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| ~ product(g2,g,f,g) ),
inference(forward_demodulation,[status(thm)],[f896,f4967]) ).
fof(f4971,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4970,f740]) ).
fof(f4972,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ18_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f4971]) ).
fof(f4987,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ product(g2,f,g,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f211,f4714]) ).
fof(f4988,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ product(g2,f,g,g) ),
inference(forward_demodulation,[status(thm)],[f87,f4987]) ).
fof(f4989,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4988,f3587]) ).
fof(f4990,plain,
( ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f4989]) ).
fof(f5020,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| product(g1,b,d2,b) ),
inference(backward_demodulation,[status(thm)],[f231,f1160]) ).
fof(f5068,plain,
! [X0] :
( ~ sQ21_spl
| X0 = h
| X0 = f
| X0 = f
| ~ group_member(X0,g2) ),
inference(forward_demodulation,[status(thm)],[f1090,f67]) ).
fof(f5069,plain,
! [X0] :
( ~ sQ21_spl
| X0 = h
| X0 = f
| ~ group_member(X0,g2) ),
inference(duplicate_literals_removal,[status(thm)],[f5068]) ).
fof(f5070,plain,
( ~ sQ21_spl
| h = h
| h = f ),
inference(resolution,[status(thm)],[f5069,f65]) ).
fof(f5072,plain,
( ~ sQ21_spl
| f = h
| f = f ),
inference(resolution,[status(thm)],[f5069,f63]) ).
fof(f5075,plain,
( ~ sQ21_spl
| sQ20_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f5070,f264,f270,f274]) ).
fof(f5076,plain,
( ~ sQ21_spl
| sQ18_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f5072,f281,f264,f274]) ).
fof(f5082,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ product(g2,h,g,h) ),
inference(forward_demodulation,[status(thm)],[f88,f4193]) ).
fof(f5127,plain,
( ~ sQ19_spl
| product(g2,h,g,g) ),
inference(backward_demodulation,[status(thm)],[f3663,f85]) ).
fof(f5128,plain,
( ~ sQ19_spl
| product(g2,g,g,g) ),
inference(backward_demodulation,[status(thm)],[f3663,f82]) ).
fof(f5134,plain,
( ~ sQ19_spl
| product(g2,g,g,g) ),
inference(forward_demodulation,[status(thm)],[f3663,f5127]) ).
fof(f5136,plain,
( ~ sQ19_spl
| product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f3663,f83]) ).
fof(f5164,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ product(g2,g,g,h) ),
inference(forward_demodulation,[status(thm)],[f3663,f5082]) ).
fof(f5165,plain,
( ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ product(g2,g,g,g) ),
inference(forward_demodulation,[status(thm)],[f3663,f5164]) ).
fof(f5229,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| product(g1,c,d2,c) ),
inference(forward_demodulation,[status(thm)],[f234,f3857]) ).
fof(f5304,plain,
( ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f234,f93]) ).
fof(f5305,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ product(g2,g,an_isomorphism(d2),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f448,f5304]) ).
fof(f5353,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5134,f5165]) ).
fof(f5354,plain,
( ~ sQ19_spl
| ~ sQ5_spl
| ~ sQ7_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f5353]) ).
fof(f5395,plain,
( ~ sQ5_spl
| product(g1,d1,d2,c) ),
inference(forward_demodulation,[status(thm)],[f214,f92]) ).
fof(f5441,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4578,f5136]) ).
fof(f5442,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f5441]) ).
fof(f5498,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ8_spl
| ~ product(g2,g,an_isomorphism(c),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f224,f5305]) ).
fof(f5499,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ8_spl
| ~ product(g2,g,g,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f448,f5498]) ).
fof(f5500,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ product(g2,g,g,an_isomorphism(a)) ),
inference(forward_demodulation,[status(thm)],[f208,f5499]) ).
fof(f5501,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ8_spl
| ~ sQ3_spl
| ~ product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f86,f5500]) ).
fof(f5502,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ8_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5501,f5136]) ).
fof(f5503,plain,
( ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ8_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f5502]) ).
fof(f5527,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),g,g) ),
inference(forward_demodulation,[status(thm)],[f234,f1531]) ).
fof(f5528,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ product(g2,g,g,g) ),
inference(forward_demodulation,[status(thm)],[f448,f5527]) ).
fof(f5529,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5528,f5128]) ).
fof(f5530,plain,
( ~ sQ4_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f5529]) ).
fof(f5577,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ3_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f4667,f227,f207,f217,f248]) ).
fof(f5578,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),f,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f234,f2439]) ).
fof(f5579,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ product(g2,g,f,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f448,f5578]) ).
fof(f5660,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ product(g2,g,an_isomorphism(c),an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f224,f3215]) ).
fof(f5661,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ19_spl
| ~ product(g2,g,g,an_isomorphism(d3)) ),
inference(forward_demodulation,[status(thm)],[f448,f5660]) ).
fof(f5662,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ product(g2,g,g,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f211,f5661]) ).
fof(f5663,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ product(g2,g,g,g) ),
inference(forward_demodulation,[status(thm)],[f87,f5662]) ).
fof(f5664,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5663,f5128]) ).
fof(f5665,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ19_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f5664]) ).
fof(f5694,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| product(g1,d1,b,b) ),
inference(forward_demodulation,[status(thm)],[f211,f542]) ).
fof(f5743,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ product(g2,g,f,an_isomorphism(b)) ),
inference(forward_demodulation,[status(thm)],[f211,f5579]) ).
fof(f5744,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ product(g2,g,f,g) ),
inference(forward_demodulation,[status(thm)],[f87,f5743]) ).
fof(f5745,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ24_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5744,f740]) ).
fof(f5746,plain,
( ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ19_spl
| ~ sQ4_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f5745]) ).
fof(f5752,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ product(g2,an_isomorphism(d1),an_isomorphism(c),g) ),
inference(backward_demodulation,[status(thm)],[f224,f1445]) ).
fof(f5834,plain,
! [X0] :
( ~ sQ10_spl
| d3 = X0
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f231,f118]) ).
fof(f5835,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ8_spl
| d3 = X0
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f224,f5834]) ).
fof(f5836,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| b = X0
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f211,f5835]) ).
fof(f5838,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| b = a ),
inference(resolution,[status(thm)],[f5836,f74]) ).
fof(f5839,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ group_member(c,g1)
| ~ group_member(b,g1)
| b = multiply(g1,b,c) ),
inference(resolution,[status(thm)],[f5836,f52]) ).
fof(f5840,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f5838,f237,f210,f223,f230]) ).
fof(f5841,definition,
( sQ41_spl
<=> b = multiply(g1,b,c) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f5842,plain,
( ~ sQ41_spl
| b = multiply(g1,b,c) ),
inference(component_clause,[status(thm)],[f5841]) ).
fof(f5844,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ4_spl
| ~ sQ29_spl
| ~ sQ30_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f5839,f5841,f1654,f1376,f210,f223,f230]) ).
fof(f5959,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ7_spl
| product(g1,b,b,b) ),
inference(forward_demodulation,[status(thm)],[f221,f5020]) ).
fof(f5996,plain,
h = multiply(g2,identity_for(g2),h),
inference(resolution,[status(thm)],[f151,f65]) ).
fof(f5997,plain,
g = multiply(g2,identity_for(g2),g),
inference(resolution,[status(thm)],[f151,f64]) ).
fof(f5998,plain,
c = multiply(g1,identity_for(g1),c),
inference(resolution,[status(thm)],[f151,f62]) ).
fof(f5999,plain,
b = multiply(g1,identity_for(g1),b),
inference(resolution,[status(thm)],[f151,f61]) ).
fof(f6001,plain,
f = multiply(g2,identity_for(g2),f),
inference(resolution,[status(thm)],[f151,f63]) ).
fof(f6003,plain,
a = multiply(g1,identity_for(g1),a),
inference(resolution,[status(thm)],[f151,f60]) ).
fof(f6005,plain,
( ~ sQ24_spl
| h = multiply(g2,f,h) ),
inference(forward_demodulation,[status(thm)],[f3590,f5996]) ).
fof(f6006,plain,
( ~ sQ24_spl
| g = multiply(g2,f,g) ),
inference(forward_demodulation,[status(thm)],[f3590,f5997]) ).
fof(f6007,plain,
( ~ sQ15_spl
| c = multiply(g1,a,c) ),
inference(forward_demodulation,[status(thm)],[f249,f5998]) ).
fof(f6008,plain,
( ~ sQ15_spl
| b = multiply(g1,a,b) ),
inference(forward_demodulation,[status(thm)],[f249,f5999]) ).
fof(f6009,plain,
( ~ sQ24_spl
| f = multiply(g2,f,f) ),
inference(forward_demodulation,[status(thm)],[f3590,f6001]) ).
fof(f6010,plain,
( ~ sQ15_spl
| a = multiply(g1,a,a) ),
inference(forward_demodulation,[status(thm)],[f249,f6003]) ).
fof(f6012,plain,
( ~ sQ24_spl
| product(g2,f,h,h)
| ~ group_member(h,g2)
| ~ group_member(f,g2) ),
inference(paramodulation,[status(thm)],[f6005,f52]) ).
fof(f6013,definition,
( sQ42_spl
<=> group_member(h,g2) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f6015,plain,
( sQ42_spl
| ~ group_member(h,g2) ),
inference(component_clause,[status(thm)],[f6013]) ).
fof(f6017,definition,
( sQ43_spl
<=> product(g2,f,h,h) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f6020,plain,
( ~ sQ24_spl
| sQ43_spl
| ~ sQ42_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f6012,f1661,f6013,f6017,f285]) ).
fof(f6021,plain,
( sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6015,f65]) ).
fof(f6022,plain,
sQ42_spl,
inference(contradiction_clause,[status(thm)],[f6021]) ).
fof(f6040,plain,
( ~ sQ24_spl
| product(g2,f,g,g)
| ~ group_member(g,g2)
| ~ group_member(f,g2) ),
inference(paramodulation,[status(thm)],[f6006,f52]) ).
fof(f6042,definition,
( sQ44_spl
<=> product(g2,f,g,g) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f6045,plain,
( ~ sQ24_spl
| sQ44_spl
| ~ sQ28_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f6040,f1661,f1205,f6042,f285]) ).
fof(f6047,plain,
( ~ sQ15_spl
| product(g1,a,c,c)
| ~ group_member(c,g1)
| ~ group_member(a,g1) ),
inference(paramodulation,[status(thm)],[f6007,f52]) ).
fof(f6049,definition,
( sQ45_spl
<=> product(g1,a,c,c) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f6052,plain,
( ~ sQ15_spl
| sQ45_spl
| ~ sQ29_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6047,f783,f1376,f6049,f248]) ).
fof(f6053,plain,
( sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1378,f62]) ).
fof(f6054,plain,
sQ29_spl,
inference(contradiction_clause,[status(thm)],[f6053]) ).
fof(f6056,plain,
( ~ sQ15_spl
| product(g1,a,b,b)
| ~ group_member(b,g1)
| ~ group_member(a,g1) ),
inference(paramodulation,[status(thm)],[f6008,f52]) ).
fof(f6058,definition,
( sQ46_spl
<=> product(g1,a,b,b) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f6061,plain,
( ~ sQ15_spl
| sQ46_spl
| ~ sQ30_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6056,f783,f1654,f6058,f248]) ).
fof(f6113,plain,
( ~ sQ24_spl
| product(g2,f,f,f)
| ~ group_member(f,g2)
| ~ group_member(f,g2) ),
inference(paramodulation,[status(thm)],[f6009,f52]) ).
fof(f6115,definition,
( sQ47_spl
<=> product(g2,f,f,f) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f6118,plain,
( ~ sQ24_spl
| sQ47_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f6113,f1661,f6115,f285]) ).
fof(f6120,plain,
( ~ sQ15_spl
| product(g1,a,a,a)
| ~ group_member(a,g1)
| ~ group_member(a,g1) ),
inference(paramodulation,[status(thm)],[f6010,f52]) ).
fof(f6122,definition,
( sQ48_spl
<=> product(g1,a,a,a) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f6125,plain,
( ~ sQ15_spl
| sQ48_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f6120,f783,f6122,f248]) ).
fof(f6126,plain,
h = multiply(g2,h,identity_for(g2)),
inference(resolution,[status(thm)],[f164,f65]) ).
fof(f6127,plain,
g = multiply(g2,g,identity_for(g2)),
inference(resolution,[status(thm)],[f164,f64]) ).
fof(f6128,plain,
c = multiply(g1,c,identity_for(g1)),
inference(resolution,[status(thm)],[f164,f62]) ).
fof(f6129,plain,
b = multiply(g1,b,identity_for(g1)),
inference(resolution,[status(thm)],[f164,f61]) ).
fof(f6135,plain,
( ~ sQ24_spl
| h = multiply(g2,h,f) ),
inference(forward_demodulation,[status(thm)],[f3590,f6126]) ).
fof(f6136,plain,
( ~ sQ24_spl
| g = multiply(g2,g,f) ),
inference(forward_demodulation,[status(thm)],[f3590,f6127]) ).
fof(f6137,plain,
( ~ sQ15_spl
| c = multiply(g1,c,a) ),
inference(forward_demodulation,[status(thm)],[f249,f6128]) ).
fof(f6138,plain,
( ~ sQ15_spl
| b = multiply(g1,b,a) ),
inference(forward_demodulation,[status(thm)],[f249,f6129]) ).
fof(f6170,plain,
( ~ sQ24_spl
| product(g2,h,f,h)
| ~ group_member(f,g2)
| ~ group_member(h,g2) ),
inference(paramodulation,[status(thm)],[f6135,f52]) ).
fof(f6172,definition,
( sQ49_spl
<=> product(g2,h,f,h) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f6175,plain,
( ~ sQ24_spl
| sQ49_spl
| ~ sQ31_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f6170,f6013,f1661,f6172,f285]) ).
fof(f6177,plain,
( ~ sQ24_spl
| product(g2,g,f,g)
| ~ group_member(f,g2)
| ~ group_member(g,g2) ),
inference(paramodulation,[status(thm)],[f6136,f52]) ).
fof(f6179,definition,
( sQ50_spl
<=> product(g2,g,f,g) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f6182,plain,
( ~ sQ24_spl
| sQ50_spl
| ~ sQ31_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f6177,f1205,f1661,f6179,f285]) ).
fof(f6184,plain,
( ~ sQ15_spl
| product(g1,c,a,c)
| ~ group_member(a,g1)
| ~ group_member(c,g1) ),
inference(paramodulation,[status(thm)],[f6137,f52]) ).
fof(f6186,definition,
( sQ51_spl
<=> product(g1,c,a,c) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f6189,plain,
( ~ sQ15_spl
| sQ51_spl
| ~ sQ27_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6184,f1376,f783,f6186,f248]) ).
fof(f6221,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ7_spl
| product(g1,b,identity_for(g1),identity_for(g1)) ),
inference(resolution,[status(thm)],[f132,f5959]) ).
fof(f6232,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ15_spl
| product(g1,b,a,identity_for(g1)) ),
inference(forward_demodulation,[status(thm)],[f249,f6221]) ).
fof(f6233,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ7_spl
| ~ sQ15_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f249,f6232]) ).
fof(f6240,plain,
( ~ sQ15_spl
| product(g1,b,a,b)
| ~ group_member(a,g1)
| ~ group_member(b,g1) ),
inference(paramodulation,[status(thm)],[f6138,f52]) ).
fof(f6242,definition,
( sQ52_spl
<=> product(g1,b,a,b) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f6245,plain,
( ~ sQ15_spl
| sQ52_spl
| ~ sQ27_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6240,f1654,f783,f6242,f248]) ).
fof(f6259,plain,
( ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ7_spl
| b = a ),
inference(resolution,[status(thm)],[f6233,f501]) ).
fof(f6270,plain,
( ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f6259,f237,f220,f230,f210,f248]) ).
fof(f6357,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| product(g1,d1,identity_for(g1),identity_for(g1)) ),
inference(resolution,[status(thm)],[f5694,f132]) ).
fof(f6367,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ15_spl
| product(g1,d1,a,identity_for(g1)) ),
inference(forward_demodulation,[status(thm)],[f249,f6357]) ).
fof(f6368,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ15_spl
| product(g1,d1,a,a) ),
inference(forward_demodulation,[status(thm)],[f249,f6367]) ).
fof(f6394,plain,
( ~ sQ41_spl
| product(g1,b,c,b)
| ~ group_member(c,g1)
| ~ group_member(b,g1) ),
inference(paramodulation,[status(thm)],[f5842,f52]) ).
fof(f6396,definition,
( sQ53_spl
<=> product(g1,b,c,b) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f6397,plain,
( ~ sQ53_spl
| product(g1,b,c,b) ),
inference(component_clause,[status(thm)],[f6396]) ).
fof(f6399,plain,
( ~ sQ41_spl
| sQ53_spl
| ~ sQ29_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6394,f1654,f1376,f6396,f5841]) ).
fof(f6406,plain,
( ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ15_spl
| ~ sQ11_spl
| product(g1,c,a,a) ),
inference(forward_demodulation,[status(thm)],[f234,f6368]) ).
fof(f6407,plain,
( ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ11_spl
| c = a ),
inference(resolution,[status(thm)],[f6406,f501]) ).
fof(f6418,plain,
( ~ sQ15_spl
| ~ sQ7_spl
| ~ sQ4_spl
| ~ sQ11_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6407,f197,f233,f210,f220,f248]) ).
fof(f6430,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ product(g2,an_isomorphism(c),an_isomorphism(c),g) ),
inference(forward_demodulation,[status(thm)],[f234,f5752]) ).
fof(f6431,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ product(g2,h,an_isomorphism(c),g) ),
inference(forward_demodulation,[status(thm)],[f88,f6430]) ).
fof(f6432,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ product(g2,h,h,g) ),
inference(forward_demodulation,[status(thm)],[f88,f6431]) ).
fof(f6433,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6432,f85]) ).
fof(f6434,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f6433]) ).
fof(f6457,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ11_spl
| c = d3 ),
inference(forward_demodulation,[status(thm)],[f234,f2716]) ).
fof(f6458,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ4_spl
| c = b ),
inference(forward_demodulation,[status(thm)],[f211,f6457]) ).
fof(f6459,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ4_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6458,f202]) ).
fof(f6460,plain,
( ~ sQ15_spl
| ~ sQ6_spl
| ~ sQ11_spl
| ~ sQ4_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f6459]) ).
fof(f6462,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ8_spl
| ~ product(g2,g,h,f) ),
inference(forward_demodulation,[status(thm)],[f88,f4657]) ).
fof(f6463,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6462,f83]) ).
fof(f6464,plain,
( ~ sQ10_spl
| ~ sQ3_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f6463]) ).
fof(f6467,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ product(g2,h,an_isomorphism(d2),f) ),
inference(forward_demodulation,[status(thm)],[f88,f4754]) ).
fof(f6503,plain,
( sQ4_spl
| ~ sQ3_spl
| a != b ),
inference(backward_demodulation,[status(thm)],[f208,f212]) ).
fof(f6531,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| product(g1,c,d2,a) ),
inference(forward_demodulation,[status(thm)],[f234,f3273]) ).
fof(f6532,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ8_spl
| product(g1,c,c,a) ),
inference(forward_demodulation,[status(thm)],[f224,f6531]) ).
fof(f6633,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ8_spl
| b = a ),
inference(resolution,[status(thm)],[f564,f6532]) ).
fof(f6635,plain,
( ~ group_member(c,g1)
| ~ group_member(c,g1)
| b = multiply(g1,c,c) ),
inference(resolution,[status(thm)],[f564,f52]) ).
fof(f6636,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f6633,f237,f223,f233,f207]) ).
fof(f6637,definition,
( sQ54_spl
<=> b = multiply(g1,c,c) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f6638,plain,
( ~ sQ54_spl
| b = multiply(g1,c,c) ),
inference(component_clause,[status(thm)],[f6637]) ).
fof(f6640,plain,
( ~ sQ29_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f6635,f6637,f1376]) ).
fof(f6758,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ7_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f221,f3251]) ).
fof(f6772,plain,
( ~ sQ54_spl
| product(g1,c,c,b)
| ~ group_member(c,g1)
| ~ group_member(c,g1) ),
inference(paramodulation,[status(thm)],[f6638,f52]) ).
fof(f6774,definition,
( sQ55_spl
<=> product(g1,c,c,b) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f6777,plain,
( ~ sQ54_spl
| sQ55_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6772,f1376,f6774,f6637]) ).
fof(f6850,definition,
! [X0] :
( sQ56_spl
<=> ( product(g2,f,multiply(g2,f,X0),multiply(g2,f,X0))
| ~ group_member(X0,g2) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f6854,definition,
! [X0] :
( sQ57_spl
<=> ( product(g1,a,multiply(g1,a,X0),multiply(g1,a,X0))
| ~ group_member(X0,g1) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f6865,plain,
( ~ group_member(b,g1)
| ~ group_member(c,g1)
| a = multiply(g1,c,b) ),
inference(resolution,[status(thm)],[f571,f52]) ).
fof(f6866,definition,
( sQ58_spl
<=> a = multiply(g1,c,b) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f6867,plain,
( ~ sQ58_spl
| a = multiply(g1,c,b) ),
inference(component_clause,[status(thm)],[f6866]) ).
fof(f6869,plain,
( ~ sQ30_spl
| ~ sQ29_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f6865,f6866,f1376,f1654]) ).
fof(f6889,plain,
( ~ sQ58_spl
| product(g1,c,b,a)
| ~ group_member(b,g1)
| ~ group_member(c,g1) ),
inference(paramodulation,[status(thm)],[f6867,f52]) ).
fof(f6891,definition,
( sQ59_spl
<=> product(g1,c,b,a) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f6894,plain,
( ~ sQ58_spl
| sQ59_spl
| ~ sQ30_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f6889,f1376,f1654,f6891,f6866]) ).
fof(f6906,plain,
( ~ group_member(a,g1)
| ~ group_member(a,g1)
| product(g1,multiply(g1,a,a),a,a) ),
inference(resolution,[status(thm)],[f170,f52]) ).
fof(f6907,definition,
( sQ60_spl
<=> product(g1,multiply(g1,a,a),a,a) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f6910,plain,
( ~ sQ27_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f6906,f6907,f783]) ).
fof(f6917,plain,
! [X0,X1] :
( ~ group_member(X0,g1)
| ~ group_member(a,g1)
| product(g1,multiply(g1,a,X0),X1,a)
| ~ product(g1,X0,X1,a) ),
inference(resolution,[status(thm)],[f171,f52]) ).
fof(f6920,definition,
! [X0,X1] :
( sQ61_spl
<=> ( ~ group_member(X0,g1)
| product(g1,multiply(g1,a,X0),X1,a)
| ~ product(g1,X0,X1,a) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f6923,plain,
( ~ sQ27_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f6917,f6920,f783]) ).
fof(f6924,plain,
( ~ sQ53_spl
| a = b ),
inference(resolution,[status(thm)],[f754,f6397]) ).
fof(f6926,plain,
( ~ group_member(c,g1)
| ~ group_member(b,g1)
| a = multiply(g1,b,c) ),
inference(resolution,[status(thm)],[f754,f52]) ).
fof(f6927,plain,
( ~ sQ53_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f6924,f237,f6396]) ).
fof(f6928,definition,
( sQ62_spl
<=> a = multiply(g1,b,c) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f6929,plain,
( ~ sQ62_spl
| a = multiply(g1,b,c) ),
inference(component_clause,[status(thm)],[f6928]) ).
fof(f6931,plain,
( ~ sQ29_spl
| ~ sQ30_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f6926,f6928,f1654,f1376]) ).
fof(f6933,plain,
( ~ sQ62_spl
| product(g1,b,c,a)
| ~ group_member(c,g1)
| ~ group_member(b,g1) ),
inference(paramodulation,[status(thm)],[f6929,f52]) ).
fof(f6935,definition,
( sQ63_spl
<=> product(g1,b,c,a) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f6938,plain,
( ~ sQ62_spl
| sQ63_spl
| ~ sQ29_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f6933,f1654,f1376,f6935,f6928]) ).
fof(f6943,plain,
! [X0,X1] :
( ~ group_member(a,g1)
| ~ group_member(X0,g1)
| product(g1,X1,a,multiply(g1,X0,a))
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f173,f52]) ).
fof(f6947,definition,
! [X0,X1] :
( sQ64_spl
<=> ( ~ group_member(X0,g1)
| product(g1,X1,a,multiply(g1,X0,a))
| ~ product(g1,X0,a,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f6950,plain,
( ~ sQ27_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f6943,f6947,f783]) ).
fof(f6955,plain,
! [X0,X1] :
( ~ group_member(a,g1)
| ~ group_member(X1,g1)
| product(g1,X0,multiply(g1,X1,a),a)
| ~ product(g1,X0,X1,a) ),
inference(resolution,[status(thm)],[f175,f52]) ).
fof(f6957,definition,
! [X0,X1] :
( sQ65_spl
<=> ( ~ group_member(X1,g1)
| product(g1,X0,multiply(g1,X1,a),a)
| ~ product(g1,X0,X1,a) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f6960,plain,
( ~ sQ27_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f6955,f6957,f783]) ).
fof(f6965,plain,
! [X0,X1] :
( ~ group_member(a,g1)
| ~ group_member(X1,g1)
| product(g1,X0,a,multiply(g1,X1,a))
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f177,f52]) ).
fof(f6967,definition,
! [X0,X1] :
( sQ66_spl
<=> ( ~ group_member(X1,g1)
| product(g1,X0,a,multiply(g1,X1,a))
| ~ product(g1,X0,a,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f6970,plain,
( ~ sQ27_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f6965,f6967,f783]) ).
fof(f6972,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ7_spl
| c = a ),
inference(resolution,[status(thm)],[f761,f6758]) ).
fof(f6974,plain,
( ~ group_member(b,g1)
| ~ group_member(b,g1)
| c = multiply(g1,b,b) ),
inference(resolution,[status(thm)],[f761,f52]) ).
fof(f6975,plain,
( ~ sQ3_spl
| ~ sQ10_spl
| ~ sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f6972,f197,f220,f230,f207]) ).
fof(f6976,definition,
( sQ67_spl
<=> c = multiply(g1,b,b) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f6977,plain,
( ~ sQ67_spl
| c = multiply(g1,b,b) ),
inference(component_clause,[status(thm)],[f6976]) ).
fof(f6979,plain,
( ~ sQ30_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f6974,f6976,f1654]) ).
fof(f7038,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ product(g2,h,an_isomorphism(b),f) ),
inference(forward_demodulation,[status(thm)],[f221,f6467]) ).
fof(f7039,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ product(g2,h,g,f) ),
inference(forward_demodulation,[status(thm)],[f87,f7038]) ).
fof(f7040,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7039,f84]) ).
fof(f7041,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f7040]) ).
fof(f7085,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| product(g1,c,d2,c) ),
inference(forward_demodulation,[status(thm)],[f234,f5395]) ).
fof(f7086,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ8_spl
| product(g1,c,c,c) ),
inference(forward_demodulation,[status(thm)],[f224,f7085]) ).
fof(f7087,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ8_spl
| b = c ),
inference(resolution,[status(thm)],[f7086,f564]) ).
fof(f7099,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f7087,f200,f223,f233,f213]) ).
fof(f7234,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ7_spl
| product(g1,c,b,c) ),
inference(forward_demodulation,[status(thm)],[f221,f5229]) ).
fof(f7235,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ7_spl
| a = c ),
inference(resolution,[status(thm)],[f7234,f571]) ).
fof(f7243,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ7_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7235,f197,f220,f233,f213]) ).
fof(f7295,plain,
( ~ sQ10_spl
| product(g1,b,d2,d3) ),
inference(forward_demodulation,[status(thm)],[f231,f92]) ).
fof(f7296,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| product(g1,b,c,d3) ),
inference(forward_demodulation,[status(thm)],[f224,f7295]) ).
fof(f7297,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl
| product(g1,b,c,c) ),
inference(forward_demodulation,[status(thm)],[f214,f7296]) ).
fof(f7298,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl
| a = c ),
inference(resolution,[status(thm)],[f7297,f754]) ).
fof(f7310,plain,
( ~ sQ10_spl
| ~ sQ8_spl
| ~ sQ5_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7298,f197,f213,f223,f230]) ).
fof(f7321,plain,
( sQ7_spl
| ~ sQ6_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f3366,f237,f217,f220]) ).
fof(f7328,plain,
( sQ4_spl
| ~ sQ3_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f6503,f237,f207,f210]) ).
fof(f7385,plain,
! [X0] :
( product(g1,a,multiply(g1,c,X0),multiply(g1,c,X0))
| ~ group_member(X0,g1)
| ~ group_member(c,g1) ),
inference(resolution,[status(thm)],[f71,f140]) ).
fof(f7396,definition,
! [X0] :
( sQ70_spl
<=> ( product(g1,a,multiply(g1,c,X0),multiply(g1,c,X0))
| ~ group_member(X0,g1) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f7399,plain,
( sQ70_spl
| ~ sQ29_spl ),
inference(split_clause,[status(thm)],[f7385,f1376,f7396]) ).
fof(f7401,plain,
! [X0] :
( product(g1,a,multiply(g1,b,X0),multiply(g1,b,X0))
| ~ group_member(X0,g1)
| ~ group_member(b,g1) ),
inference(resolution,[status(thm)],[f69,f140]) ).
fof(f7412,definition,
! [X0] :
( sQ71_spl
<=> ( product(g1,a,multiply(g1,b,X0),multiply(g1,b,X0))
| ~ group_member(X0,g1) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f7415,plain,
( sQ71_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f7401,f1654,f7412]) ).
fof(f7447,plain,
! [X0] :
( product(g1,a,multiply(g1,a,X0),multiply(g1,a,X0))
| ~ group_member(X0,g1)
| ~ group_member(a,g1) ),
inference(resolution,[status(thm)],[f68,f140]) ).
fof(f7458,plain,
( sQ57_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f7447,f783,f6854]) ).
fof(f7459,plain,
! [X0] :
( product(g2,f,multiply(g2,h,X0),multiply(g2,h,X0))
| ~ group_member(X0,g2)
| ~ group_member(h,g2) ),
inference(resolution,[status(thm)],[f80,f140]) ).
fof(f7470,definition,
! [X0] :
( sQ72_spl
<=> ( product(g2,f,multiply(g2,h,X0),multiply(g2,h,X0))
| ~ group_member(X0,g2) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f7473,plain,
( sQ72_spl
| ~ sQ42_spl ),
inference(split_clause,[status(thm)],[f7459,f6013,f7470]) ).
fof(f7479,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ19_spl
| ~ product(g2,f,g,g) ),
inference(backward_demodulation,[status(thm)],[f3663,f2094]) ).
fof(f7502,plain,
! [X0] :
( product(g2,f,multiply(g2,g,X0),multiply(g2,g,X0))
| ~ group_member(X0,g2)
| ~ group_member(g,g2) ),
inference(resolution,[status(thm)],[f78,f140]) ).
fof(f7513,definition,
! [X0] :
( sQ73_spl
<=> ( product(g2,f,multiply(g2,g,X0),multiply(g2,g,X0))
| ~ group_member(X0,g2) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f7516,plain,
( sQ73_spl
| ~ sQ28_spl ),
inference(split_clause,[status(thm)],[f7502,f1205,f7513]) ).
fof(f7517,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7479,f78]) ).
fof(f7518,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ19_spl ),
inference(contradiction_clause,[status(thm)],[f7517]) ).
fof(f7523,plain,
! [X0] :
( product(g2,f,multiply(g2,f,X0),multiply(g2,f,X0))
| ~ group_member(X0,g2)
| ~ group_member(f,g2) ),
inference(resolution,[status(thm)],[f77,f140]) ).
fof(f7534,plain,
( sQ56_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f7523,f1661,f6850]) ).
fof(f7574,plain,
( ~ sQ67_spl
| product(g1,b,b,c)
| ~ group_member(b,g1)
| ~ group_member(b,g1) ),
inference(paramodulation,[status(thm)],[f6977,f52]) ).
fof(f7576,definition,
( sQ74_spl
<=> product(g1,b,b,c) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f7579,plain,
( ~ sQ67_spl
| sQ74_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f7574,f1654,f7576,f6976]) ).
fof(f7627,plain,
( ~ sQ17_spl
| a = c ),
inference(resolution,[status(thm)],[f1216,f71]) ).
fof(f7628,plain,
( ~ sQ17_spl
| c = b ),
inference(resolution,[status(thm)],[f1216,f76]) ).
fof(f7633,plain,
( ~ sQ17_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f7627,f197,f254]) ).
fof(f7634,plain,
( ~ sQ17_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f7628,f200,f254]) ).
fof(f7641,plain,
$false,
inference(sat_refutation,[status(thm)],[f206,f216,f226,f236,f243,f247,f257,f273,f280,f284,f294,f427,f446,f540,f554,f575,f693,f694,f826,f864,f928,f934,f974,f975,f979,f1048,f1049,f1050,f1069,f1100,f1256,f1444,f1503,f1550,f1718,f1723,f1725,f1758,f1815,f2030,f2131,f2160,f2161,f2270,f2586,f2592,f2594,f2634,f2665,f2755,f2797,f2958,f2963,f3092,f3154,f3237,f3272,f3307,f3364,f3432,f3433,f3854,f3913,f3959,f4218,f4230,f4232,f4401,f4423,f4446,f4624,f4663,f4764,f4782,f4786,f4890,f4972,f4990,f5075,f5076,f5354,f5442,f5503,f5530,f5577,f5665,f5746,f5840,f5844,f6020,f6022,f6045,f6052,f6054,f6061,f6118,f6125,f6175,f6182,f6189,f6245,f6270,f6399,f6418,f6434,f6460,f6464,f6636,f6640,f6777,f6869,f6894,f6910,f6923,f6927,f6931,f6938,f6950,f6960,f6970,f6975,f6979,f7041,f7099,f7243,f7310,f7321,f7328,f7399,f7415,f7458,f7473,f7516,f7518,f7534,f7579,f7633,f7634]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP026-1 : TPTP v9.3.1. Bugfixed v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.33 % Computer : n017.cluster.edu
% 0.07/0.33 % Model : x86_64 x86_64
% 0.07/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.33 % Memory : 8046.5625MB
% 0.07/0.33 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Sun Sep 20 19:49:27 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.07/0.35 % Drodi V4.1.1
% 12.83/2.05 % Refutation found
% 12.83/2.05 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 12.83/2.05 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 12.83/2.10 % Elapsed time: 1.743084 seconds
% 12.83/2.10 % CPU time: 13.389819 seconds
% 12.83/2.10 % Total memory used: 199.107 MB
% 12.83/2.10 % Net memory used: 187.839 MB
%------------------------------------------------------------------------------