%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP026-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 12:35:29 PM UTC 2026
% Result : Satisfiable 4.90s 1.04s
% Output : Saturation 0.47s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% 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(f4,axiom,
! [X,Xg] :
( group_member(inverse(Xg,X),Xg)
| ~ group_member(X,Xg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Xg,X] : product(Xg,inverse(Xg,X),X,identity_for(Xg)),
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(f8,axiom,
! [X,Xg,Y] :
( group_member(multiply(Xg,X,Y),Xg)
| ~ 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,axiom,
! [Xg,X,Z,Y,W] :
( W = Z
| ~ product(Xg,X,W,Y)
| ~ product(Xg,X,Z,Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Xg,Z,Y,X,W] :
( W = Z
| ~ product(Xg,W,Y,X)
| ~ product(Xg,Z,Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
g1 != g2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
group_member(a,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
group_member(b,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
group_member(c,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
a != b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
c != a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
b != c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
group_member(f,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
group_member(g,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
group_member(h,g2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
f != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
h != f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
g != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
! [X] :
( X = c
| X = b
| X = a
| ~ group_member(X,g1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
! [X] :
( X = h
| X = g
| X = f
| ~ group_member(X,g2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
identity_for(g1) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
identity_for(g2) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
! [X] : product(g1,a,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
! [X] : product(g1,X,a,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
! [X] : product(g2,f,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
! [X] : product(g2,X,f,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f35,hypothesis,
isomorphism1(a) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,hypothesis,
isomorphism1(b) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,hypothesis,
isomorphism1(c) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,hypothesis,
isomorphism2(a) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,hypothesis,
isomorphism2(b) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,hypothesis,
isomorphism2(c) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,hypothesis,
isomorphism3(a) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,hypothesis,
isomorphism3(b) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,hypothesis,
isomorphism3(c) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,hypothesis,
isomorphism4(a) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,hypothesis,
isomorphism4(b) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,hypothesis,
isomorphism4(c) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,hypothesis,
isomorphism5(a) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,hypothesis,
isomorphism5(b) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,hypothesis,
isomorphism5(c) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,hypothesis,
isomorphism6(a) = h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,hypothesis,
isomorphism6(b) = f,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,hypothesis,
isomorphism6(c) = g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,negated_conjecture,
group_member(d1,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,negated_conjecture,
group_member(d2,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,negated_conjecture,
group_member(d3,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,negated_conjecture,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,negated_conjecture,
( ~ product(g2,isomorphism6(d1),isomorphism6(d2),isomorphism6(d3))
| ~ product(g2,isomorphism5(d1),isomorphism5(d2),isomorphism5(d3))
| ~ product(g2,isomorphism4(d1),isomorphism4(d2),isomorphism4(d3))
| ~ product(g2,isomorphism3(d1),isomorphism3(d2),isomorphism3(d3))
| ~ product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3))
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,plain,
! [X0] : group_member(identity_for(X0),X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f59,plain,
! [X0,X1] : product(X0,identity_for(X0),X1,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f60,plain,
! [X0,X1] : product(X0,X1,identity_for(X0),X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f61,plain,
! [X0,X1] :
( group_member(inverse(X1,X0),X1)
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f62,plain,
! [X0,X1] : product(X0,inverse(X0,X1),X1,identity_for(X0)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f63,plain,
! [X0,X1] : product(X0,X1,inverse(X0,X1),identity_for(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f64,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(f65,plain,
! [X0,X1,X2] :
( group_member(multiply(X1,X0,X2),X1)
| ~ group_member(X2,X1)
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f66,plain,
! [Z,W] :
( W = Z
| ! [Xg,X,Y] :
( ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f67,plain,
! [X0,X1,X2,X3,X4] :
( X4 = X3
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f68,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(f69,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)],[f68]) ).
fof(f70,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(f71,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)],[f70]) ).
fof(f72,plain,
! [Z,W] :
( W = Z
| ! [Xg,X,Y] :
( ~ product(Xg,X,W,Y)
| ~ product(Xg,X,Z,Y) ) ),
inference(miniscoping,[status(thm)],[f12]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( X4 = X2
| ~ product(X0,X1,X4,X3)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f74,plain,
! [Z,W] :
( W = Z
| ! [Xg,Y,X] :
( ~ product(Xg,W,Y,X)
| ~ product(Xg,Z,Y,X) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f75,plain,
! [X0,X1,X2,X3,X4] :
( X4 = X1
| ~ product(X0,X4,X2,X3)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f76,plain,
g1 != g2,
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f77,plain,
group_member(a,g1),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f78,plain,
group_member(b,g1),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f79,plain,
group_member(c,g1),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f80,plain,
a != b,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f81,plain,
c != a,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f82,plain,
b != c,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f83,plain,
group_member(f,g2),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f84,plain,
group_member(g,g2),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f85,plain,
group_member(h,g2),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f86,plain,
f != g,
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f87,plain,
h != f,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f88,plain,
g != h,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f89,plain,
! [X0] :
( X0 = c
| X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f90,plain,
! [X0] :
( X0 = h
| X0 = g
| X0 = f
| ~ group_member(X0,g2) ),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f91,plain,
identity_for(g1) = a,
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f92,plain,
identity_for(g2) = f,
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f93,plain,
! [X0] : product(g1,a,X0,X0),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f94,plain,
! [X0] : product(g1,X0,a,X0),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f95,plain,
! [X0] : product(g2,f,X0,X0),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f96,plain,
! [X0] : product(g2,X0,f,X0),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f97,plain,
isomorphism1(a) = f,
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f98,plain,
isomorphism1(b) = g,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f99,plain,
isomorphism1(c) = h,
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f100,plain,
isomorphism2(a) = f,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f101,plain,
isomorphism2(b) = h,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f102,plain,
isomorphism2(c) = g,
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f103,plain,
isomorphism3(a) = g,
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f104,plain,
isomorphism3(b) = f,
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f105,plain,
isomorphism3(c) = h,
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f106,plain,
isomorphism4(a) = g,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f107,plain,
isomorphism4(b) = h,
inference(cnf_transformation,[status(thm)],[f45]) ).
fof(f108,plain,
isomorphism4(c) = f,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f109,plain,
isomorphism5(a) = h,
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f110,plain,
isomorphism5(b) = g,
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f111,plain,
isomorphism5(c) = f,
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f112,plain,
isomorphism6(a) = h,
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f113,plain,
isomorphism6(b) = f,
inference(cnf_transformation,[status(thm)],[f51]) ).
fof(f114,plain,
isomorphism6(c) = g,
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f115,plain,
group_member(d1,g1),
inference(cnf_transformation,[status(thm)],[f53]) ).
fof(f116,plain,
group_member(d2,g1),
inference(cnf_transformation,[status(thm)],[f54]) ).
fof(f117,plain,
group_member(d3,g1),
inference(cnf_transformation,[status(thm)],[f55]) ).
fof(f118,plain,
product(g1,d1,d2,d3),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f119,plain,
( ~ product(g2,isomorphism6(d1),isomorphism6(d2),isomorphism6(d3))
| ~ product(g2,isomorphism5(d1),isomorphism5(d2),isomorphism5(d3))
| ~ product(g2,isomorphism4(d1),isomorphism4(d2),isomorphism4(d3))
| ~ product(g2,isomorphism3(d1),isomorphism3(d2),isomorphism3(d3))
| ~ product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3))
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f120,definition,
( sQ0_spl
<=> product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f121,plain,
( ~ sQ0_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f122,plain,
( sQ0_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
( sQ1_spl
<=> product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f124,plain,
( ~ sQ1_spl
| product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3)) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f125,plain,
( sQ1_spl
| ~ product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3)) ),
inference(component_clause,[status(thm)],[f123]) ).
fof(f126,definition,
( sQ2_spl
<=> product(g2,isomorphism3(d1),isomorphism3(d2),isomorphism3(d3)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ2_spl
| product(g2,isomorphism3(d1),isomorphism3(d2),isomorphism3(d3)) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f128,plain,
( sQ2_spl
| ~ product(g2,isomorphism3(d1),isomorphism3(d2),isomorphism3(d3)) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,definition,
( sQ3_spl
<=> product(g2,isomorphism4(d1),isomorphism4(d2),isomorphism4(d3)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f131,plain,
( sQ3_spl
| ~ product(g2,isomorphism4(d1),isomorphism4(d2),isomorphism4(d3)) ),
inference(component_clause,[status(thm)],[f129]) ).
fof(f132,definition,
( sQ4_spl
<=> product(g2,isomorphism5(d1),isomorphism5(d2),isomorphism5(d3)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f134,plain,
( sQ4_spl
| ~ product(g2,isomorphism5(d1),isomorphism5(d2),isomorphism5(d3)) ),
inference(component_clause,[status(thm)],[f132]) ).
fof(f135,definition,
( sQ5_spl
<=> product(g2,isomorphism6(d1),isomorphism6(d2),isomorphism6(d3)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f136,plain,
( ~ sQ5_spl
| product(g2,isomorphism6(d1),isomorphism6(d2),isomorphism6(d3)) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f137,plain,
( sQ5_spl
| ~ product(g2,isomorphism6(d1),isomorphism6(d2),isomorphism6(d3)) ),
inference(component_clause,[status(thm)],[f135]) ).
fof(f138,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl
| ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f119,f120,f123,f126,f129,f132,f135]) ).
fof(f139,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,identity_for(X0),X3,X4)
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f59,f69]) ).
fof(f140,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(resolution,[status(thm)],[f59,f67]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,X3,X2,X4)
| ~ product(X0,X3,X1,X4)
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(resolution,[status(thm)],[f60,f69]) ).
fof(f142,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,X1,identity_for(X0),X2) ),
inference(resolution,[status(thm)],[f60,f67]) ).
fof(f143,plain,
! [X0,X1,X2] :
( product(g1,d1,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f118,f69]) ).
fof(f144,plain,
! [X0] :
( X0 = d3
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f118,f67]) ).
fof(f145,plain,
! [X0,X1,X2] :
( product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f71,f118]) ).
fof(f146,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,X1,X2,X4)
| ~ product(X0,identity_for(X0),X3,X4)
| ~ product(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f71,f59]) ).
fof(f147,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,X3,X1,X4)
| ~ product(X0,X3,X2,X4)
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(resolution,[status(thm)],[f71,f60]) ).
fof(f148,plain,
! [X0] :
( X0 = d2
| ~ product(g1,d1,X0,d3) ),
inference(resolution,[status(thm)],[f73,f118]) ).
fof(f150,plain,
! [X0,X1,X2] :
( X2 = identity_for(X0)
| ~ product(X0,X1,X2,X1) ),
inference(resolution,[status(thm)],[f73,f60]) ).
fof(f151,plain,
group_member(inverse(g1,d3),g1),
inference(resolution,[status(thm)],[f61,f117]) ).
fof(f154,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f61,f116]) ).
fof(f155,plain,
group_member(inverse(g1,d1),g1),
inference(resolution,[status(thm)],[f61,f115]) ).
fof(f156,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,inverse(X0,X1),X2,identity_for(X0)) ),
inference(resolution,[status(thm)],[f62,f73]) ).
fof(f157,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,identity_for(X0),X2,X4)
| ~ product(X0,inverse(X0,X1),X3,X4)
| ~ product(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f62,f71]) ).
fof(f158,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,inverse(X0,X1),X3,X4)
| ~ product(X0,identity_for(X0),X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[f62,f69]) ).
fof(f159,plain,
! [X0,X1,X2] :
( X2 = identity_for(X0)
| ~ product(X0,inverse(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f62,f67]) ).
fof(f160,plain,
! [X0,X1,X2] :
( X2 = inverse(X0,X1)
| ~ product(X0,X1,X2,identity_for(X0)) ),
inference(resolution,[status(thm)],[f63,f73]) ).
fof(f161,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,identity_for(X0),X2,X4)
| ~ product(X0,X1,X3,X4)
| ~ product(X0,inverse(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f63,f71]) ).
fof(f162,plain,
! [X0,X1,X2,X3,X4] :
( product(X0,X1,X3,X4)
| ~ product(X0,identity_for(X0),X2,X4)
| ~ product(X0,inverse(X0,X1),X2,X3) ),
inference(resolution,[status(thm)],[f63,f69]) ).
fof(f163,plain,
! [X0,X1,X2] :
( X2 = identity_for(X0)
| ~ product(X0,X1,inverse(X0,X1),X2) ),
inference(resolution,[status(thm)],[f63,f67]) ).
fof(f164,plain,
group_member(inverse(g1,inverse(g1,d3)),g1),
inference(resolution,[status(thm)],[f151,f61]) ).
fof(f165,plain,
! [X0] :
( X0 = d1
| ~ product(g1,X0,d2,d3) ),
inference(resolution,[status(thm)],[f75,f118]) ).
fof(f166,plain,
! [X0,X1,X2] :
( X1 = inverse(X0,X2)
| ~ product(X0,X1,X2,identity_for(X0)) ),
inference(resolution,[status(thm)],[f75,f62]) ).
fof(f167,plain,
! [X0,X1,X2] :
( X1 = identity_for(X0)
| ~ product(X0,X1,X2,X2) ),
inference(resolution,[status(thm)],[f75,f59]) ).
fof(f168,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ product(X0,X1,inverse(X0,X2),identity_for(X0)) ),
inference(resolution,[status(thm)],[f75,f63]) ).
fof(f170,plain,
! [X0,X1] :
( X0 = a
| ~ product(g1,X0,X1,X1) ),
inference(resolution,[status(thm)],[f93,f75]) ).
fof(f171,plain,
! [X0,X1] :
( X0 = X1
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f93,f73]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( product(g1,X0,X1,X3)
| ~ product(g1,a,X2,X3)
| ~ product(g1,X0,X1,X2) ),
inference(resolution,[status(thm)],[f93,f71]) ).
fof(f173,plain,
! [X0,X1,X2,X3] :
( product(g1,a,X2,X3)
| ~ product(g1,X0,X1,X3)
| ~ product(g1,X0,X1,X2) ),
inference(resolution,[status(thm)],[f93,f69]) ).
fof(f175,plain,
group_member(inverse(g1,b),g1),
inference(resolution,[status(thm)],[f78,f61]) ).
fof(f176,plain,
group_member(inverse(g1,c),g1),
inference(resolution,[status(thm)],[f79,f61]) ).
fof(f178,plain,
! [X0] :
( product(g2,f,X0,multiply(g2,f,X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f64,f83]) ).
fof(f179,plain,
! [X0] :
( product(g1,c,X0,multiply(g1,c,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f64,f79]) ).
fof(f180,plain,
! [X0] :
( product(g1,b,X0,multiply(g1,b,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f64,f78]) ).
fof(f181,plain,
! [X0] :
( product(g1,inverse(g1,d3),X0,multiply(g1,inverse(g1,d3),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f64,f151]) ).
fof(f182,plain,
! [X0] :
( product(g1,d3,X0,multiply(g1,d3,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f64,f117]) ).
fof(f183,plain,
! [X0,X1] :
( product(X1,identity_for(X1),X0,multiply(X1,identity_for(X1),X0))
| ~ group_member(X0,X1) ),
inference(resolution,[status(thm)],[f64,f58]) ).
fof(f184,plain,
! [X0] :
( product(g1,a,X0,multiply(g1,a,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f64,f77]) ).
fof(f185,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f64,f116]) ).
fof(f186,plain,
! [X0] :
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f64,f115]) ).
fof(f187,plain,
! [X0] :
( group_member(multiply(g2,f,X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f65,f83]) ).
fof(f188,plain,
! [X0] :
( group_member(multiply(g1,c,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f65,f79]) ).
fof(f189,plain,
! [X0] :
( group_member(multiply(g1,b,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f65,f78]) ).
fof(f190,plain,
! [X0] :
( group_member(multiply(g1,inverse(g1,d3),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f65,f151]) ).
fof(f191,plain,
! [X0] :
( group_member(multiply(g1,d3,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f65,f117]) ).
fof(f192,plain,
! [X0,X1] :
( group_member(multiply(X1,identity_for(X1),X0),X1)
| ~ group_member(X0,X1) ),
inference(resolution,[status(thm)],[f65,f58]) ).
fof(f193,plain,
! [X0] :
( group_member(multiply(g1,a,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f65,f77]) ).
fof(f194,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f65,f116]) ).
fof(f195,plain,
! [X0] :
( group_member(multiply(g1,d1,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f65,f115]) ).
fof(f196,plain,
! [X0] :
( group_member(multiply(g2,g,X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f84,f65]) ).
fof(f197,plain,
! [X0] :
( product(g2,g,X0,multiply(g2,g,X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f84,f64]) ).
fof(f198,plain,
group_member(inverse(g2,g),g2),
inference(resolution,[status(thm)],[f84,f61]) ).
fof(f199,plain,
! [X0] :
( group_member(multiply(g1,inverse(g1,d2),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f154,f65]) ).
fof(f200,plain,
! [X0] :
( product(g1,inverse(g1,d2),X0,multiply(g1,inverse(g1,d2),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f154,f64]) ).
fof(f201,plain,
group_member(inverse(g1,inverse(g1,d2)),g1),
inference(resolution,[status(thm)],[f154,f61]) ).
fof(f202,plain,
! [X0] :
( product(g1,d1,identity_for(g1),X0)
| ~ product(g1,d3,inverse(g1,d2),X0) ),
inference(resolution,[status(thm)],[f143,f63]) ).
fof(f203,plain,
! [X0] :
( product(g1,d1,d2,X0)
| ~ product(g1,d3,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f143,f60]) ).
fof(f204,plain,
! [X0] :
( product(g1,d1,d2,X0)
| ~ product(g1,d3,a,X0) ),
inference(resolution,[status(thm)],[f94,f143]) ).
fof(f205,plain,
! [X0,X1] :
( X0 = X1
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f94,f75]) ).
fof(f206,plain,
! [X0,X1] :
( X1 = a
| ~ product(g1,X0,X1,X0) ),
inference(resolution,[status(thm)],[f94,f73]) ).
fof(f207,plain,
! [X0,X1,X2,X3] :
( product(g1,X2,X0,X3)
| ~ product(g1,X2,X1,X3)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f94,f71]) ).
fof(f208,plain,
! [X0,X1,X2,X3] :
( product(g1,X2,X1,X3)
| ~ product(g1,X2,X0,X3)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f94,f69]) ).
fof(f210,plain,
! [X0] :
( group_member(multiply(g2,h,X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f85,f65]) ).
fof(f211,plain,
! [X0] :
( product(g2,h,X0,multiply(g2,h,X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f85,f64]) ).
fof(f212,plain,
group_member(inverse(g2,h),g2),
inference(resolution,[status(thm)],[f85,f61]) ).
fof(f213,plain,
! [X0] : product(g1,X0,inverse(g1,X0),a),
inference(paramodulation,[status(thm)],[f91,f63]) ).
fof(f214,plain,
! [X0] : product(g1,inverse(g1,X0),X0,a),
inference(paramodulation,[status(thm)],[f91,f62]) ).
fof(f218,plain,
! [X0] : product(g2,X0,inverse(g2,X0),f),
inference(paramodulation,[status(thm)],[f92,f63]) ).
fof(f219,plain,
! [X0] : product(g2,inverse(g2,X0),X0,f),
inference(paramodulation,[status(thm)],[f92,f62]) ).
fof(f223,plain,
( c = c
| c = b
| c = a ),
inference(resolution,[status(thm)],[f89,f79]) ).
fof(f224,plain,
( b = c
| b = b
| b = a ),
inference(resolution,[status(thm)],[f89,f78]) ).
fof(f225,plain,
( inverse(g1,d2) = c
| inverse(g1,d2) = b
| inverse(g1,d2) = a ),
inference(resolution,[status(thm)],[f89,f154]) ).
fof(f226,plain,
( inverse(g1,d3) = c
| inverse(g1,d3) = b
| inverse(g1,d3) = a ),
inference(resolution,[status(thm)],[f89,f151]) ).
fof(f227,plain,
( d3 = c
| d3 = b
| d3 = a ),
inference(resolution,[status(thm)],[f89,f117]) ).
fof(f228,plain,
( identity_for(g1) = c
| identity_for(g1) = b
| identity_for(g1) = a ),
inference(resolution,[status(thm)],[f89,f58]) ).
fof(f229,plain,
( a = c
| a = b
| a = a ),
inference(resolution,[status(thm)],[f89,f77]) ).
fof(f230,plain,
( d2 = c
| d2 = b
| d2 = a ),
inference(resolution,[status(thm)],[f89,f116]) ).
fof(f231,plain,
( d1 = c
| d1 = b
| d1 = a ),
inference(resolution,[status(thm)],[f89,f115]) ).
fof(f232,definition,
( sQ6_spl
<=> c = a ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f233,plain,
( ~ sQ6_spl
| c = a ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,definition,
( sQ7_spl
<=> c = b ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f236,plain,
( ~ sQ7_spl
| c = b ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,definition,
( sQ8_spl
<=> c = c ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f241,plain,
( sQ8_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f223,f232,f235,f238]) ).
fof(f242,definition,
( sQ9_spl
<=> b = a ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f243,plain,
( ~ sQ9_spl
| b = a ),
inference(component_clause,[status(thm)],[f242]) ).
fof(f245,definition,
( sQ10_spl
<=> b = b ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f248,plain,
( sQ7_spl
| sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f224,f242,f245,f235]) ).
fof(f249,definition,
( sQ11_spl
<=> inverse(g1,d2) = a ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f250,plain,
( ~ sQ11_spl
| inverse(g1,d2) = a ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f251,plain,
( sQ11_spl
| inverse(g1,d2) != a ),
inference(component_clause,[status(thm)],[f249]) ).
fof(f252,definition,
( sQ12_spl
<=> inverse(g1,d2) = b ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f253,plain,
( ~ sQ12_spl
| inverse(g1,d2) = b ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f254,plain,
( sQ12_spl
| inverse(g1,d2) != b ),
inference(component_clause,[status(thm)],[f252]) ).
fof(f255,definition,
( sQ13_spl
<=> inverse(g1,d2) = c ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f256,plain,
( ~ sQ13_spl
| inverse(g1,d2) = c ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f257,plain,
( sQ13_spl
| inverse(g1,d2) != c ),
inference(component_clause,[status(thm)],[f255]) ).
fof(f258,plain,
( sQ13_spl
| sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f225,f249,f252,f255]) ).
fof(f259,definition,
( sQ14_spl
<=> inverse(g1,d3) = a ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f260,plain,
( ~ sQ14_spl
| inverse(g1,d3) = a ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f261,plain,
( sQ14_spl
| inverse(g1,d3) != a ),
inference(component_clause,[status(thm)],[f259]) ).
fof(f262,definition,
( sQ15_spl
<=> inverse(g1,d3) = b ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f263,plain,
( ~ sQ15_spl
| inverse(g1,d3) = b ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f264,plain,
( sQ15_spl
| inverse(g1,d3) != b ),
inference(component_clause,[status(thm)],[f262]) ).
fof(f265,definition,
( sQ16_spl
<=> inverse(g1,d3) = c ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f266,plain,
( ~ sQ16_spl
| inverse(g1,d3) = c ),
inference(component_clause,[status(thm)],[f265]) ).
fof(f268,plain,
( sQ16_spl
| sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f226,f259,f262,f265]) ).
fof(f269,definition,
( sQ17_spl
<=> d3 = a ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f270,plain,
( ~ sQ17_spl
| d3 = a ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f271,plain,
( sQ17_spl
| d3 != a ),
inference(component_clause,[status(thm)],[f269]) ).
fof(f272,definition,
( sQ18_spl
<=> d3 = b ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f273,plain,
( ~ sQ18_spl
| d3 = b ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f274,plain,
( sQ18_spl
| d3 != b ),
inference(component_clause,[status(thm)],[f272]) ).
fof(f275,definition,
( sQ19_spl
<=> d3 = c ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f276,plain,
( ~ sQ19_spl
| d3 = c ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f277,plain,
( sQ19_spl
| d3 != c ),
inference(component_clause,[status(thm)],[f275]) ).
fof(f278,plain,
( sQ19_spl
| sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f227,f269,f272,f275]) ).
fof(f279,definition,
( sQ20_spl
<=> identity_for(g1) = a ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f282,definition,
( sQ21_spl
<=> identity_for(g1) = b ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f283,plain,
( ~ sQ21_spl
| identity_for(g1) = b ),
inference(component_clause,[status(thm)],[f282]) ).
fof(f285,definition,
( sQ22_spl
<=> identity_for(g1) = c ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f286,plain,
( ~ sQ22_spl
| identity_for(g1) = c ),
inference(component_clause,[status(thm)],[f285]) ).
fof(f288,plain,
( sQ22_spl
| sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f228,f279,f282,f285]) ).
fof(f289,definition,
( sQ23_spl
<=> a = a ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f292,plain,
( sQ6_spl
| sQ9_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f229,f289,f242,f232]) ).
fof(f293,definition,
( sQ24_spl
<=> d2 = a ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f294,plain,
( ~ sQ24_spl
| d2 = a ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f295,plain,
( sQ24_spl
| d2 != a ),
inference(component_clause,[status(thm)],[f293]) ).
fof(f296,definition,
( sQ25_spl
<=> d2 = b ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f297,plain,
( ~ sQ25_spl
| d2 = b ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f298,plain,
( sQ25_spl
| d2 != b ),
inference(component_clause,[status(thm)],[f296]) ).
fof(f299,definition,
( sQ26_spl
<=> d2 = c ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f300,plain,
( ~ sQ26_spl
| d2 = c ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f301,plain,
( sQ26_spl
| d2 != c ),
inference(component_clause,[status(thm)],[f299]) ).
fof(f302,plain,
( sQ26_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f230,f293,f296,f299]) ).
fof(f303,definition,
( sQ27_spl
<=> d1 = a ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f304,plain,
( ~ sQ27_spl
| d1 = a ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f305,plain,
( sQ27_spl
| d1 != a ),
inference(component_clause,[status(thm)],[f303]) ).
fof(f306,definition,
( sQ28_spl
<=> d1 = b ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f307,plain,
( ~ sQ28_spl
| d1 = b ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f308,plain,
( sQ28_spl
| d1 != b ),
inference(component_clause,[status(thm)],[f306]) ).
fof(f309,definition,
( sQ29_spl
<=> d1 = c ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f310,plain,
( ~ sQ29_spl
| d1 = c ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f311,plain,
( sQ29_spl
| d1 != c ),
inference(component_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( sQ29_spl
| sQ28_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f231,f303,f306,f309]) ).
fof(f313,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f233,f81]) ).
fof(f314,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f313]) ).
fof(f315,plain,
( ~ sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f243,f80]) ).
fof(f316,plain,
~ sQ9_spl,
inference(contradiction_clause,[status(thm)],[f315]) ).
fof(f317,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f82]) ).
fof(f318,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f317]) ).
fof(f319,plain,
( ~ sQ22_spl
| a = c ),
inference(forward_demodulation,[status(thm)],[f91,f286]) ).
fof(f320,plain,
( ~ sQ22_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f319,f81]) ).
fof(f321,plain,
~ sQ22_spl,
inference(contradiction_clause,[status(thm)],[f320]) ).
fof(f322,plain,
( ~ sQ21_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f91,f283]) ).
fof(f323,plain,
( ~ sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f80]) ).
fof(f324,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f327,plain,
( h = h
| h = g
| h = f ),
inference(resolution,[status(thm)],[f90,f85]) ).
fof(f328,plain,
( g = h
| g = g
| g = f ),
inference(resolution,[status(thm)],[f90,f84]) ).
fof(f329,plain,
( f = h
| f = g
| f = f ),
inference(resolution,[status(thm)],[f90,f83]) ).
fof(f330,plain,
( identity_for(g2) = h
| identity_for(g2) = g
| identity_for(g2) = f ),
inference(resolution,[status(thm)],[f90,f58]) ).
fof(f331,definition,
( sQ30_spl
<=> h = f ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f332,plain,
( ~ sQ30_spl
| h = f ),
inference(component_clause,[status(thm)],[f331]) ).
fof(f334,definition,
( sQ31_spl
<=> h = g ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f335,plain,
( ~ sQ31_spl
| h = g ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f337,definition,
( sQ32_spl
<=> h = h ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f340,plain,
( sQ32_spl
| sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f327,f331,f334,f337]) ).
fof(f341,definition,
( sQ33_spl
<=> g = f ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f342,plain,
( ~ sQ33_spl
| g = f ),
inference(component_clause,[status(thm)],[f341]) ).
fof(f344,definition,
( sQ34_spl
<=> g = g ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f347,plain,
( sQ31_spl
| sQ34_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f328,f341,f344,f334]) ).
fof(f348,definition,
( sQ35_spl
<=> f = f ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f351,plain,
( sQ30_spl
| sQ33_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f329,f348,f341,f331]) ).
fof(f352,definition,
( sQ36_spl
<=> identity_for(g2) = f ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f355,definition,
( sQ37_spl
<=> identity_for(g2) = g ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f356,plain,
( ~ sQ37_spl
| identity_for(g2) = g ),
inference(component_clause,[status(thm)],[f355]) ).
fof(f358,definition,
( sQ38_spl
<=> identity_for(g2) = h ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f359,plain,
( ~ sQ38_spl
| identity_for(g2) = h ),
inference(component_clause,[status(thm)],[f358]) ).
fof(f361,plain,
( sQ38_spl
| sQ37_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f330,f352,f355,f358]) ).
fof(f362,plain,
( ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f332,f87]) ).
fof(f363,plain,
~ sQ30_spl,
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f364,plain,
( ~ sQ33_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f342,f86]) ).
fof(f365,plain,
~ sQ33_spl,
inference(contradiction_clause,[status(thm)],[f364]) ).
fof(f366,plain,
( ~ sQ31_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f88]) ).
fof(f367,plain,
~ sQ31_spl,
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f368,plain,
( ~ sQ38_spl
| f = h ),
inference(forward_demodulation,[status(thm)],[f92,f359]) ).
fof(f369,plain,
( ~ sQ38_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f368,f87]) ).
fof(f370,plain,
~ sQ38_spl,
inference(contradiction_clause,[status(thm)],[f369]) ).
fof(f371,plain,
( ~ sQ37_spl
| f = g ),
inference(forward_demodulation,[status(thm)],[f92,f356]) ).
fof(f372,plain,
( ~ sQ37_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f371,f86]) ).
fof(f373,plain,
~ sQ37_spl,
inference(contradiction_clause,[status(thm)],[f372]) ).
fof(f376,plain,
! [X0,X1] :
( X0 = f
| ~ product(g2,X0,X1,X1) ),
inference(resolution,[status(thm)],[f95,f75]) ).
fof(f377,plain,
! [X0,X1] :
( X0 = X1
| ~ product(g2,f,X0,X1) ),
inference(resolution,[status(thm)],[f95,f73]) ).
fof(f378,plain,
! [X0,X1,X2,X3] :
( product(g2,X0,X1,X3)
| ~ product(g2,f,X2,X3)
| ~ product(g2,X0,X1,X2) ),
inference(resolution,[status(thm)],[f95,f71]) ).
fof(f379,plain,
! [X0,X1,X2,X3] :
( product(g2,f,X2,X3)
| ~ product(g2,X0,X1,X3)
| ~ product(g2,X0,X1,X2) ),
inference(resolution,[status(thm)],[f95,f69]) ).
fof(f381,plain,
! [X0,X1,X2] :
( ~ sQ29_spl
| product(g1,c,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(backward_demodulation,[status(thm)],[f310,f143]) ).
fof(f382,plain,
( sQ5_spl
| ~ sQ29_spl
| ~ product(g2,isomorphism6(c),isomorphism6(d2),isomorphism6(d3)) ),
inference(backward_demodulation,[status(thm)],[f310,f137]) ).
fof(f383,plain,
( ~ sQ29_spl
| product(g1,c,d2,d3) ),
inference(backward_demodulation,[status(thm)],[f310,f118]) ).
fof(f385,plain,
( ~ sQ29_spl
| ~ sQ28_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f307,f310]) ).
fof(f386,plain,
( ~ sQ29_spl
| ~ sQ28_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f385,f235,f306,f309]) ).
fof(f387,plain,
( ~ sQ26_spl
| group_member(inverse(g1,c),g1) ),
inference(backward_demodulation,[status(thm)],[f300,f154]) ).
fof(f389,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f297,f300]) ).
fof(f390,plain,
( ~ sQ26_spl
| ~ sQ25_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f389,f235,f296,f299]) ).
fof(f391,plain,
! [X0,X1] :
( X0 = X1
| ~ product(g2,X0,f,X1) ),
inference(resolution,[status(thm)],[f96,f75]) ).
fof(f392,plain,
! [X0,X1] :
( X1 = f
| ~ product(g2,X0,X1,X0) ),
inference(resolution,[status(thm)],[f96,f73]) ).
fof(f393,plain,
! [X0,X1,X2,X3] :
( product(g2,X2,X0,X3)
| ~ product(g2,X2,X1,X3)
| ~ product(g2,f,X0,X1) ),
inference(resolution,[status(thm)],[f96,f71]) ).
fof(f394,plain,
! [X0,X1,X2,X3] :
( product(g2,X2,X1,X3)
| ~ product(g2,X2,X0,X3)
| ~ product(g2,f,X0,X1) ),
inference(resolution,[status(thm)],[f96,f69]) ).
fof(f396,plain,
( ~ sQ19_spl
| group_member(inverse(g1,c),g1) ),
inference(backward_demodulation,[status(thm)],[f276,f151]) ).
fof(f398,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism6(a),isomorphism6(d2),isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f304,f137]) ).
fof(f399,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,isomorphism6(a),isomorphism6(a),isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f294,f398]) ).
fof(f400,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ19_spl
| ~ product(g2,isomorphism6(a),isomorphism6(a),isomorphism6(c)) ),
inference(forward_demodulation,[status(thm)],[f276,f399]) ).
fof(f401,plain,
( ~ sQ19_spl
| ~ sQ18_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f273,f276]) ).
fof(f402,plain,
( ~ sQ19_spl
| ~ sQ18_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f401,f235,f272,f275]) ).
fof(f407,plain,
( ~ sQ27_spl
| product(g1,a,d2,d3) ),
inference(forward_demodulation,[status(thm)],[f304,f118]) ).
fof(f408,plain,
( ~ sQ27_spl
| ~ sQ24_spl
| product(g1,a,a,d3) ),
inference(forward_demodulation,[status(thm)],[f294,f407]) ).
fof(f411,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,h,isomorphism6(a),isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f112,f399]) ).
fof(f412,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,h,h,isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f112,f411]) ).
fof(f413,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ17_spl
| ~ product(g2,h,h,isomorphism6(a)) ),
inference(forward_demodulation,[status(thm)],[f270,f412]) ).
fof(f414,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ17_spl
| ~ product(g2,h,h,h) ),
inference(forward_demodulation,[status(thm)],[f112,f413]) ).
fof(f417,plain,
! [X0,X1] :
( product(g2,identity_for(g2),X0,X1)
| ~ product(g2,X0,f,X1) ),
inference(resolution,[status(thm)],[f139,f96]) ).
fof(f419,plain,
! [X0,X1] :
( product(g1,identity_for(g1),X0,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f139,f94]) ).
fof(f420,plain,
! [X0,X1,X2] :
( product(X0,identity_for(X0),identity_for(X0),X2)
| ~ product(X0,inverse(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f139,f62]) ).
fof(f422,plain,
! [X0,X1,X2] :
( product(X0,identity_for(X0),identity_for(X0),X2)
| ~ product(X0,X1,inverse(X0,X1),X2) ),
inference(resolution,[status(thm)],[f139,f63]) ).
fof(f423,plain,
! [X0,X1,X2] :
( product(X0,identity_for(X0),X1,X2)
| ~ product(X0,X1,identity_for(X0),X2) ),
inference(resolution,[status(thm)],[f139,f60]) ).
fof(f424,plain,
! [X0,X1] :
( product(g2,f,X0,X1)
| ~ product(g2,X0,f,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f417]) ).
fof(f425,plain,
! [X0,X1] :
( product(g1,a,X0,X1)
| ~ product(g1,X0,a,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f419]) ).
fof(f429,plain,
! [X0] : identity_for(X0) = inverse(X0,identity_for(X0)),
inference(resolution,[status(thm)],[f140,f63]) ).
fof(f440,plain,
( ~ sQ16_spl
| ~ sQ17_spl
| inverse(g1,a) = c ),
inference(forward_demodulation,[status(thm)],[f270,f266]) ).
fof(f441,plain,
( ~ sQ16_spl
| ~ sQ17_spl
| product(g1,a,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f440,f63]) ).
fof(f442,plain,
( ~ sQ16_spl
| ~ sQ17_spl
| product(g1,c,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f440,f62]) ).
fof(f443,plain,
( ~ sQ16_spl
| ~ sQ17_spl
| product(g1,a,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f441]) ).
fof(f444,plain,
( ~ sQ16_spl
| ~ sQ17_spl
| product(g1,c,a,a) ),
inference(forward_demodulation,[status(thm)],[f91,f442]) ).
fof(f445,plain,
! [X0] :
( ~ sQ27_spl
| X0 = d3
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f304,f144]) ).
fof(f446,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| X0 = d3
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f294,f445]) ).
fof(f450,plain,
( ~ sQ16_spl
| ~ sQ17_spl
| ~ sQ15_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f451,f440]) ).
fof(f451,plain,
( ~ sQ15_spl
| ~ sQ17_spl
| inverse(g1,a) = b ),
inference(forward_demodulation,[status(thm)],[f270,f263]) ).
fof(f452,plain,
( ~ sQ15_spl
| ~ sQ17_spl
| product(g1,a,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f451,f63]) ).
fof(f453,plain,
( ~ sQ15_spl
| ~ sQ17_spl
| product(g1,b,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f451,f62]) ).
fof(f454,plain,
( ~ sQ16_spl
| ~ sQ17_spl
| ~ sQ15_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f450,f235,f262,f269,f265]) ).
fof(f455,plain,
( ~ sQ15_spl
| ~ sQ17_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f452]) ).
fof(f456,plain,
( ~ sQ15_spl
| ~ sQ17_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f91,f453]) ).
fof(f458,plain,
( ~ sQ14_spl
| ~ sQ17_spl
| inverse(g1,a) = a ),
inference(forward_demodulation,[status(thm)],[f270,f260]) ).
fof(f470,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f294,f145]) ).
fof(f471,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| ~ sQ27_spl
| product(g1,d3,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f304,f470]) ).
fof(f472,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| ~ sQ27_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f471]) ).
fof(f475,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ27_spl
| ~ sQ17_spl
| product(g1,a,inverse(g1,a),X0)
| ~ product(g1,a,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f472,f63]) ).
fof(f477,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ27_spl
| ~ sQ17_spl
| product(g1,a,inverse(g1,a),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f475]) ).
fof(f478,plain,
( ~ sQ13_spl
| ~ sQ24_spl
| inverse(g1,a) = c ),
inference(forward_demodulation,[status(thm)],[f294,f256]) ).
fof(f479,plain,
( ~ sQ13_spl
| ~ sQ24_spl
| ~ sQ14_spl
| ~ sQ17_spl
| a = c ),
inference(forward_demodulation,[status(thm)],[f458,f478]) ).
fof(f480,plain,
( ~ sQ13_spl
| ~ sQ24_spl
| ~ sQ14_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f81]) ).
fof(f481,plain,
( ~ sQ13_spl
| ~ sQ24_spl
| ~ sQ14_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f480]) ).
fof(f482,plain,
( sQ13_spl
| ~ sQ24_spl
| inverse(g1,a) != c ),
inference(forward_demodulation,[status(thm)],[f294,f257]) ).
fof(f484,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| inverse(g1,a) = b ),
inference(forward_demodulation,[status(thm)],[f294,f253]) ).
fof(f485,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| ~ sQ14_spl
| ~ sQ17_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f458,f484]) ).
fof(f486,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| ~ sQ14_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f80]) ).
fof(f487,plain,
( ~ sQ12_spl
| ~ sQ24_spl
| ~ sQ14_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f486]) ).
fof(f490,plain,
( ~ sQ11_spl
| ~ sQ24_spl
| inverse(g1,a) = a ),
inference(forward_demodulation,[status(thm)],[f294,f250]) ).
fof(f492,plain,
! [X0,X1] :
( product(g2,X0,f,X1)
| ~ product(g2,identity_for(g2),X0,X1) ),
inference(resolution,[status(thm)],[f146,f96]) ).
fof(f494,plain,
! [X0,X1] :
( product(g1,X0,a,X1)
| ~ product(g1,identity_for(g1),X0,X1) ),
inference(resolution,[status(thm)],[f146,f94]) ).
fof(f495,plain,
! [X0,X1,X2] :
( product(X0,inverse(X0,X2),X2,X1)
| ~ product(X0,identity_for(X0),identity_for(X0),X1) ),
inference(resolution,[status(thm)],[f146,f62]) ).
fof(f497,plain,
! [X0,X1,X2] :
( product(X0,X2,inverse(X0,X2),X1)
| ~ product(X0,identity_for(X0),identity_for(X0),X1) ),
inference(resolution,[status(thm)],[f146,f63]) ).
fof(f498,plain,
! [X0,X1,X2] :
( product(X0,X1,identity_for(X0),X2)
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(resolution,[status(thm)],[f146,f60]) ).
fof(f499,plain,
! [X0,X1] :
( product(g2,X0,f,X1)
| ~ product(g2,f,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f492]) ).
fof(f500,plain,
! [X0,X1] :
( product(g1,X0,a,X1)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f494]) ).
fof(f508,plain,
! [X0] :
( ~ sQ27_spl
| X0 = d2
| ~ product(g1,a,X0,d3) ),
inference(forward_demodulation,[status(thm)],[f304,f148]) ).
fof(f509,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ17_spl
| X0 = d2
| ~ product(g1,a,X0,a) ),
inference(forward_demodulation,[status(thm)],[f270,f508]) ).
fof(f517,plain,
identity_for(g2) = inverse(g2,f),
inference(paramodulation,[status(thm)],[f92,f429]) ).
fof(f521,plain,
f = inverse(g2,f),
inference(forward_demodulation,[status(thm)],[f92,f517]) ).
fof(f537,plain,
! [X0,X1] : inverse(X0,inverse(X0,X1)) = X1,
inference(resolution,[status(thm)],[f156,f63]) ).
fof(f541,plain,
! [X0,X1] :
( X1 = X0
| ~ product(g2,inverse(g2,X0),X1,f) ),
inference(paramodulation,[status(thm)],[f92,f156]) ).
fof(f542,plain,
! [X0,X1] :
( X1 = X0
| ~ product(g1,inverse(g1,X0),X1,a) ),
inference(paramodulation,[status(thm)],[f91,f156]) ).
fof(f546,plain,
! [X0,X1] :
( product(g2,identity_for(g2),f,X1)
| ~ product(g2,inverse(g2,X0),X0,X1) ),
inference(resolution,[status(thm)],[f157,f96]) ).
fof(f548,plain,
! [X0,X1] :
( product(g1,identity_for(g1),a,X1)
| ~ product(g1,inverse(g1,X0),X0,X1) ),
inference(resolution,[status(thm)],[f157,f94]) ).
fof(f554,plain,
! [X0,X1] :
( product(g2,f,f,X1)
| ~ product(g2,inverse(g2,X0),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f546]) ).
fof(f556,plain,
! [X0,X1] :
( product(g1,a,a,X1)
| ~ product(g1,inverse(g1,X0),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f548]) ).
fof(f558,plain,
! [X0,X1] :
( product(g2,inverse(g2,X1),X1,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f158,f96]) ).
fof(f560,plain,
! [X0,X1] :
( product(g1,inverse(g1,X1),X1,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f158,f94]) ).
fof(f566,plain,
! [X0,X1] :
( product(g2,inverse(g2,X1),X1,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f558]) ).
fof(f568,plain,
! [X0,X1] :
( product(g1,inverse(g1,X1),X1,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f560]) ).
fof(f571,plain,
! [X0] :
( ~ sQ24_spl
| X0 = d1
| ~ product(g1,X0,a,d3) ),
inference(forward_demodulation,[status(thm)],[f294,f165]) ).
fof(f572,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ17_spl
| X0 = d1
| ~ product(g1,X0,a,a) ),
inference(forward_demodulation,[status(thm)],[f270,f571]) ).
fof(f611,plain,
! [X0,X1] :
( X1 = inverse(g2,X0)
| ~ product(g2,X0,X1,f) ),
inference(paramodulation,[status(thm)],[f92,f160]) ).
fof(f612,plain,
! [X0,X1] :
( X1 = inverse(g1,X0)
| ~ product(g1,X0,X1,a) ),
inference(paramodulation,[status(thm)],[f91,f160]) ).
fof(f628,plain,
! [X0,X1] :
( product(g2,identity_for(g2),f,X1)
| ~ product(g2,X0,inverse(g2,X0),X1) ),
inference(resolution,[status(thm)],[f161,f96]) ).
fof(f629,plain,
! [X0,X1] :
( product(g1,identity_for(g1),a,X1)
| ~ product(g1,X0,inverse(g1,X0),X1) ),
inference(resolution,[status(thm)],[f161,f94]) ).
fof(f637,plain,
! [X0,X1] :
( product(g2,f,f,X1)
| ~ product(g2,X0,inverse(g2,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f92,f628]) ).
fof(f638,plain,
! [X0,X1] :
( product(g1,a,a,X1)
| ~ product(g1,X0,inverse(g1,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f91,f629]) ).
fof(f642,plain,
! [X0,X1] :
( product(g2,X1,inverse(g2,X1),X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f162,f96]) ).
fof(f643,plain,
! [X0,X1] :
( product(g1,X1,inverse(g1,X1),X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f162,f94]) ).
fof(f651,plain,
! [X0,X1] :
( product(g2,X1,inverse(g2,X1),X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f642]) ).
fof(f652,plain,
! [X0,X1] :
( product(g1,X1,inverse(g1,X1),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f643]) ).
fof(f670,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,a,X0,multiply(g1,d3,X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f270,f182]) ).
fof(f671,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,a,X0,multiply(g1,a,X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f270,f670]) ).
fof(f672,plain,
( ~ sQ17_spl
| product(g1,a,c,multiply(g1,a,c)) ),
inference(resolution,[status(thm)],[f671,f79]) ).
fof(f673,plain,
( ~ sQ17_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(resolution,[status(thm)],[f671,f78]) ).
fof(f674,plain,
( ~ sQ17_spl
| product(g1,a,identity_for(g1),multiply(g1,a,identity_for(g1))) ),
inference(resolution,[status(thm)],[f671,f58]) ).
fof(f675,plain,
( ~ sQ17_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(resolution,[status(thm)],[f671,f77]) ).
fof(f676,plain,
( ~ sQ17_spl
| product(g1,a,a,multiply(g1,a,identity_for(g1))) ),
inference(forward_demodulation,[status(thm)],[f91,f674]) ).
fof(f677,plain,
( ~ sQ17_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f91,f676]) ).
fof(f691,plain,
! [X0,X1] :
( X0 = inverse(g2,X1)
| ~ product(g2,X0,X1,f) ),
inference(paramodulation,[status(thm)],[f92,f166]) ).
fof(f692,plain,
! [X0,X1] :
( X0 = inverse(g1,X1)
| ~ product(g1,X0,X1,a) ),
inference(paramodulation,[status(thm)],[f91,f166]) ).
fof(f703,plain,
! [X0,X1] :
( X0 = X1
| ~ product(g2,X0,inverse(g2,X1),f) ),
inference(paramodulation,[status(thm)],[f92,f168]) ).
fof(f704,plain,
! [X0,X1] :
( X0 = X1
| ~ product(g1,X0,inverse(g1,X1),a) ),
inference(paramodulation,[status(thm)],[f91,f168]) ).
fof(f707,plain,
( ~ sQ17_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f175,f671]) ).
fof(f708,plain,
( inverse(g1,b) = c
| inverse(g1,b) = b
| inverse(g1,b) = a ),
inference(resolution,[status(thm)],[f175,f89]) ).
fof(f709,plain,
! [X0] :
( group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f175,f65]) ).
fof(f710,plain,
! [X0] :
( product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f175,f64]) ).
fof(f712,definition,
( sQ39_spl
<=> inverse(g1,b) = a ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f713,plain,
( ~ sQ39_spl
| inverse(g1,b) = a ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f714,plain,
( sQ39_spl
| inverse(g1,b) != a ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f715,definition,
( sQ40_spl
<=> inverse(g1,b) = b ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f716,plain,
( ~ sQ40_spl
| inverse(g1,b) = b ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f717,plain,
( sQ40_spl
| inverse(g1,b) != b ),
inference(component_clause,[status(thm)],[f715]) ).
fof(f718,definition,
( sQ41_spl
<=> inverse(g1,b) = c ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f719,plain,
( ~ sQ41_spl
| inverse(g1,b) = c ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f720,plain,
( sQ41_spl
| inverse(g1,b) != c ),
inference(component_clause,[status(thm)],[f718]) ).
fof(f721,plain,
( sQ41_spl
| sQ40_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f708,f712,f715,f718]) ).
fof(f724,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,X0,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f719,f168]) ).
fof(f725,plain,
! [X0] :
( ~ sQ41_spl
| X0 = identity_for(g1)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f719,f163]) ).
fof(f726,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f719,f162]) ).
fof(f727,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f719,f161]) ).
fof(f728,plain,
! [X0] :
( ~ sQ41_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f719,f159]) ).
fof(f729,plain,
( ~ sQ41_spl
| inverse(g1,c) = b ),
inference(paramodulation,[status(thm)],[f719,f537]) ).
fof(f730,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,c,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f719,f156]) ).
fof(f732,plain,
( ~ sQ41_spl
| product(g1,c,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f719,f62]) ).
fof(f733,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,X0,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f724]) ).
fof(f734,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f725]) ).
fof(f735,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f726]) ).
fof(f736,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f727]) ).
fof(f737,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f728]) ).
fof(f738,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f730]) ).
fof(f740,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f732]) ).
fof(f741,plain,
( ~ sQ41_spl
| ~ sQ40_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f716,f719]) ).
fof(f742,plain,
! [X0] :
( ~ sQ40_spl
| X0 = b
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f716,f168]) ).
fof(f743,plain,
! [X0] :
( ~ sQ40_spl
| X0 = identity_for(g1)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f716,f163]) ).
fof(f744,plain,
! [X0,X1,X2] :
( ~ sQ40_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f716,f162]) ).
fof(f745,plain,
! [X0,X1,X2] :
( ~ sQ40_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f716,f161]) ).
fof(f746,plain,
! [X0] :
( ~ sQ40_spl
| X0 = identity_for(g1)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f716,f159]) ).
fof(f748,plain,
! [X0] :
( ~ sQ40_spl
| X0 = b
| ~ product(g1,b,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f716,f156]) ).
fof(f749,plain,
( ~ sQ40_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f716,f63]) ).
fof(f750,plain,
( ~ sQ40_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f716,f62]) ).
fof(f751,plain,
( ~ sQ41_spl
| ~ sQ40_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f741,f235,f715,f718]) ).
fof(f752,plain,
! [X0] :
( ~ sQ40_spl
| X0 = b
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f742]) ).
fof(f753,plain,
! [X0] :
( ~ sQ40_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f743]) ).
fof(f754,plain,
! [X0,X1,X2] :
( ~ sQ40_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f744]) ).
fof(f755,plain,
! [X0,X1,X2] :
( ~ sQ40_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f745]) ).
fof(f756,plain,
! [X0] :
( ~ sQ40_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f746]) ).
fof(f757,plain,
! [X0] :
( ~ sQ40_spl
| X0 = b
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f748]) ).
fof(f758,plain,
( ~ sQ40_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f749]) ).
fof(f759,plain,
( ~ sQ40_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f750]) ).
fof(f778,plain,
( ~ sQ17_spl
| product(g1,a,inverse(g1,c),multiply(g1,a,inverse(g1,c))) ),
inference(resolution,[status(thm)],[f176,f671]) ).
fof(f779,plain,
( inverse(g1,c) = c
| inverse(g1,c) = b
| inverse(g1,c) = a ),
inference(resolution,[status(thm)],[f176,f89]) ).
fof(f780,plain,
! [X0] :
( group_member(multiply(g1,inverse(g1,c),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f176,f65]) ).
fof(f781,plain,
! [X0] :
( product(g1,inverse(g1,c),X0,multiply(g1,inverse(g1,c),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f176,f64]) ).
fof(f783,definition,
( sQ42_spl
<=> inverse(g1,c) = a ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f784,plain,
( ~ sQ42_spl
| inverse(g1,c) = a ),
inference(component_clause,[status(thm)],[f783]) ).
fof(f785,plain,
( sQ42_spl
| inverse(g1,c) != a ),
inference(component_clause,[status(thm)],[f783]) ).
fof(f786,definition,
( sQ43_spl
<=> inverse(g1,c) = b ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f787,plain,
( ~ sQ43_spl
| inverse(g1,c) = b ),
inference(component_clause,[status(thm)],[f786]) ).
fof(f788,plain,
( sQ43_spl
| inverse(g1,c) != b ),
inference(component_clause,[status(thm)],[f786]) ).
fof(f789,definition,
( sQ44_spl
<=> inverse(g1,c) = c ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f790,plain,
( ~ sQ44_spl
| inverse(g1,c) = c ),
inference(component_clause,[status(thm)],[f789]) ).
fof(f791,plain,
( sQ44_spl
| inverse(g1,c) != c ),
inference(component_clause,[status(thm)],[f789]) ).
fof(f792,plain,
( sQ44_spl
| sQ43_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f779,f783,f786,f789]) ).
fof(f794,plain,
group_member(d3,g1),
inference(forward_demodulation,[status(thm)],[f537,f164]) ).
fof(f806,plain,
! [X0] :
( ~ sQ39_spl
| X0 = b
| ~ product(g1,X0,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f713,f168]) ).
fof(f807,plain,
! [X0] :
( ~ sQ39_spl
| X0 = identity_for(g1)
| ~ product(g1,b,a,X0) ),
inference(paramodulation,[status(thm)],[f713,f163]) ).
fof(f808,plain,
! [X0,X1,X2] :
( ~ sQ39_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f713,f162]) ).
fof(f809,plain,
! [X0,X1,X2] :
( ~ sQ39_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f713,f161]) ).
fof(f810,plain,
! [X0] :
( ~ sQ39_spl
| X0 = identity_for(g1)
| ~ product(g1,a,b,X0) ),
inference(paramodulation,[status(thm)],[f713,f159]) ).
fof(f811,plain,
( ~ sQ39_spl
| inverse(g1,a) = b ),
inference(paramodulation,[status(thm)],[f713,f537]) ).
fof(f812,plain,
! [X0] :
( ~ sQ39_spl
| X0 = b
| ~ product(g1,a,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f713,f156]) ).
fof(f813,plain,
( ~ sQ39_spl
| product(g1,b,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f713,f63]) ).
fof(f814,plain,
( ~ sQ39_spl
| product(g1,a,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f713,f62]) ).
fof(f815,plain,
! [X0] :
( ~ sQ39_spl
| X0 = b
| ~ product(g1,X0,a,a) ),
inference(forward_demodulation,[status(thm)],[f91,f806]) ).
fof(f816,plain,
! [X0] :
( ~ sQ39_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f807]) ).
fof(f817,plain,
! [X0,X1,X2] :
( ~ sQ39_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f808]) ).
fof(f818,plain,
! [X0,X1,X2] :
( ~ sQ39_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f809]) ).
fof(f819,plain,
! [X0] :
( ~ sQ39_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f810]) ).
fof(f824,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,X0,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f790,f168]) ).
fof(f825,plain,
! [X0] :
( ~ sQ44_spl
| X0 = identity_for(g1)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f163]) ).
fof(f826,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f162]) ).
fof(f827,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f161]) ).
fof(f830,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,c,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f790,f156]) ).
fof(f831,plain,
( ~ sQ44_spl
| product(g1,c,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f790,f63]) ).
fof(f833,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,X0,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f824]) ).
fof(f834,plain,
! [X0] :
( ~ sQ44_spl
| X0 = a
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f825]) ).
fof(f835,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f826]) ).
fof(f836,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f827]) ).
fof(f838,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,c,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f830]) ).
fof(f839,plain,
( ~ sQ44_spl
| product(g1,c,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f831]) ).
fof(f841,plain,
( ~ sQ44_spl
| ~ sQ43_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f787,f790]) ).
fof(f842,plain,
! [X0] :
( ~ sQ43_spl
| X0 = c
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f787,f168]) ).
fof(f843,plain,
! [X0] :
( ~ sQ43_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f787,f163]) ).
fof(f844,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f787,f162]) ).
fof(f845,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f787,f161]) ).
fof(f846,plain,
! [X0] :
( ~ sQ43_spl
| X0 = identity_for(g1)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f787,f159]) ).
fof(f847,plain,
( ~ sQ43_spl
| inverse(g1,b) = c ),
inference(paramodulation,[status(thm)],[f787,f537]) ).
fof(f848,plain,
! [X0] :
( ~ sQ43_spl
| X0 = c
| ~ product(g1,b,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f787,f156]) ).
fof(f849,plain,
( ~ sQ43_spl
| product(g1,c,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f787,f63]) ).
fof(f850,plain,
( ~ sQ43_spl
| product(g1,b,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f787,f62]) ).
fof(f851,plain,
( ~ sQ44_spl
| ~ sQ43_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f841,f235,f786,f789]) ).
fof(f852,plain,
! [X0] :
( ~ sQ43_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f842]) ).
fof(f853,plain,
! [X0] :
( ~ sQ43_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f843]) ).
fof(f854,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f844]) ).
fof(f855,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f845]) ).
fof(f856,plain,
! [X0] :
( ~ sQ43_spl
| X0 = a
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f846]) ).
fof(f857,plain,
( ~ sQ43_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f847,f718,f786]) ).
fof(f858,plain,
! [X0] :
( ~ sQ43_spl
| X0 = c
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f848]) ).
fof(f859,plain,
( ~ sQ43_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f849]) ).
fof(f860,plain,
( ~ sQ43_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f850]) ).
fof(f861,plain,
( ~ sQ41_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f729,f786,f718]) ).
fof(f863,plain,
product(g2,f,h,multiply(g2,f,h)),
inference(resolution,[status(thm)],[f178,f85]) ).
fof(f864,plain,
product(g2,f,g,multiply(g2,f,g)),
inference(resolution,[status(thm)],[f178,f84]) ).
fof(f865,plain,
product(g2,f,f,multiply(g2,f,f)),
inference(resolution,[status(thm)],[f178,f83]) ).
fof(f869,plain,
product(g1,c,c,multiply(g1,c,c)),
inference(resolution,[status(thm)],[f179,f79]) ).
fof(f870,plain,
product(g1,c,b,multiply(g1,c,b)),
inference(resolution,[status(thm)],[f179,f78]) ).
fof(f871,plain,
product(g1,c,identity_for(g1),multiply(g1,c,identity_for(g1))),
inference(resolution,[status(thm)],[f179,f58]) ).
fof(f872,plain,
product(g1,c,a,multiply(g1,c,a)),
inference(resolution,[status(thm)],[f179,f77]) ).
fof(f873,plain,
product(g1,c,a,multiply(g1,c,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f871]) ).
fof(f874,plain,
product(g1,c,a,multiply(g1,c,a)),
inference(forward_demodulation,[status(thm)],[f91,f873]) ).
fof(f875,plain,
group_member(d2,g1),
inference(forward_demodulation,[status(thm)],[f537,f201]) ).
fof(f877,plain,
! [X0] :
( ~ sQ17_spl
| group_member(multiply(g1,a,X0),g1)
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f270,f191]) ).
fof(f878,plain,
( ~ sQ17_spl
| group_member(multiply(g1,a,c),g1) ),
inference(resolution,[status(thm)],[f877,f79]) ).
fof(f879,plain,
( ~ sQ17_spl
| group_member(multiply(g1,a,b),g1) ),
inference(resolution,[status(thm)],[f877,f78]) ).
fof(f880,plain,
( ~ sQ17_spl
| group_member(multiply(g1,a,identity_for(g1)),g1) ),
inference(resolution,[status(thm)],[f877,f58]) ).
fof(f881,plain,
( ~ sQ17_spl
| group_member(multiply(g1,a,a),g1) ),
inference(resolution,[status(thm)],[f877,f77]) ).
fof(f882,plain,
( ~ sQ17_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f880]) ).
fof(f895,plain,
! [X0] :
( ~ sQ42_spl
| X0 = c
| ~ product(g1,X0,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f784,f168]) ).
fof(f896,plain,
! [X0] :
( ~ sQ42_spl
| X0 = identity_for(g1)
| ~ product(g1,c,a,X0) ),
inference(paramodulation,[status(thm)],[f784,f163]) ).
fof(f897,plain,
! [X0,X1,X2] :
( ~ sQ42_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f784,f162]) ).
fof(f898,plain,
! [X0,X1,X2] :
( ~ sQ42_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f784,f161]) ).
fof(f899,plain,
! [X0] :
( ~ sQ42_spl
| X0 = identity_for(g1)
| ~ product(g1,a,c,X0) ),
inference(paramodulation,[status(thm)],[f784,f159]) ).
fof(f900,plain,
( ~ sQ42_spl
| inverse(g1,a) = c ),
inference(paramodulation,[status(thm)],[f784,f537]) ).
fof(f901,plain,
! [X0] :
( ~ sQ42_spl
| X0 = c
| ~ product(g1,a,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f784,f156]) ).
fof(f902,plain,
( ~ sQ42_spl
| product(g1,c,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f784,f63]) ).
fof(f903,plain,
( ~ sQ42_spl
| product(g1,a,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f784,f62]) ).
fof(f904,plain,
! [X0] :
( ~ sQ42_spl
| X0 = c
| ~ product(g1,X0,a,a) ),
inference(forward_demodulation,[status(thm)],[f91,f895]) ).
fof(f905,plain,
! [X0] :
( ~ sQ42_spl
| X0 = a
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f896]) ).
fof(f906,plain,
! [X0,X1,X2] :
( ~ sQ42_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f897]) ).
fof(f907,plain,
! [X0,X1,X2] :
( ~ sQ42_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f898]) ).
fof(f908,plain,
! [X0] :
( ~ sQ42_spl
| X0 = a
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f899]) ).
fof(f912,plain,
product(g1,b,c,multiply(g1,b,c)),
inference(resolution,[status(thm)],[f180,f79]) ).
fof(f913,plain,
product(g1,b,b,multiply(g1,b,b)),
inference(resolution,[status(thm)],[f180,f78]) ).
fof(f914,plain,
product(g1,b,identity_for(g1),multiply(g1,b,identity_for(g1))),
inference(resolution,[status(thm)],[f180,f58]) ).
fof(f915,plain,
product(g1,b,a,multiply(g1,b,a)),
inference(resolution,[status(thm)],[f180,f77]) ).
fof(f916,plain,
product(g1,b,a,multiply(g1,b,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f914]) ).
fof(f917,plain,
product(g1,b,a,multiply(g1,b,a)),
inference(forward_demodulation,[status(thm)],[f91,f916]) ).
fof(f921,plain,
product(g1,identity_for(g1),c,multiply(g1,identity_for(g1),c)),
inference(resolution,[status(thm)],[f183,f79]) ).
fof(f922,plain,
product(g1,identity_for(g1),b,multiply(g1,identity_for(g1),b)),
inference(resolution,[status(thm)],[f183,f78]) ).
fof(f923,plain,
! [X0] : product(X0,identity_for(X0),identity_for(X0),multiply(X0,identity_for(X0),identity_for(X0))),
inference(resolution,[status(thm)],[f183,f58]) ).
fof(f924,plain,
product(g1,identity_for(g1),a,multiply(g1,identity_for(g1),a)),
inference(resolution,[status(thm)],[f183,f77]) ).
fof(f931,plain,
product(g1,a,c,multiply(g1,identity_for(g1),c)),
inference(forward_demodulation,[status(thm)],[f91,f921]) ).
fof(f932,plain,
product(g1,a,c,multiply(g1,a,c)),
inference(forward_demodulation,[status(thm)],[f91,f931]) ).
fof(f933,plain,
product(g1,a,b,multiply(g1,identity_for(g1),b)),
inference(forward_demodulation,[status(thm)],[f91,f922]) ).
fof(f934,plain,
product(g1,a,b,multiply(g1,a,b)),
inference(forward_demodulation,[status(thm)],[f91,f933]) ).
fof(f935,plain,
product(g1,a,a,multiply(g1,identity_for(g1),a)),
inference(forward_demodulation,[status(thm)],[f91,f924]) ).
fof(f936,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f91,f935]) ).
fof(f942,plain,
( ~ sQ17_spl
| product(g1,b,multiply(g1,a,c),multiply(g1,b,multiply(g1,a,c))) ),
inference(resolution,[status(thm)],[f878,f180]) ).
fof(f944,plain,
( ~ sQ17_spl
| product(g1,c,multiply(g1,a,c),multiply(g1,c,multiply(g1,a,c))) ),
inference(resolution,[status(thm)],[f878,f179]) ).
fof(f950,plain,
( ~ sQ17_spl
| group_member(inverse(g1,multiply(g1,a,c)),g1) ),
inference(resolution,[status(thm)],[f878,f61]) ).
fof(f951,definition,
( sQ45_spl
<=> multiply(g1,a,c) = a ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f952,plain,
( ~ sQ45_spl
| multiply(g1,a,c) = a ),
inference(component_clause,[status(thm)],[f951]) ).
fof(f954,definition,
( sQ46_spl
<=> multiply(g1,a,c) = b ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f955,plain,
( ~ sQ46_spl
| multiply(g1,a,c) = b ),
inference(component_clause,[status(thm)],[f954]) ).
fof(f957,definition,
( sQ47_spl
<=> multiply(g1,a,c) = c ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f958,plain,
( ~ sQ47_spl
| multiply(g1,a,c) = c ),
inference(component_clause,[status(thm)],[f957]) ).
fof(f959,plain,
( sQ47_spl
| multiply(g1,a,c) != c ),
inference(component_clause,[status(thm)],[f957]) ).
fof(f980,plain,
! [X0] :
( ~ sQ43_spl
| X0 = c
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f787,f168]) ).
fof(f981,plain,
! [X0] :
( ~ sQ43_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f787,f163]) ).
fof(f982,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f787,f162]) ).
fof(f983,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f787,f161]) ).
fof(f984,plain,
! [X0] :
( ~ sQ43_spl
| X0 = identity_for(g1)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f787,f159]) ).
fof(f985,plain,
( ~ sQ43_spl
| inverse(g1,b) = c ),
inference(paramodulation,[status(thm)],[f787,f537]) ).
fof(f986,plain,
! [X0] :
( ~ sQ43_spl
| X0 = c
| ~ product(g1,b,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f787,f156]) ).
fof(f987,plain,
( ~ sQ43_spl
| product(g1,c,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f787,f63]) ).
fof(f988,plain,
( ~ sQ43_spl
| product(g1,b,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f787,f62]) ).
fof(f989,plain,
! [X0] :
( ~ sQ43_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f980]) ).
fof(f990,plain,
! [X0] :
( ~ sQ43_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f981]) ).
fof(f991,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f982]) ).
fof(f992,plain,
! [X0,X1,X2] :
( ~ sQ43_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f983]) ).
fof(f993,plain,
! [X0] :
( ~ sQ43_spl
| X0 = a
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f984]) ).
fof(f994,plain,
! [X0] :
( ~ sQ43_spl
| X0 = c
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f986]) ).
fof(f995,plain,
( ~ sQ43_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f987]) ).
fof(f996,plain,
( ~ sQ43_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f988]) ).
fof(f1001,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f719,f162]) ).
fof(f1002,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f719,f161]) ).
fof(f1003,plain,
! [X0] :
( ~ sQ41_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f719,f159]) ).
fof(f1004,plain,
( ~ sQ41_spl
| inverse(g1,c) = b ),
inference(paramodulation,[status(thm)],[f719,f537]) ).
fof(f1005,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,c,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f719,f156]) ).
fof(f1007,plain,
( ~ sQ41_spl
| product(g1,c,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f719,f62]) ).
fof(f1010,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f1001]) ).
fof(f1011,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f1002]) ).
fof(f1012,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1003]) ).
fof(f1013,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f1005]) ).
fof(f1015,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f1007]) ).
fof(f1016,plain,
( ~ sQ17_spl
| group_member(multiply(g1,c,multiply(g1,a,c)),g1) ),
inference(resolution,[status(thm)],[f188,f878]) ).
fof(f1017,plain,
group_member(multiply(g1,c,c),g1),
inference(resolution,[status(thm)],[f188,f79]) ).
fof(f1018,plain,
group_member(multiply(g1,c,b),g1),
inference(resolution,[status(thm)],[f188,f78]) ).
fof(f1019,plain,
group_member(multiply(g1,c,identity_for(g1)),g1),
inference(resolution,[status(thm)],[f188,f58]) ).
fof(f1020,plain,
group_member(multiply(g1,c,a),g1),
inference(resolution,[status(thm)],[f188,f77]) ).
fof(f1021,plain,
group_member(multiply(g1,c,a),g1),
inference(forward_demodulation,[status(thm)],[f91,f1019]) ).
fof(f1022,plain,
( ~ sQ17_spl
| group_member(multiply(g1,b,multiply(g1,a,c)),g1) ),
inference(resolution,[status(thm)],[f189,f878]) ).
fof(f1023,plain,
group_member(multiply(g1,b,c),g1),
inference(resolution,[status(thm)],[f189,f79]) ).
fof(f1024,plain,
group_member(multiply(g1,b,b),g1),
inference(resolution,[status(thm)],[f189,f78]) ).
fof(f1025,plain,
group_member(multiply(g1,b,identity_for(g1)),g1),
inference(resolution,[status(thm)],[f189,f58]) ).
fof(f1026,plain,
group_member(multiply(g1,b,a),g1),
inference(resolution,[status(thm)],[f189,f77]) ).
fof(f1027,plain,
group_member(multiply(g1,b,a),g1),
inference(forward_demodulation,[status(thm)],[f91,f1025]) ).
fof(f1033,plain,
group_member(multiply(g1,identity_for(g1),b),g1),
inference(resolution,[status(thm)],[f192,f78]) ).
fof(f1034,plain,
! [X0] : group_member(multiply(X0,identity_for(X0),identity_for(X0)),X0),
inference(resolution,[status(thm)],[f192,f58]) ).
fof(f1035,plain,
group_member(multiply(g1,identity_for(g1),a),g1),
inference(resolution,[status(thm)],[f192,f77]) ).
fof(f1041,plain,
group_member(multiply(g1,a,b),g1),
inference(forward_demodulation,[status(thm)],[f91,f1033]) ).
fof(f1042,plain,
group_member(multiply(g1,a,a),g1),
inference(forward_demodulation,[status(thm)],[f91,f1035]) ).
fof(f1044,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| product(g1,d1,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f294,f143]) ).
fof(f1045,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| ~ sQ17_spl
| product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f1044]) ).
fof(f1072,plain,
group_member(multiply(g2,f,inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f187]) ).
fof(f1073,plain,
product(g2,f,inverse(g2,g),multiply(g2,f,inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f178]) ).
fof(f1074,plain,
( inverse(g2,g) = h
| inverse(g2,g) = g
| inverse(g2,g) = f ),
inference(resolution,[status(thm)],[f198,f90]) ).
fof(f1075,plain,
group_member(multiply(g2,identity_for(g2),inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f192]) ).
fof(f1076,plain,
product(g2,identity_for(g2),inverse(g2,g),multiply(g2,identity_for(g2),inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f183]) ).
fof(f1077,plain,
! [X0] :
( group_member(multiply(g2,inverse(g2,g),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f198,f65]) ).
fof(f1078,plain,
! [X0] :
( product(g2,inverse(g2,g),X0,multiply(g2,inverse(g2,g),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f198,f64]) ).
fof(f1080,definition,
( sQ48_spl
<=> inverse(g2,g) = f ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1081,plain,
( ~ sQ48_spl
| inverse(g2,g) = f ),
inference(component_clause,[status(thm)],[f1080]) ).
fof(f1082,plain,
( sQ48_spl
| inverse(g2,g) != f ),
inference(component_clause,[status(thm)],[f1080]) ).
fof(f1083,definition,
( sQ49_spl
<=> inverse(g2,g) = g ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1084,plain,
( ~ sQ49_spl
| inverse(g2,g) = g ),
inference(component_clause,[status(thm)],[f1083]) ).
fof(f1085,plain,
( sQ49_spl
| inverse(g2,g) != g ),
inference(component_clause,[status(thm)],[f1083]) ).
fof(f1086,definition,
( sQ50_spl
<=> inverse(g2,g) = h ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1087,plain,
( ~ sQ50_spl
| inverse(g2,g) = h ),
inference(component_clause,[status(thm)],[f1086]) ).
fof(f1088,plain,
( sQ50_spl
| inverse(g2,g) != h ),
inference(component_clause,[status(thm)],[f1086]) ).
fof(f1089,plain,
( sQ50_spl
| sQ49_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f1074,f1080,f1083,f1086]) ).
fof(f1090,plain,
group_member(multiply(g2,f,inverse(g2,g)),g2),
inference(forward_demodulation,[status(thm)],[f92,f1075]) ).
fof(f1091,plain,
product(g2,f,inverse(g2,g),multiply(g2,identity_for(g2),inverse(g2,g))),
inference(forward_demodulation,[status(thm)],[f92,f1076]) ).
fof(f1092,plain,
product(g2,f,inverse(g2,g),multiply(g2,f,inverse(g2,g))),
inference(forward_demodulation,[status(thm)],[f92,f1091]) ).
fof(f1095,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1087,f168]) ).
fof(f1096,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1087,f163]) ).
fof(f1097,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1087,f162]) ).
fof(f1098,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1087,f161]) ).
fof(f1099,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1087,f159]) ).
fof(f1100,plain,
( ~ sQ50_spl
| inverse(g2,h) = g ),
inference(paramodulation,[status(thm)],[f1087,f537]) ).
fof(f1104,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1095]) ).
fof(f1105,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1096]) ).
fof(f1106,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1097]) ).
fof(f1107,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1098]) ).
fof(f1108,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1099]) ).
fof(f1112,plain,
group_member(multiply(g2,g,h),g2),
inference(resolution,[status(thm)],[f196,f85]) ).
fof(f1113,plain,
group_member(multiply(g2,g,g),g2),
inference(resolution,[status(thm)],[f196,f84]) ).
fof(f1114,plain,
group_member(multiply(g2,g,f),g2),
inference(resolution,[status(thm)],[f196,f83]) ).
fof(f1117,plain,
product(g2,g,h,multiply(g2,g,h)),
inference(resolution,[status(thm)],[f197,f85]) ).
fof(f1118,plain,
product(g2,g,g,multiply(g2,g,g)),
inference(resolution,[status(thm)],[f197,f84]) ).
fof(f1119,plain,
product(g2,g,f,multiply(g2,g,f)),
inference(resolution,[status(thm)],[f197,f83]) ).
fof(f1120,plain,
product(g2,g,identity_for(g2),multiply(g2,g,identity_for(g2))),
inference(resolution,[status(thm)],[f197,f58]) ).
fof(f1121,plain,
product(g2,g,f,multiply(g2,g,identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f92,f1120]) ).
fof(f1122,plain,
product(g2,g,f,multiply(g2,g,f)),
inference(forward_demodulation,[status(thm)],[f92,f1121]) ).
fof(f1123,plain,
group_member(multiply(g2,h,h),g2),
inference(resolution,[status(thm)],[f210,f85]) ).
fof(f1124,plain,
group_member(multiply(g2,h,g),g2),
inference(resolution,[status(thm)],[f210,f84]) ).
fof(f1125,plain,
group_member(multiply(g2,h,f),g2),
inference(resolution,[status(thm)],[f210,f83]) ).
fof(f1128,plain,
( ~ sQ47_spl
| ~ sQ46_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f955,f958]) ).
fof(f1129,plain,
( ~ sQ47_spl
| ~ sQ46_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f1128,f235,f954,f957]) ).
fof(f1134,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1100,f168]) ).
fof(f1140,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1100,f156]) ).
fof(f1141,plain,
( ~ sQ50_spl
| product(g2,h,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1100,f63]) ).
fof(f1142,plain,
( ~ sQ50_spl
| product(g2,g,h,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1100,f62]) ).
fof(f1143,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1134]) ).
fof(f1148,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1140]) ).
fof(f1149,plain,
( ~ sQ50_spl
| product(g2,h,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1141]) ).
fof(f1150,plain,
( ~ sQ50_spl
| product(g2,g,h,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1142]) ).
fof(f1161,plain,
( ~ sQ50_spl
| ~ sQ49_spl
| g = h ),
inference(backward_demodulation,[status(thm)],[f1084,f1087]) ).
fof(f1162,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,X0,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1084,f168]) ).
fof(f1163,plain,
! [X0] :
( ~ sQ49_spl
| X0 = identity_for(g2)
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f163]) ).
fof(f1164,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,g,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(paramodulation,[status(thm)],[f1084,f162]) ).
fof(f1165,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(paramodulation,[status(thm)],[f1084,f161]) ).
fof(f1168,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,g,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1084,f156]) ).
fof(f1169,plain,
( ~ sQ49_spl
| product(g2,g,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1084,f63]) ).
fof(f1171,plain,
( ~ sQ50_spl
| ~ sQ49_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f1161,f334,f1083,f1086]) ).
fof(f1172,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,X0,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1162]) ).
fof(f1173,plain,
! [X0] :
( ~ sQ49_spl
| X0 = f
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1163]) ).
fof(f1174,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1164]) ).
fof(f1175,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1165]) ).
fof(f1177,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,g,X0,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1168]) ).
fof(f1178,plain,
( ~ sQ49_spl
| product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1169]) ).
fof(f1180,plain,
! [X0] :
( ~ sQ48_spl
| X0 = g
| ~ product(g2,X0,f,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1081,f168]) ).
fof(f1181,plain,
! [X0] :
( ~ sQ48_spl
| X0 = identity_for(g2)
| ~ product(g2,g,f,X0) ),
inference(paramodulation,[status(thm)],[f1081,f163]) ).
fof(f1182,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| product(g2,g,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,f,X0,X1) ),
inference(paramodulation,[status(thm)],[f1081,f162]) ).
fof(f1183,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,f,X0,X1) ),
inference(paramodulation,[status(thm)],[f1081,f161]) ).
fof(f1184,plain,
! [X0] :
( ~ sQ48_spl
| X0 = identity_for(g2)
| ~ product(g2,f,g,X0) ),
inference(paramodulation,[status(thm)],[f1081,f159]) ).
fof(f1185,plain,
( ~ sQ48_spl
| inverse(g2,f) = g ),
inference(paramodulation,[status(thm)],[f1081,f537]) ).
fof(f1186,plain,
! [X0] :
( ~ sQ48_spl
| X0 = g
| ~ product(g2,f,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1081,f156]) ).
fof(f1187,plain,
( ~ sQ48_spl
| product(g2,g,f,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1081,f63]) ).
fof(f1188,plain,
( ~ sQ48_spl
| product(g2,f,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1081,f62]) ).
fof(f1189,plain,
! [X0] :
( ~ sQ48_spl
| X0 = g
| ~ product(g2,X0,f,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1180]) ).
fof(f1190,plain,
! [X0] :
( ~ sQ48_spl
| X0 = f
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1181]) ).
fof(f1191,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,f,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1182]) ).
fof(f1192,plain,
! [X0,X1,X2] :
( ~ sQ48_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,f,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1183]) ).
fof(f1193,plain,
! [X0] :
( ~ sQ48_spl
| X0 = f
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1184]) ).
fof(f1194,plain,
( ~ sQ48_spl
| f = g ),
inference(forward_demodulation,[status(thm)],[f521,f1185]) ).
fof(f1195,plain,
( ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1194,f86]) ).
fof(f1196,plain,
~ sQ48_spl,
inference(contradiction_clause,[status(thm)],[f1195]) ).
fof(f1197,plain,
product(g2,h,h,multiply(g2,h,h)),
inference(resolution,[status(thm)],[f211,f85]) ).
fof(f1198,plain,
product(g2,h,g,multiply(g2,h,g)),
inference(resolution,[status(thm)],[f211,f84]) ).
fof(f1199,plain,
product(g2,h,f,multiply(g2,h,f)),
inference(resolution,[status(thm)],[f211,f83]) ).
fof(f1203,plain,
product(g2,h,inverse(g2,h),multiply(g2,h,inverse(g2,h))),
inference(resolution,[status(thm)],[f212,f211]) ).
fof(f1204,plain,
group_member(multiply(g2,h,inverse(g2,h)),g2),
inference(resolution,[status(thm)],[f212,f210]) ).
fof(f1205,plain,
product(g2,g,inverse(g2,h),multiply(g2,g,inverse(g2,h))),
inference(resolution,[status(thm)],[f212,f197]) ).
fof(f1206,plain,
group_member(multiply(g2,g,inverse(g2,h)),g2),
inference(resolution,[status(thm)],[f212,f196]) ).
fof(f1207,plain,
group_member(multiply(g2,f,inverse(g2,h)),g2),
inference(resolution,[status(thm)],[f212,f187]) ).
fof(f1208,plain,
product(g2,f,inverse(g2,h),multiply(g2,f,inverse(g2,h))),
inference(resolution,[status(thm)],[f212,f178]) ).
fof(f1209,plain,
( inverse(g2,h) = h
| inverse(g2,h) = g
| inverse(g2,h) = f ),
inference(resolution,[status(thm)],[f212,f90]) ).
fof(f1210,plain,
group_member(multiply(g2,identity_for(g2),inverse(g2,h)),g2),
inference(resolution,[status(thm)],[f212,f192]) ).
fof(f1211,plain,
product(g2,identity_for(g2),inverse(g2,h),multiply(g2,identity_for(g2),inverse(g2,h))),
inference(resolution,[status(thm)],[f212,f183]) ).
fof(f1212,plain,
! [X0] :
( group_member(multiply(g2,inverse(g2,h),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f212,f65]) ).
fof(f1213,plain,
! [X0] :
( product(g2,inverse(g2,h),X0,multiply(g2,inverse(g2,h),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f212,f64]) ).
fof(f1215,definition,
( sQ51_spl
<=> inverse(g2,h) = f ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1216,plain,
( ~ sQ51_spl
| inverse(g2,h) = f ),
inference(component_clause,[status(thm)],[f1215]) ).
fof(f1217,plain,
( sQ51_spl
| inverse(g2,h) != f ),
inference(component_clause,[status(thm)],[f1215]) ).
fof(f1218,definition,
( sQ52_spl
<=> inverse(g2,h) = g ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1219,plain,
( ~ sQ52_spl
| inverse(g2,h) = g ),
inference(component_clause,[status(thm)],[f1218]) ).
fof(f1220,plain,
( sQ52_spl
| inverse(g2,h) != g ),
inference(component_clause,[status(thm)],[f1218]) ).
fof(f1221,definition,
( sQ53_spl
<=> inverse(g2,h) = h ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1222,plain,
( ~ sQ53_spl
| inverse(g2,h) = h ),
inference(component_clause,[status(thm)],[f1221]) ).
fof(f1223,plain,
( sQ53_spl
| inverse(g2,h) != h ),
inference(component_clause,[status(thm)],[f1221]) ).
fof(f1224,plain,
( sQ53_spl
| sQ52_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f1209,f1215,f1218,f1221]) ).
fof(f1225,plain,
group_member(multiply(g2,f,inverse(g2,h)),g2),
inference(forward_demodulation,[status(thm)],[f92,f1210]) ).
fof(f1226,plain,
product(g2,f,inverse(g2,h),multiply(g2,identity_for(g2),inverse(g2,h))),
inference(forward_demodulation,[status(thm)],[f92,f1211]) ).
fof(f1227,plain,
product(g2,f,inverse(g2,h),multiply(g2,f,inverse(g2,h))),
inference(forward_demodulation,[status(thm)],[f92,f1226]) ).
fof(f1248,plain,
! [X0,X1,X2,X3] :
( product(g1,a,X1,X3)
| ~ product(g1,X0,X2,X3)
| ~ product(g1,inverse(g1,X0),X1,X2) ),
inference(resolution,[status(thm)],[f213,f71]) ).
fof(f1249,plain,
! [X0,X1,X2,X3] :
( product(g1,X0,X2,X3)
| ~ product(g1,a,X1,X3)
| ~ product(g1,inverse(g1,X0),X1,X2) ),
inference(resolution,[status(thm)],[f213,f69]) ).
fof(f1250,plain,
! [X0,X1] :
( X1 = a
| ~ product(g1,X0,inverse(g1,X0),X1) ),
inference(resolution,[status(thm)],[f213,f67]) ).
fof(f1252,plain,
( ~ sQ43_spl
| product(g1,c,b,a) ),
inference(paramodulation,[status(thm)],[f787,f213]) ).
fof(f1278,plain,
( ~ sQ50_spl
| inverse(g2,g) = h ),
inference(paramodulation,[status(thm)],[f1100,f537]) ).
fof(f1293,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1278,f162]) ).
fof(f1294,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1278,f161]) ).
fof(f1295,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1278,f159]) ).
fof(f1297,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,h,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1278,f156]) ).
fof(f1302,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1293]) ).
fof(f1303,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1294]) ).
fof(f1304,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1295]) ).
fof(f1305,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,h,X0,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1297]) ).
fof(f1315,plain,
( ~ sQ53_spl
| ~ sQ50_spl
| g = h ),
inference(forward_demodulation,[status(thm)],[f1100,f1222]) ).
fof(f1316,plain,
( ~ sQ53_spl
| ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1315,f88]) ).
fof(f1317,plain,
( ~ sQ53_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f1316]) ).
fof(f1326,plain,
inverse(g1,a) = identity_for(g1),
inference(resolution,[status(thm)],[f214,f167]) ).
fof(f1333,plain,
! [X0,X1,X2,X3] :
( product(g1,a,X1,X3)
| ~ product(g1,inverse(g1,X0),X2,X3)
| ~ product(g1,X0,X1,X2) ),
inference(resolution,[status(thm)],[f214,f71]) ).
fof(f1334,plain,
! [X0,X1,X2,X3] :
( product(g1,inverse(g1,X0),X2,X3)
| ~ product(g1,a,X1,X3)
| ~ product(g1,X0,X1,X2) ),
inference(resolution,[status(thm)],[f214,f69]) ).
fof(f1335,plain,
! [X0,X1] :
( X1 = a
| ~ product(g1,inverse(g1,X0),X0,X1) ),
inference(resolution,[status(thm)],[f214,f67]) ).
fof(f1336,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(paramodulation,[status(thm)],[f719,f214]) ).
fof(f1337,plain,
( ~ sQ43_spl
| product(g1,b,c,a) ),
inference(paramodulation,[status(thm)],[f787,f214]) ).
fof(f1372,plain,
! [X0,X1,X2,X3] :
( product(g2,f,X1,X3)
| ~ product(g2,X0,X2,X3)
| ~ product(g2,inverse(g2,X0),X1,X2) ),
inference(resolution,[status(thm)],[f218,f71]) ).
fof(f1373,plain,
! [X0,X1,X2,X3] :
( product(g2,X0,X2,X3)
| ~ product(g2,f,X1,X3)
| ~ product(g2,inverse(g2,X0),X1,X2) ),
inference(resolution,[status(thm)],[f218,f69]) ).
fof(f1374,plain,
! [X0,X1] :
( X1 = f
| ~ product(g2,X0,inverse(g2,X0),X1) ),
inference(resolution,[status(thm)],[f218,f67]) ).
fof(f1407,plain,
! [X0,X1,X2,X3] :
( product(g2,f,X1,X3)
| ~ product(g2,inverse(g2,X0),X2,X3)
| ~ product(g2,X0,X1,X2) ),
inference(resolution,[status(thm)],[f219,f71]) ).
fof(f1408,plain,
! [X0,X1,X2,X3] :
( product(g2,inverse(g2,X0),X2,X3)
| ~ product(g2,f,X1,X3)
| ~ product(g2,X0,X1,X2) ),
inference(resolution,[status(thm)],[f219,f69]) ).
fof(f1409,plain,
! [X0,X1] :
( X1 = f
| ~ product(g2,inverse(g2,X0),X0,X1) ),
inference(resolution,[status(thm)],[f219,f67]) ).
fof(f1426,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,identity_for(g1),X0)
| ~ product(g1,a,inverse(g1,d2),X0) ),
inference(forward_demodulation,[status(thm)],[f270,f202]) ).
fof(f1427,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ24_spl
| product(g1,d1,identity_for(g1),X0)
| ~ product(g1,a,inverse(g1,a),X0) ),
inference(forward_demodulation,[status(thm)],[f294,f1426]) ).
fof(f1428,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ24_spl
| ~ sQ14_spl
| product(g1,d1,identity_for(g1),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f458,f1427]) ).
fof(f1430,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,identity_for(g1),X0) ),
inference(forward_demodulation,[status(thm)],[f270,f203]) ).
fof(f1431,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1430]) ).
fof(f1432,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ27_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f304,f1431]) ).
fof(f1433,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f204]) ).
fof(f1434,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ27_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f304,f1433]) ).
fof(f1435,plain,
( ~ sQ52_spl
| product(g2,g,h,f) ),
inference(paramodulation,[status(thm)],[f1219,f219]) ).
fof(f1436,plain,
( ~ sQ52_spl
| product(g2,h,g,f) ),
inference(paramodulation,[status(thm)],[f1219,f218]) ).
fof(f1437,plain,
! [X0] :
( ~ sQ52_spl
| X0 = h
| ~ product(g2,X0,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1219,f168]) ).
fof(f1438,plain,
! [X0] :
( ~ sQ52_spl
| X0 = identity_for(g2)
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1219,f163]) ).
fof(f1439,plain,
! [X0,X1,X2] :
( ~ sQ52_spl
| product(g2,h,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(paramodulation,[status(thm)],[f1219,f162]) ).
fof(f1440,plain,
! [X0,X1,X2] :
( ~ sQ52_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(paramodulation,[status(thm)],[f1219,f161]) ).
fof(f1441,plain,
! [X0] :
( ~ sQ52_spl
| X0 = identity_for(g2)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1219,f159]) ).
fof(f1442,plain,
( ~ sQ52_spl
| inverse(g2,g) = h ),
inference(paramodulation,[status(thm)],[f1219,f537]) ).
fof(f1443,plain,
! [X0] :
( ~ sQ52_spl
| X0 = h
| ~ product(g2,g,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1219,f156]) ).
fof(f1444,plain,
( ~ sQ52_spl
| product(g2,h,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1219,f63]) ).
fof(f1445,plain,
( ~ sQ52_spl
| product(g2,g,h,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1219,f62]) ).
fof(f1446,plain,
! [X0] :
( ~ sQ52_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1437]) ).
fof(f1447,plain,
! [X0] :
( ~ sQ52_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1438]) ).
fof(f1448,plain,
! [X0,X1,X2] :
( ~ sQ52_spl
| product(g2,h,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1439]) ).
fof(f1449,plain,
! [X0,X1,X2] :
( ~ sQ52_spl
| product(g2,f,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1440]) ).
fof(f1450,plain,
! [X0] :
( ~ sQ52_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1441]) ).
fof(f1451,plain,
( ~ sQ52_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f1442,f1086,f1218]) ).
fof(f1452,plain,
! [X0] :
( ~ sQ52_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1443]) ).
fof(f1453,plain,
( ~ sQ52_spl
| product(g2,h,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1444]) ).
fof(f1454,plain,
( ~ sQ52_spl
| product(g2,g,h,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1445]) ).
fof(f1455,plain,
( ~ sQ51_spl
| product(g2,f,h,f) ),
inference(paramodulation,[status(thm)],[f1216,f219]) ).
fof(f1456,plain,
( ~ sQ51_spl
| product(g2,h,f,f) ),
inference(paramodulation,[status(thm)],[f1216,f218]) ).
fof(f1457,plain,
! [X0] :
( ~ sQ51_spl
| X0 = h
| ~ product(g2,X0,f,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1216,f168]) ).
fof(f1458,plain,
! [X0] :
( ~ sQ51_spl
| X0 = identity_for(g2)
| ~ product(g2,h,f,X0) ),
inference(paramodulation,[status(thm)],[f1216,f163]) ).
fof(f1459,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| product(g2,h,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,f,X0,X1) ),
inference(paramodulation,[status(thm)],[f1216,f162]) ).
fof(f1460,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,f,X0,X1) ),
inference(paramodulation,[status(thm)],[f1216,f161]) ).
fof(f1461,plain,
! [X0] :
( ~ sQ51_spl
| X0 = identity_for(g2)
| ~ product(g2,f,h,X0) ),
inference(paramodulation,[status(thm)],[f1216,f159]) ).
fof(f1462,plain,
( ~ sQ51_spl
| inverse(g2,f) = h ),
inference(paramodulation,[status(thm)],[f1216,f537]) ).
fof(f1463,plain,
! [X0] :
( ~ sQ51_spl
| X0 = h
| ~ product(g2,f,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1216,f156]) ).
fof(f1464,plain,
( ~ sQ51_spl
| product(g2,h,f,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1216,f63]) ).
fof(f1465,plain,
( ~ sQ51_spl
| product(g2,f,h,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1216,f62]) ).
fof(f1466,plain,
! [X0] :
( ~ sQ51_spl
| X0 = h
| ~ product(g2,X0,f,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1457]) ).
fof(f1467,plain,
! [X0] :
( ~ sQ51_spl
| X0 = f
| ~ product(g2,h,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1458]) ).
fof(f1468,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| product(g2,h,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,f,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1459]) ).
fof(f1469,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| product(g2,f,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,f,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1460]) ).
fof(f1470,plain,
! [X0] :
( ~ sQ51_spl
| X0 = f
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1461]) ).
fof(f1471,plain,
( ~ sQ51_spl
| f = h ),
inference(forward_demodulation,[status(thm)],[f521,f1462]) ).
fof(f1472,plain,
( ~ sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1471,f87]) ).
fof(f1473,plain,
~ sQ51_spl,
inference(contradiction_clause,[status(thm)],[f1472]) ).
fof(f1476,plain,
product(g2,h,inverse(g2,g),multiply(g2,h,inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f211]) ).
fof(f1477,plain,
group_member(multiply(g2,h,inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f210]) ).
fof(f1478,plain,
product(g2,g,inverse(g2,g),multiply(g2,g,inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f197]) ).
fof(f1479,plain,
group_member(multiply(g2,g,inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f196]) ).
fof(f1480,plain,
group_member(multiply(g2,f,inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f187]) ).
fof(f1481,plain,
product(g2,f,inverse(g2,g),multiply(g2,f,inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f178]) ).
fof(f1483,plain,
group_member(multiply(g2,identity_for(g2),inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f192]) ).
fof(f1484,plain,
product(g2,identity_for(g2),inverse(g2,g),multiply(g2,identity_for(g2),inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f183]) ).
fof(f1485,plain,
! [X0] :
( group_member(multiply(g2,inverse(g2,g),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f198,f65]) ).
fof(f1486,plain,
! [X0] :
( product(g2,inverse(g2,g),X0,multiply(g2,inverse(g2,g),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f198,f64]) ).
fof(f1489,plain,
group_member(multiply(g2,f,inverse(g2,g)),g2),
inference(forward_demodulation,[status(thm)],[f92,f1483]) ).
fof(f1490,plain,
product(g2,f,inverse(g2,g),multiply(g2,identity_for(g2),inverse(g2,g))),
inference(forward_demodulation,[status(thm)],[f92,f1484]) ).
fof(f1491,plain,
product(g2,f,inverse(g2,g),multiply(g2,f,inverse(g2,g))),
inference(forward_demodulation,[status(thm)],[f92,f1490]) ).
fof(f1493,plain,
( ~ sQ17_spl
| group_member(multiply(g1,b,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f879,f189]) ).
fof(f1494,plain,
( ~ sQ17_spl
| group_member(multiply(g1,c,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f879,f188]) ).
fof(f1495,plain,
( ~ sQ17_spl
| product(g1,b,multiply(g1,a,b),multiply(g1,b,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f879,f180]) ).
fof(f1496,plain,
( ~ sQ17_spl
| group_member(multiply(g1,a,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f879,f877]) ).
fof(f1497,plain,
( ~ sQ17_spl
| product(g1,c,multiply(g1,a,b),multiply(g1,c,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f879,f179]) ).
fof(f1498,plain,
( ~ sQ17_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f879,f671]) ).
fof(f1500,plain,
( ~ sQ17_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f879,f192]) ).
fof(f1501,plain,
( ~ sQ17_spl
| product(g1,identity_for(g1),multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f879,f183]) ).
fof(f1502,plain,
! [X0] :
( ~ sQ17_spl
| group_member(multiply(g1,multiply(g1,a,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f879,f65]) ).
fof(f1503,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,multiply(g1,a,b),X0,multiply(g1,multiply(g1,a,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f879,f64]) ).
fof(f1504,plain,
( ~ sQ17_spl
| group_member(inverse(g1,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f879,f61]) ).
fof(f1505,definition,
( sQ54_spl
<=> multiply(g1,a,b) = a ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1506,plain,
( ~ sQ54_spl
| multiply(g1,a,b) = a ),
inference(component_clause,[status(thm)],[f1505]) ).
fof(f1507,plain,
( sQ54_spl
| multiply(g1,a,b) != a ),
inference(component_clause,[status(thm)],[f1505]) ).
fof(f1508,definition,
( sQ55_spl
<=> multiply(g1,a,b) = b ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1509,plain,
( ~ sQ55_spl
| multiply(g1,a,b) = b ),
inference(component_clause,[status(thm)],[f1508]) ).
fof(f1510,plain,
( sQ55_spl
| multiply(g1,a,b) != b ),
inference(component_clause,[status(thm)],[f1508]) ).
fof(f1511,definition,
( sQ56_spl
<=> multiply(g1,a,b) = c ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1512,plain,
( ~ sQ56_spl
| multiply(g1,a,b) = c ),
inference(component_clause,[status(thm)],[f1511]) ).
fof(f1513,plain,
( sQ56_spl
| multiply(g1,a,b) != c ),
inference(component_clause,[status(thm)],[f1511]) ).
fof(f1515,plain,
( ~ sQ17_spl
| group_member(multiply(g1,a,multiply(g1,a,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f1500]) ).
fof(f1516,plain,
( ~ sQ17_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f1501]) ).
fof(f1517,plain,
( ~ sQ17_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f1516]) ).
fof(f1518,plain,
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,a,c,a) ),
inference(forward_demodulation,[status(thm)],[f952,f672]) ).
fof(f1519,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,X0,a,X1)
| ~ product(g1,X0,c,X1) ),
inference(resolution,[status(thm)],[f1518,f208]) ).
fof(f1520,plain,
! [X0,X1] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,X0,c,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f1518,f207]) ).
fof(f1521,plain,
( ~ sQ17_spl
| ~ sQ45_spl
| c = a ),
inference(resolution,[status(thm)],[f1518,f171]) ).
fof(f1523,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,a,a,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f1518,f173]) ).
fof(f1524,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,a,c,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f1518,f172]) ).
fof(f1525,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f1518,f158]) ).
fof(f1526,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f1518,f157]) ).
fof(f1527,plain,
( ~ sQ17_spl
| ~ sQ45_spl
| c = identity_for(g1) ),
inference(resolution,[status(thm)],[f1518,f150]) ).
fof(f1528,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,a,c,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f1518,f146]) ).
fof(f1529,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f1518,f139]) ).
fof(f1530,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| X0 = a
| ~ product(g1,X0,c,a) ),
inference(resolution,[status(thm)],[f1518,f75]) ).
fof(f1531,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| X0 = c
| ~ product(g1,a,X0,a) ),
inference(resolution,[status(thm)],[f1518,f73]) ).
fof(f1532,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f1518,f71]) ).
fof(f1533,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f1518,f69]) ).
fof(f1534,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| X0 = a
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f1518,f67]) ).
fof(f1535,plain,
( ~ sQ17_spl
| ~ sQ45_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1521,f232,f951,f269]) ).
fof(f1537,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1525]) ).
fof(f1538,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| ~ sQ14_spl
| product(g1,a,a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f458,f1537]) ).
fof(f1539,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| ~ sQ14_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f458,f1526]) ).
fof(f1540,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| ~ sQ14_spl
| product(g1,a,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1539]) ).
fof(f1541,plain,
( ~ sQ17_spl
| ~ sQ45_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f1527,f285,f951,f269]) ).
fof(f1542,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,a,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1528]) ).
fof(f1543,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ45_spl
| product(g1,a,a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1529]) ).
fof(f1544,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism5(a),isomorphism5(d2),isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f304,f134]) ).
fof(f1545,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ product(g2,h,isomorphism5(d2),isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f109,f1544]) ).
fof(f1546,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,h,isomorphism5(a),isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f294,f1545]) ).
fof(f1547,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,h,h,isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f109,f1546]) ).
fof(f1548,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism4(a),isomorphism4(d2),isomorphism4(d3)) ),
inference(forward_demodulation,[status(thm)],[f304,f131]) ).
fof(f1549,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ product(g2,g,isomorphism4(d2),isomorphism4(d3)) ),
inference(forward_demodulation,[status(thm)],[f106,f1548]) ).
fof(f1550,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,g,isomorphism4(a),isomorphism4(d3)) ),
inference(forward_demodulation,[status(thm)],[f294,f1549]) ).
fof(f1551,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,g,g,isomorphism4(d3)) ),
inference(forward_demodulation,[status(thm)],[f106,f1550]) ).
fof(f1552,plain,
( sQ2_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism3(a),isomorphism3(d2),isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f304,f128]) ).
fof(f1553,plain,
( sQ2_spl
| ~ sQ27_spl
| ~ product(g2,g,isomorphism3(d2),isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f103,f1552]) ).
fof(f1554,plain,
( sQ2_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,g,isomorphism3(a),isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f294,f1553]) ).
fof(f1555,plain,
( sQ2_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,g,g,isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f103,f1554]) ).
fof(f1556,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism2(a),isomorphism2(d2),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f304,f125]) ).
fof(f1557,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ product(g2,f,isomorphism2(d2),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f100,f1556]) ).
fof(f1558,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,f,isomorphism2(a),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f294,f1557]) ).
fof(f1559,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,f,f,isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f100,f1558]) ).
fof(f1560,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism1(a),isomorphism1(d2),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f304,f122]) ).
fof(f1561,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ product(g2,f,isomorphism1(d2),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f97,f1560]) ).
fof(f1562,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,f,isomorphism1(a),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f294,f1561]) ).
fof(f1563,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ product(g2,f,f,isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f97,f1562]) ).
fof(f1564,plain,
! [X0] :
( ~ sQ27_spl
| product(g1,a,d2,X0)
| ~ product(g1,d3,a,X0) ),
inference(forward_demodulation,[status(thm)],[f304,f204]) ).
fof(f1565,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| product(g1,a,a,X0)
| ~ product(g1,d3,a,X0) ),
inference(forward_demodulation,[status(thm)],[f294,f1564]) ).
fof(f1566,plain,
! [X0] :
( product(g1,d1,d2,X0)
| ~ product(g1,d3,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f203]) ).
fof(f1567,plain,
! [X0] :
( ~ sQ27_spl
| product(g1,a,d2,X0)
| ~ product(g1,d3,a,X0) ),
inference(forward_demodulation,[status(thm)],[f304,f1566]) ).
fof(f1568,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| product(g1,a,a,X0)
| ~ product(g1,d3,a,X0) ),
inference(forward_demodulation,[status(thm)],[f294,f1567]) ).
fof(f1569,plain,
! [X0] :
( ~ sQ24_spl
| product(g1,d1,identity_for(g1),X0)
| ~ product(g1,d3,inverse(g1,a),X0) ),
inference(forward_demodulation,[status(thm)],[f294,f202]) ).
fof(f1570,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ27_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,d3,inverse(g1,a),X0) ),
inference(forward_demodulation,[status(thm)],[f304,f1569]) ).
fof(f1571,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,d3,inverse(g1,a),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1570]) ).
fof(f1572,plain,
inverse(g1,a) = a,
inference(forward_demodulation,[status(thm)],[f91,f1326]) ).
fof(f1575,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| ~ sQ27_spl
| product(g1,a,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f304,f1044]) ).
fof(f1581,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ27_spl
| X0 = a
| ~ product(g1,X0,a,d3) ),
inference(forward_demodulation,[status(thm)],[f304,f571]) ).
fof(f1583,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| X0 = a
| ~ product(g1,a,X0,d3) ),
inference(forward_demodulation,[status(thm)],[f294,f508]) ).
fof(f1584,plain,
! [X0] :
( ~ sQ39_spl
| X0 = b
| ~ product(g1,a,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f812]) ).
fof(f1585,plain,
( ~ sQ39_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f91,f813]) ).
fof(f1586,plain,
( ~ sQ39_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f814]) ).
fof(f1587,plain,
! [X0] :
( ~ sQ42_spl
| X0 = c
| ~ product(g1,a,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f901]) ).
fof(f1588,plain,
( ~ sQ42_spl
| product(g1,c,a,a) ),
inference(forward_demodulation,[status(thm)],[f91,f902]) ).
fof(f1589,plain,
( ~ sQ42_spl
| product(g1,a,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f903]) ).
fof(f1591,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,h,h,isomorphism5(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1547]) ).
fof(f1592,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,h,h,g) ),
inference(forward_demodulation,[status(thm)],[f110,f1591]) ).
fof(f1593,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,g,g,isomorphism4(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1551]) ).
fof(f1594,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,g,g,h) ),
inference(forward_demodulation,[status(thm)],[f107,f1593]) ).
fof(f1598,plain,
( sQ2_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,g,g,isomorphism3(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1555]) ).
fof(f1599,plain,
( sQ2_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f104,f1598]) ).
fof(f1600,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,f,f,isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1559]) ).
fof(f1601,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,f,f,h) ),
inference(forward_demodulation,[status(thm)],[f101,f1600]) ).
fof(f1602,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,f,f,isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1563]) ).
fof(f1603,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,f,f,g) ),
inference(forward_demodulation,[status(thm)],[f98,f1602]) ).
fof(f1623,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,h,h,isomorphism6(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f412]) ).
fof(f1624,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ product(g2,h,h,f) ),
inference(forward_demodulation,[status(thm)],[f113,f1623]) ).
fof(f1627,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1100,f168]) ).
fof(f1628,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1100,f163]) ).
fof(f1631,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1100,f159]) ).
fof(f1633,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1100,f156]) ).
fof(f1636,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1627]) ).
fof(f1637,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1628]) ).
fof(f1640,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1631]) ).
fof(f1641,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1633]) ).
fof(f1648,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1278,f168]) ).
fof(f1649,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1278,f163]) ).
fof(f1650,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1278,f162]) ).
fof(f1651,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1278,f161]) ).
fof(f1652,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1278,f159]) ).
fof(f1657,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,f) ),
inference(forward_demodulation,[status(thm)],[f92,f1648]) ).
fof(f1658,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1649]) ).
fof(f1659,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1650]) ).
fof(f1660,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f1651]) ).
fof(f1661,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f1652]) ).
fof(f1665,plain,
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,a,a,b) ),
inference(forward_demodulation,[status(thm)],[f273,f408]) ).
fof(f1666,plain,
! [X0,X1] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f1665,f208]) ).
fof(f1667,plain,
! [X0,X1] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,X0,a,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f1665,f207]) ).
fof(f1668,plain,
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| a = b ),
inference(resolution,[status(thm)],[f1665,f171]) ).
fof(f1670,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f1665,f173]) ).
fof(f1671,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1665,f172]) ).
fof(f1672,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,inverse(g1,a),b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f1665,f158]) ).
fof(f1673,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,inverse(g1,a),b,X0) ),
inference(resolution,[status(thm)],[f1665,f157]) ).
fof(f1674,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1665,f146]) ).
fof(f1675,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f1665,f139]) ).
fof(f1676,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,X0,a,b) ),
inference(resolution,[status(thm)],[f1665,f75]) ).
fof(f1677,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,a,X0,b) ),
inference(resolution,[status(thm)],[f1665,f73]) ).
fof(f1678,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,b,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f1665,f71]) ).
fof(f1679,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,a,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f1665,f69]) ).
fof(f1680,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f1665,f67]) ).
fof(f1681,plain,
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1668,f242,f272,f293,f303]) ).
fof(f1683,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,inverse(g1,a),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1672]) ).
fof(f1684,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ sQ11_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f490,f1683]) ).
fof(f1685,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ sQ11_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f490,f1673]) ).
fof(f1686,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| ~ sQ11_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1685]) ).
fof(f1687,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1674]) ).
fof(f1688,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ24_spl
| ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1675]) ).
fof(f1689,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ18_spl
| X0 = d2
| ~ product(g1,a,X0,b) ),
inference(forward_demodulation,[status(thm)],[f273,f508]) ).
fof(f1690,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,identity_for(g1),X0)
| ~ product(g1,b,inverse(g1,d2),X0) ),
inference(forward_demodulation,[status(thm)],[f273,f202]) ).
fof(f1691,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ27_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,inverse(g1,d2),X0) ),
inference(forward_demodulation,[status(thm)],[f304,f1690]) ).
fof(f1692,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,b,inverse(g1,d2),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1691]) ).
fof(f1693,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ18_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1567]) ).
fof(f1694,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ18_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1564]) ).
fof(f1695,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,f,isomorphism1(d2),isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1561]) ).
fof(f1696,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,f,isomorphism1(d2),g) ),
inference(forward_demodulation,[status(thm)],[f98,f1695]) ).
fof(f1697,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,f,isomorphism2(d2),isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1557]) ).
fof(f1698,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,f,isomorphism2(d2),h) ),
inference(forward_demodulation,[status(thm)],[f101,f1697]) ).
fof(f1699,plain,
( sQ2_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,g,isomorphism3(d2),isomorphism3(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1553]) ).
fof(f1700,plain,
( sQ2_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,g,isomorphism3(d2),f) ),
inference(forward_demodulation,[status(thm)],[f104,f1699]) ).
fof(f1701,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,g,isomorphism4(d2),isomorphism4(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1549]) ).
fof(f1702,plain,
( sQ3_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,g,isomorphism4(d2),h) ),
inference(forward_demodulation,[status(thm)],[f107,f1701]) ).
fof(f1703,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,h,isomorphism5(d2),isomorphism5(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1545]) ).
fof(f1704,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,h,isomorphism5(d2),g) ),
inference(forward_demodulation,[status(thm)],[f110,f1703]) ).
fof(f1705,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f273,f143]) ).
fof(f1706,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ27_spl
| product(g1,a,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f304,f1705]) ).
fof(f1707,plain,
! [X0] :
( ~ sQ18_spl
| X0 = d1
| ~ product(g1,X0,d2,b) ),
inference(forward_demodulation,[status(thm)],[f273,f165]) ).
fof(f1708,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ27_spl
| X0 = a
| ~ product(g1,X0,d2,b) ),
inference(forward_demodulation,[status(thm)],[f304,f1707]) ).
fof(f1709,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| product(g1,d3,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f304,f145]) ).
fof(f1710,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sQ18_spl
| product(g1,b,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f273,f1709]) ).
fof(f1711,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f445]) ).
fof(f1712,plain,
( ~ sQ27_spl
| ~ sQ18_spl
| product(g1,a,d2,b) ),
inference(forward_demodulation,[status(thm)],[f273,f407]) ).
fof(f1713,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ product(g2,h,isomorphism6(d2),isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f112,f398]) ).
fof(f1714,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,h,isomorphism6(d2),isomorphism6(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1713]) ).
fof(f1715,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ product(g2,h,isomorphism6(d2),f) ),
inference(forward_demodulation,[status(thm)],[f113,f1714]) ).
fof(f1717,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ sQ25_spl
| ~ product(g2,f,isomorphism1(b),g) ),
inference(backward_demodulation,[status(thm)],[f297,f1696]) ).
fof(f1718,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ sQ25_spl
| ~ product(g2,f,g,g) ),
inference(forward_demodulation,[status(thm)],[f98,f1717]) ).
fof(f1719,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1718,f95]) ).
fof(f1720,plain,
( sQ0_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f1719]) ).
fof(f1721,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f297,f145]) ).
fof(f1722,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ18_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f273,f1721]) ).
fof(f1723,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| X0 = d1
| ~ product(g1,X0,b,b) ),
inference(forward_demodulation,[status(thm)],[f297,f1707]) ).
fof(f1724,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ25_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f297,f1705]) ).
fof(f1725,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| product(g1,d1,identity_for(g1),X0)
| ~ product(g1,b,inverse(g1,b),X0) ),
inference(forward_demodulation,[status(thm)],[f297,f1690]) ).
fof(f1726,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| product(g1,d1,a,X0)
| ~ product(g1,b,inverse(g1,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1725]) ).
fof(f1727,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,d2,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1566]) ).
fof(f1728,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| product(g1,d1,b,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f1727]) ).
fof(f1729,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,d2,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f204]) ).
fof(f1730,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| product(g1,d1,b,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f1729]) ).
fof(f1731,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism2(d1),isomorphism2(b),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f125]) ).
fof(f1732,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism2(d1),h,isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f101,f1731]) ).
fof(f1733,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism2(d1),h,isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1732]) ).
fof(f1734,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism2(d1),h,h) ),
inference(forward_demodulation,[status(thm)],[f101,f1733]) ).
fof(f1735,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism3(d1),isomorphism3(b),isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f128]) ).
fof(f1736,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism3(d1),f,isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f104,f1735]) ).
fof(f1737,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism3(d1),f,isomorphism3(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1736]) ).
fof(f1738,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism3(d1),f,f) ),
inference(forward_demodulation,[status(thm)],[f104,f1737]) ).
fof(f1739,plain,
( sQ3_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism4(d1),isomorphism4(b),isomorphism4(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f131]) ).
fof(f1740,plain,
( sQ3_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism4(d1),h,isomorphism4(d3)) ),
inference(forward_demodulation,[status(thm)],[f107,f1739]) ).
fof(f1741,plain,
( sQ3_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism4(d1),h,isomorphism4(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1740]) ).
fof(f1742,plain,
( sQ3_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism4(d1),h,h) ),
inference(forward_demodulation,[status(thm)],[f107,f1741]) ).
fof(f1743,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism5(d1),isomorphism5(b),isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f134]) ).
fof(f1744,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism5(d1),g,isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f110,f1743]) ).
fof(f1745,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism5(d1),g,isomorphism5(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1744]) ).
fof(f1746,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism5(d1),g,g) ),
inference(forward_demodulation,[status(thm)],[f110,f1745]) ).
fof(f1747,plain,
! [X0] :
( ~ sQ18_spl
| X0 = d2
| ~ product(g1,d1,X0,b) ),
inference(forward_demodulation,[status(thm)],[f273,f148]) ).
fof(f1748,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,d1,X0,b) ),
inference(forward_demodulation,[status(thm)],[f297,f1747]) ).
fof(f1749,plain,
! [X0] :
( ~ sQ25_spl
| X0 = d3
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f144]) ).
fof(f1750,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1749]) ).
fof(f1751,plain,
( ~ sQ25_spl
| product(g1,d1,b,d3) ),
inference(forward_demodulation,[status(thm)],[f297,f118]) ).
fof(f1752,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| product(g1,d1,b,b) ),
inference(forward_demodulation,[status(thm)],[f273,f1751]) ).
fof(f1753,plain,
( sQ5_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism6(d1),isomorphism6(b),isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f137]) ).
fof(f1754,plain,
( sQ5_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism6(d1),f,isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f113,f1753]) ).
fof(f1755,plain,
( sQ5_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism6(d1),f,isomorphism6(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1754]) ).
fof(f1756,plain,
( sQ5_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism6(d1),f,f) ),
inference(forward_demodulation,[status(thm)],[f113,f1755]) ).
fof(f1759,plain,
( sQ3_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism4(b),h,h) ),
inference(backward_demodulation,[status(thm)],[f307,f1742]) ).
fof(f1761,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism3(b),f,f) ),
inference(backward_demodulation,[status(thm)],[f307,f1738]) ).
fof(f1762,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism2(b),h,h) ),
inference(backward_demodulation,[status(thm)],[f307,f1734]) ).
fof(f1763,plain,
( sQ3_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,h,h) ),
inference(forward_demodulation,[status(thm)],[f107,f1759]) ).
fof(f1764,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,f,f,f) ),
inference(forward_demodulation,[status(thm)],[f104,f1761]) ).
fof(f1765,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1764,f95]) ).
fof(f1766,plain,
( sQ2_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl ),
inference(contradiction_clause,[status(thm)],[f1765]) ).
fof(f1767,plain,
( sQ1_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,h,h) ),
inference(forward_demodulation,[status(thm)],[f101,f1762]) ).
fof(f1768,plain,
( ~ sQ2_spl
| ~ sQ28_spl
| product(g2,isomorphism3(b),isomorphism3(d2),isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f307,f127]) ).
fof(f1769,plain,
( ~ sQ2_spl
| ~ sQ28_spl
| product(g2,f,isomorphism3(d2),isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f104,f1768]) ).
fof(f1770,plain,
( ~ sQ2_spl
| ~ sQ28_spl
| ~ sQ25_spl
| product(g2,f,isomorphism3(b),isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f1769]) ).
fof(f1771,plain,
( ~ sQ2_spl
| ~ sQ28_spl
| ~ sQ25_spl
| product(g2,f,f,isomorphism3(d3)) ),
inference(forward_demodulation,[status(thm)],[f104,f1770]) ).
fof(f1775,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism5(b),g,g) ),
inference(forward_demodulation,[status(thm)],[f307,f1746]) ).
fof(f1776,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,g,g) ),
inference(forward_demodulation,[status(thm)],[f110,f1775]) ).
fof(f1777,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,b,b) ),
inference(forward_demodulation,[status(thm)],[f307,f1752]) ).
fof(f1778,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| b = a ),
inference(resolution,[status(thm)],[f1777,f206]) ).
fof(f1779,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,a,b,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f1777,f173]) ).
fof(f1780,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1777,f172]) ).
fof(f1782,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| b = identity_for(g1) ),
inference(resolution,[status(thm)],[f1777,f167]) ).
fof(f1783,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1777,f158]) ).
fof(f1784,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(resolution,[status(thm)],[f1777,f157]) ).
fof(f1786,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1777,f146]) ).
fof(f1787,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f1777,f139]) ).
fof(f1788,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| X0 = b
| ~ product(g1,X0,b,b) ),
inference(resolution,[status(thm)],[f1777,f75]) ).
fof(f1789,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| X0 = b
| ~ product(g1,b,X0,b) ),
inference(resolution,[status(thm)],[f1777,f73]) ).
fof(f1790,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1777,f71]) ).
fof(f1791,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1777,f69]) ).
fof(f1792,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| X0 = b
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f1777,f67]) ).
fof(f1793,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f1778,f242,f306,f272,f296]) ).
fof(f1795,plain,
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f1782,f282,f306,f272,f296]) ).
fof(f1796,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1783]) ).
fof(f1797,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1784]) ).
fof(f1799,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1786]) ).
fof(f1800,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ28_spl
| product(g1,a,b,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1787]) ).
fof(f1805,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ sQ25_spl
| ~ product(g2,f,isomorphism2(b),h) ),
inference(forward_demodulation,[status(thm)],[f297,f1698]) ).
fof(f1806,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ sQ25_spl
| ~ product(g2,f,h,h) ),
inference(forward_demodulation,[status(thm)],[f101,f1805]) ).
fof(f1807,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1806,f95]) ).
fof(f1808,plain,
( sQ1_spl
| ~ sQ27_spl
| ~ sQ18_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f1807]) ).
fof(f1820,plain,
( ~ sQ0_spl
| ~ sQ25_spl
| product(g2,isomorphism1(d1),isomorphism1(b),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f121]) ).
fof(f1821,plain,
( ~ sQ0_spl
| ~ sQ25_spl
| product(g2,isomorphism1(d1),g,isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f98,f1820]) ).
fof(f1822,plain,
( ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ18_spl
| product(g2,isomorphism1(d1),g,isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1821]) ).
fof(f1823,plain,
( ~ sQ0_spl
| ~ sQ25_spl
| ~ sQ18_spl
| product(g2,isomorphism1(d1),g,g) ),
inference(forward_demodulation,[status(thm)],[f98,f1822]) ).
fof(f1824,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| product(g2,isomorphism2(d1),isomorphism2(b),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f124]) ).
fof(f1825,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| product(g2,isomorphism2(d1),h,isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f101,f1824]) ).
fof(f1826,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ18_spl
| product(g2,isomorphism2(d1),h,isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f1825]) ).
fof(f1827,plain,
( ~ sQ1_spl
| ~ sQ25_spl
| ~ sQ18_spl
| product(g2,isomorphism2(d1),h,h) ),
inference(forward_demodulation,[status(thm)],[f101,f1826]) ).
fof(f1831,plain,
( sQ5_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism6(a),f,f) ),
inference(forward_demodulation,[status(thm)],[f304,f1756]) ).
fof(f1832,plain,
( sQ5_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ27_spl
| ~ product(g2,h,f,f) ),
inference(forward_demodulation,[status(thm)],[f112,f1831]) ).
fof(f1834,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| inverse(g1,b) = b ),
inference(forward_demodulation,[status(thm)],[f273,f263]) ).
fof(f1835,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,b,a) ),
inference(paramodulation,[status(thm)],[f1834,f214]) ).
fof(f1837,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1834,f168]) ).
fof(f1838,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| X0 = identity_for(g1)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f1834,f163]) ).
fof(f1839,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1834,f162]) ).
fof(f1840,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1834,f161]) ).
fof(f1842,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| inverse(g1,b) = b ),
inference(paramodulation,[status(thm)],[f1834,f537]) ).
fof(f1843,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,b,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1834,f156]) ).
fof(f1846,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f1837]) ).
fof(f1847,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1838]) ).
fof(f1848,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f1839]) ).
fof(f1849,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f1840]) ).
fof(f1851,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1842,f715,f272,f262]) ).
fof(f1852,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f1843]) ).
fof(f1855,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism5(a),g,g) ),
inference(forward_demodulation,[status(thm)],[f304,f1746]) ).
fof(f1856,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ27_spl
| ~ product(g2,h,g,g) ),
inference(forward_demodulation,[status(thm)],[f109,f1855]) ).
fof(f1876,plain,
( sQ3_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism4(a),h,h) ),
inference(forward_demodulation,[status(thm)],[f304,f1742]) ).
fof(f1877,plain,
( sQ3_spl
| ~ sQ25_spl
| ~ sQ18_spl
| ~ sQ27_spl
| ~ product(g2,g,h,h) ),
inference(forward_demodulation,[status(thm)],[f106,f1876]) ).
fof(f1883,plain,
( sQ14_spl
| ~ sQ18_spl
| inverse(g1,b) != a ),
inference(forward_demodulation,[status(thm)],[f273,f261]) ).
fof(f1888,plain,
group_member(multiply(g1,a,b),g1),
inference(resolution,[status(thm)],[f193,f78]) ).
fof(f1889,plain,
group_member(multiply(g1,a,identity_for(g1)),g1),
inference(resolution,[status(thm)],[f193,f58]) ).
fof(f1890,plain,
group_member(multiply(g1,a,a),g1),
inference(resolution,[status(thm)],[f193,f77]) ).
fof(f1891,plain,
group_member(multiply(g1,a,a),g1),
inference(forward_demodulation,[status(thm)],[f91,f1889]) ).
fof(f1895,plain,
product(g1,a,b,multiply(g1,a,b)),
inference(resolution,[status(thm)],[f184,f78]) ).
fof(f1896,plain,
product(g1,a,identity_for(g1),multiply(g1,a,identity_for(g1))),
inference(resolution,[status(thm)],[f184,f58]) ).
fof(f1897,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(resolution,[status(thm)],[f184,f77]) ).
fof(f1898,plain,
product(g1,a,a,multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f1896]) ).
fof(f1899,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f91,f1898]) ).
fof(f1903,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| inverse(g1,b) = a ),
inference(forward_demodulation,[status(thm)],[f297,f250]) ).
fof(f1904,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| product(g1,a,b,a) ),
inference(paramodulation,[status(thm)],[f1903,f214]) ).
fof(f1905,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| product(g1,b,a,a) ),
inference(paramodulation,[status(thm)],[f1903,f213]) ).
fof(f1906,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,X0,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1903,f168]) ).
fof(f1907,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ25_spl
| X0 = identity_for(g1)
| ~ product(g1,b,a,X0) ),
inference(paramodulation,[status(thm)],[f1903,f163]) ).
fof(f1908,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ25_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f1903,f162]) ).
fof(f1909,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f1903,f161]) ).
fof(f1910,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ25_spl
| X0 = identity_for(g1)
| ~ product(g1,a,b,X0) ),
inference(paramodulation,[status(thm)],[f1903,f159]) ).
fof(f1911,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| inverse(g1,a) = b ),
inference(paramodulation,[status(thm)],[f1903,f537]) ).
fof(f1912,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,a,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1903,f156]) ).
fof(f1913,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| product(g1,b,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1903,f63]) ).
fof(f1914,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| product(g1,a,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1903,f62]) ).
fof(f1916,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,X0,a,a) ),
inference(forward_demodulation,[status(thm)],[f91,f1906]) ).
fof(f1917,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1907]) ).
fof(f1918,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ25_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f1908]) ).
fof(f1919,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ25_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f1909]) ).
fof(f1920,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1910]) ).
fof(f1921,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f1572,f1911]) ).
fof(f1922,plain,
( ~ sQ11_spl
| ~ sQ25_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1921,f80]) ).
fof(f1923,plain,
( ~ sQ11_spl
| ~ sQ25_spl ),
inference(contradiction_clause,[status(thm)],[f1922]) ).
fof(f1924,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| inverse(g1,b) = a ),
inference(forward_demodulation,[status(thm)],[f273,f260]) ).
fof(f1925,plain,
( sQ15_spl
| ~ sQ18_spl
| inverse(g1,b) != b ),
inference(forward_demodulation,[status(thm)],[f273,f264]) ).
fof(f1927,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| inverse(g1,b) = b ),
inference(forward_demodulation,[status(thm)],[f297,f253]) ).
fof(f1928,plain,
( ~ sQ39_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f1572,f811]) ).
fof(f1929,plain,
( ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1928,f80]) ).
fof(f1930,plain,
~ sQ39_spl,
inference(contradiction_clause,[status(thm)],[f1929]) ).
fof(f1931,plain,
( ~ sQ18_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f273,f151]) ).
fof(f1932,plain,
( ~ sQ18_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f1931,f184]) ).
fof(f1933,plain,
( ~ sQ18_spl
| group_member(multiply(g1,a,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f1931,f193]) ).
fof(f1934,plain,
( ~ sQ18_spl
| group_member(multiply(g1,b,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f1931,f189]) ).
fof(f1935,plain,
( ~ sQ18_spl
| group_member(multiply(g1,c,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f1931,f188]) ).
fof(f1936,plain,
( ~ sQ18_spl
| product(g1,b,inverse(g1,b),multiply(g1,b,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f1931,f180]) ).
fof(f1937,plain,
( ~ sQ18_spl
| product(g1,c,inverse(g1,b),multiply(g1,c,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f1931,f179]) ).
fof(f1939,plain,
( ~ sQ18_spl
| group_member(multiply(g1,identity_for(g1),inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f1931,f192]) ).
fof(f1940,plain,
( ~ sQ18_spl
| product(g1,identity_for(g1),inverse(g1,b),multiply(g1,identity_for(g1),inverse(g1,b))) ),
inference(resolution,[status(thm)],[f1931,f183]) ).
fof(f1941,plain,
! [X0] :
( ~ sQ18_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1931,f65]) ).
fof(f1942,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1931,f64]) ).
fof(f1945,plain,
( ~ sQ18_spl
| group_member(multiply(g1,a,inverse(g1,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f1939]) ).
fof(f1946,plain,
( ~ sQ18_spl
| product(g1,a,inverse(g1,b),multiply(g1,identity_for(g1),inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f1940]) ).
fof(f1947,plain,
( ~ sQ18_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f1946]) ).
fof(f1951,plain,
product(g1,a,inverse(g1,c),multiply(g1,a,inverse(g1,c))),
inference(resolution,[status(thm)],[f176,f184]) ).
fof(f1952,plain,
group_member(multiply(g1,a,inverse(g1,c)),g1),
inference(resolution,[status(thm)],[f176,f193]) ).
fof(f1953,plain,
group_member(multiply(g1,b,inverse(g1,c)),g1),
inference(resolution,[status(thm)],[f176,f189]) ).
fof(f1954,plain,
group_member(multiply(g1,c,inverse(g1,c)),g1),
inference(resolution,[status(thm)],[f176,f188]) ).
fof(f1955,plain,
product(g1,b,inverse(g1,c),multiply(g1,b,inverse(g1,c))),
inference(resolution,[status(thm)],[f176,f180]) ).
fof(f1956,plain,
product(g1,c,inverse(g1,c),multiply(g1,c,inverse(g1,c))),
inference(resolution,[status(thm)],[f176,f179]) ).
fof(f1958,plain,
group_member(multiply(g1,identity_for(g1),inverse(g1,c)),g1),
inference(resolution,[status(thm)],[f176,f192]) ).
fof(f1959,plain,
product(g1,identity_for(g1),inverse(g1,c),multiply(g1,identity_for(g1),inverse(g1,c))),
inference(resolution,[status(thm)],[f176,f183]) ).
fof(f1960,plain,
! [X0] :
( group_member(multiply(g1,inverse(g1,c),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f176,f65]) ).
fof(f1961,plain,
! [X0] :
( product(g1,inverse(g1,c),X0,multiply(g1,inverse(g1,c),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f176,f64]) ).
fof(f1964,plain,
group_member(multiply(g1,a,inverse(g1,c)),g1),
inference(forward_demodulation,[status(thm)],[f91,f1958]) ).
fof(f1965,plain,
product(g1,a,inverse(g1,c),multiply(g1,identity_for(g1),inverse(g1,c))),
inference(forward_demodulation,[status(thm)],[f91,f1959]) ).
fof(f1966,plain,
product(g1,a,inverse(g1,c),multiply(g1,a,inverse(g1,c))),
inference(forward_demodulation,[status(thm)],[f91,f1965]) ).
fof(f1971,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| product(g1,a,b,a) ),
inference(paramodulation,[status(thm)],[f1924,f214]) ).
fof(f1972,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| product(g1,b,a,a) ),
inference(paramodulation,[status(thm)],[f1924,f213]) ).
fof(f1973,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,X0,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1924,f168]) ).
fof(f1974,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ18_spl
| X0 = identity_for(g1)
| ~ product(g1,b,a,X0) ),
inference(paramodulation,[status(thm)],[f1924,f163]) ).
fof(f1975,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f1924,f162]) ).
fof(f1976,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f1924,f161]) ).
fof(f1977,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ18_spl
| X0 = identity_for(g1)
| ~ product(g1,a,b,X0) ),
inference(paramodulation,[status(thm)],[f1924,f159]) ).
fof(f1978,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| inverse(g1,a) = b ),
inference(paramodulation,[status(thm)],[f1924,f537]) ).
fof(f1979,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,a,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1924,f156]) ).
fof(f1980,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| product(g1,b,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1924,f63]) ).
fof(f1981,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| product(g1,a,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1924,f62]) ).
fof(f1982,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,X0,a,a) ),
inference(forward_demodulation,[status(thm)],[f91,f1973]) ).
fof(f1983,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1974]) ).
fof(f1984,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f1975]) ).
fof(f1985,plain,
! [X0,X1,X2] :
( ~ sQ14_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f1976]) ).
fof(f1986,plain,
! [X0] :
( ~ sQ14_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1977]) ).
fof(f1987,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f1572,f1978]) ).
fof(f1988,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1987,f80]) ).
fof(f1989,plain,
( ~ sQ14_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f1988]) ).
fof(f1990,plain,
( ~ sQ42_spl
| a = c ),
inference(forward_demodulation,[status(thm)],[f1572,f900]) ).
fof(f1991,plain,
( ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1990,f81]) ).
fof(f1992,plain,
~ sQ42_spl,
inference(contradiction_clause,[status(thm)],[f1991]) ).
fof(f1993,plain,
( ~ sQ25_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f154]) ).
fof(f1994,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f1993,f184]) ).
fof(f1995,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f1993,f193]) ).
fof(f1996,plain,
( ~ sQ25_spl
| group_member(multiply(g1,b,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f1993,f189]) ).
fof(f1997,plain,
( ~ sQ25_spl
| group_member(multiply(g1,c,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f1993,f188]) ).
fof(f1998,plain,
( ~ sQ25_spl
| product(g1,b,inverse(g1,b),multiply(g1,b,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f1993,f180]) ).
fof(f1999,plain,
( ~ sQ25_spl
| product(g1,c,inverse(g1,b),multiply(g1,c,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f1993,f179]) ).
fof(f2001,plain,
( ~ sQ25_spl
| group_member(multiply(g1,identity_for(g1),inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f1993,f192]) ).
fof(f2002,plain,
( ~ sQ25_spl
| product(g1,identity_for(g1),inverse(g1,b),multiply(g1,identity_for(g1),inverse(g1,b))) ),
inference(resolution,[status(thm)],[f1993,f183]) ).
fof(f2003,plain,
! [X0] :
( ~ sQ25_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1993,f65]) ).
fof(f2004,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1993,f64]) ).
fof(f2007,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,inverse(g1,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f2001]) ).
fof(f2008,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,identity_for(g1),inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f2002]) ).
fof(f2009,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f2008]) ).
fof(f2015,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,a) ),
inference(paramodulation,[status(thm)],[f1927,f214]) ).
fof(f2016,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,a) ),
inference(paramodulation,[status(thm)],[f1927,f213]) ).
fof(f2017,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1927,f168]) ).
fof(f2018,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = identity_for(g1)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f1927,f163]) ).
fof(f2019,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1927,f162]) ).
fof(f2020,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1927,f161]) ).
fof(f2021,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = identity_for(g1)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f1927,f159]) ).
fof(f2023,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,b,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1927,f156]) ).
fof(f2024,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1927,f63]) ).
fof(f2025,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1927,f62]) ).
fof(f2026,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f2017]) ).
fof(f2027,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2018]) ).
fof(f2028,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f2019]) ).
fof(f2029,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f2020]) ).
fof(f2030,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2021]) ).
fof(f2031,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f2023]) ).
fof(f2032,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f2024]) ).
fof(f2033,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f2025]) ).
fof(f2053,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(resolution,[status(thm)],[f1149,f75]) ).
fof(f2057,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f1149,f67]) ).
fof(f2089,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f162]) ).
fof(f2090,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f161]) ).
fof(f2098,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f2089]) ).
fof(f2099,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f2090]) ).
fof(f2110,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f420]) ).
fof(f2111,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f1927,f420]) ).
fof(f2114,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1100,f420]) ).
fof(f2129,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2110]) ).
fof(f2130,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2129]) ).
fof(f2131,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2111]) ).
fof(f2132,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2131]) ).
fof(f2136,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,identity_for(g2),X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f2114]) ).
fof(f2137,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f2136]) ).
fof(f2145,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f422]) ).
fof(f2146,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f1927,f422]) ).
fof(f2148,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1278,f422]) ).
fof(f2164,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2145]) ).
fof(f2165,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2164]) ).
fof(f2166,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2146]) ).
fof(f2167,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2166]) ).
fof(f2169,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,identity_for(g2),X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f2148]) ).
fof(f2170,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f2169]) ).
fof(f2196,plain,
( ~ sQ56_spl
| ~ sQ55_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f1509,f1512]) ).
fof(f2197,plain,
( ~ sQ56_spl
| ~ sQ55_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f2196,f235,f1508,f1511]) ).
fof(f2198,plain,
! [X0] :
( ~ sQ18_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f273,f190]) ).
fof(f2200,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f1150,f379]) ).
fof(f2201,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,h,X0)
| ~ product(g2,f,f,X0) ),
inference(resolution,[status(thm)],[f1150,f378]) ).
fof(f2204,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,h,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f1150,f146]) ).
fof(f2205,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f1150,f139]) ).
fof(f2206,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,f) ),
inference(resolution,[status(thm)],[f1150,f75]) ).
fof(f2207,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(resolution,[status(thm)],[f1150,f73]) ).
fof(f2208,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f1150,f71]) ).
fof(f2209,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f1150,f69]) ).
fof(f2210,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f1150,f67]) ).
fof(f2215,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,h,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f2204]) ).
fof(f2216,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f2205]) ).
fof(f2235,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,d3),X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f273,f181]) ).
fof(f2281,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,d2),X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f297,f200]) ).
fof(f2288,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(paramodulation,[status(thm)],[f1100,f541]) ).
fof(f2297,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,b,X0,a) ),
inference(paramodulation,[status(thm)],[f1927,f542]) ).
fof(f2308,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1100,f554]) ).
fof(f2321,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f556]) ).
fof(f2322,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f1927,f556]) ).
fof(f2331,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f1835,f173]) ).
fof(f2332,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f1835,f172]) ).
fof(f2333,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1835,f158]) ).
fof(f2334,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f1835,f157]) ).
fof(f2335,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f1835,f146]) ).
fof(f2336,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f1835,f139]) ).
fof(f2339,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1835,f71]) ).
fof(f2340,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1835,f69]) ).
fof(f2342,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2333]) ).
fof(f2346,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2335]) ).
fof(f2347,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2336]) ).
fof(f2348,plain,
! [X0] :
( ~ sQ25_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f297,f199]) ).
fof(f2355,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| ~ sQ12_spl
| product(g1,d1,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1927,f1726]) ).
fof(f2356,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f304,f2355]) ).
fof(f2359,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f839,f173]) ).
fof(f2360,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,c,c,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f839,f172]) ).
fof(f2363,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,c,c,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f839,f146]) ).
fof(f2364,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f839,f139]) ).
fof(f2367,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f839,f71]) ).
fof(f2368,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f839,f69]) ).
fof(f2374,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,c,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2363]) ).
fof(f2375,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2364]) ).
fof(f2401,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1278,f637]) ).
fof(f2415,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f638]) ).
fof(f2416,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f1927,f638]) ).
fof(f2434,plain,
product(g1,a,multiply(g1,c,a),multiply(g1,a,multiply(g1,c,a))),
inference(resolution,[status(thm)],[f1020,f184]) ).
fof(f2435,plain,
group_member(multiply(g1,a,multiply(g1,c,a)),g1),
inference(resolution,[status(thm)],[f1020,f193]) ).
fof(f2436,plain,
group_member(multiply(g1,b,multiply(g1,c,a)),g1),
inference(resolution,[status(thm)],[f1020,f189]) ).
fof(f2437,plain,
group_member(multiply(g1,c,multiply(g1,c,a)),g1),
inference(resolution,[status(thm)],[f1020,f188]) ).
fof(f2438,plain,
product(g1,b,multiply(g1,c,a),multiply(g1,b,multiply(g1,c,a))),
inference(resolution,[status(thm)],[f1020,f180]) ).
fof(f2439,plain,
product(g1,c,multiply(g1,c,a),multiply(g1,c,multiply(g1,c,a))),
inference(resolution,[status(thm)],[f1020,f179]) ).
fof(f2440,plain,
( multiply(g1,c,a) = c
| multiply(g1,c,a) = b
| multiply(g1,c,a) = a ),
inference(resolution,[status(thm)],[f1020,f89]) ).
fof(f2441,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,c,a)),g1),
inference(resolution,[status(thm)],[f1020,f192]) ).
fof(f2442,plain,
product(g1,identity_for(g1),multiply(g1,c,a),multiply(g1,identity_for(g1),multiply(g1,c,a))),
inference(resolution,[status(thm)],[f1020,f183]) ).
fof(f2443,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,c,a),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1020,f65]) ).
fof(f2444,plain,
! [X0] :
( product(g1,multiply(g1,c,a),X0,multiply(g1,multiply(g1,c,a),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1020,f64]) ).
fof(f2445,plain,
group_member(inverse(g1,multiply(g1,c,a)),g1),
inference(resolution,[status(thm)],[f1020,f61]) ).
fof(f2446,definition,
( sQ57_spl
<=> multiply(g1,c,a) = a ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f2447,plain,
( ~ sQ57_spl
| multiply(g1,c,a) = a ),
inference(component_clause,[status(thm)],[f2446]) ).
fof(f2448,plain,
( sQ57_spl
| multiply(g1,c,a) != a ),
inference(component_clause,[status(thm)],[f2446]) ).
fof(f2449,definition,
( sQ58_spl
<=> multiply(g1,c,a) = b ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f2450,plain,
( ~ sQ58_spl
| multiply(g1,c,a) = b ),
inference(component_clause,[status(thm)],[f2449]) ).
fof(f2451,plain,
( sQ58_spl
| multiply(g1,c,a) != b ),
inference(component_clause,[status(thm)],[f2449]) ).
fof(f2452,definition,
( sQ59_spl
<=> multiply(g1,c,a) = c ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f2453,plain,
( ~ sQ59_spl
| multiply(g1,c,a) = c ),
inference(component_clause,[status(thm)],[f2452]) ).
fof(f2455,plain,
( sQ59_spl
| sQ58_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f2440,f2446,f2449,f2452]) ).
fof(f2456,plain,
group_member(multiply(g1,a,multiply(g1,c,a)),g1),
inference(forward_demodulation,[status(thm)],[f91,f2441]) ).
fof(f2457,plain,
product(g1,a,multiply(g1,c,a),multiply(g1,identity_for(g1),multiply(g1,c,a))),
inference(forward_demodulation,[status(thm)],[f91,f2442]) ).
fof(f2458,plain,
product(g1,a,multiply(g1,c,a),multiply(g1,a,multiply(g1,c,a))),
inference(forward_demodulation,[status(thm)],[f91,f2457]) ).
fof(f2480,plain,
( ~ sQ59_spl
| ~ sQ58_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f2450,f2453]) ).
fof(f2481,plain,
( ~ sQ59_spl
| ~ sQ58_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f2480,f235,f2449,f2452]) ).
fof(f2484,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,f) ),
inference(paramodulation,[status(thm)],[f1278,f703]) ).
fof(f2485,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(paramodulation,[status(thm)],[f1100,f703]) ).
fof(f2494,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,X0,b,a) ),
inference(paramodulation,[status(thm)],[f1927,f704]) ).
fof(f2503,plain,
product(g1,a,multiply(g1,b,a),multiply(g1,a,multiply(g1,b,a))),
inference(resolution,[status(thm)],[f1026,f184]) ).
fof(f2504,plain,
group_member(multiply(g1,a,multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f1026,f193]) ).
fof(f2505,plain,
group_member(multiply(g1,b,multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f1026,f189]) ).
fof(f2506,plain,
group_member(multiply(g1,c,multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f1026,f188]) ).
fof(f2507,plain,
product(g1,b,multiply(g1,b,a),multiply(g1,b,multiply(g1,b,a))),
inference(resolution,[status(thm)],[f1026,f180]) ).
fof(f2508,plain,
product(g1,c,multiply(g1,b,a),multiply(g1,c,multiply(g1,b,a))),
inference(resolution,[status(thm)],[f1026,f179]) ).
fof(f2509,plain,
( multiply(g1,b,a) = c
| multiply(g1,b,a) = b
| multiply(g1,b,a) = a ),
inference(resolution,[status(thm)],[f1026,f89]) ).
fof(f2510,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f1026,f192]) ).
fof(f2511,plain,
product(g1,identity_for(g1),multiply(g1,b,a),multiply(g1,identity_for(g1),multiply(g1,b,a))),
inference(resolution,[status(thm)],[f1026,f183]) ).
fof(f2512,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,b,a),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1026,f65]) ).
fof(f2513,plain,
! [X0] :
( product(g1,multiply(g1,b,a),X0,multiply(g1,multiply(g1,b,a),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1026,f64]) ).
fof(f2514,plain,
group_member(inverse(g1,multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f1026,f61]) ).
fof(f2515,definition,
( sQ60_spl
<=> multiply(g1,b,a) = a ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f2516,plain,
( ~ sQ60_spl
| multiply(g1,b,a) = a ),
inference(component_clause,[status(thm)],[f2515]) ).
fof(f2517,plain,
( sQ60_spl
| multiply(g1,b,a) != a ),
inference(component_clause,[status(thm)],[f2515]) ).
fof(f2518,definition,
( sQ61_spl
<=> multiply(g1,b,a) = b ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f2519,plain,
( ~ sQ61_spl
| multiply(g1,b,a) = b ),
inference(component_clause,[status(thm)],[f2518]) ).
fof(f2520,plain,
( sQ61_spl
| multiply(g1,b,a) != b ),
inference(component_clause,[status(thm)],[f2518]) ).
fof(f2521,definition,
( sQ62_spl
<=> multiply(g1,b,a) = c ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f2522,plain,
( ~ sQ62_spl
| multiply(g1,b,a) = c ),
inference(component_clause,[status(thm)],[f2521]) ).
fof(f2523,plain,
( sQ62_spl
| multiply(g1,b,a) != c ),
inference(component_clause,[status(thm)],[f2521]) ).
fof(f2524,plain,
( sQ62_spl
| sQ61_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f2509,f2515,f2518,f2521]) ).
fof(f2525,plain,
group_member(multiply(g1,a,multiply(g1,b,a)),g1),
inference(forward_demodulation,[status(thm)],[f91,f2510]) ).
fof(f2526,plain,
product(g1,a,multiply(g1,b,a),multiply(g1,identity_for(g1),multiply(g1,b,a))),
inference(forward_demodulation,[status(thm)],[f91,f2511]) ).
fof(f2527,plain,
product(g1,a,multiply(g1,b,a),multiply(g1,a,multiply(g1,b,a))),
inference(forward_demodulation,[status(thm)],[f91,f2526]) ).
fof(f2534,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,a,a))),
inference(resolution,[status(thm)],[f1042,f184]) ).
fof(f2535,plain,
group_member(multiply(g1,a,multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f1042,f193]) ).
fof(f2536,plain,
group_member(multiply(g1,b,multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f1042,f189]) ).
fof(f2537,plain,
group_member(multiply(g1,c,multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f1042,f188]) ).
fof(f2538,plain,
product(g1,b,multiply(g1,a,a),multiply(g1,b,multiply(g1,a,a))),
inference(resolution,[status(thm)],[f1042,f180]) ).
fof(f2539,plain,
product(g1,c,multiply(g1,a,a),multiply(g1,c,multiply(g1,a,a))),
inference(resolution,[status(thm)],[f1042,f179]) ).
fof(f2540,plain,
( multiply(g1,a,a) = c
| multiply(g1,a,a) = b
| multiply(g1,a,a) = a ),
inference(resolution,[status(thm)],[f1042,f89]) ).
fof(f2541,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f1042,f192]) ).
fof(f2542,plain,
product(g1,identity_for(g1),multiply(g1,a,a),multiply(g1,identity_for(g1),multiply(g1,a,a))),
inference(resolution,[status(thm)],[f1042,f183]) ).
fof(f2543,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,a,a),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1042,f65]) ).
fof(f2544,plain,
! [X0] :
( product(g1,multiply(g1,a,a),X0,multiply(g1,multiply(g1,a,a),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1042,f64]) ).
fof(f2545,plain,
group_member(inverse(g1,multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f1042,f61]) ).
fof(f2546,definition,
( sQ63_spl
<=> multiply(g1,a,a) = a ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f2547,plain,
( ~ sQ63_spl
| multiply(g1,a,a) = a ),
inference(component_clause,[status(thm)],[f2546]) ).
fof(f2549,definition,
( sQ64_spl
<=> multiply(g1,a,a) = b ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f2550,plain,
( ~ sQ64_spl
| multiply(g1,a,a) = b ),
inference(component_clause,[status(thm)],[f2549]) ).
fof(f2551,plain,
( sQ64_spl
| multiply(g1,a,a) != b ),
inference(component_clause,[status(thm)],[f2549]) ).
fof(f2552,definition,
( sQ65_spl
<=> multiply(g1,a,a) = c ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f2553,plain,
( ~ sQ65_spl
| multiply(g1,a,a) = c ),
inference(component_clause,[status(thm)],[f2552]) ).
fof(f2555,plain,
( sQ65_spl
| sQ64_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f2540,f2546,f2549,f2552]) ).
fof(f2556,plain,
group_member(multiply(g1,a,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f91,f2541]) ).
fof(f2557,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,identity_for(g1),multiply(g1,a,a))),
inference(forward_demodulation,[status(thm)],[f91,f2542]) ).
fof(f2558,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,a,a))),
inference(forward_demodulation,[status(thm)],[f91,f2557]) ).
fof(f2560,plain,
( ~ sQ65_spl
| ~ sQ64_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f2550,f2553]) ).
fof(f2561,plain,
( ~ sQ65_spl
| ~ sQ64_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f2560,f235,f2549,f2552]) ).
fof(f2564,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| inverse(g1,b) = b ),
inference(resolution,[status(thm)],[f1852,f213]) ).
fof(f2565,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f1927,f1932]) ).
fof(f2566,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1927,f2565]) ).
fof(f2567,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f1506,f2566]) ).
fof(f2568,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,b,a,a) ),
inference(resolution,[status(thm)],[f2567,f500]) ).
fof(f2569,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,X0,a,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f2567,f208]) ).
fof(f2570,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f2567,f207]) ).
fof(f2575,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| b = a ),
inference(resolution,[status(thm)],[f2567,f206]) ).
fof(f2576,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f2567,f173]) ).
fof(f2577,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f2567,f172]) ).
fof(f2578,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f2567,f158]) ).
fof(f2579,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f2567,f157]) ).
fof(f2580,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| b = identity_for(g1) ),
inference(resolution,[status(thm)],[f2567,f150]) ).
fof(f2581,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2567,f146]) ).
fof(f2582,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f2567,f139]) ).
fof(f2583,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| X0 = a
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f2567,f75]) ).
fof(f2584,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| X0 = b
| ~ product(g1,a,X0,a) ),
inference(resolution,[status(thm)],[f2567,f73]) ).
fof(f2585,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f2567,f71]) ).
fof(f2586,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f2567,f69]) ).
fof(f2587,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ54_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f2567,f67]) ).
fof(f2595,plain,
( ~ sQ57_spl
| product(g1,c,a,a) ),
inference(forward_demodulation,[status(thm)],[f2447,f872]) ).
fof(f2596,plain,
( ~ sQ57_spl
| product(g1,a,c,a) ),
inference(resolution,[status(thm)],[f2595,f425]) ).
fof(f2598,plain,
( ~ sQ57_spl
| c = inverse(g1,a) ),
inference(resolution,[status(thm)],[f2595,f692]) ).
fof(f2599,plain,
( ~ sQ57_spl
| a = inverse(g1,c) ),
inference(resolution,[status(thm)],[f2595,f612]) ).
fof(f2600,plain,
! [X0] :
( ~ sQ57_spl
| product(g1,a,a,X0)
| ~ product(g1,c,a,X0) ),
inference(resolution,[status(thm)],[f2595,f173]) ).
fof(f2601,plain,
! [X0] :
( ~ sQ57_spl
| product(g1,c,a,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f2595,f172]) ).
fof(f2602,plain,
( ~ sQ57_spl
| c = a ),
inference(resolution,[status(thm)],[f2595,f170]) ).
fof(f2603,plain,
( ~ sQ57_spl
| c = identity_for(g1) ),
inference(resolution,[status(thm)],[f2595,f167]) ).
fof(f2604,plain,
! [X0] :
( ~ sQ57_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2595,f158]) ).
fof(f2605,plain,
! [X0] :
( ~ sQ57_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f2595,f157]) ).
fof(f2606,plain,
! [X0] :
( ~ sQ57_spl
| product(g1,c,a,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2595,f146]) ).
fof(f2607,plain,
! [X0] :
( ~ sQ57_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,c,a,X0) ),
inference(resolution,[status(thm)],[f2595,f139]) ).
fof(f2608,plain,
! [X0] :
( ~ sQ57_spl
| X0 = c
| ~ product(g1,X0,a,a) ),
inference(resolution,[status(thm)],[f2595,f75]) ).
fof(f2609,plain,
! [X0] :
( ~ sQ57_spl
| X0 = a
| ~ product(g1,c,X0,a) ),
inference(resolution,[status(thm)],[f2595,f73]) ).
fof(f2610,plain,
! [X0,X1,X2] :
( ~ sQ57_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2595,f71]) ).
fof(f2611,plain,
! [X0,X1,X2] :
( ~ sQ57_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2595,f69]) ).
fof(f2612,plain,
! [X0] :
( ~ sQ57_spl
| X0 = a
| ~ product(g1,c,a,X0) ),
inference(resolution,[status(thm)],[f2595,f67]) ).
fof(f2614,plain,
( ~ sQ57_spl
| c = a ),
inference(forward_demodulation,[status(thm)],[f1572,f2598]) ).
fof(f2615,plain,
( ~ sQ57_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2614,f81]) ).
fof(f2616,plain,
~ sQ57_spl,
inference(contradiction_clause,[status(thm)],[f2615]) ).
fof(f2617,plain,
( ~ sQ60_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f2516,f915]) ).
fof(f2619,plain,
( ~ sQ60_spl
| product(g1,a,b,a) ),
inference(resolution,[status(thm)],[f2617,f425]) ).
fof(f2621,plain,
( ~ sQ60_spl
| b = inverse(g1,a) ),
inference(resolution,[status(thm)],[f2617,f692]) ).
fof(f2622,plain,
( ~ sQ60_spl
| a = inverse(g1,b) ),
inference(resolution,[status(thm)],[f2617,f612]) ).
fof(f2623,plain,
! [X0] :
( ~ sQ60_spl
| product(g1,a,a,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f2617,f173]) ).
fof(f2624,plain,
! [X0] :
( ~ sQ60_spl
| product(g1,b,a,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f2617,f172]) ).
fof(f2625,plain,
( ~ sQ60_spl
| b = a ),
inference(resolution,[status(thm)],[f2617,f170]) ).
fof(f2626,plain,
( ~ sQ60_spl
| b = identity_for(g1) ),
inference(resolution,[status(thm)],[f2617,f167]) ).
fof(f2627,plain,
! [X0] :
( ~ sQ60_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2617,f158]) ).
fof(f2628,plain,
! [X0] :
( ~ sQ60_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f2617,f157]) ).
fof(f2629,plain,
! [X0] :
( ~ sQ60_spl
| product(g1,b,a,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2617,f146]) ).
fof(f2630,plain,
! [X0] :
( ~ sQ60_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f2617,f139]) ).
fof(f2631,plain,
! [X0] :
( ~ sQ60_spl
| X0 = b
| ~ product(g1,X0,a,a) ),
inference(resolution,[status(thm)],[f2617,f75]) ).
fof(f2632,plain,
! [X0] :
( ~ sQ60_spl
| X0 = a
| ~ product(g1,b,X0,a) ),
inference(resolution,[status(thm)],[f2617,f73]) ).
fof(f2633,plain,
! [X0,X1,X2] :
( ~ sQ60_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2617,f71]) ).
fof(f2634,plain,
! [X0,X1,X2] :
( ~ sQ60_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2617,f69]) ).
fof(f2635,plain,
! [X0] :
( ~ sQ60_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f2617,f67]) ).
fof(f2638,plain,
( ~ sQ60_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f1572,f2621]) ).
fof(f2639,plain,
( ~ sQ60_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2638,f80]) ).
fof(f2640,plain,
~ sQ60_spl,
inference(contradiction_clause,[status(thm)],[f2639]) ).
fof(f2646,plain,
h = multiply(g2,f,h),
inference(resolution,[status(thm)],[f863,f377]) ).
fof(f2667,plain,
g = multiply(g2,f,g),
inference(resolution,[status(thm)],[f864,f377]) ).
fof(f2685,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1927,f1933]) ).
fof(f2686,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f2685,f184]) ).
fof(f2687,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,a,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f2685,f193]) ).
fof(f2688,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,b,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f2685,f189]) ).
fof(f2689,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,c,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f2685,f188]) ).
fof(f2690,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,multiply(g1,a,b),multiply(g1,b,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f2685,f180]) ).
fof(f2691,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,c,multiply(g1,a,b),multiply(g1,c,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f2685,f179]) ).
fof(f2693,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f2685,f192]) ).
fof(f2694,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f2685,f183]) ).
fof(f2695,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,multiply(g1,a,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f2685,f65]) ).
fof(f2696,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,multiply(g1,a,b),X0,multiply(g1,multiply(g1,a,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f2685,f64]) ).
fof(f2697,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(inverse(g1,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f2685,f61]) ).
fof(f2699,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,a,multiply(g1,a,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f2693]) ).
fof(f2700,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f2694]) ).
fof(f2701,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f2700]) ).
fof(f2713,plain,
f = multiply(g2,f,f),
inference(resolution,[status(thm)],[f865,f377]) ).
fof(f2733,plain,
! [X0] :
( product(g1,a,multiply(g1,c,c),X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f869,f173]) ).
fof(f2734,plain,
! [X0] :
( product(g1,c,c,X0)
| ~ product(g1,a,multiply(g1,c,c),X0) ),
inference(resolution,[status(thm)],[f869,f172]) ).
fof(f2735,plain,
! [X0] :
( product(g1,inverse(g1,c),multiply(g1,c,c),X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f869,f158]) ).
fof(f2736,plain,
! [X0] :
( product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,c),multiply(g1,c,c),X0) ),
inference(resolution,[status(thm)],[f869,f157]) ).
fof(f2737,plain,
! [X0] :
( product(g1,c,c,X0)
| ~ product(g1,identity_for(g1),multiply(g1,c,c),X0) ),
inference(resolution,[status(thm)],[f869,f146]) ).
fof(f2738,plain,
! [X0] :
( product(g1,identity_for(g1),multiply(g1,c,c),X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f869,f139]) ).
fof(f2739,plain,
! [X0] :
( X0 = c
| ~ product(g1,X0,c,multiply(g1,c,c)) ),
inference(resolution,[status(thm)],[f869,f75]) ).
fof(f2740,plain,
! [X0] :
( X0 = c
| ~ product(g1,c,X0,multiply(g1,c,c)) ),
inference(resolution,[status(thm)],[f869,f73]) ).
fof(f2741,plain,
! [X0,X1,X2] :
( product(g1,multiply(g1,c,c),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f869,f71]) ).
fof(f2742,plain,
! [X0,X1,X2] :
( product(g1,c,X1,X2)
| ~ product(g1,multiply(g1,c,c),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f869,f69]) ).
fof(f2743,plain,
! [X0] :
( X0 = multiply(g1,c,c)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f869,f67]) ).
fof(f2744,plain,
! [X0] :
( product(g1,inverse(g1,c),multiply(g1,c,c),X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2735]) ).
fof(f2745,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,c,multiply(g1,c,c),X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f2744]) ).
fof(f2746,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,c,multiply(g1,c,c),X0) ),
inference(forward_demodulation,[status(thm)],[f790,f2736]) ).
fof(f2747,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,c,X0)
| ~ product(g1,c,multiply(g1,c,c),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2746]) ).
fof(f2748,plain,
! [X0] :
( product(g1,c,c,X0)
| ~ product(g1,a,multiply(g1,c,c),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2737]) ).
fof(f2749,plain,
! [X0] :
( product(g1,a,multiply(g1,c,c),X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2738]) ).
fof(f2752,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1927,f1934]) ).
fof(f2753,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,a,multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f2752,f184]) ).
fof(f2754,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,a,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f2752,f193]) ).
fof(f2755,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,b,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f2752,f189]) ).
fof(f2756,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,c,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f2752,f188]) ).
fof(f2757,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,multiply(g1,b,b),multiply(g1,b,multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f2752,f180]) ).
fof(f2758,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,c,multiply(g1,b,b),multiply(g1,c,multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f2752,f179]) ).
fof(f2760,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f2752,f192]) ).
fof(f2761,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),multiply(g1,b,b),multiply(g1,identity_for(g1),multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f2752,f183]) ).
fof(f2762,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,multiply(g1,b,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f2752,f65]) ).
fof(f2763,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,multiply(g1,b,b),X0,multiply(g1,multiply(g1,b,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f2752,f64]) ).
fof(f2764,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(inverse(g1,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f2752,f61]) ).
fof(f2765,definition,
( sQ66_spl
<=> multiply(g1,b,b) = a ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f2766,plain,
( ~ sQ66_spl
| multiply(g1,b,b) = a ),
inference(component_clause,[status(thm)],[f2765]) ).
fof(f2767,plain,
( sQ66_spl
| multiply(g1,b,b) != a ),
inference(component_clause,[status(thm)],[f2765]) ).
fof(f2768,definition,
( sQ67_spl
<=> multiply(g1,b,b) = b ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f2769,plain,
( ~ sQ67_spl
| multiply(g1,b,b) = b ),
inference(component_clause,[status(thm)],[f2768]) ).
fof(f2770,plain,
( sQ67_spl
| multiply(g1,b,b) != b ),
inference(component_clause,[status(thm)],[f2768]) ).
fof(f2771,definition,
( sQ68_spl
<=> multiply(g1,b,b) = c ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f2772,plain,
( ~ sQ68_spl
| multiply(g1,b,b) = c ),
inference(component_clause,[status(thm)],[f2771]) ).
fof(f2773,plain,
( sQ68_spl
| multiply(g1,b,b) != c ),
inference(component_clause,[status(thm)],[f2771]) ).
fof(f2775,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,a,multiply(g1,b,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f2760]) ).
fof(f2776,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,identity_for(g1),multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f2761]) ).
fof(f2777,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,a,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f2776]) ).
fof(f2782,plain,
! [X0] :
( product(g1,a,multiply(g1,c,b),X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f870,f173]) ).
fof(f2783,plain,
! [X0] :
( product(g1,c,b,X0)
| ~ product(g1,a,multiply(g1,c,b),X0) ),
inference(resolution,[status(thm)],[f870,f172]) ).
fof(f2784,plain,
! [X0] :
( product(g1,inverse(g1,c),multiply(g1,c,b),X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f870,f158]) ).
fof(f2785,plain,
! [X0] :
( product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),multiply(g1,c,b),X0) ),
inference(resolution,[status(thm)],[f870,f157]) ).
fof(f2786,plain,
! [X0] :
( product(g1,c,b,X0)
| ~ product(g1,identity_for(g1),multiply(g1,c,b),X0) ),
inference(resolution,[status(thm)],[f870,f146]) ).
fof(f2787,plain,
! [X0] :
( product(g1,identity_for(g1),multiply(g1,c,b),X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f870,f139]) ).
fof(f2788,plain,
! [X0] :
( X0 = c
| ~ product(g1,X0,b,multiply(g1,c,b)) ),
inference(resolution,[status(thm)],[f870,f75]) ).
fof(f2789,plain,
! [X0] :
( X0 = b
| ~ product(g1,c,X0,multiply(g1,c,b)) ),
inference(resolution,[status(thm)],[f870,f73]) ).
fof(f2790,plain,
! [X0,X1,X2] :
( product(g1,multiply(g1,c,b),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f870,f71]) ).
fof(f2791,plain,
! [X0,X1,X2] :
( product(g1,c,X1,X2)
| ~ product(g1,multiply(g1,c,b),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f870,f69]) ).
fof(f2792,plain,
! [X0] :
( X0 = multiply(g1,c,b)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f870,f67]) ).
fof(f2793,plain,
! [X0] :
( product(g1,inverse(g1,c),multiply(g1,c,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2784]) ).
fof(f2794,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,c,multiply(g1,c,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f2793]) ).
fof(f2795,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f790,f2785]) ).
fof(f2796,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2795]) ).
fof(f2797,plain,
! [X0] :
( product(g1,c,b,X0)
| ~ product(g1,a,multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2786]) ).
fof(f2798,plain,
! [X0] :
( product(g1,a,multiply(g1,c,b),X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2787]) ).
fof(f2800,plain,
! [X0] :
( product(g1,a,multiply(g1,b,c),X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f912,f173]) ).
fof(f2801,plain,
! [X0] :
( product(g1,b,c,X0)
| ~ product(g1,a,multiply(g1,b,c),X0) ),
inference(resolution,[status(thm)],[f912,f172]) ).
fof(f2802,plain,
! [X0] :
( product(g1,inverse(g1,b),multiply(g1,b,c),X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f912,f158]) ).
fof(f2803,plain,
! [X0] :
( product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,b),multiply(g1,b,c),X0) ),
inference(resolution,[status(thm)],[f912,f157]) ).
fof(f2804,plain,
! [X0] :
( product(g1,b,c,X0)
| ~ product(g1,identity_for(g1),multiply(g1,b,c),X0) ),
inference(resolution,[status(thm)],[f912,f146]) ).
fof(f2805,plain,
! [X0] :
( product(g1,identity_for(g1),multiply(g1,b,c),X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f912,f139]) ).
fof(f2806,plain,
! [X0] :
( X0 = b
| ~ product(g1,X0,c,multiply(g1,b,c)) ),
inference(resolution,[status(thm)],[f912,f75]) ).
fof(f2807,plain,
! [X0] :
( X0 = c
| ~ product(g1,b,X0,multiply(g1,b,c)) ),
inference(resolution,[status(thm)],[f912,f73]) ).
fof(f2808,plain,
! [X0,X1,X2] :
( product(g1,multiply(g1,b,c),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f912,f71]) ).
fof(f2809,plain,
! [X0,X1,X2] :
( product(g1,b,X1,X2)
| ~ product(g1,multiply(g1,b,c),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f912,f69]) ).
fof(f2810,plain,
! [X0] :
( X0 = multiply(g1,b,c)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f912,f67]) ).
fof(f2811,plain,
! [X0] :
( product(g1,inverse(g1,b),multiply(g1,b,c),X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2802]) ).
fof(f2812,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,multiply(g1,b,c),X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f1927,f2811]) ).
fof(f2813,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,b,multiply(g1,b,c),X0) ),
inference(forward_demodulation,[status(thm)],[f1927,f2803]) ).
fof(f2814,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,c,X0)
| ~ product(g1,b,multiply(g1,b,c),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2813]) ).
fof(f2815,plain,
! [X0] :
( product(g1,b,c,X0)
| ~ product(g1,a,multiply(g1,b,c),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2804]) ).
fof(f2816,plain,
! [X0] :
( product(g1,a,multiply(g1,b,c),X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2805]) ).
fof(f2817,plain,
( ~ sQ68_spl
| ~ sQ67_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f2769,f2772]) ).
fof(f2818,plain,
( ~ sQ68_spl
| ~ sQ67_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f2817,f235,f2768,f2771]) ).
fof(f2819,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1927,f1935]) ).
fof(f2820,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,c,b),multiply(g1,a,multiply(g1,c,b))) ),
inference(resolution,[status(thm)],[f2819,f184]) ).
fof(f2821,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,a,multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f2819,f193]) ).
fof(f2822,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,b,multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f2819,f189]) ).
fof(f2823,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,c,multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f2819,f188]) ).
fof(f2824,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,multiply(g1,c,b),multiply(g1,b,multiply(g1,c,b))) ),
inference(resolution,[status(thm)],[f2819,f180]) ).
fof(f2825,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,c,multiply(g1,c,b),multiply(g1,c,multiply(g1,c,b))) ),
inference(resolution,[status(thm)],[f2819,f179]) ).
fof(f2827,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f2819,f192]) ).
fof(f2828,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),multiply(g1,c,b),multiply(g1,identity_for(g1),multiply(g1,c,b))) ),
inference(resolution,[status(thm)],[f2819,f183]) ).
fof(f2829,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,multiply(g1,c,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f2819,f65]) ).
fof(f2830,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,multiply(g1,c,b),X0,multiply(g1,multiply(g1,c,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f2819,f64]) ).
fof(f2831,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(inverse(g1,multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f2819,f61]) ).
fof(f2832,definition,
( sQ69_spl
<=> multiply(g1,c,b) = a ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f2833,plain,
( ~ sQ69_spl
| multiply(g1,c,b) = a ),
inference(component_clause,[status(thm)],[f2832]) ).
fof(f2834,plain,
( sQ69_spl
| multiply(g1,c,b) != a ),
inference(component_clause,[status(thm)],[f2832]) ).
fof(f2835,definition,
( sQ70_spl
<=> multiply(g1,c,b) = b ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f2836,plain,
( ~ sQ70_spl
| multiply(g1,c,b) = b ),
inference(component_clause,[status(thm)],[f2835]) ).
fof(f2837,plain,
( sQ70_spl
| multiply(g1,c,b) != b ),
inference(component_clause,[status(thm)],[f2835]) ).
fof(f2838,definition,
( sQ71_spl
<=> multiply(g1,c,b) = c ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f2839,plain,
( ~ sQ71_spl
| multiply(g1,c,b) = c ),
inference(component_clause,[status(thm)],[f2838]) ).
fof(f2840,plain,
( sQ71_spl
| multiply(g1,c,b) != c ),
inference(component_clause,[status(thm)],[f2838]) ).
fof(f2842,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,a,multiply(g1,c,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f2827]) ).
fof(f2843,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,c,b),multiply(g1,identity_for(g1),multiply(g1,c,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f2828]) ).
fof(f2844,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,multiply(g1,c,b),multiply(g1,a,multiply(g1,c,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f2843]) ).
fof(f2847,plain,
( ~ sQ71_spl
| product(g1,c,b,c) ),
inference(backward_demodulation,[status(thm)],[f2839,f870]) ).
fof(f2848,plain,
( ~ sQ71_spl
| ~ sQ70_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f2836,f2839]) ).
fof(f2849,plain,
( ~ sQ71_spl
| ~ sQ70_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f2848,f235,f2835,f2838]) ).
fof(f2850,plain,
( ~ sQ66_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f2766,f913]) ).
fof(f2851,plain,
( ~ sQ62_spl
| product(g1,b,a,c) ),
inference(forward_demodulation,[status(thm)],[f2522,f917]) ).
fof(f2852,plain,
( ~ sQ62_spl
| product(g1,a,b,c) ),
inference(resolution,[status(thm)],[f2851,f425]) ).
fof(f2853,plain,
( ~ sQ62_spl
| b = c ),
inference(resolution,[status(thm)],[f2851,f205]) ).
fof(f2854,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,a,c,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f2851,f173]) ).
fof(f2855,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,b,a,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f2851,f172]) ).
fof(f2856,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,inverse(g1,b),c,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2851,f158]) ).
fof(f2857,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,inverse(g1,b),c,X0) ),
inference(resolution,[status(thm)],[f2851,f157]) ).
fof(f2858,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,b,a,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f2851,f146]) ).
fof(f2859,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f2851,f139]) ).
fof(f2860,plain,
! [X0] :
( ~ sQ62_spl
| X0 = b
| ~ product(g1,X0,a,c) ),
inference(resolution,[status(thm)],[f2851,f75]) ).
fof(f2861,plain,
! [X0] :
( ~ sQ62_spl
| X0 = a
| ~ product(g1,b,X0,c) ),
inference(resolution,[status(thm)],[f2851,f73]) ).
fof(f2862,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| product(g1,c,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2851,f71]) ).
fof(f2863,plain,
! [X0,X1,X2] :
( ~ sQ62_spl
| product(g1,b,X1,X2)
| ~ product(g1,c,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2851,f69]) ).
fof(f2864,plain,
! [X0] :
( ~ sQ62_spl
| X0 = c
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f2851,f67]) ).
fof(f2865,plain,
( ~ sQ62_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f2853,f235,f2521]) ).
fof(f2866,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,inverse(g1,b),c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2856]) ).
fof(f2867,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f1927,f2866]) ).
fof(f2868,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f1927,f2857]) ).
fof(f2869,plain,
! [X0] :
( ~ sQ62_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2868]) ).
fof(f2870,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,b,a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2858]) ).
fof(f2871,plain,
! [X0] :
( ~ sQ62_spl
| product(g1,a,c,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2859]) ).
fof(f2874,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f1927,f1936]) ).
fof(f2875,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f1927,f2874]) ).
fof(f2876,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f2766,f2875]) ).
fof(f2886,plain,
c = multiply(g1,a,c),
inference(resolution,[status(thm)],[f932,f171]) ).
fof(f2904,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,c,b,multiply(g1,c,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f1927,f1937]) ).
fof(f2905,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f1927,f2904]) ).
fof(f2906,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f2905]) ).
fof(f2908,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| c = inverse(g1,b) ),
inference(resolution,[status(thm)],[f2906,f692]) ).
fof(f2909,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| b = inverse(g1,c) ),
inference(resolution,[status(thm)],[f2906,f612]) ).
fof(f2910,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f2906,f173]) ).
fof(f2911,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f2906,f172]) ).
fof(f2912,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f2906,f158]) ).
fof(f2913,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f2906,f157]) ).
fof(f2914,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,c,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2906,f146]) ).
fof(f2915,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f2906,f139]) ).
fof(f2916,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f2906,f75]) ).
fof(f2917,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(resolution,[status(thm)],[f2906,f73]) ).
fof(f2918,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f2906,f71]) ).
fof(f2919,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f2906,f69]) ).
fof(f2920,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f2906,f67]) ).
fof(f2922,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f2908,f718,f2832,f296,f252,f272]) ).
fof(f2923,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f2909,f786,f2832,f296,f252,f272]) ).
fof(f2924,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2912]) ).
fof(f2925,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| ~ sQ44_spl
| product(g1,c,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f2924]) ).
fof(f2926,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| ~ sQ44_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f2913]) ).
fof(f2927,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2926]) ).
fof(f2928,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2914]) ).
fof(f2929,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2915]) ).
fof(f2936,plain,
! [X0] :
( product(g1,a,multiply(g1,identity_for(g1),identity_for(g1)),X0)
| ~ product(g1,identity_for(g1),identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f923,f173]) ).
fof(f2937,plain,
! [X0] :
( product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,a,multiply(g1,identity_for(g1),identity_for(g1)),X0) ),
inference(resolution,[status(thm)],[f923,f172]) ).
fof(f2945,plain,
! [X0] : multiply(X0,identity_for(X0),identity_for(X0)) = identity_for(X0),
inference(resolution,[status(thm)],[f923,f140]) ).
fof(f2958,plain,
product(g1,a,identity_for(g1),multiply(g1,identity_for(g1),identity_for(g1))),
inference(paramodulation,[status(thm)],[f91,f923]) ).
fof(f2960,plain,
product(g1,identity_for(g1),a,multiply(g1,identity_for(g1),identity_for(g1))),
inference(paramodulation,[status(thm)],[f91,f923]) ).
fof(f2962,plain,
product(g1,identity_for(g1),identity_for(g1),multiply(g1,a,identity_for(g1))),
inference(paramodulation,[status(thm)],[f91,f923]) ).
fof(f2964,plain,
product(g1,identity_for(g1),identity_for(g1),multiply(g1,identity_for(g1),a)),
inference(paramodulation,[status(thm)],[f91,f923]) ).
fof(f2965,plain,
! [X0] :
( product(g1,a,multiply(g1,identity_for(g1),identity_for(g1)),X0)
| ~ product(g1,a,identity_for(g1),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2936]) ).
fof(f2966,plain,
! [X0] :
( product(g1,a,multiply(g1,identity_for(g1),identity_for(g1)),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2965]) ).
fof(f2967,plain,
! [X0] :
( product(g1,a,multiply(g1,a,identity_for(g1)),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2966]) ).
fof(f2968,plain,
! [X0] :
( product(g1,a,multiply(g1,a,a),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2967]) ).
fof(f2969,plain,
! [X0] :
( product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,a,multiply(g1,a,identity_for(g1)),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2937]) ).
fof(f2970,plain,
! [X0] :
( product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,a,multiply(g1,a,a),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2969]) ).
fof(f2987,plain,
product(g1,a,a,multiply(g1,identity_for(g1),identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f2958]) ).
fof(f2988,plain,
product(g1,a,a,multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f2987]) ).
fof(f2989,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f91,f2988]) ).
fof(f2995,plain,
product(g1,a,a,multiply(g1,identity_for(g1),identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f2960]) ).
fof(f2996,plain,
product(g1,a,a,multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f2995]) ).
fof(f2997,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f91,f2996]) ).
fof(f3003,plain,
product(g1,a,identity_for(g1),multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f2962]) ).
fof(f3004,plain,
product(g1,a,a,multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f91,f3003]) ).
fof(f3005,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f91,f3004]) ).
fof(f3011,plain,
product(g1,a,identity_for(g1),multiply(g1,identity_for(g1),a)),
inference(forward_demodulation,[status(thm)],[f91,f2964]) ).
fof(f3012,plain,
product(g1,a,a,multiply(g1,identity_for(g1),a)),
inference(forward_demodulation,[status(thm)],[f91,f3011]) ).
fof(f3013,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f91,f3012]) ).
fof(f3016,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1927,f1945]) ).
fof(f3018,plain,
product(g1,a,multiply(g1,c,c),multiply(g1,a,multiply(g1,c,c))),
inference(resolution,[status(thm)],[f1017,f184]) ).
fof(f3019,plain,
group_member(multiply(g1,a,multiply(g1,c,c)),g1),
inference(resolution,[status(thm)],[f1017,f193]) ).
fof(f3020,plain,
group_member(multiply(g1,b,multiply(g1,c,c)),g1),
inference(resolution,[status(thm)],[f1017,f189]) ).
fof(f3021,plain,
group_member(multiply(g1,c,multiply(g1,c,c)),g1),
inference(resolution,[status(thm)],[f1017,f188]) ).
fof(f3022,plain,
product(g1,b,multiply(g1,c,c),multiply(g1,b,multiply(g1,c,c))),
inference(resolution,[status(thm)],[f1017,f180]) ).
fof(f3023,plain,
product(g1,c,multiply(g1,c,c),multiply(g1,c,multiply(g1,c,c))),
inference(resolution,[status(thm)],[f1017,f179]) ).
fof(f3024,plain,
( multiply(g1,c,c) = c
| multiply(g1,c,c) = b
| multiply(g1,c,c) = a ),
inference(resolution,[status(thm)],[f1017,f89]) ).
fof(f3025,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,c,c)),g1),
inference(resolution,[status(thm)],[f1017,f192]) ).
fof(f3026,plain,
product(g1,identity_for(g1),multiply(g1,c,c),multiply(g1,identity_for(g1),multiply(g1,c,c))),
inference(resolution,[status(thm)],[f1017,f183]) ).
fof(f3027,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,c,c),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1017,f65]) ).
fof(f3028,plain,
! [X0] :
( product(g1,multiply(g1,c,c),X0,multiply(g1,multiply(g1,c,c),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1017,f64]) ).
fof(f3029,plain,
group_member(inverse(g1,multiply(g1,c,c)),g1),
inference(resolution,[status(thm)],[f1017,f61]) ).
fof(f3030,definition,
( sQ72_spl
<=> multiply(g1,c,c) = a ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f3031,plain,
( ~ sQ72_spl
| multiply(g1,c,c) = a ),
inference(component_clause,[status(thm)],[f3030]) ).
fof(f3032,plain,
( sQ72_spl
| multiply(g1,c,c) != a ),
inference(component_clause,[status(thm)],[f3030]) ).
fof(f3033,definition,
( sQ73_spl
<=> multiply(g1,c,c) = b ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f3034,plain,
( ~ sQ73_spl
| multiply(g1,c,c) = b ),
inference(component_clause,[status(thm)],[f3033]) ).
fof(f3035,plain,
( sQ73_spl
| multiply(g1,c,c) != b ),
inference(component_clause,[status(thm)],[f3033]) ).
fof(f3036,definition,
( sQ74_spl
<=> multiply(g1,c,c) = c ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f3037,plain,
( ~ sQ74_spl
| multiply(g1,c,c) = c ),
inference(component_clause,[status(thm)],[f3036]) ).
fof(f3038,plain,
( sQ74_spl
| multiply(g1,c,c) != c ),
inference(component_clause,[status(thm)],[f3036]) ).
fof(f3039,plain,
( sQ74_spl
| sQ73_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f3024,f3030,f3033,f3036]) ).
fof(f3040,plain,
group_member(multiply(g1,a,multiply(g1,c,c)),g1),
inference(forward_demodulation,[status(thm)],[f91,f3025]) ).
fof(f3041,plain,
product(g1,a,multiply(g1,c,c),multiply(g1,identity_for(g1),multiply(g1,c,c))),
inference(forward_demodulation,[status(thm)],[f91,f3026]) ).
fof(f3042,plain,
product(g1,a,multiply(g1,c,c),multiply(g1,a,multiply(g1,c,c))),
inference(forward_demodulation,[status(thm)],[f91,f3041]) ).
fof(f3044,plain,
( ~ sQ74_spl
| product(g1,c,c,c) ),
inference(backward_demodulation,[status(thm)],[f3037,f869]) ).
fof(f3045,plain,
( ~ sQ74_spl
| ~ sQ73_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f3034,f3037]) ).
fof(f3046,plain,
( ~ sQ74_spl
| ~ sQ73_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f3045,f235,f3033,f3036]) ).
fof(f3049,plain,
product(g1,a,multiply(g1,b,c),multiply(g1,a,multiply(g1,b,c))),
inference(resolution,[status(thm)],[f1023,f184]) ).
fof(f3050,plain,
group_member(multiply(g1,a,multiply(g1,b,c)),g1),
inference(resolution,[status(thm)],[f1023,f193]) ).
fof(f3051,plain,
group_member(multiply(g1,b,multiply(g1,b,c)),g1),
inference(resolution,[status(thm)],[f1023,f189]) ).
fof(f3052,plain,
group_member(multiply(g1,c,multiply(g1,b,c)),g1),
inference(resolution,[status(thm)],[f1023,f188]) ).
fof(f3053,plain,
product(g1,b,multiply(g1,b,c),multiply(g1,b,multiply(g1,b,c))),
inference(resolution,[status(thm)],[f1023,f180]) ).
fof(f3054,plain,
product(g1,c,multiply(g1,b,c),multiply(g1,c,multiply(g1,b,c))),
inference(resolution,[status(thm)],[f1023,f179]) ).
fof(f3055,plain,
( multiply(g1,b,c) = c
| multiply(g1,b,c) = b
| multiply(g1,b,c) = a ),
inference(resolution,[status(thm)],[f1023,f89]) ).
fof(f3056,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,b,c)),g1),
inference(resolution,[status(thm)],[f1023,f192]) ).
fof(f3057,plain,
product(g1,identity_for(g1),multiply(g1,b,c),multiply(g1,identity_for(g1),multiply(g1,b,c))),
inference(resolution,[status(thm)],[f1023,f183]) ).
fof(f3058,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,b,c),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1023,f65]) ).
fof(f3059,plain,
! [X0] :
( product(g1,multiply(g1,b,c),X0,multiply(g1,multiply(g1,b,c),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1023,f64]) ).
fof(f3060,plain,
group_member(inverse(g1,multiply(g1,b,c)),g1),
inference(resolution,[status(thm)],[f1023,f61]) ).
fof(f3061,definition,
( sQ75_spl
<=> multiply(g1,b,c) = a ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f3062,plain,
( ~ sQ75_spl
| multiply(g1,b,c) = a ),
inference(component_clause,[status(thm)],[f3061]) ).
fof(f3063,plain,
( sQ75_spl
| multiply(g1,b,c) != a ),
inference(component_clause,[status(thm)],[f3061]) ).
fof(f3064,definition,
( sQ76_spl
<=> multiply(g1,b,c) = b ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f3065,plain,
( ~ sQ76_spl
| multiply(g1,b,c) = b ),
inference(component_clause,[status(thm)],[f3064]) ).
fof(f3066,plain,
( sQ76_spl
| multiply(g1,b,c) != b ),
inference(component_clause,[status(thm)],[f3064]) ).
fof(f3067,definition,
( sQ77_spl
<=> multiply(g1,b,c) = c ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f3068,plain,
( ~ sQ77_spl
| multiply(g1,b,c) = c ),
inference(component_clause,[status(thm)],[f3067]) ).
fof(f3069,plain,
( sQ77_spl
| multiply(g1,b,c) != c ),
inference(component_clause,[status(thm)],[f3067]) ).
fof(f3070,plain,
( sQ77_spl
| sQ76_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f3055,f3061,f3064,f3067]) ).
fof(f3071,plain,
group_member(multiply(g1,a,multiply(g1,b,c)),g1),
inference(forward_demodulation,[status(thm)],[f91,f3056]) ).
fof(f3072,plain,
product(g1,a,multiply(g1,b,c),multiply(g1,identity_for(g1),multiply(g1,b,c))),
inference(forward_demodulation,[status(thm)],[f91,f3057]) ).
fof(f3073,plain,
product(g1,a,multiply(g1,b,c),multiply(g1,a,multiply(g1,b,c))),
inference(forward_demodulation,[status(thm)],[f91,f3072]) ).
fof(f3074,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f1927,f1947]) ).
fof(f3075,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1927,f3074]) ).
fof(f3082,plain,
( ~ sQ77_spl
| product(g1,b,c,c) ),
inference(backward_demodulation,[status(thm)],[f3068,f912]) ).
fof(f3090,plain,
( ~ sQ77_spl
| ~ sQ76_spl
| b = c ),
inference(backward_demodulation,[status(thm)],[f3065,f3068]) ).
fof(f3091,plain,
( ~ sQ77_spl
| ~ sQ76_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f3090,f235,f3064,f3067]) ).
fof(f3106,plain,
( multiply(g2,identity_for(g2),identity_for(g2)) = h
| multiply(g2,identity_for(g2),identity_for(g2)) = g
| multiply(g2,identity_for(g2),identity_for(g2)) = f ),
inference(resolution,[status(thm)],[f1034,f90]) ).
fof(f3107,plain,
product(g1,a,multiply(g1,identity_for(g1),identity_for(g1)),multiply(g1,a,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(resolution,[status(thm)],[f1034,f184]) ).
fof(f3108,plain,
group_member(multiply(g1,a,multiply(g1,identity_for(g1),identity_for(g1))),g1),
inference(resolution,[status(thm)],[f1034,f193]) ).
fof(f3109,plain,
group_member(multiply(g1,b,multiply(g1,identity_for(g1),identity_for(g1))),g1),
inference(resolution,[status(thm)],[f1034,f189]) ).
fof(f3110,plain,
group_member(multiply(g1,c,multiply(g1,identity_for(g1),identity_for(g1))),g1),
inference(resolution,[status(thm)],[f1034,f188]) ).
fof(f3111,plain,
product(g1,b,multiply(g1,identity_for(g1),identity_for(g1)),multiply(g1,b,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(resolution,[status(thm)],[f1034,f180]) ).
fof(f3112,plain,
product(g1,c,multiply(g1,identity_for(g1),identity_for(g1)),multiply(g1,c,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(resolution,[status(thm)],[f1034,f179]) ).
fof(f3113,plain,
( multiply(g1,identity_for(g1),identity_for(g1)) = c
| multiply(g1,identity_for(g1),identity_for(g1)) = b
| multiply(g1,identity_for(g1),identity_for(g1)) = a ),
inference(resolution,[status(thm)],[f1034,f89]) ).
fof(f3120,plain,
group_member(multiply(g1,a,identity_for(g1)),g1),
inference(paramodulation,[status(thm)],[f91,f1034]) ).
fof(f3122,plain,
group_member(multiply(g1,identity_for(g1),a),g1),
inference(paramodulation,[status(thm)],[f91,f1034]) ).
fof(f3152,definition,
( sQ78_spl
<=> multiply(g2,identity_for(g2),identity_for(g2)) = f ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f3155,definition,
( sQ79_spl
<=> multiply(g2,identity_for(g2),identity_for(g2)) = g ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f3156,plain,
( ~ sQ79_spl
| multiply(g2,identity_for(g2),identity_for(g2)) = g ),
inference(component_clause,[status(thm)],[f3155]) ).
fof(f3158,definition,
( sQ80_spl
<=> multiply(g2,identity_for(g2),identity_for(g2)) = h ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f3159,plain,
( ~ sQ80_spl
| multiply(g2,identity_for(g2),identity_for(g2)) = h ),
inference(component_clause,[status(thm)],[f3158]) ).
fof(f3161,plain,
( sQ80_spl
| sQ79_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f3106,f3152,f3155,f3158]) ).
fof(f3162,plain,
product(g1,a,multiply(g1,a,identity_for(g1)),multiply(g1,a,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f91,f3107]) ).
fof(f3163,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f91,f3162]) ).
fof(f3169,plain,
group_member(multiply(g1,a,multiply(g1,a,identity_for(g1))),g1),
inference(forward_demodulation,[status(thm)],[f91,f3108]) ).
fof(f3170,plain,
group_member(multiply(g1,a,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f91,f3169]) ).
fof(f3173,plain,
group_member(multiply(g1,b,multiply(g1,a,identity_for(g1))),g1),
inference(forward_demodulation,[status(thm)],[f91,f3109]) ).
fof(f3174,plain,
group_member(multiply(g1,b,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f91,f3173]) ).
fof(f3175,plain,
( ~ sQ63_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2547,f3174]) ).
fof(f3177,plain,
group_member(multiply(g1,c,multiply(g1,a,identity_for(g1))),g1),
inference(forward_demodulation,[status(thm)],[f91,f3110]) ).
fof(f3178,plain,
group_member(multiply(g1,c,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f91,f3177]) ).
fof(f3179,plain,
( ~ sQ63_spl
| group_member(multiply(g1,c,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2547,f3178]) ).
fof(f3181,plain,
product(g1,b,multiply(g1,a,identity_for(g1)),multiply(g1,b,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f91,f3111]) ).
fof(f3182,plain,
product(g1,b,multiply(g1,a,a),multiply(g1,b,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f91,f3181]) ).
fof(f3183,plain,
( ~ sQ63_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,identity_for(g1),identity_for(g1)))) ),
inference(forward_demodulation,[status(thm)],[f2547,f3182]) ).
fof(f3184,plain,
( ~ sQ63_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,a,identity_for(g1)))) ),
inference(forward_demodulation,[status(thm)],[f91,f3183]) ).
fof(f3185,plain,
( ~ sQ63_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f91,f3184]) ).
fof(f3186,plain,
( ~ sQ63_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f2547,f3185]) ).
fof(f3188,plain,
product(g1,c,multiply(g1,a,identity_for(g1)),multiply(g1,c,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f91,f3112]) ).
fof(f3189,plain,
product(g1,c,multiply(g1,a,a),multiply(g1,c,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f91,f3188]) ).
fof(f3190,plain,
( ~ sQ63_spl
| product(g1,c,a,multiply(g1,c,multiply(g1,identity_for(g1),identity_for(g1)))) ),
inference(forward_demodulation,[status(thm)],[f2547,f3189]) ).
fof(f3191,plain,
( ~ sQ63_spl
| product(g1,c,a,multiply(g1,c,multiply(g1,a,identity_for(g1)))) ),
inference(forward_demodulation,[status(thm)],[f91,f3190]) ).
fof(f3192,plain,
( ~ sQ63_spl
| product(g1,c,a,multiply(g1,c,multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f91,f3191]) ).
fof(f3193,plain,
( ~ sQ63_spl
| product(g1,c,a,multiply(g1,c,a)) ),
inference(forward_demodulation,[status(thm)],[f2547,f3192]) ).
fof(f3195,definition,
( sQ81_spl
<=> multiply(g1,identity_for(g1),identity_for(g1)) = a ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f3196,plain,
( ~ sQ81_spl
| multiply(g1,identity_for(g1),identity_for(g1)) = a ),
inference(component_clause,[status(thm)],[f3195]) ).
fof(f3198,definition,
( sQ82_spl
<=> multiply(g1,identity_for(g1),identity_for(g1)) = b ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f3199,plain,
( ~ sQ82_spl
| multiply(g1,identity_for(g1),identity_for(g1)) = b ),
inference(component_clause,[status(thm)],[f3198]) ).
fof(f3200,plain,
( sQ82_spl
| multiply(g1,identity_for(g1),identity_for(g1)) != b ),
inference(component_clause,[status(thm)],[f3198]) ).
fof(f3201,definition,
( sQ83_spl
<=> multiply(g1,identity_for(g1),identity_for(g1)) = c ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f3202,plain,
( ~ sQ83_spl
| multiply(g1,identity_for(g1),identity_for(g1)) = c ),
inference(component_clause,[status(thm)],[f3201]) ).
fof(f3203,plain,
( sQ83_spl
| multiply(g1,identity_for(g1),identity_for(g1)) != c ),
inference(component_clause,[status(thm)],[f3201]) ).
fof(f3204,plain,
( sQ83_spl
| sQ82_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f3113,f3195,f3198,f3201]) ).
fof(f3207,plain,
group_member(multiply(g1,a,a),g1),
inference(forward_demodulation,[status(thm)],[f91,f3120]) ).
fof(f3211,plain,
group_member(multiply(g1,a,a),g1),
inference(forward_demodulation,[status(thm)],[f91,f3122]) ).
fof(f3213,plain,
( ~ sQ83_spl
| multiply(g1,a,identity_for(g1)) = c ),
inference(forward_demodulation,[status(thm)],[f91,f3202]) ).
fof(f3214,plain,
( ~ sQ83_spl
| multiply(g1,a,a) = c ),
inference(forward_demodulation,[status(thm)],[f91,f3213]) ).
fof(f3215,plain,
( ~ sQ83_spl
| ~ sQ63_spl
| a = c ),
inference(forward_demodulation,[status(thm)],[f2547,f3214]) ).
fof(f3216,plain,
( ~ sQ83_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3215,f81]) ).
fof(f3217,plain,
( ~ sQ83_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f3216]) ).
fof(f3218,plain,
( ~ sQ82_spl
| multiply(g1,a,identity_for(g1)) = b ),
inference(forward_demodulation,[status(thm)],[f91,f3199]) ).
fof(f3219,plain,
( ~ sQ82_spl
| multiply(g1,a,a) = b ),
inference(forward_demodulation,[status(thm)],[f91,f3218]) ).
fof(f3220,plain,
( ~ sQ82_spl
| ~ sQ63_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f2547,f3219]) ).
fof(f3221,plain,
( ~ sQ82_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3220,f80]) ).
fof(f3222,plain,
( ~ sQ82_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f3221]) ).
fof(f3223,plain,
( ~ sQ81_spl
| multiply(g1,a,identity_for(g1)) = a ),
inference(forward_demodulation,[status(thm)],[f91,f3196]) ).
fof(f3224,plain,
( ~ sQ81_spl
| multiply(g1,a,a) = a ),
inference(forward_demodulation,[status(thm)],[f91,f3223]) ).
fof(f3225,plain,
( ~ sQ80_spl
| multiply(g2,f,identity_for(g2)) = h ),
inference(forward_demodulation,[status(thm)],[f92,f3159]) ).
fof(f3226,plain,
( ~ sQ80_spl
| multiply(g2,f,f) = h ),
inference(forward_demodulation,[status(thm)],[f92,f3225]) ).
fof(f3227,plain,
( ~ sQ80_spl
| f = h ),
inference(forward_demodulation,[status(thm)],[f2713,f3226]) ).
fof(f3228,plain,
( ~ sQ80_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3227,f87]) ).
fof(f3229,plain,
~ sQ80_spl,
inference(contradiction_clause,[status(thm)],[f3228]) ).
fof(f3230,plain,
( ~ sQ79_spl
| multiply(g2,f,identity_for(g2)) = g ),
inference(forward_demodulation,[status(thm)],[f92,f3156]) ).
fof(f3231,plain,
( ~ sQ79_spl
| multiply(g2,f,f) = g ),
inference(forward_demodulation,[status(thm)],[f92,f3230]) ).
fof(f3232,plain,
( ~ sQ79_spl
| f = g ),
inference(forward_demodulation,[status(thm)],[f2713,f3231]) ).
fof(f3233,plain,
( ~ sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3232,f86]) ).
fof(f3234,plain,
~ sQ79_spl,
inference(contradiction_clause,[status(thm)],[f3233]) ).
fof(f3237,plain,
( sQ83_spl
| multiply(g1,a,identity_for(g1)) != c ),
inference(forward_demodulation,[status(thm)],[f91,f3203]) ).
fof(f3238,plain,
( sQ83_spl
| multiply(g1,a,a) != c ),
inference(forward_demodulation,[status(thm)],[f91,f3237]) ).
fof(f3240,plain,
( sQ82_spl
| multiply(g1,a,identity_for(g1)) != b ),
inference(forward_demodulation,[status(thm)],[f91,f3200]) ).
fof(f3241,plain,
( sQ82_spl
| multiply(g1,a,a) != b ),
inference(forward_demodulation,[status(thm)],[f91,f3240]) ).
fof(f3249,plain,
product(g2,h,multiply(g2,g,h),multiply(g2,h,multiply(g2,g,h))),
inference(resolution,[status(thm)],[f1112,f211]) ).
fof(f3250,plain,
group_member(multiply(g2,h,multiply(g2,g,h)),g2),
inference(resolution,[status(thm)],[f1112,f210]) ).
fof(f3251,plain,
product(g2,g,multiply(g2,g,h),multiply(g2,g,multiply(g2,g,h))),
inference(resolution,[status(thm)],[f1112,f197]) ).
fof(f3252,plain,
group_member(multiply(g2,g,multiply(g2,g,h)),g2),
inference(resolution,[status(thm)],[f1112,f196]) ).
fof(f3253,plain,
group_member(multiply(g2,f,multiply(g2,g,h)),g2),
inference(resolution,[status(thm)],[f1112,f187]) ).
fof(f3254,plain,
product(g2,f,multiply(g2,g,h),multiply(g2,f,multiply(g2,g,h))),
inference(resolution,[status(thm)],[f1112,f178]) ).
fof(f3255,plain,
( multiply(g2,g,h) = h
| multiply(g2,g,h) = g
| multiply(g2,g,h) = f ),
inference(resolution,[status(thm)],[f1112,f90]) ).
fof(f3256,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,g,h)),g2),
inference(resolution,[status(thm)],[f1112,f192]) ).
fof(f3257,plain,
product(g2,identity_for(g2),multiply(g2,g,h),multiply(g2,identity_for(g2),multiply(g2,g,h))),
inference(resolution,[status(thm)],[f1112,f183]) ).
fof(f3258,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,g,h),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1112,f65]) ).
fof(f3259,plain,
! [X0] :
( product(g2,multiply(g2,g,h),X0,multiply(g2,multiply(g2,g,h),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1112,f64]) ).
fof(f3260,plain,
group_member(inverse(g2,multiply(g2,g,h)),g2),
inference(resolution,[status(thm)],[f1112,f61]) ).
fof(f3261,definition,
( sQ84_spl
<=> multiply(g2,g,h) = f ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f3262,plain,
( ~ sQ84_spl
| multiply(g2,g,h) = f ),
inference(component_clause,[status(thm)],[f3261]) ).
fof(f3263,plain,
( sQ84_spl
| multiply(g2,g,h) != f ),
inference(component_clause,[status(thm)],[f3261]) ).
fof(f3264,definition,
( sQ85_spl
<=> multiply(g2,g,h) = g ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f3265,plain,
( ~ sQ85_spl
| multiply(g2,g,h) = g ),
inference(component_clause,[status(thm)],[f3264]) ).
fof(f3266,plain,
( sQ85_spl
| multiply(g2,g,h) != g ),
inference(component_clause,[status(thm)],[f3264]) ).
fof(f3267,definition,
( sQ86_spl
<=> multiply(g2,g,h) = h ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f3268,plain,
( ~ sQ86_spl
| multiply(g2,g,h) = h ),
inference(component_clause,[status(thm)],[f3267]) ).
fof(f3269,plain,
( sQ86_spl
| multiply(g2,g,h) != h ),
inference(component_clause,[status(thm)],[f3267]) ).
fof(f3270,plain,
( sQ86_spl
| sQ85_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f3255,f3261,f3264,f3267]) ).
fof(f3271,plain,
group_member(multiply(g2,f,multiply(g2,g,h)),g2),
inference(forward_demodulation,[status(thm)],[f92,f3256]) ).
fof(f3272,plain,
product(g2,f,multiply(g2,g,h),multiply(g2,identity_for(g2),multiply(g2,g,h))),
inference(forward_demodulation,[status(thm)],[f92,f3257]) ).
fof(f3273,plain,
product(g2,f,multiply(g2,g,h),multiply(g2,f,multiply(g2,g,h))),
inference(forward_demodulation,[status(thm)],[f92,f3272]) ).
fof(f3282,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f1927,f1994]) ).
fof(f3283,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1927,f3282]) ).
fof(f3293,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f1248]) ).
fof(f3294,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1927,f1248]) ).
fof(f3305,plain,
( ~ sQ86_spl
| ~ sQ85_spl
| g = h ),
inference(backward_demodulation,[status(thm)],[f3265,f3268]) ).
fof(f3306,plain,
( ~ sQ86_spl
| ~ sQ85_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f3305,f334,f3264,f3267]) ).
fof(f3314,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1927,f1995]) ).
fof(f3322,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f1249]) ).
fof(f3323,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1927,f1249]) ).
fof(f3339,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f1927,f1250]) ).
fof(f3346,plain,
product(g2,h,multiply(g2,g,g),multiply(g2,h,multiply(g2,g,g))),
inference(resolution,[status(thm)],[f1113,f211]) ).
fof(f3347,plain,
group_member(multiply(g2,h,multiply(g2,g,g)),g2),
inference(resolution,[status(thm)],[f1113,f210]) ).
fof(f3348,plain,
product(g2,g,multiply(g2,g,g),multiply(g2,g,multiply(g2,g,g))),
inference(resolution,[status(thm)],[f1113,f197]) ).
fof(f3349,plain,
group_member(multiply(g2,g,multiply(g2,g,g)),g2),
inference(resolution,[status(thm)],[f1113,f196]) ).
fof(f3350,plain,
group_member(multiply(g2,f,multiply(g2,g,g)),g2),
inference(resolution,[status(thm)],[f1113,f187]) ).
fof(f3351,plain,
product(g2,f,multiply(g2,g,g),multiply(g2,f,multiply(g2,g,g))),
inference(resolution,[status(thm)],[f1113,f178]) ).
fof(f3352,plain,
( multiply(g2,g,g) = h
| multiply(g2,g,g) = g
| multiply(g2,g,g) = f ),
inference(resolution,[status(thm)],[f1113,f90]) ).
fof(f3353,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,g,g)),g2),
inference(resolution,[status(thm)],[f1113,f192]) ).
fof(f3354,plain,
product(g2,identity_for(g2),multiply(g2,g,g),multiply(g2,identity_for(g2),multiply(g2,g,g))),
inference(resolution,[status(thm)],[f1113,f183]) ).
fof(f3355,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,g,g),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1113,f65]) ).
fof(f3356,plain,
! [X0] :
( product(g2,multiply(g2,g,g),X0,multiply(g2,multiply(g2,g,g),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1113,f64]) ).
fof(f3357,plain,
group_member(inverse(g2,multiply(g2,g,g)),g2),
inference(resolution,[status(thm)],[f1113,f61]) ).
fof(f3358,definition,
( sQ87_spl
<=> multiply(g2,g,g) = f ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f3359,plain,
( ~ sQ87_spl
| multiply(g2,g,g) = f ),
inference(component_clause,[status(thm)],[f3358]) ).
fof(f3360,plain,
( sQ87_spl
| multiply(g2,g,g) != f ),
inference(component_clause,[status(thm)],[f3358]) ).
fof(f3361,definition,
( sQ88_spl
<=> multiply(g2,g,g) = g ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f3362,plain,
( ~ sQ88_spl
| multiply(g2,g,g) = g ),
inference(component_clause,[status(thm)],[f3361]) ).
fof(f3363,plain,
( sQ88_spl
| multiply(g2,g,g) != g ),
inference(component_clause,[status(thm)],[f3361]) ).
fof(f3364,definition,
( sQ89_spl
<=> multiply(g2,g,g) = h ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f3365,plain,
( ~ sQ89_spl
| multiply(g2,g,g) = h ),
inference(component_clause,[status(thm)],[f3364]) ).
fof(f3366,plain,
( sQ89_spl
| multiply(g2,g,g) != h ),
inference(component_clause,[status(thm)],[f3364]) ).
fof(f3367,plain,
( sQ89_spl
| sQ88_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f3352,f3358,f3361,f3364]) ).
fof(f3368,plain,
group_member(multiply(g2,f,multiply(g2,g,g)),g2),
inference(forward_demodulation,[status(thm)],[f92,f3353]) ).
fof(f3369,plain,
product(g2,f,multiply(g2,g,g),multiply(g2,identity_for(g2),multiply(g2,g,g))),
inference(forward_demodulation,[status(thm)],[f92,f3354]) ).
fof(f3370,plain,
product(g2,f,multiply(g2,g,g),multiply(g2,f,multiply(g2,g,g))),
inference(forward_demodulation,[status(thm)],[f92,f3369]) ).
fof(f3372,plain,
( ~ sQ89_spl
| ~ sQ88_spl
| g = h ),
inference(backward_demodulation,[status(thm)],[f3362,f3365]) ).
fof(f3373,plain,
( ~ sQ89_spl
| ~ sQ88_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f3372,f334,f3361,f3364]) ).
fof(f3374,plain,
product(g2,h,multiply(g2,g,f),multiply(g2,h,multiply(g2,g,f))),
inference(resolution,[status(thm)],[f1114,f211]) ).
fof(f3375,plain,
group_member(multiply(g2,h,multiply(g2,g,f)),g2),
inference(resolution,[status(thm)],[f1114,f210]) ).
fof(f3376,plain,
product(g2,g,multiply(g2,g,f),multiply(g2,g,multiply(g2,g,f))),
inference(resolution,[status(thm)],[f1114,f197]) ).
fof(f3377,plain,
group_member(multiply(g2,g,multiply(g2,g,f)),g2),
inference(resolution,[status(thm)],[f1114,f196]) ).
fof(f3380,plain,
( multiply(g2,g,f) = h
| multiply(g2,g,f) = g
| multiply(g2,g,f) = f ),
inference(resolution,[status(thm)],[f1114,f90]) ).
fof(f3385,plain,
group_member(inverse(g2,multiply(g2,g,f)),g2),
inference(resolution,[status(thm)],[f1114,f61]) ).
fof(f3386,definition,
( sQ90_spl
<=> multiply(g2,g,f) = f ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f3387,plain,
( ~ sQ90_spl
| multiply(g2,g,f) = f ),
inference(component_clause,[status(thm)],[f3386]) ).
fof(f3389,definition,
( sQ91_spl
<=> multiply(g2,g,f) = g ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f3392,definition,
( sQ92_spl
<=> multiply(g2,g,f) = h ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f3393,plain,
( ~ sQ92_spl
| multiply(g2,g,f) = h ),
inference(component_clause,[status(thm)],[f3392]) ).
fof(f3395,plain,
( sQ92_spl
| sQ91_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f3380,f3386,f3389,f3392]) ).
fof(f3399,plain,
( ~ sQ84_spl
| product(g2,g,h,f) ),
inference(forward_demodulation,[status(thm)],[f3262,f1117]) ).
fof(f3401,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1927,f1996]) ).
fof(f3405,plain,
( ~ sQ87_spl
| product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f3359,f1118]) ).
fof(f3406,plain,
( ~ sQ50_spl
| ~ sQ87_spl
| g = h ),
inference(resolution,[status(thm)],[f3405,f1148]) ).
fof(f3408,plain,
( ~ sQ87_spl
| g = inverse(g2,g) ),
inference(resolution,[status(thm)],[f3405,f691]) ).
fof(f3410,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,f,f,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f3405,f379]) ).
fof(f3411,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,g,g,X0)
| ~ product(g2,f,f,X0) ),
inference(resolution,[status(thm)],[f3405,f378]) ).
fof(f3412,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,inverse(g2,g),f,X0)
| ~ product(g2,identity_for(g2),g,X0) ),
inference(resolution,[status(thm)],[f3405,f158]) ).
fof(f3413,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,inverse(g2,g),f,X0) ),
inference(resolution,[status(thm)],[f3405,f157]) ).
fof(f3414,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,g,g,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f3405,f146]) ).
fof(f3415,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f3405,f139]) ).
fof(f3416,plain,
! [X0] :
( ~ sQ87_spl
| X0 = g
| ~ product(g2,X0,g,f) ),
inference(resolution,[status(thm)],[f3405,f75]) ).
fof(f3417,plain,
! [X0] :
( ~ sQ87_spl
| X0 = g
| ~ product(g2,g,X0,f) ),
inference(resolution,[status(thm)],[f3405,f73]) ).
fof(f3418,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f3405,f71]) ).
fof(f3419,plain,
! [X0,X1,X2] :
( ~ sQ87_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f3405,f69]) ).
fof(f3420,plain,
! [X0] :
( ~ sQ87_spl
| X0 = f
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f3405,f67]) ).
fof(f3421,plain,
( ~ sQ50_spl
| ~ sQ87_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f3406,f334,f3358,f1086]) ).
fof(f3423,plain,
( ~ sQ87_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f3408,f1083,f3358]) ).
fof(f3425,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,inverse(g2,g),f,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3412]) ).
fof(f3426,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ50_spl
| product(g2,h,f,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f3425]) ).
fof(f3427,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ50_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,h,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f3413]) ).
fof(f3428,plain,
! [X0] :
( ~ sQ87_spl
| ~ sQ50_spl
| product(g2,f,g,X0)
| ~ product(g2,h,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3427]) ).
fof(f3429,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,g,g,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3414]) ).
fof(f3430,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,f,f,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3415]) ).
fof(f3431,plain,
( ~ sQ92_spl
| product(g2,g,f,h) ),
inference(forward_demodulation,[status(thm)],[f3393,f1119]) ).
fof(f3432,plain,
( ~ sQ92_spl
| product(g2,f,g,h) ),
inference(resolution,[status(thm)],[f3431,f424]) ).
fof(f3433,plain,
( ~ sQ92_spl
| g = h ),
inference(resolution,[status(thm)],[f3431,f391]) ).
fof(f3434,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,f,h,X0)
| ~ product(g2,g,f,X0) ),
inference(resolution,[status(thm)],[f3431,f379]) ).
fof(f3435,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,g,f,X0)
| ~ product(g2,f,h,X0) ),
inference(resolution,[status(thm)],[f3431,f378]) ).
fof(f3436,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,inverse(g2,g),h,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f3431,f158]) ).
fof(f3437,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,inverse(g2,g),h,X0) ),
inference(resolution,[status(thm)],[f3431,f157]) ).
fof(f3438,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,g,f,X0)
| ~ product(g2,identity_for(g2),h,X0) ),
inference(resolution,[status(thm)],[f3431,f146]) ).
fof(f3439,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,g,f,X0) ),
inference(resolution,[status(thm)],[f3431,f139]) ).
fof(f3440,plain,
! [X0] :
( ~ sQ92_spl
| X0 = g
| ~ product(g2,X0,f,h) ),
inference(resolution,[status(thm)],[f3431,f75]) ).
fof(f3441,plain,
! [X0] :
( ~ sQ92_spl
| X0 = f
| ~ product(g2,g,X0,h) ),
inference(resolution,[status(thm)],[f3431,f73]) ).
fof(f3442,plain,
! [X0,X1,X2] :
( ~ sQ92_spl
| product(g2,h,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,f,X0,X1) ),
inference(resolution,[status(thm)],[f3431,f71]) ).
fof(f3443,plain,
! [X0,X1,X2] :
( ~ sQ92_spl
| product(g2,g,X1,X2)
| ~ product(g2,h,X0,X2)
| ~ product(g2,f,X0,X1) ),
inference(resolution,[status(thm)],[f3431,f69]) ).
fof(f3444,plain,
! [X0] :
( ~ sQ92_spl
| X0 = h
| ~ product(g2,g,f,X0) ),
inference(resolution,[status(thm)],[f3431,f67]) ).
fof(f3445,plain,
( ~ sQ92_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f3433,f334,f3392]) ).
fof(f3446,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,inverse(g2,g),h,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3436]) ).
fof(f3447,plain,
! [X0] :
( ~ sQ92_spl
| ~ sQ50_spl
| product(g2,h,h,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f3446]) ).
fof(f3448,plain,
! [X0] :
( ~ sQ92_spl
| ~ sQ50_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f3437]) ).
fof(f3449,plain,
! [X0] :
( ~ sQ92_spl
| ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3448]) ).
fof(f3450,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,g,f,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3438]) ).
fof(f3451,plain,
! [X0] :
( ~ sQ92_spl
| product(g2,f,h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3439]) ).
fof(f3453,plain,
g = multiply(g2,g,f),
inference(resolution,[status(thm)],[f1122,f391]) ).
fof(f3475,plain,
( ~ sQ90_spl
| g = f ),
inference(backward_demodulation,[status(thm)],[f3387,f3453]) ).
fof(f3476,plain,
( ~ sQ90_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f3475,f341,f3386]) ).
fof(f3477,plain,
product(g2,h,multiply(g2,h,h),multiply(g2,h,multiply(g2,h,h))),
inference(resolution,[status(thm)],[f1123,f211]) ).
fof(f3478,plain,
group_member(multiply(g2,h,multiply(g2,h,h)),g2),
inference(resolution,[status(thm)],[f1123,f210]) ).
fof(f3479,plain,
product(g2,g,multiply(g2,h,h),multiply(g2,g,multiply(g2,h,h))),
inference(resolution,[status(thm)],[f1123,f197]) ).
fof(f3480,plain,
group_member(multiply(g2,g,multiply(g2,h,h)),g2),
inference(resolution,[status(thm)],[f1123,f196]) ).
fof(f3481,plain,
group_member(multiply(g2,f,multiply(g2,h,h)),g2),
inference(resolution,[status(thm)],[f1123,f187]) ).
fof(f3482,plain,
product(g2,f,multiply(g2,h,h),multiply(g2,f,multiply(g2,h,h))),
inference(resolution,[status(thm)],[f1123,f178]) ).
fof(f3483,plain,
( multiply(g2,h,h) = h
| multiply(g2,h,h) = g
| multiply(g2,h,h) = f ),
inference(resolution,[status(thm)],[f1123,f90]) ).
fof(f3484,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,h,h)),g2),
inference(resolution,[status(thm)],[f1123,f192]) ).
fof(f3485,plain,
product(g2,identity_for(g2),multiply(g2,h,h),multiply(g2,identity_for(g2),multiply(g2,h,h))),
inference(resolution,[status(thm)],[f1123,f183]) ).
fof(f3486,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,h,h),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1123,f65]) ).
fof(f3487,plain,
! [X0] :
( product(g2,multiply(g2,h,h),X0,multiply(g2,multiply(g2,h,h),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1123,f64]) ).
fof(f3488,plain,
group_member(inverse(g2,multiply(g2,h,h)),g2),
inference(resolution,[status(thm)],[f1123,f61]) ).
fof(f3489,definition,
( sQ93_spl
<=> multiply(g2,h,h) = f ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f3490,plain,
( ~ sQ93_spl
| multiply(g2,h,h) = f ),
inference(component_clause,[status(thm)],[f3489]) ).
fof(f3491,plain,
( sQ93_spl
| multiply(g2,h,h) != f ),
inference(component_clause,[status(thm)],[f3489]) ).
fof(f3492,definition,
( sQ94_spl
<=> multiply(g2,h,h) = g ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f3493,plain,
( ~ sQ94_spl
| multiply(g2,h,h) = g ),
inference(component_clause,[status(thm)],[f3492]) ).
fof(f3494,plain,
( sQ94_spl
| multiply(g2,h,h) != g ),
inference(component_clause,[status(thm)],[f3492]) ).
fof(f3495,definition,
( sQ95_spl
<=> multiply(g2,h,h) = h ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f3496,plain,
( ~ sQ95_spl
| multiply(g2,h,h) = h ),
inference(component_clause,[status(thm)],[f3495]) ).
fof(f3497,plain,
( sQ95_spl
| multiply(g2,h,h) != h ),
inference(component_clause,[status(thm)],[f3495]) ).
fof(f3498,plain,
( sQ95_spl
| sQ94_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f3483,f3489,f3492,f3495]) ).
fof(f3499,plain,
group_member(multiply(g2,f,multiply(g2,h,h)),g2),
inference(forward_demodulation,[status(thm)],[f92,f3484]) ).
fof(f3500,plain,
product(g2,f,multiply(g2,h,h),multiply(g2,identity_for(g2),multiply(g2,h,h))),
inference(forward_demodulation,[status(thm)],[f92,f3485]) ).
fof(f3501,plain,
product(g2,f,multiply(g2,h,h),multiply(g2,f,multiply(g2,h,h))),
inference(forward_demodulation,[status(thm)],[f92,f3500]) ).
fof(f3502,plain,
product(g2,h,multiply(g2,h,g),multiply(g2,h,multiply(g2,h,g))),
inference(resolution,[status(thm)],[f1124,f211]) ).
fof(f3503,plain,
group_member(multiply(g2,h,multiply(g2,h,g)),g2),
inference(resolution,[status(thm)],[f1124,f210]) ).
fof(f3504,plain,
product(g2,g,multiply(g2,h,g),multiply(g2,g,multiply(g2,h,g))),
inference(resolution,[status(thm)],[f1124,f197]) ).
fof(f3505,plain,
group_member(multiply(g2,g,multiply(g2,h,g)),g2),
inference(resolution,[status(thm)],[f1124,f196]) ).
fof(f3506,plain,
group_member(multiply(g2,f,multiply(g2,h,g)),g2),
inference(resolution,[status(thm)],[f1124,f187]) ).
fof(f3507,plain,
product(g2,f,multiply(g2,h,g),multiply(g2,f,multiply(g2,h,g))),
inference(resolution,[status(thm)],[f1124,f178]) ).
fof(f3508,plain,
( multiply(g2,h,g) = h
| multiply(g2,h,g) = g
| multiply(g2,h,g) = f ),
inference(resolution,[status(thm)],[f1124,f90]) ).
fof(f3509,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,h,g)),g2),
inference(resolution,[status(thm)],[f1124,f192]) ).
fof(f3510,plain,
product(g2,identity_for(g2),multiply(g2,h,g),multiply(g2,identity_for(g2),multiply(g2,h,g))),
inference(resolution,[status(thm)],[f1124,f183]) ).
fof(f3511,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,h,g),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1124,f65]) ).
fof(f3512,plain,
! [X0] :
( product(g2,multiply(g2,h,g),X0,multiply(g2,multiply(g2,h,g),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1124,f64]) ).
fof(f3513,plain,
group_member(inverse(g2,multiply(g2,h,g)),g2),
inference(resolution,[status(thm)],[f1124,f61]) ).
fof(f3514,definition,
( sQ96_spl
<=> multiply(g2,h,g) = f ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f3515,plain,
( ~ sQ96_spl
| multiply(g2,h,g) = f ),
inference(component_clause,[status(thm)],[f3514]) ).
fof(f3516,plain,
( sQ96_spl
| multiply(g2,h,g) != f ),
inference(component_clause,[status(thm)],[f3514]) ).
fof(f3517,definition,
( sQ97_spl
<=> multiply(g2,h,g) = g ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f3518,plain,
( ~ sQ97_spl
| multiply(g2,h,g) = g ),
inference(component_clause,[status(thm)],[f3517]) ).
fof(f3519,plain,
( sQ97_spl
| multiply(g2,h,g) != g ),
inference(component_clause,[status(thm)],[f3517]) ).
fof(f3520,definition,
( sQ98_spl
<=> multiply(g2,h,g) = h ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f3521,plain,
( ~ sQ98_spl
| multiply(g2,h,g) = h ),
inference(component_clause,[status(thm)],[f3520]) ).
fof(f3522,plain,
( sQ98_spl
| multiply(g2,h,g) != h ),
inference(component_clause,[status(thm)],[f3520]) ).
fof(f3523,plain,
( sQ98_spl
| sQ97_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f3508,f3514,f3517,f3520]) ).
fof(f3524,plain,
group_member(multiply(g2,f,multiply(g2,h,g)),g2),
inference(forward_demodulation,[status(thm)],[f92,f3509]) ).
fof(f3525,plain,
product(g2,f,multiply(g2,h,g),multiply(g2,identity_for(g2),multiply(g2,h,g))),
inference(forward_demodulation,[status(thm)],[f92,f3510]) ).
fof(f3526,plain,
product(g2,f,multiply(g2,h,g),multiply(g2,f,multiply(g2,h,g))),
inference(forward_demodulation,[status(thm)],[f92,f3525]) ).
fof(f3527,plain,
product(g2,h,multiply(g2,h,f),multiply(g2,h,multiply(g2,h,f))),
inference(resolution,[status(thm)],[f1125,f211]) ).
fof(f3528,plain,
group_member(multiply(g2,h,multiply(g2,h,f)),g2),
inference(resolution,[status(thm)],[f1125,f210]) ).
fof(f3529,plain,
product(g2,g,multiply(g2,h,f),multiply(g2,g,multiply(g2,h,f))),
inference(resolution,[status(thm)],[f1125,f197]) ).
fof(f3530,plain,
group_member(multiply(g2,g,multiply(g2,h,f)),g2),
inference(resolution,[status(thm)],[f1125,f196]) ).
fof(f3533,plain,
( multiply(g2,h,f) = h
| multiply(g2,h,f) = g
| multiply(g2,h,f) = f ),
inference(resolution,[status(thm)],[f1125,f90]) ).
fof(f3538,plain,
group_member(inverse(g2,multiply(g2,h,f)),g2),
inference(resolution,[status(thm)],[f1125,f61]) ).
fof(f3539,definition,
( sQ99_spl
<=> multiply(g2,h,f) = f ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f3540,plain,
( ~ sQ99_spl
| multiply(g2,h,f) = f ),
inference(component_clause,[status(thm)],[f3539]) ).
fof(f3542,definition,
( sQ100_spl
<=> multiply(g2,h,f) = g ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f3543,plain,
( ~ sQ100_spl
| multiply(g2,h,f) = g ),
inference(component_clause,[status(thm)],[f3542]) ).
fof(f3545,definition,
( sQ101_spl
<=> multiply(g2,h,f) = h ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f3548,plain,
( sQ101_spl
| sQ100_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f3533,f3539,f3542,f3545]) ).
fof(f3552,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1927,f2007]) ).
fof(f3554,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| product(g1,b,b,multiply(g1,b,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f1927,f1998]) ).
fof(f3555,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f1927,f3554]) ).
fof(f3556,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ66_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f2766,f3555]) ).
fof(f3560,plain,
! [X0] :
( product(g2,f,multiply(g2,h,h),X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f1197,f379]) ).
fof(f3561,plain,
! [X0] :
( product(g2,h,h,X0)
| ~ product(g2,f,multiply(g2,h,h),X0) ),
inference(resolution,[status(thm)],[f1197,f378]) ).
fof(f3562,plain,
! [X0] :
( product(g2,inverse(g2,h),multiply(g2,h,h),X0)
| ~ product(g2,identity_for(g2),h,X0) ),
inference(resolution,[status(thm)],[f1197,f158]) ).
fof(f3563,plain,
! [X0] :
( product(g2,identity_for(g2),h,X0)
| ~ product(g2,inverse(g2,h),multiply(g2,h,h),X0) ),
inference(resolution,[status(thm)],[f1197,f157]) ).
fof(f3564,plain,
! [X0] :
( product(g2,h,h,X0)
| ~ product(g2,identity_for(g2),multiply(g2,h,h),X0) ),
inference(resolution,[status(thm)],[f1197,f146]) ).
fof(f3565,plain,
! [X0] :
( product(g2,identity_for(g2),multiply(g2,h,h),X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f1197,f139]) ).
fof(f3566,plain,
! [X0] :
( X0 = h
| ~ product(g2,X0,h,multiply(g2,h,h)) ),
inference(resolution,[status(thm)],[f1197,f75]) ).
fof(f3567,plain,
! [X0] :
( X0 = h
| ~ product(g2,h,X0,multiply(g2,h,h)) ),
inference(resolution,[status(thm)],[f1197,f73]) ).
fof(f3568,plain,
! [X0,X1,X2] :
( product(g2,multiply(g2,h,h),X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f1197,f71]) ).
fof(f3569,plain,
! [X0,X1,X2] :
( product(g2,h,X1,X2)
| ~ product(g2,multiply(g2,h,h),X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f1197,f69]) ).
fof(f3570,plain,
! [X0] :
( X0 = multiply(g2,h,h)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f1197,f67]) ).
fof(f3571,plain,
! [X0] :
( product(g2,inverse(g2,h),multiply(g2,h,h),X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3562]) ).
fof(f3572,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,multiply(g2,h,h),X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f3571]) ).
fof(f3573,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,g,multiply(g2,h,h),X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f3563]) ).
fof(f3574,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,h,X0)
| ~ product(g2,g,multiply(g2,h,h),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3573]) ).
fof(f3575,plain,
! [X0] :
( product(g2,h,h,X0)
| ~ product(g2,f,multiply(g2,h,h),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3564]) ).
fof(f3576,plain,
! [X0] :
( product(g2,f,multiply(g2,h,h),X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3565]) ).
fof(f3577,plain,
( ~ sQ50_spl
| multiply(g2,h,g) = f ),
inference(resolution,[status(thm)],[f1198,f1108]) ).
fof(f3578,plain,
! [X0] :
( product(g2,f,multiply(g2,h,g),X0)
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f1198,f379]) ).
fof(f3579,plain,
! [X0] :
( product(g2,h,g,X0)
| ~ product(g2,f,multiply(g2,h,g),X0) ),
inference(resolution,[status(thm)],[f1198,f378]) ).
fof(f3580,plain,
! [X0] :
( product(g2,inverse(g2,h),multiply(g2,h,g),X0)
| ~ product(g2,identity_for(g2),g,X0) ),
inference(resolution,[status(thm)],[f1198,f158]) ).
fof(f3581,plain,
! [X0] :
( product(g2,identity_for(g2),g,X0)
| ~ product(g2,inverse(g2,h),multiply(g2,h,g),X0) ),
inference(resolution,[status(thm)],[f1198,f157]) ).
fof(f3582,plain,
! [X0] :
( product(g2,h,g,X0)
| ~ product(g2,identity_for(g2),multiply(g2,h,g),X0) ),
inference(resolution,[status(thm)],[f1198,f146]) ).
fof(f3583,plain,
! [X0] :
( product(g2,identity_for(g2),multiply(g2,h,g),X0)
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f1198,f139]) ).
fof(f3584,plain,
! [X0] :
( X0 = h
| ~ product(g2,X0,g,multiply(g2,h,g)) ),
inference(resolution,[status(thm)],[f1198,f75]) ).
fof(f3585,plain,
! [X0] :
( X0 = g
| ~ product(g2,h,X0,multiply(g2,h,g)) ),
inference(resolution,[status(thm)],[f1198,f73]) ).
fof(f3586,plain,
! [X0,X1,X2] :
( product(g2,multiply(g2,h,g),X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f1198,f71]) ).
fof(f3587,plain,
! [X0,X1,X2] :
( product(g2,h,X1,X2)
| ~ product(g2,multiply(g2,h,g),X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f1198,f69]) ).
fof(f3588,plain,
! [X0] :
( X0 = multiply(g2,h,g)
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f1198,f67]) ).
fof(f3589,plain,
! [X0] :
( product(g2,inverse(g2,h),multiply(g2,h,g),X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3580]) ).
fof(f3593,plain,
! [X0] :
( product(g2,h,g,X0)
| ~ product(g2,f,multiply(g2,h,g),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3582]) ).
fof(f3594,plain,
! [X0] :
( product(g2,f,multiply(g2,h,g),X0)
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3583]) ).
fof(f3596,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| product(g1,c,b,multiply(g1,c,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f1927,f1999]) ).
fof(f3597,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f1927,f3596]) ).
fof(f3598,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,c,b,b) ),
inference(forward_demodulation,[status(thm)],[f2836,f3597]) ).
fof(f3599,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f3598,f173]) ).
fof(f3600,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f3598,f172]) ).
fof(f3603,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,inverse(g1,c),b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f3598,f158]) ).
fof(f3604,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),b,X0) ),
inference(resolution,[status(thm)],[f3598,f157]) ).
fof(f3605,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,c,b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f3598,f146]) ).
fof(f3606,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f3598,f139]) ).
fof(f3607,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| X0 = c
| ~ product(g1,X0,b,b) ),
inference(resolution,[status(thm)],[f3598,f75]) ).
fof(f3608,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| X0 = b
| ~ product(g1,c,X0,b) ),
inference(resolution,[status(thm)],[f3598,f73]) ).
fof(f3609,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,b,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f3598,f71]) ).
fof(f3610,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,c,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f3598,f69]) ).
fof(f3611,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| X0 = b
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f3598,f67]) ).
fof(f3614,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,inverse(g1,c),b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3603]) ).
fof(f3615,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| ~ sQ44_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f3614]) ).
fof(f3616,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| ~ sQ44_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f3604]) ).
fof(f3617,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3616]) ).
fof(f3618,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3605]) ).
fof(f3619,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ70_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3606]) ).
fof(f3623,plain,
( ~ sQ95_spl
| product(g2,h,h,h) ),
inference(backward_demodulation,[status(thm)],[f3496,f1197]) ).
fof(f3625,plain,
( ~ sQ95_spl
| ~ sQ94_spl
| g = h ),
inference(backward_demodulation,[status(thm)],[f3493,f3496]) ).
fof(f3626,plain,
( ~ sQ95_spl
| ~ sQ94_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f3625,f334,f3492,f3495]) ).
fof(f3628,plain,
h = multiply(g2,h,f),
inference(resolution,[status(thm)],[f1199,f391]) ).
fof(f3631,plain,
! [X0] :
( product(g2,inverse(g2,h),multiply(g2,h,f),X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f1199,f158]) ).
fof(f3632,plain,
! [X0] :
( product(g2,identity_for(g2),f,X0)
| ~ product(g2,inverse(g2,h),multiply(g2,h,f),X0) ),
inference(resolution,[status(thm)],[f1199,f157]) ).
fof(f3640,plain,
! [X0] :
( product(g2,inverse(g2,h),multiply(g2,h,f),X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3631]) ).
fof(f3641,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,multiply(g2,h,f),X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f3640]) ).
fof(f3642,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,g,multiply(g2,h,f),X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f3632]) ).
fof(f3643,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,multiply(g2,h,f),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3642]) ).
fof(f3649,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f1927,f2009]) ).
fof(f3650,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1927,f3649]) ).
fof(f3652,plain,
( ~ sQ71_spl
| b = a ),
inference(resolution,[status(thm)],[f2847,f206]) ).
fof(f3653,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,a,c,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f2847,f173]) ).
fof(f3654,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,c,b,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f2847,f172]) ).
fof(f3655,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,inverse(g1,c),c,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f2847,f158]) ).
fof(f3656,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),c,X0) ),
inference(resolution,[status(thm)],[f2847,f157]) ).
fof(f3657,plain,
( ~ sQ71_spl
| b = identity_for(g1) ),
inference(resolution,[status(thm)],[f2847,f150]) ).
fof(f3658,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,c,b,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f2847,f146]) ).
fof(f3659,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f2847,f139]) ).
fof(f3660,plain,
! [X0] :
( ~ sQ71_spl
| X0 = c
| ~ product(g1,X0,b,c) ),
inference(resolution,[status(thm)],[f2847,f75]) ).
fof(f3661,plain,
! [X0] :
( ~ sQ71_spl
| X0 = b
| ~ product(g1,c,X0,c) ),
inference(resolution,[status(thm)],[f2847,f73]) ).
fof(f3662,plain,
! [X0,X1,X2] :
( ~ sQ71_spl
| product(g1,c,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f2847,f71]) ).
fof(f3663,plain,
! [X0,X1,X2] :
( ~ sQ71_spl
| product(g1,c,X1,X2)
| ~ product(g1,c,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f2847,f69]) ).
fof(f3664,plain,
! [X0] :
( ~ sQ71_spl
| X0 = c
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f2847,f67]) ).
fof(f3665,plain,
( ~ sQ71_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f3652,f242,f2838]) ).
fof(f3666,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,inverse(g1,c),c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3655]) ).
fof(f3667,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ44_spl
| product(g1,c,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f3666]) ).
fof(f3668,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ44_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f3656]) ).
fof(f3669,plain,
! [X0] :
( ~ sQ71_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3668]) ).
fof(f3670,plain,
( ~ sQ71_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f3657,f282,f2838]) ).
fof(f3671,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,c,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3658]) ).
fof(f3672,plain,
! [X0] :
( ~ sQ71_spl
| product(g1,a,c,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3659]) ).
fof(f3673,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(forward_demodulation,[status(thm)],[f3062,f2803]) ).
fof(f3674,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,a,c,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3673]) ).
fof(f3675,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f3062,f2811]) ).
fof(f3677,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2334]) ).
fof(f3678,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f297,f2281]) ).
fof(f3679,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f273,f2235]) ).
fof(f3680,plain,
( sQ12_spl
| ~ sQ25_spl
| inverse(g1,b) != b ),
inference(forward_demodulation,[status(thm)],[f297,f254]) ).
fof(f3681,plain,
( ~ sQ13_spl
| ~ sQ25_spl
| inverse(g1,b) = c ),
inference(forward_demodulation,[status(thm)],[f297,f256]) ).
fof(f3683,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f2564,f1249]) ).
fof(f3684,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f2564,f1248]) ).
fof(f3686,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f2564,f638]) ).
fof(f3687,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f2564,f556]) ).
fof(f3691,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f2564,f422]) ).
fof(f3692,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f2564,f420]) ).
fof(f3695,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f2564,f162]) ).
fof(f3696,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f2564,f161]) ).
fof(f3702,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3691]) ).
fof(f3703,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3702]) ).
fof(f3704,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3692]) ).
fof(f3705,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3704]) ).
fof(f3708,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f3695]) ).
fof(f3709,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f3696]) ).
fof(f3718,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,inverse(g2,h))) ),
inference(forward_demodulation,[status(thm)],[f1100,f1205]) ).
fof(f3719,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,g)) ),
inference(forward_demodulation,[status(thm)],[f1100,f3718]) ).
fof(f3720,plain,
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,g,g,g) ),
inference(forward_demodulation,[status(thm)],[f3362,f3719]) ).
fof(f3721,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,f,g,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f3720,f379]) ).
fof(f3722,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,g,g,X0)
| ~ product(g2,f,g,X0) ),
inference(resolution,[status(thm)],[f3720,f378]) ).
fof(f3723,plain,
( ~ sQ50_spl
| ~ sQ88_spl
| g = f ),
inference(resolution,[status(thm)],[f3720,f392]) ).
fof(f3725,plain,
( ~ sQ50_spl
| ~ sQ88_spl
| g = identity_for(g2) ),
inference(resolution,[status(thm)],[f3720,f167]) ).
fof(f3726,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,inverse(g2,g),g,X0)
| ~ product(g2,identity_for(g2),g,X0) ),
inference(resolution,[status(thm)],[f3720,f158]) ).
fof(f3727,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,inverse(g2,g),g,X0) ),
inference(resolution,[status(thm)],[f3720,f157]) ).
fof(f3729,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,g,g,X0)
| ~ product(g2,identity_for(g2),g,X0) ),
inference(resolution,[status(thm)],[f3720,f146]) ).
fof(f3730,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f3720,f139]) ).
fof(f3731,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| X0 = g
| ~ product(g2,X0,g,g) ),
inference(resolution,[status(thm)],[f3720,f75]) ).
fof(f3732,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| X0 = g
| ~ product(g2,g,X0,g) ),
inference(resolution,[status(thm)],[f3720,f73]) ).
fof(f3733,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,g,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f3720,f71]) ).
fof(f3734,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,g,X1,X2)
| ~ product(g2,g,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f3720,f69]) ).
fof(f3735,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| X0 = g
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f3720,f67]) ).
fof(f3736,plain,
( ~ sQ50_spl
| ~ sQ88_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f3723,f341,f3361,f1086]) ).
fof(f3738,plain,
( ~ sQ50_spl
| ~ sQ88_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f3725,f355,f3361,f1086]) ).
fof(f3739,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,inverse(g2,g),g,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3726]) ).
fof(f3740,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,h,g,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f3739]) ).
fof(f3741,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f3727]) ).
fof(f3742,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,f,g,X0)
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3741]) ).
fof(f3744,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,g,g,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3729]) ).
fof(f3745,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ88_spl
| product(g2,f,g,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3730]) ).
fof(f3746,plain,
! [X0] :
( product(g2,f,f,X0)
| ~ product(g2,inverse(g2,h),multiply(g2,h,f),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3632]) ).
fof(f3747,plain,
! [X0] :
( product(g2,f,g,X0)
| ~ product(g2,inverse(g2,h),multiply(g2,h,g),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3581]) ).
fof(f3748,plain,
! [X0] :
( product(g2,f,h,X0)
| ~ product(g2,inverse(g2,h),multiply(g2,h,h),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3563]) ).
fof(f3752,plain,
! [X0] :
( ~ sQ87_spl
| product(g2,f,g,X0)
| ~ product(g2,inverse(g2,g),f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3413]) ).
fof(f3753,plain,
product(g2,h,inverse(g2,h),multiply(g2,h,inverse(g2,h))),
inference(resolution,[status(thm)],[f212,f211]) ).
fof(f3754,plain,
group_member(multiply(g2,h,inverse(g2,h)),g2),
inference(resolution,[status(thm)],[f212,f210]) ).
fof(f3755,plain,
product(g2,g,inverse(g2,h),multiply(g2,g,inverse(g2,h))),
inference(resolution,[status(thm)],[f212,f197]) ).
fof(f3756,plain,
group_member(multiply(g2,g,inverse(g2,h)),g2),
inference(resolution,[status(thm)],[f212,f196]) ).
fof(f3757,plain,
group_member(multiply(g2,f,inverse(g2,h)),g2),
inference(resolution,[status(thm)],[f212,f187]) ).
fof(f3758,plain,
product(g2,f,inverse(g2,h),multiply(g2,f,inverse(g2,h))),
inference(resolution,[status(thm)],[f212,f178]) ).
fof(f3760,plain,
group_member(multiply(g2,identity_for(g2),inverse(g2,h)),g2),
inference(resolution,[status(thm)],[f212,f192]) ).
fof(f3761,plain,
product(g2,identity_for(g2),inverse(g2,h),multiply(g2,identity_for(g2),inverse(g2,h))),
inference(resolution,[status(thm)],[f212,f183]) ).
fof(f3762,plain,
! [X0] :
( group_member(multiply(g2,inverse(g2,h),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f212,f65]) ).
fof(f3763,plain,
! [X0] :
( product(g2,inverse(g2,h),X0,multiply(g2,inverse(g2,h),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f212,f64]) ).
fof(f3766,plain,
group_member(multiply(g2,f,inverse(g2,h)),g2),
inference(forward_demodulation,[status(thm)],[f92,f3760]) ).
fof(f3767,plain,
product(g2,f,inverse(g2,h),multiply(g2,identity_for(g2),inverse(g2,h))),
inference(forward_demodulation,[status(thm)],[f92,f3761]) ).
fof(f3768,plain,
product(g2,f,inverse(g2,h),multiply(g2,f,inverse(g2,h))),
inference(forward_demodulation,[status(thm)],[f92,f3767]) ).
fof(f3775,plain,
product(g2,h,inverse(g2,g),multiply(g2,h,inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f211]) ).
fof(f3776,plain,
group_member(multiply(g2,h,inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f210]) ).
fof(f3777,plain,
product(g2,g,inverse(g2,g),multiply(g2,g,inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f197]) ).
fof(f3778,plain,
group_member(multiply(g2,g,inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f196]) ).
fof(f3779,plain,
group_member(multiply(g2,f,inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f187]) ).
fof(f3780,plain,
product(g2,f,inverse(g2,g),multiply(g2,f,inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f178]) ).
fof(f3782,plain,
group_member(multiply(g2,identity_for(g2),inverse(g2,g)),g2),
inference(resolution,[status(thm)],[f198,f192]) ).
fof(f3783,plain,
product(g2,identity_for(g2),inverse(g2,g),multiply(g2,identity_for(g2),inverse(g2,g))),
inference(resolution,[status(thm)],[f198,f183]) ).
fof(f3784,plain,
! [X0] :
( group_member(multiply(g2,inverse(g2,g),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f198,f65]) ).
fof(f3785,plain,
! [X0] :
( product(g2,inverse(g2,g),X0,multiply(g2,inverse(g2,g),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f198,f64]) ).
fof(f3788,plain,
group_member(multiply(g2,f,inverse(g2,g)),g2),
inference(forward_demodulation,[status(thm)],[f92,f3782]) ).
fof(f3789,plain,
product(g2,f,inverse(g2,g),multiply(g2,identity_for(g2),inverse(g2,g))),
inference(forward_demodulation,[status(thm)],[f92,f3783]) ).
fof(f3790,plain,
product(g2,f,inverse(g2,g),multiply(g2,f,inverse(g2,g))),
inference(forward_demodulation,[status(thm)],[f92,f3789]) ).
fof(f3792,plain,
product(g2,h,multiply(g2,g,inverse(g2,h)),multiply(g2,h,multiply(g2,g,inverse(g2,h)))),
inference(resolution,[status(thm)],[f1206,f211]) ).
fof(f3793,plain,
group_member(multiply(g2,h,multiply(g2,g,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1206,f210]) ).
fof(f3794,plain,
product(g2,g,multiply(g2,g,inverse(g2,h)),multiply(g2,g,multiply(g2,g,inverse(g2,h)))),
inference(resolution,[status(thm)],[f1206,f197]) ).
fof(f3795,plain,
group_member(multiply(g2,g,multiply(g2,g,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1206,f196]) ).
fof(f3796,plain,
group_member(multiply(g2,f,multiply(g2,g,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1206,f187]) ).
fof(f3797,plain,
product(g2,f,multiply(g2,g,inverse(g2,h)),multiply(g2,f,multiply(g2,g,inverse(g2,h)))),
inference(resolution,[status(thm)],[f1206,f178]) ).
fof(f3798,plain,
( multiply(g2,g,inverse(g2,h)) = h
| multiply(g2,g,inverse(g2,h)) = g
| multiply(g2,g,inverse(g2,h)) = f ),
inference(resolution,[status(thm)],[f1206,f90]) ).
fof(f3799,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,g,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1206,f192]) ).
fof(f3800,plain,
product(g2,identity_for(g2),multiply(g2,g,inverse(g2,h)),multiply(g2,identity_for(g2),multiply(g2,g,inverse(g2,h)))),
inference(resolution,[status(thm)],[f1206,f183]) ).
fof(f3801,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,g,inverse(g2,h)),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1206,f65]) ).
fof(f3802,plain,
! [X0] :
( product(g2,multiply(g2,g,inverse(g2,h)),X0,multiply(g2,multiply(g2,g,inverse(g2,h)),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1206,f64]) ).
fof(f3803,plain,
group_member(inverse(g2,multiply(g2,g,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1206,f61]) ).
fof(f3804,definition,
( sQ102_spl
<=> multiply(g2,g,inverse(g2,h)) = f ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f3805,plain,
( ~ sQ102_spl
| multiply(g2,g,inverse(g2,h)) = f ),
inference(component_clause,[status(thm)],[f3804]) ).
fof(f3806,plain,
( sQ102_spl
| multiply(g2,g,inverse(g2,h)) != f ),
inference(component_clause,[status(thm)],[f3804]) ).
fof(f3807,definition,
( sQ103_spl
<=> multiply(g2,g,inverse(g2,h)) = g ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f3808,plain,
( ~ sQ103_spl
| multiply(g2,g,inverse(g2,h)) = g ),
inference(component_clause,[status(thm)],[f3807]) ).
fof(f3809,plain,
( sQ103_spl
| multiply(g2,g,inverse(g2,h)) != g ),
inference(component_clause,[status(thm)],[f3807]) ).
fof(f3810,definition,
( sQ104_spl
<=> multiply(g2,g,inverse(g2,h)) = h ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f3811,plain,
( ~ sQ104_spl
| multiply(g2,g,inverse(g2,h)) = h ),
inference(component_clause,[status(thm)],[f3810]) ).
fof(f3813,plain,
( sQ104_spl
| sQ103_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f3798,f3804,f3807,f3810]) ).
fof(f3814,plain,
group_member(multiply(g2,f,multiply(g2,g,inverse(g2,h))),g2),
inference(forward_demodulation,[status(thm)],[f92,f3799]) ).
fof(f3815,plain,
product(g2,f,multiply(g2,g,inverse(g2,h)),multiply(g2,identity_for(g2),multiply(g2,g,inverse(g2,h)))),
inference(forward_demodulation,[status(thm)],[f92,f3800]) ).
fof(f3816,plain,
product(g2,f,multiply(g2,g,inverse(g2,h)),multiply(g2,f,multiply(g2,g,inverse(g2,h)))),
inference(forward_demodulation,[status(thm)],[f92,f3815]) ).
fof(f3817,plain,
product(g2,h,multiply(g2,f,inverse(g2,h)),multiply(g2,h,multiply(g2,f,inverse(g2,h)))),
inference(resolution,[status(thm)],[f1207,f211]) ).
fof(f3818,plain,
group_member(multiply(g2,h,multiply(g2,f,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1207,f210]) ).
fof(f3819,plain,
product(g2,g,multiply(g2,f,inverse(g2,h)),multiply(g2,g,multiply(g2,f,inverse(g2,h)))),
inference(resolution,[status(thm)],[f1207,f197]) ).
fof(f3820,plain,
group_member(multiply(g2,g,multiply(g2,f,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1207,f196]) ).
fof(f3821,plain,
group_member(multiply(g2,f,multiply(g2,f,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1207,f187]) ).
fof(f3822,plain,
product(g2,f,multiply(g2,f,inverse(g2,h)),multiply(g2,f,multiply(g2,f,inverse(g2,h)))),
inference(resolution,[status(thm)],[f1207,f178]) ).
fof(f3823,plain,
( multiply(g2,f,inverse(g2,h)) = h
| multiply(g2,f,inverse(g2,h)) = g
| multiply(g2,f,inverse(g2,h)) = f ),
inference(resolution,[status(thm)],[f1207,f90]) ).
fof(f3824,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,f,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1207,f192]) ).
fof(f3825,plain,
product(g2,identity_for(g2),multiply(g2,f,inverse(g2,h)),multiply(g2,identity_for(g2),multiply(g2,f,inverse(g2,h)))),
inference(resolution,[status(thm)],[f1207,f183]) ).
fof(f3826,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,f,inverse(g2,h)),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1207,f65]) ).
fof(f3827,plain,
! [X0] :
( product(g2,multiply(g2,f,inverse(g2,h)),X0,multiply(g2,multiply(g2,f,inverse(g2,h)),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f1207,f64]) ).
fof(f3828,plain,
group_member(inverse(g2,multiply(g2,f,inverse(g2,h))),g2),
inference(resolution,[status(thm)],[f1207,f61]) ).
fof(f3829,definition,
( sQ105_spl
<=> multiply(g2,f,inverse(g2,h)) = f ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f3830,plain,
( ~ sQ105_spl
| multiply(g2,f,inverse(g2,h)) = f ),
inference(component_clause,[status(thm)],[f3829]) ).
fof(f3831,plain,
( sQ105_spl
| multiply(g2,f,inverse(g2,h)) != f ),
inference(component_clause,[status(thm)],[f3829]) ).
fof(f3832,definition,
( sQ106_spl
<=> multiply(g2,f,inverse(g2,h)) = g ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f3833,plain,
( ~ sQ106_spl
| multiply(g2,f,inverse(g2,h)) = g ),
inference(component_clause,[status(thm)],[f3832]) ).
fof(f3835,definition,
( sQ107_spl
<=> multiply(g2,f,inverse(g2,h)) = h ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f3836,plain,
( ~ sQ107_spl
| multiply(g2,f,inverse(g2,h)) = h ),
inference(component_clause,[status(thm)],[f3835]) ).
fof(f3837,plain,
( sQ107_spl
| multiply(g2,f,inverse(g2,h)) != h ),
inference(component_clause,[status(thm)],[f3835]) ).
fof(f3838,plain,
( sQ107_spl
| sQ106_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f3823,f3829,f3832,f3835]) ).
fof(f3839,plain,
group_member(multiply(g2,f,multiply(g2,f,inverse(g2,h))),g2),
inference(forward_demodulation,[status(thm)],[f92,f3824]) ).
fof(f3840,plain,
product(g2,f,multiply(g2,f,inverse(g2,h)),multiply(g2,identity_for(g2),multiply(g2,f,inverse(g2,h)))),
inference(forward_demodulation,[status(thm)],[f92,f3825]) ).
fof(f3841,plain,
product(g2,f,multiply(g2,f,inverse(g2,h)),multiply(g2,f,multiply(g2,f,inverse(g2,h)))),
inference(forward_demodulation,[status(thm)],[f92,f3840]) ).
fof(f3842,plain,
( sQ12_spl
| ~ sQ25_spl
| ~ sQ15_spl
| ~ sQ18_spl
| b != b ),
inference(forward_demodulation,[status(thm)],[f2564,f3680]) ).
fof(f3843,plain,
( sQ12_spl
| ~ sQ25_spl
| ~ sQ15_spl
| ~ sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3842]) ).
fof(f3844,plain,
( sQ12_spl
| ~ sQ25_spl
| ~ sQ15_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f3843]) ).
fof(f3845,plain,
( sQ5_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism6(d1),isomorphism6(d2),isomorphism6(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f137]) ).
fof(f3846,plain,
( sQ5_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism6(d1),isomorphism6(d2),f) ),
inference(forward_demodulation,[status(thm)],[f113,f3845]) ).
fof(f3847,plain,
( ~ sQ18_spl
| product(g1,d1,d2,b) ),
inference(forward_demodulation,[status(thm)],[f273,f118]) ).
fof(f3848,plain,
! [X0] :
( ~ sQ18_spl
| X0 = b
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f273,f144]) ).
fof(f3849,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism5(d1),isomorphism5(d2),isomorphism5(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f134]) ).
fof(f3850,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism5(d1),isomorphism5(d2),g) ),
inference(forward_demodulation,[status(thm)],[f110,f3849]) ).
fof(f3851,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism4(d1),isomorphism4(d2),isomorphism4(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f131]) ).
fof(f3852,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ product(g2,isomorphism4(d1),isomorphism4(d2),h) ),
inference(forward_demodulation,[status(thm)],[f107,f3851]) ).
fof(f3853,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,a,X0)
| ~ product(g1,b,inverse(g1,d2),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1690]) ).
fof(f3854,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f273,f145]) ).
fof(f3859,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ18_spl
| X0 = d1
| ~ product(g1,X0,a,b) ),
inference(forward_demodulation,[status(thm)],[f273,f571]) ).
fof(f3860,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| ~ sQ18_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f273,f1044]) ).
fof(f3861,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ18_spl
| product(g1,d1,identity_for(g1),X0)
| ~ product(g1,b,inverse(g1,a),X0) ),
inference(forward_demodulation,[status(thm)],[f273,f1569]) ).
fof(f3862,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ18_spl
| product(g1,d1,identity_for(g1),X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f3861]) ).
fof(f3863,plain,
! [X0] :
( ~ sQ24_spl
| ~ sQ18_spl
| product(g1,d1,a,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3862]) ).
fof(f3865,plain,
! [X0,X1,X2] :
( ~ sQ24_spl
| ~ sQ18_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f273,f470]) ).
fof(f3866,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(resolution,[status(thm)],[f116,f184]) ).
fof(f3867,plain,
group_member(multiply(g1,a,d2),g1),
inference(resolution,[status(thm)],[f116,f193]) ).
fof(f3868,plain,
group_member(multiply(g1,b,d2),g1),
inference(resolution,[status(thm)],[f116,f189]) ).
fof(f3869,plain,
group_member(multiply(g1,c,d2),g1),
inference(resolution,[status(thm)],[f116,f188]) ).
fof(f3870,plain,
product(g1,b,d2,multiply(g1,b,d2)),
inference(resolution,[status(thm)],[f116,f180]) ).
fof(f3871,plain,
product(g1,c,d2,multiply(g1,c,d2)),
inference(resolution,[status(thm)],[f116,f179]) ).
fof(f3873,plain,
group_member(multiply(g1,identity_for(g1),d2),g1),
inference(resolution,[status(thm)],[f116,f192]) ).
fof(f3874,plain,
product(g1,identity_for(g1),d2,multiply(g1,identity_for(g1),d2)),
inference(resolution,[status(thm)],[f116,f183]) ).
fof(f3875,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f116,f65]) ).
fof(f3876,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f116,f64]) ).
fof(f3877,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f116,f61]) ).
fof(f3879,plain,
group_member(multiply(g1,a,d2),g1),
inference(forward_demodulation,[status(thm)],[f91,f3873]) ).
fof(f3880,plain,
product(g1,a,d2,multiply(g1,identity_for(g1),d2)),
inference(forward_demodulation,[status(thm)],[f91,f3874]) ).
fof(f3881,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(forward_demodulation,[status(thm)],[f91,f3880]) ).
fof(f3884,plain,
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,d2,b) ),
inference(forward_demodulation,[status(thm)],[f307,f3847]) ).
fof(f3886,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(resolution,[status(thm)],[f3884,f173]) ).
fof(f3887,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f3884,f172]) ).
fof(f3888,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,identity_for(g1),d2,X0) ),
inference(resolution,[status(thm)],[f3884,f158]) ).
fof(f3889,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(resolution,[status(thm)],[f3884,f157]) ).
fof(f3890,plain,
( ~ sQ18_spl
| ~ sQ28_spl
| d2 = identity_for(g1) ),
inference(resolution,[status(thm)],[f3884,f150]) ).
fof(f3891,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,d2,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f3884,f146]) ).
fof(f3892,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,b,d2,X0) ),
inference(resolution,[status(thm)],[f3884,f139]) ).
fof(f3898,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3888]) ).
fof(f3899,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ15_spl
| product(g1,b,b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f2564,f3898]) ).
fof(f3900,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ15_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f2564,f3889]) ).
fof(f3901,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ15_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3900]) ).
fof(f3902,plain,
( ~ sQ18_spl
| ~ sQ28_spl
| d2 = a ),
inference(forward_demodulation,[status(thm)],[f91,f3890]) ).
fof(f3903,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3891]) ).
fof(f3904,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3892]) ).
fof(f3912,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism5(b),isomorphism5(d2),g) ),
inference(forward_demodulation,[status(thm)],[f307,f3850]) ).
fof(f3913,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,isomorphism5(d2),g) ),
inference(forward_demodulation,[status(thm)],[f110,f3912]) ).
fof(f3914,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ24_spl
| ~ product(g2,g,isomorphism5(a),g) ),
inference(forward_demodulation,[status(thm)],[f294,f3913]) ).
fof(f3915,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ24_spl
| ~ product(g2,g,h,g) ),
inference(forward_demodulation,[status(thm)],[f109,f3914]) ).
fof(f3916,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism4(b),isomorphism4(d2),h) ),
inference(forward_demodulation,[status(thm)],[f307,f3852]) ).
fof(f3917,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,isomorphism4(d2),h) ),
inference(forward_demodulation,[status(thm)],[f107,f3916]) ).
fof(f3918,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ24_spl
| ~ product(g2,h,isomorphism4(a),h) ),
inference(forward_demodulation,[status(thm)],[f294,f3917]) ).
fof(f3919,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ24_spl
| ~ product(g2,h,g,h) ),
inference(forward_demodulation,[status(thm)],[f106,f3918]) ).
fof(f3933,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ24_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f294,f1705]) ).
fof(f3938,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ24_spl
| X0 = d1
| ~ product(g1,X0,a,b) ),
inference(forward_demodulation,[status(thm)],[f294,f1707]) ).
fof(f3940,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ24_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f294,f3854]) ).
fof(f3945,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,X0,g,f) ),
inference(paramodulation,[status(thm)],[f1084,f703]) ).
fof(f3946,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,f,f,X0)
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f637]) ).
fof(f3947,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,f,f,X0)
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f554]) ).
fof(f3948,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,g,X0,f) ),
inference(paramodulation,[status(thm)],[f1084,f541]) ).
fof(f3951,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f422]) ).
fof(f3952,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f420]) ).
fof(f3953,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,X0,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1084,f168]) ).
fof(f3954,plain,
! [X0] :
( ~ sQ49_spl
| X0 = identity_for(g2)
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f163]) ).
fof(f3955,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,g,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(paramodulation,[status(thm)],[f1084,f162]) ).
fof(f3956,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(paramodulation,[status(thm)],[f1084,f161]) ).
fof(f3957,plain,
! [X0] :
( ~ sQ49_spl
| X0 = identity_for(g2)
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f159]) ).
fof(f3959,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,g,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1084,f156]) ).
fof(f3962,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,f,identity_for(g2),X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3951]) ).
fof(f3963,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,f,f,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3962]) ).
fof(f3964,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,f,identity_for(g2),X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3952]) ).
fof(f3965,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,f,f,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3964]) ).
fof(f3966,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,X0,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f3953]) ).
fof(f3967,plain,
! [X0] :
( ~ sQ49_spl
| X0 = f
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3954]) ).
fof(f3968,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f3955]) ).
fof(f3969,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f3956]) ).
fof(f3970,plain,
! [X0] :
( ~ sQ49_spl
| X0 = f
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3957]) ).
fof(f3971,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,g,X0,f) ),
inference(forward_demodulation,[status(thm)],[f92,f3959]) ).
fof(f3977,plain,
( ~ sQ53_spl
| group_member(multiply(g2,g,h),g2) ),
inference(backward_demodulation,[status(thm)],[f1222,f1206]) ).
fof(f3979,plain,
! [X0] :
( ~ sQ53_spl
| X0 = h
| ~ product(g2,X0,h,f) ),
inference(paramodulation,[status(thm)],[f1222,f703]) ).
fof(f3980,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(paramodulation,[status(thm)],[f1222,f637]) ).
fof(f3981,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(paramodulation,[status(thm)],[f1222,f554]) ).
fof(f3982,plain,
! [X0] :
( ~ sQ53_spl
| X0 = h
| ~ product(g2,h,X0,f) ),
inference(paramodulation,[status(thm)],[f1222,f541]) ).
fof(f3983,plain,
( ~ sQ53_spl
| product(g2,h,h,f) ),
inference(paramodulation,[status(thm)],[f1222,f219]) ).
fof(f3985,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,h,h,X0) ),
inference(paramodulation,[status(thm)],[f1222,f422]) ).
fof(f3986,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,h,h,X0) ),
inference(paramodulation,[status(thm)],[f1222,f420]) ).
fof(f3987,plain,
! [X0] :
( ~ sQ53_spl
| X0 = h
| ~ product(g2,X0,h,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1222,f168]) ).
fof(f3988,plain,
! [X0] :
( ~ sQ53_spl
| X0 = identity_for(g2)
| ~ product(g2,h,h,X0) ),
inference(paramodulation,[status(thm)],[f1222,f163]) ).
fof(f3989,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| product(g2,h,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1222,f162]) ).
fof(f3990,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1222,f161]) ).
fof(f3991,plain,
! [X0] :
( ~ sQ53_spl
| X0 = identity_for(g2)
| ~ product(g2,h,h,X0) ),
inference(paramodulation,[status(thm)],[f1222,f159]) ).
fof(f3993,plain,
! [X0] :
( ~ sQ53_spl
| X0 = h
| ~ product(g2,h,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1222,f156]) ).
fof(f3998,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,f,identity_for(g2),X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3985]) ).
fof(f3999,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3998]) ).
fof(f4000,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,f,identity_for(g2),X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3986]) ).
fof(f4001,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4000]) ).
fof(f4002,plain,
! [X0] :
( ~ sQ53_spl
| X0 = h
| ~ product(g2,X0,h,f) ),
inference(forward_demodulation,[status(thm)],[f92,f3987]) ).
fof(f4003,plain,
! [X0] :
( ~ sQ53_spl
| X0 = f
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3988]) ).
fof(f4004,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| product(g2,h,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f3989]) ).
fof(f4005,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| product(g2,f,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f3990]) ).
fof(f4006,plain,
! [X0] :
( ~ sQ53_spl
| X0 = f
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f3991]) ).
fof(f4007,plain,
! [X0] :
( ~ sQ53_spl
| X0 = h
| ~ product(g2,h,X0,f) ),
inference(forward_demodulation,[status(thm)],[f92,f3993]) ).
fof(f4013,plain,
( ~ sQ28_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f307,f155]) ).
fof(f4020,plain,
( ~ sQ98_spl
| ~ sQ97_spl
| g = h ),
inference(backward_demodulation,[status(thm)],[f3518,f3521]) ).
fof(f4021,plain,
( ~ sQ98_spl
| ~ sQ97_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f4020,f334,f3517,f3520]) ).
fof(f4026,plain,
( ~ sQ24_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f294,f3867]) ).
fof(f4030,plain,
product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))),
inference(resolution,[status(thm)],[f1888,f184]) ).
fof(f4031,plain,
group_member(multiply(g1,a,multiply(g1,a,b)),g1),
inference(resolution,[status(thm)],[f1888,f193]) ).
fof(f4032,plain,
group_member(multiply(g1,b,multiply(g1,a,b)),g1),
inference(resolution,[status(thm)],[f1888,f189]) ).
fof(f4033,plain,
group_member(multiply(g1,c,multiply(g1,a,b)),g1),
inference(resolution,[status(thm)],[f1888,f188]) ).
fof(f4034,plain,
product(g1,b,multiply(g1,a,b),multiply(g1,b,multiply(g1,a,b))),
inference(resolution,[status(thm)],[f1888,f180]) ).
fof(f4035,plain,
product(g1,c,multiply(g1,a,b),multiply(g1,c,multiply(g1,a,b))),
inference(resolution,[status(thm)],[f1888,f179]) ).
fof(f4036,plain,
( multiply(g1,a,b) = c
| multiply(g1,a,b) = b
| multiply(g1,a,b) = a ),
inference(resolution,[status(thm)],[f1888,f89]) ).
fof(f4037,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,a,b)),g1),
inference(resolution,[status(thm)],[f1888,f192]) ).
fof(f4038,plain,
product(g1,identity_for(g1),multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))),
inference(resolution,[status(thm)],[f1888,f183]) ).
fof(f4039,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,a,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1888,f65]) ).
fof(f4040,plain,
! [X0] :
( product(g1,multiply(g1,a,b),X0,multiply(g1,multiply(g1,a,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1888,f64]) ).
fof(f4041,plain,
group_member(inverse(g1,multiply(g1,a,b)),g1),
inference(resolution,[status(thm)],[f1888,f61]) ).
fof(f4042,plain,
( sQ56_spl
| sQ55_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f4036,f1505,f1508,f1511]) ).
fof(f4043,plain,
group_member(multiply(g1,a,multiply(g1,a,b)),g1),
inference(forward_demodulation,[status(thm)],[f91,f4037]) ).
fof(f4044,plain,
product(g1,a,multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))),
inference(forward_demodulation,[status(thm)],[f91,f4038]) ).
fof(f4045,plain,
product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))),
inference(forward_demodulation,[status(thm)],[f91,f4044]) ).
fof(f4048,plain,
( ~ sQ100_spl
| h = g ),
inference(backward_demodulation,[status(thm)],[f3543,f3628]) ).
fof(f4049,plain,
( ~ sQ100_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f4048,f334,f3542]) ).
fof(f4068,plain,
! [X0] :
( product(g1,a,identity_for(g1),X0)
| ~ product(g1,inverse(g1,identity_for(g1)),multiply(g1,identity_for(g1),identity_for(g1)),X0) ),
inference(resolution,[status(thm)],[f1333,f923]) ).
fof(f4077,plain,
! [X0] :
( product(g1,a,identity_for(g1),X0)
| ~ product(g1,identity_for(g1),multiply(g1,identity_for(g1),identity_for(g1)),X0) ),
inference(forward_demodulation,[status(thm)],[f429,f4068]) ).
fof(f4078,plain,
! [X0] :
( product(g1,a,identity_for(g1),X0)
| ~ product(g1,a,multiply(g1,identity_for(g1),identity_for(g1)),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4077]) ).
fof(f4079,plain,
! [X0] :
( product(g1,a,identity_for(g1),X0)
| ~ product(g1,a,multiply(g1,a,identity_for(g1)),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4078]) ).
fof(f4080,plain,
! [X0] :
( product(g1,a,identity_for(g1),X0)
| ~ product(g1,a,multiply(g1,a,a),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4079]) ).
fof(f4092,plain,
! [X0] :
( product(g1,inverse(g1,identity_for(g1)),multiply(g1,identity_for(g1),identity_for(g1)),X0)
| ~ product(g1,a,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f1334,f923]) ).
fof(f4101,plain,
! [X0] :
( product(g1,inverse(g1,identity_for(g1)),multiply(g1,identity_for(g1),identity_for(g1)),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4092]) ).
fof(f4102,plain,
! [X0] :
( product(g1,identity_for(g1),multiply(g1,identity_for(g1),identity_for(g1)),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f429,f4101]) ).
fof(f4103,plain,
! [X0] :
( product(g1,a,multiply(g1,identity_for(g1),identity_for(g1)),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4102]) ).
fof(f4104,plain,
! [X0] :
( product(g1,a,multiply(g1,a,identity_for(g1)),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4103]) ).
fof(f4105,plain,
! [X0] :
( product(g1,a,multiply(g1,a,a),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4104]) ).
fof(f4109,plain,
( ~ sQ99_spl
| h = f ),
inference(backward_demodulation,[status(thm)],[f3540,f3628]) ).
fof(f4110,plain,
( ~ sQ99_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f4109,f331,f3539]) ).
fof(f4112,plain,
( ~ sQ84_spl
| g = inverse(g2,h) ),
inference(resolution,[status(thm)],[f3399,f691]) ).
fof(f4113,plain,
( ~ sQ84_spl
| h = inverse(g2,g) ),
inference(resolution,[status(thm)],[f3399,f611]) ).
fof(f4114,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f3399,f379]) ).
fof(f4115,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,g,h,X0)
| ~ product(g2,f,f,X0) ),
inference(resolution,[status(thm)],[f3399,f378]) ).
fof(f4116,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,inverse(g2,g),f,X0)
| ~ product(g2,identity_for(g2),h,X0) ),
inference(resolution,[status(thm)],[f3399,f158]) ).
fof(f4117,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,inverse(g2,g),f,X0) ),
inference(resolution,[status(thm)],[f3399,f157]) ).
fof(f4120,plain,
! [X0] :
( ~ sQ84_spl
| X0 = g
| ~ product(g2,X0,h,f) ),
inference(resolution,[status(thm)],[f3399,f75]) ).
fof(f4121,plain,
! [X0] :
( ~ sQ84_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(resolution,[status(thm)],[f3399,f73]) ).
fof(f4122,plain,
! [X0,X1,X2] :
( ~ sQ84_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f3399,f71]) ).
fof(f4123,plain,
! [X0,X1,X2] :
( ~ sQ84_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f3399,f69]) ).
fof(f4124,plain,
! [X0] :
( ~ sQ84_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f3399,f67]) ).
fof(f4125,plain,
( ~ sQ84_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f4112,f1218,f3261]) ).
fof(f4126,plain,
( ~ sQ84_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f4113,f1086,f3261]) ).
fof(f4127,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,inverse(g2,g),f,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4116]) ).
fof(f4128,plain,
! [X0] :
( ~ sQ84_spl
| ~ sQ49_spl
| product(g2,g,f,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1084,f4127]) ).
fof(f4129,plain,
! [X0] :
( ~ sQ84_spl
| ~ sQ49_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1084,f4117]) ).
fof(f4130,plain,
! [X0] :
( ~ sQ84_spl
| ~ sQ49_spl
| product(g2,f,h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4129]) ).
fof(f4139,plain,
( ~ sQ24_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f294,f3868]) ).
fof(f4148,plain,
! [X0] :
( ~ sQ44_spl
| X0 = a
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f1335]) ).
fof(f4157,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,f,f,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f1178,f379]) ).
fof(f4158,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,g,g,X0)
| ~ product(g2,f,f,X0) ),
inference(resolution,[status(thm)],[f1178,f378]) ).
fof(f4161,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,g,g,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f1178,f146]) ).
fof(f4162,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f1178,f139]) ).
fof(f4163,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,X0,g,f) ),
inference(resolution,[status(thm)],[f1178,f75]) ).
fof(f4164,plain,
! [X0] :
( ~ sQ49_spl
| X0 = g
| ~ product(g2,g,X0,f) ),
inference(resolution,[status(thm)],[f1178,f73]) ).
fof(f4165,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f1178,f71]) ).
fof(f4166,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f1178,f69]) ).
fof(f4167,plain,
! [X0] :
( ~ sQ49_spl
| X0 = f
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f1178,f67]) ).
fof(f4172,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,g,g,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4161]) ).
fof(f4173,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,f,f,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4162]) ).
fof(f4174,plain,
( ~ sQ24_spl
| group_member(multiply(g1,c,a),g1) ),
inference(forward_demodulation,[status(thm)],[f294,f3869]) ).
fof(f4176,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f2564,f1947]) ).
fof(f4177,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f2564,f4176]) ).
fof(f4178,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,b,c) ),
inference(forward_demodulation,[status(thm)],[f1512,f4177]) ).
fof(f4179,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,b,a,c) ),
inference(resolution,[status(thm)],[f4178,f500]) ).
fof(f4180,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,X0,c,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f4178,f208]) ).
fof(f4181,plain,
! [X0,X1] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,c,X1) ),
inference(resolution,[status(thm)],[f4178,f207]) ).
fof(f4182,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| b = c ),
inference(resolution,[status(thm)],[f4178,f171]) ).
fof(f4183,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,inverse(g1,a),c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4178,f1334]) ).
fof(f4184,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,a),c,X0) ),
inference(resolution,[status(thm)],[f4178,f1333]) ).
fof(f4185,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4178,f173]) ).
fof(f4186,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f4178,f172]) ).
fof(f4187,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,inverse(g1,a),c,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f4178,f158]) ).
fof(f4188,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,a),c,X0) ),
inference(resolution,[status(thm)],[f4178,f157]) ).
fof(f4189,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f4178,f146]) ).
fof(f4190,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4178,f139]) ).
fof(f4191,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| X0 = a
| ~ product(g1,X0,b,c) ),
inference(resolution,[status(thm)],[f4178,f75]) ).
fof(f4192,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| X0 = b
| ~ product(g1,a,X0,c) ),
inference(resolution,[status(thm)],[f4178,f73]) ).
fof(f4193,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,c,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4178,f71]) ).
fof(f4194,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,X1,X2)
| ~ product(g1,c,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4178,f69]) ).
fof(f4195,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| X0 = c
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4178,f67]) ).
fof(f4196,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f4182,f235,f1511,f262,f272]) ).
fof(f4197,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f4183]) ).
fof(f4198,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f4184]) ).
fof(f4199,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,inverse(g1,a),c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4187]) ).
fof(f4200,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f4199]) ).
fof(f4201,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f4188]) ).
fof(f4202,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4201]) ).
fof(f4203,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4189]) ).
fof(f4204,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ56_spl
| product(g1,a,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4190]) ).
fof(f4207,plain,
( ~ sQ24_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f294,f3879]) ).
fof(f4209,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2564,f1945]) ).
fof(f4217,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| product(g2,f,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1222,f1372]) ).
fof(f4218,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(paramodulation,[status(thm)],[f1084,f1372]) ).
fof(f4235,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| product(g2,h,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1222,f1373]) ).
fof(f4236,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(paramodulation,[status(thm)],[f1084,f1373]) ).
fof(f4251,plain,
! [X0] :
( ~ sQ53_spl
| X0 = f
| ~ product(g2,h,h,X0) ),
inference(paramodulation,[status(thm)],[f1222,f1374]) ).
fof(f4252,plain,
! [X0] :
( ~ sQ49_spl
| X0 = f
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f1374]) ).
fof(f4259,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2564,f1935]) ).
fof(f4260,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,multiply(g1,c,b),multiply(g1,a,multiply(g1,c,b))) ),
inference(resolution,[status(thm)],[f4259,f184]) ).
fof(f4261,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,a,multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f4259,f193]) ).
fof(f4262,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,b,multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f4259,f189]) ).
fof(f4263,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,c,multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f4259,f188]) ).
fof(f4264,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,b,multiply(g1,c,b),multiply(g1,b,multiply(g1,c,b))) ),
inference(resolution,[status(thm)],[f4259,f180]) ).
fof(f4265,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,c,multiply(g1,c,b),multiply(g1,c,multiply(g1,c,b))) ),
inference(resolution,[status(thm)],[f4259,f179]) ).
fof(f4267,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f4259,f192]) ).
fof(f4268,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,identity_for(g1),multiply(g1,c,b),multiply(g1,identity_for(g1),multiply(g1,c,b))) ),
inference(resolution,[status(thm)],[f4259,f183]) ).
fof(f4269,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,multiply(g1,c,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f4259,f65]) ).
fof(f4270,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,multiply(g1,c,b),X0,multiply(g1,multiply(g1,c,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f4259,f64]) ).
fof(f4271,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(inverse(g1,multiply(g1,c,b)),g1) ),
inference(resolution,[status(thm)],[f4259,f61]) ).
fof(f4273,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,a,multiply(g1,c,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f4267]) ).
fof(f4274,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,multiply(g1,c,b),multiply(g1,identity_for(g1),multiply(g1,c,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f4268]) ).
fof(f4275,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,multiply(g1,c,b),multiply(g1,a,multiply(g1,c,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f4274]) ).
fof(f4276,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,c,b,multiply(g1,c,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f2564,f1937]) ).
fof(f4277,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f2564,f4276]) ).
fof(f4278,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,inverse(g1,c),multiply(g1,c,b),X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4277,f1334]) ).
fof(f4279,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),multiply(g1,c,b),X0) ),
inference(resolution,[status(thm)],[f4277,f1333]) ).
fof(f4280,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,multiply(g1,c,b),X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4277,f173]) ).
fof(f4281,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,c,b,X0)
| ~ product(g1,a,multiply(g1,c,b),X0) ),
inference(resolution,[status(thm)],[f4277,f172]) ).
fof(f4282,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,inverse(g1,c),multiply(g1,c,b),X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f4277,f158]) ).
fof(f4283,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),multiply(g1,c,b),X0) ),
inference(resolution,[status(thm)],[f4277,f157]) ).
fof(f4284,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,c,b,X0)
| ~ product(g1,identity_for(g1),multiply(g1,c,b),X0) ),
inference(resolution,[status(thm)],[f4277,f146]) ).
fof(f4285,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,identity_for(g1),multiply(g1,c,b),X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4277,f139]) ).
fof(f4286,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| X0 = c
| ~ product(g1,X0,b,multiply(g1,c,b)) ),
inference(resolution,[status(thm)],[f4277,f75]) ).
fof(f4287,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| X0 = b
| ~ product(g1,c,X0,multiply(g1,c,b)) ),
inference(resolution,[status(thm)],[f4277,f73]) ).
fof(f4288,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,multiply(g1,c,b),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4277,f71]) ).
fof(f4289,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,c,X1,X2)
| ~ product(g1,multiply(g1,c,b),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4277,f69]) ).
fof(f4290,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| X0 = multiply(g1,c,b)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4277,f67]) ).
fof(f4291,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ44_spl
| product(g1,c,multiply(g1,c,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4278]) ).
fof(f4292,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4279]) ).
fof(f4293,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,inverse(g1,c),multiply(g1,c,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4282]) ).
fof(f4294,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ44_spl
| product(g1,c,multiply(g1,c,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4293]) ).
fof(f4295,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ44_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4283]) ).
fof(f4296,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4295]) ).
fof(f4297,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,c,b,X0)
| ~ product(g1,a,multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4284]) ).
fof(f4298,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,multiply(g1,c,b),X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4285]) ).
fof(f4299,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(backward_demodulation,[status(thm)],[f2833,f4277]) ).
fof(f4302,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ69_spl
| c = b ),
inference(resolution,[status(thm)],[f4299,f1846]) ).
fof(f4303,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| c = inverse(g1,b) ),
inference(resolution,[status(thm)],[f4299,f692]) ).
fof(f4304,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| b = inverse(g1,c) ),
inference(resolution,[status(thm)],[f4299,f612]) ).
fof(f4305,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4299,f1334]) ).
fof(f4306,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f4299,f1333]) ).
fof(f4307,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4299,f173]) ).
fof(f4308,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f4299,f172]) ).
fof(f4309,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f4299,f158]) ).
fof(f4310,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f4299,f157]) ).
fof(f4311,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,c,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f4299,f146]) ).
fof(f4312,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4299,f139]) ).
fof(f4313,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f4299,f75]) ).
fof(f4314,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(resolution,[status(thm)],[f4299,f73]) ).
fof(f4315,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4299,f71]) ).
fof(f4316,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4299,f69]) ).
fof(f4317,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4299,f67]) ).
fof(f4318,plain,
( ~ sQ15_spl
| ~ sQ18_spl
| ~ sQ69_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f4302,f235,f2832,f272,f262]) ).
fof(f4319,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f4303,f718,f2832,f262,f272]) ).
fof(f4320,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f4304,f786,f2832,f262,f272]) ).
fof(f4321,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| ~ sQ44_spl
| product(g1,c,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4305]) ).
fof(f4322,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4306]) ).
fof(f4323,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4309]) ).
fof(f4324,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| ~ sQ44_spl
| product(g1,c,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4323]) ).
fof(f4325,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| ~ sQ44_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4310]) ).
fof(f4326,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4325]) ).
fof(f4327,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4311]) ).
fof(f4328,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ15_spl
| ~ sQ69_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4312]) ).
fof(f4331,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f3983,f379]) ).
fof(f4332,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,h,h,X0)
| ~ product(g2,f,f,X0) ),
inference(resolution,[status(thm)],[f3983,f378]) ).
fof(f4335,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,h,h,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f3983,f146]) ).
fof(f4336,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f3983,f139]) ).
fof(f4337,plain,
! [X0] :
( ~ sQ53_spl
| X0 = h
| ~ product(g2,X0,h,f) ),
inference(resolution,[status(thm)],[f3983,f75]) ).
fof(f4338,plain,
! [X0] :
( ~ sQ53_spl
| X0 = h
| ~ product(g2,h,X0,f) ),
inference(resolution,[status(thm)],[f3983,f73]) ).
fof(f4339,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| product(g2,f,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f3983,f71]) ).
fof(f4340,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| product(g2,h,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f3983,f69]) ).
fof(f4341,plain,
! [X0] :
( ~ sQ53_spl
| X0 = f
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f3983,f67]) ).
fof(f4346,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,h,h,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4335]) ).
fof(f4347,plain,
! [X0] :
( ~ sQ53_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4336]) ).
fof(f4348,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,b,b,multiply(g1,b,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f2564,f1936]) ).
fof(f4349,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f2564,f4348]) ).
fof(f4380,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2564,f1934]) ).
fof(f4410,plain,
! [X0] :
( ~ sQ53_spl
| X0 = f
| ~ product(g2,h,h,X0) ),
inference(paramodulation,[status(thm)],[f1222,f1409]) ).
fof(f4411,plain,
! [X0] :
( ~ sQ49_spl
| X0 = f
| ~ product(g2,g,g,X0) ),
inference(paramodulation,[status(thm)],[f1084,f1409]) ).
fof(f4420,plain,
( ~ sQ49_spl
| product(g2,h,g,multiply(g2,h,inverse(g2,g))) ),
inference(forward_demodulation,[status(thm)],[f1084,f1476]) ).
fof(f4421,plain,
( ~ sQ49_spl
| product(g2,h,g,multiply(g2,h,g)) ),
inference(forward_demodulation,[status(thm)],[f1084,f4420]) ).
fof(f4422,plain,
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,h,g,f) ),
inference(forward_demodulation,[status(thm)],[f3515,f4421]) ).
fof(f4423,plain,
( ~ sQ49_spl
| ~ sQ96_spl
| h = inverse(g2,g) ),
inference(resolution,[status(thm)],[f4422,f691]) ).
fof(f4424,plain,
( ~ sQ49_spl
| ~ sQ96_spl
| g = inverse(g2,h) ),
inference(resolution,[status(thm)],[f4422,f611]) ).
fof(f4425,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,inverse(g2,h),f,X0)
| ~ product(g2,f,g,X0) ),
inference(resolution,[status(thm)],[f4422,f1408]) ).
fof(f4426,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,f,g,X0)
| ~ product(g2,inverse(g2,h),f,X0) ),
inference(resolution,[status(thm)],[f4422,f1407]) ).
fof(f4427,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,f,f,X0)
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f4422,f379]) ).
fof(f4428,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,h,g,X0)
| ~ product(g2,f,f,X0) ),
inference(resolution,[status(thm)],[f4422,f378]) ).
fof(f4429,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,inverse(g2,h),f,X0)
| ~ product(g2,identity_for(g2),g,X0) ),
inference(resolution,[status(thm)],[f4422,f158]) ).
fof(f4430,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,inverse(g2,h),f,X0) ),
inference(resolution,[status(thm)],[f4422,f157]) ).
fof(f4431,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,h,g,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f4422,f146]) ).
fof(f4432,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f4422,f139]) ).
fof(f4433,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(resolution,[status(thm)],[f4422,f75]) ).
fof(f4434,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| X0 = g
| ~ product(g2,h,X0,f) ),
inference(resolution,[status(thm)],[f4422,f73]) ).
fof(f4435,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,f,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f4422,f71]) ).
fof(f4436,plain,
! [X0,X1,X2] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,h,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f4422,f69]) ).
fof(f4437,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f4422,f67]) ).
fof(f4438,plain,
( ~ sQ49_spl
| ~ sQ96_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f4423,f1086,f3514,f1083]) ).
fof(f4439,plain,
( ~ sQ49_spl
| ~ sQ96_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f4424,f1218,f3514,f1083]) ).
fof(f4440,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| ~ sQ53_spl
| product(g2,h,f,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1222,f4425]) ).
fof(f4441,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| ~ sQ53_spl
| product(g2,f,g,X0)
| ~ product(g2,h,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1222,f4426]) ).
fof(f4442,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,inverse(g2,h),f,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4429]) ).
fof(f4443,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| ~ sQ53_spl
| product(g2,h,f,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1222,f4442]) ).
fof(f4444,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| ~ sQ53_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,h,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1222,f4430]) ).
fof(f4445,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| ~ sQ53_spl
| product(g2,f,g,X0)
| ~ product(g2,h,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4444]) ).
fof(f4446,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,h,g,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4431]) ).
fof(f4447,plain,
! [X0] :
( ~ sQ49_spl
| ~ sQ96_spl
| product(g2,f,f,X0)
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4432]) ).
fof(f4448,plain,
( ~ sQ49_spl
| group_member(multiply(g2,h,g),g2) ),
inference(forward_demodulation,[status(thm)],[f1084,f1477]) ).
fof(f4449,plain,
( ~ sQ49_spl
| product(g2,h,multiply(g2,h,g),multiply(g2,h,multiply(g2,h,g))) ),
inference(resolution,[status(thm)],[f4448,f211]) ).
fof(f4450,plain,
( ~ sQ49_spl
| group_member(multiply(g2,h,multiply(g2,h,g)),g2) ),
inference(resolution,[status(thm)],[f4448,f210]) ).
fof(f4451,plain,
( ~ sQ49_spl
| product(g2,g,multiply(g2,h,g),multiply(g2,g,multiply(g2,h,g))) ),
inference(resolution,[status(thm)],[f4448,f197]) ).
fof(f4452,plain,
( ~ sQ49_spl
| group_member(multiply(g2,g,multiply(g2,h,g)),g2) ),
inference(resolution,[status(thm)],[f4448,f196]) ).
fof(f4453,plain,
( ~ sQ49_spl
| group_member(multiply(g2,f,multiply(g2,h,g)),g2) ),
inference(resolution,[status(thm)],[f4448,f187]) ).
fof(f4454,plain,
( ~ sQ49_spl
| product(g2,f,multiply(g2,h,g),multiply(g2,f,multiply(g2,h,g))) ),
inference(resolution,[status(thm)],[f4448,f178]) ).
fof(f4456,plain,
( ~ sQ49_spl
| group_member(multiply(g2,identity_for(g2),multiply(g2,h,g)),g2) ),
inference(resolution,[status(thm)],[f4448,f192]) ).
fof(f4457,plain,
( ~ sQ49_spl
| product(g2,identity_for(g2),multiply(g2,h,g),multiply(g2,identity_for(g2),multiply(g2,h,g))) ),
inference(resolution,[status(thm)],[f4448,f183]) ).
fof(f4458,plain,
! [X0] :
( ~ sQ49_spl
| group_member(multiply(g2,multiply(g2,h,g),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f4448,f65]) ).
fof(f4459,plain,
! [X0] :
( ~ sQ49_spl
| product(g2,multiply(g2,h,g),X0,multiply(g2,multiply(g2,h,g),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f4448,f64]) ).
fof(f4460,plain,
( ~ sQ49_spl
| group_member(inverse(g2,multiply(g2,h,g)),g2) ),
inference(resolution,[status(thm)],[f4448,f61]) ).
fof(f4462,plain,
( ~ sQ49_spl
| group_member(multiply(g2,f,multiply(g2,h,g)),g2) ),
inference(forward_demodulation,[status(thm)],[f92,f4456]) ).
fof(f4463,plain,
( ~ sQ49_spl
| product(g2,f,multiply(g2,h,g),multiply(g2,identity_for(g2),multiply(g2,h,g))) ),
inference(forward_demodulation,[status(thm)],[f92,f4457]) ).
fof(f4464,plain,
( ~ sQ49_spl
| product(g2,f,multiply(g2,h,g),multiply(g2,f,multiply(g2,h,g))) ),
inference(forward_demodulation,[status(thm)],[f92,f4463]) ).
fof(f4465,plain,
( ~ sQ49_spl
| product(g2,g,g,multiply(g2,g,inverse(g2,g))) ),
inference(forward_demodulation,[status(thm)],[f1084,f1478]) ).
fof(f4466,plain,
( ~ sQ49_spl
| product(g2,g,g,multiply(g2,g,g)) ),
inference(forward_demodulation,[status(thm)],[f1084,f4465]) ).
fof(f4468,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2564,f1933]) ).
fof(f4470,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f2564,f1932]) ).
fof(f4471,plain,
( ~ sQ18_spl
| ~ sQ15_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f2564,f4470]) ).
fof(f4479,plain,
( ~ sQ49_spl
| group_member(multiply(g2,g,g),g2) ),
inference(forward_demodulation,[status(thm)],[f1084,f1479]) ).
fof(f4486,plain,
( ~ sQ24_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f294,f3866]) ).
fof(f4487,plain,
( ~ sQ24_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f294,f4486]) ).
fof(f4501,plain,
( ~ sQ24_spl
| product(g1,b,a,multiply(g1,b,d2)) ),
inference(forward_demodulation,[status(thm)],[f294,f3870]) ).
fof(f4502,plain,
( ~ sQ24_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f294,f4501]) ).
fof(f4509,plain,
( ~ sQ24_spl
| product(g1,c,a,multiply(g1,c,d2)) ),
inference(forward_demodulation,[status(thm)],[f294,f3871]) ).
fof(f4510,plain,
( ~ sQ24_spl
| product(g1,c,a,multiply(g1,c,a)) ),
inference(forward_demodulation,[status(thm)],[f294,f4509]) ).
fof(f4523,plain,
( ~ sQ44_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f790,f1953]) ).
fof(f4525,plain,
( ~ sQ24_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f294,f3881]) ).
fof(f4526,plain,
( ~ sQ24_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f294,f4525]) ).
fof(f4536,plain,
multiply(g1,a,identity_for(g1)) = identity_for(g1),
inference(paramodulation,[status(thm)],[f91,f2945]) ).
fof(f4538,plain,
multiply(g1,identity_for(g1),a) = identity_for(g1),
inference(paramodulation,[status(thm)],[f91,f2945]) ).
fof(f4541,plain,
multiply(g1,a,a) = identity_for(g1),
inference(forward_demodulation,[status(thm)],[f91,f4536]) ).
fof(f4545,plain,
multiply(g1,a,a) = identity_for(g1),
inference(forward_demodulation,[status(thm)],[f91,f4538]) ).
fof(f4551,plain,
( ~ sQ44_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f790,f1954]) ).
fof(f4553,plain,
( ~ sQ44_spl
| product(g1,b,c,multiply(g1,b,inverse(g1,c))) ),
inference(forward_demodulation,[status(thm)],[f790,f1955]) ).
fof(f4554,plain,
( ~ sQ44_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f790,f4553]) ).
fof(f4555,plain,
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f4554]) ).
fof(f4557,plain,
( ~ sQ44_spl
| ~ sQ75_spl
| b = c ),
inference(resolution,[status(thm)],[f4555,f833]) ).
fof(f4558,plain,
( ~ sQ44_spl
| ~ sQ75_spl
| b = inverse(g1,c) ),
inference(resolution,[status(thm)],[f4555,f692]) ).
fof(f4559,plain,
( ~ sQ44_spl
| ~ sQ75_spl
| c = inverse(g1,b) ),
inference(resolution,[status(thm)],[f4555,f612]) ).
fof(f4560,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f4555,f1334]) ).
fof(f4561,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,a,c,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f4555,f1333]) ).
fof(f4562,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f4555,f173]) ).
fof(f4563,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,b,c,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f4555,f172]) ).
fof(f4564,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f4555,f158]) ).
fof(f4565,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f4555,f157]) ).
fof(f4566,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,b,c,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f4555,f146]) ).
fof(f4567,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f4555,f139]) ).
fof(f4568,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| X0 = b
| ~ product(g1,X0,c,a) ),
inference(resolution,[status(thm)],[f4555,f75]) ).
fof(f4569,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| X0 = c
| ~ product(g1,b,X0,a) ),
inference(resolution,[status(thm)],[f4555,f73]) ).
fof(f4570,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f4555,f71]) ).
fof(f4571,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f4555,f69]) ).
fof(f4572,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| X0 = a
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f4555,f67]) ).
fof(f4574,plain,
( ~ sQ44_spl
| ~ sQ75_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f4557,f235,f3061,f789]) ).
fof(f4575,plain,
( ~ sQ44_spl
| ~ sQ75_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f4558,f786,f3061,f789]) ).
fof(f4576,plain,
( ~ sQ44_spl
| ~ sQ75_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f4559,f718,f3061,f789]) ).
fof(f4577,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f2564,f4560]) ).
fof(f4578,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,c,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f2564,f4561]) ).
fof(f4579,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4564]) ).
fof(f4580,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f2564,f4579]) ).
fof(f4581,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| ~ sQ15_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f2564,f4565]) ).
fof(f4582,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,c,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4581]) ).
fof(f4583,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,b,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4566]) ).
fof(f4584,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ75_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4567]) ).
fof(f4585,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,b,multiply(g1,b,c),X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f2564,f2811]) ).
fof(f4586,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,b,multiply(g1,b,c),X0) ),
inference(forward_demodulation,[status(thm)],[f2564,f2803]) ).
fof(f4587,plain,
! [X0] :
( ~ sQ15_spl
| ~ sQ18_spl
| product(g1,a,c,X0)
| ~ product(g1,b,multiply(g1,b,c),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4586]) ).
fof(f4588,plain,
( ~ sQ44_spl
| product(g1,c,c,multiply(g1,c,inverse(g1,c))) ),
inference(forward_demodulation,[status(thm)],[f790,f1956]) ).
fof(f4589,plain,
( ~ sQ44_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f790,f4588]) ).
fof(f4592,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,d2,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f307,f1729]) ).
fof(f4595,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,b,d2,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f307,f1727]) ).
fof(f4596,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ24_spl
| product(g1,d1,a,X0)
| ~ product(g1,b,inverse(g1,a),X0) ),
inference(forward_demodulation,[status(thm)],[f294,f3853]) ).
fof(f4597,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ24_spl
| product(g1,d1,a,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f4596]) ).
fof(f4617,plain,
( ~ sQ70_spl
| product(g1,c,b,b) ),
inference(forward_demodulation,[status(thm)],[f2836,f870]) ).
fof(f4618,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,inverse(g1,c),b,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4617,f1334]) ).
fof(f4619,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),b,X0) ),
inference(resolution,[status(thm)],[f4617,f1333]) ).
fof(f4620,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4617,f173]) ).
fof(f4621,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4617,f172]) ).
fof(f4622,plain,
( ~ sQ70_spl
| c = a ),
inference(resolution,[status(thm)],[f4617,f170]) ).
fof(f4623,plain,
( ~ sQ70_spl
| c = identity_for(g1) ),
inference(resolution,[status(thm)],[f4617,f167]) ).
fof(f4624,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,inverse(g1,c),b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f4617,f158]) ).
fof(f4625,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),b,X0) ),
inference(resolution,[status(thm)],[f4617,f157]) ).
fof(f4626,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,c,b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f4617,f146]) ).
fof(f4627,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4617,f139]) ).
fof(f4628,plain,
! [X0] :
( ~ sQ70_spl
| X0 = c
| ~ product(g1,X0,b,b) ),
inference(resolution,[status(thm)],[f4617,f75]) ).
fof(f4629,plain,
! [X0] :
( ~ sQ70_spl
| X0 = b
| ~ product(g1,c,X0,b) ),
inference(resolution,[status(thm)],[f4617,f73]) ).
fof(f4630,plain,
! [X0,X1,X2] :
( ~ sQ70_spl
| product(g1,b,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4617,f71]) ).
fof(f4631,plain,
! [X0,X1,X2] :
( ~ sQ70_spl
| product(g1,c,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4617,f69]) ).
fof(f4632,plain,
! [X0] :
( ~ sQ70_spl
| X0 = b
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4617,f67]) ).
fof(f4633,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ44_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4618]) ).
fof(f4634,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4619]) ).
fof(f4635,plain,
( ~ sQ70_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f4622,f232,f2835]) ).
fof(f4636,plain,
( ~ sQ70_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f4623,f285,f2835]) ).
fof(f4637,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,inverse(g1,c),b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4624]) ).
fof(f4638,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ44_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4637]) ).
fof(f4639,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ44_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f790,f4625]) ).
fof(f4640,plain,
! [X0] :
( ~ sQ70_spl
| ~ sQ44_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4639]) ).
fof(f4641,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4626]) ).
fof(f4642,plain,
! [X0] :
( ~ sQ70_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4627]) ).
fof(f4643,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1927,f715,f296,f252]) ).
fof(f4649,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ55_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f2688]) ).
fof(f4651,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ55_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f2689]) ).
fof(f4652,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ55_spl
| product(g1,b,b,multiply(g1,b,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f1509,f2690]) ).
fof(f4653,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ55_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f1509,f4652]) ).
fof(f4654,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ55_spl
| ~ sQ66_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f2766,f4653]) ).
fof(f4655,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ55_spl
| product(g1,c,b,multiply(g1,c,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f1509,f2691]) ).
fof(f4656,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ55_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f1509,f4655]) ).
fof(f4665,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ55_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f2697]) ).
fof(f4666,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,a,a,multiply(g1,a,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f2766,f2753]) ).
fof(f4667,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f2766,f4666]) ).
fof(f4669,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2766,f2754]) ).
fof(f4671,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2766,f2755]) ).
fof(f4673,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| group_member(multiply(g1,c,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2766,f2756]) ).
fof(f4675,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f2766,f2757]) ).
fof(f4676,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f2766,f4675]) ).
fof(f4678,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,c,a,multiply(g1,c,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f2766,f2758]) ).
fof(f4679,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,c,a,multiply(g1,c,a)) ),
inference(forward_demodulation,[status(thm)],[f2766,f4678]) ).
fof(f4681,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2766,f2775]) ).
fof(f4683,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,a,a,multiply(g1,a,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f2766,f2777]) ).
fof(f4684,plain,
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ66_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f2766,f4683]) ).
fof(f4699,plain,
! [X0] :
( product(g1,a,c,X0)
| ~ product(g1,inverse(g1,b),multiply(g1,b,c),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2803]) ).
fof(f4700,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ12_spl
| ~ sQ25_spl
| ~ sQ69_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2913]) ).
fof(f4701,plain,
! [X0] :
( product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2785]) ).
fof(f4702,plain,
! [X0] :
( ~ sQ72_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f3031,f2736]) ).
fof(f4703,plain,
! [X0] :
( ~ sQ72_spl
| product(g1,a,c,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4702]) ).
fof(f4704,plain,
! [X0] :
( ~ sQ72_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f3031,f2744]) ).
fof(f4705,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| inverse(g1,b) = c ),
inference(forward_demodulation,[status(thm)],[f273,f266]) ).
fof(f4707,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f121]) ).
fof(f4708,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),g) ),
inference(forward_demodulation,[status(thm)],[f98,f4707]) ).
fof(f4709,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f273,f124]) ).
fof(f4710,plain,
( ~ sQ1_spl
| ~ sQ18_spl
| product(g2,isomorphism2(d1),isomorphism2(d2),h) ),
inference(forward_demodulation,[status(thm)],[f101,f4709]) ).
fof(f4711,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f3889]) ).
fof(f4712,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(resolution,[status(thm)],[f115,f184]) ).
fof(f4713,plain,
group_member(multiply(g1,a,d1),g1),
inference(resolution,[status(thm)],[f115,f193]) ).
fof(f4714,plain,
group_member(multiply(g1,b,d1),g1),
inference(resolution,[status(thm)],[f115,f189]) ).
fof(f4715,plain,
group_member(multiply(g1,c,d1),g1),
inference(resolution,[status(thm)],[f115,f188]) ).
fof(f4716,plain,
product(g1,b,d1,multiply(g1,b,d1)),
inference(resolution,[status(thm)],[f115,f180]) ).
fof(f4717,plain,
product(g1,c,d1,multiply(g1,c,d1)),
inference(resolution,[status(thm)],[f115,f179]) ).
fof(f4719,plain,
group_member(multiply(g1,identity_for(g1),d1),g1),
inference(resolution,[status(thm)],[f115,f192]) ).
fof(f4720,plain,
product(g1,identity_for(g1),d1,multiply(g1,identity_for(g1),d1)),
inference(resolution,[status(thm)],[f115,f183]) ).
fof(f4721,plain,
! [X0] :
( group_member(multiply(g1,d1,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f115,f65]) ).
fof(f4722,plain,
! [X0] :
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f115,f64]) ).
fof(f4723,plain,
group_member(inverse(g1,d1),g1),
inference(resolution,[status(thm)],[f115,f61]) ).
fof(f4725,plain,
group_member(multiply(g1,a,d1),g1),
inference(forward_demodulation,[status(thm)],[f91,f4719]) ).
fof(f4726,plain,
product(g1,a,d1,multiply(g1,identity_for(g1),d1)),
inference(forward_demodulation,[status(thm)],[f91,f4720]) ).
fof(f4727,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(forward_demodulation,[status(thm)],[f91,f4726]) ).
fof(f4728,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f3847,f1334]) ).
fof(f4729,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f3847,f1333]) ).
fof(f4730,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f3847,f173]) ).
fof(f4731,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f3847,f172]) ).
fof(f4732,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,identity_for(g1),d2,X0) ),
inference(resolution,[status(thm)],[f3847,f158]) ).
fof(f4733,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f3847,f157]) ).
fof(f4734,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,d2,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f3847,f146]) ).
fof(f4735,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f3847,f139]) ).
fof(f4736,plain,
! [X0] :
( ~ sQ18_spl
| X0 = d1
| ~ product(g1,X0,d2,b) ),
inference(resolution,[status(thm)],[f3847,f75]) ).
fof(f4737,plain,
! [X0] :
( ~ sQ18_spl
| X0 = d2
| ~ product(g1,d1,X0,b) ),
inference(resolution,[status(thm)],[f3847,f73]) ).
fof(f4738,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f3847,f71]) ).
fof(f4739,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f3847,f69]) ).
fof(f4740,plain,
! [X0] :
( ~ sQ18_spl
| X0 = b
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f3847,f67]) ).
fof(f4741,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4732]) ).
fof(f4742,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4733]) ).
fof(f4743,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4734]) ).
fof(f4744,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4735]) ).
fof(f4748,plain,
( sQ5_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism6(b),isomorphism6(d2),f) ),
inference(forward_demodulation,[status(thm)],[f307,f3846]) ).
fof(f4749,plain,
( sQ5_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,f,isomorphism6(d2),f) ),
inference(forward_demodulation,[status(thm)],[f113,f4748]) ).
fof(f4750,plain,
( sQ5_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,f,isomorphism6(a),f) ),
inference(forward_demodulation,[status(thm)],[f3902,f4749]) ).
fof(f4751,plain,
( sQ5_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,f,h,f) ),
inference(forward_demodulation,[status(thm)],[f112,f4750]) ).
fof(f4754,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,isomorphism5(a),g) ),
inference(forward_demodulation,[status(thm)],[f3902,f3913]) ).
fof(f4755,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,h,g) ),
inference(forward_demodulation,[status(thm)],[f109,f4754]) ).
fof(f4756,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism5(b),isomorphism5(d2),g) ),
inference(forward_demodulation,[status(thm)],[f307,f3850]) ).
fof(f4757,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,isomorphism5(d2),g) ),
inference(forward_demodulation,[status(thm)],[f110,f4756]) ).
fof(f4758,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,isomorphism5(a),g) ),
inference(forward_demodulation,[status(thm)],[f3902,f4757]) ).
fof(f4759,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,h,g) ),
inference(forward_demodulation,[status(thm)],[f109,f4758]) ).
fof(f4762,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,isomorphism4(a),h) ),
inference(forward_demodulation,[status(thm)],[f3902,f3917]) ).
fof(f4763,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,g,h) ),
inference(forward_demodulation,[status(thm)],[f106,f4762]) ).
fof(f4764,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism4(b),isomorphism4(d2),h) ),
inference(forward_demodulation,[status(thm)],[f307,f3852]) ).
fof(f4765,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,isomorphism4(d2),h) ),
inference(forward_demodulation,[status(thm)],[f107,f4764]) ).
fof(f4766,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,isomorphism4(a),h) ),
inference(forward_demodulation,[status(thm)],[f3902,f4765]) ).
fof(f4767,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,g,h) ),
inference(forward_demodulation,[status(thm)],[f106,f4766]) ).
fof(f4773,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f4705,f1335]) ).
fof(f4774,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f4705,f1250]) ).
fof(f4775,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f4705,f1249]) ).
fof(f4776,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f4705,f1248]) ).
fof(f4777,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,X0,c,a) ),
inference(paramodulation,[status(thm)],[f4705,f704]) ).
fof(f4778,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f4705,f638]) ).
fof(f4779,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f4705,f556]) ).
fof(f4780,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(paramodulation,[status(thm)],[f4705,f542]) ).
fof(f4781,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,b,a) ),
inference(paramodulation,[status(thm)],[f4705,f214]) ).
fof(f4782,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,c,a) ),
inference(paramodulation,[status(thm)],[f4705,f213]) ).
fof(f4783,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f4705,f422]) ).
fof(f4784,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f4705,f420]) ).
fof(f4785,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,X0,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f4705,f168]) ).
fof(f4786,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = identity_for(g1)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f4705,f163]) ).
fof(f4787,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f4705,f162]) ).
fof(f4788,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f4705,f161]) ).
fof(f4789,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f4705,f159]) ).
fof(f4790,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| inverse(g1,c) = b ),
inference(paramodulation,[status(thm)],[f4705,f537]) ).
fof(f4791,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,c,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f4705,f156]) ).
fof(f4794,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4783]) ).
fof(f4795,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4794]) ).
fof(f4796,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4784]) ).
fof(f4797,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4796]) ).
fof(f4798,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,X0,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f4785]) ).
fof(f4799,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4786]) ).
fof(f4800,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f4787]) ).
fof(f4801,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f4788]) ).
fof(f4802,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4789]) ).
fof(f4803,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f4791]) ).
fof(f4809,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f1250]) ).
fof(f4810,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f1249]) ).
fof(f4811,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f1248]) ).
fof(f4812,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(paramodulation,[status(thm)],[f1004,f704]) ).
fof(f4813,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f638]) ).
fof(f4814,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f1004,f556]) ).
fof(f4815,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,b,X0,a) ),
inference(paramodulation,[status(thm)],[f1004,f542]) ).
fof(f4817,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(paramodulation,[status(thm)],[f1004,f213]) ).
fof(f4818,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f422]) ).
fof(f4819,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f1004,f420]) ).
fof(f4820,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1004,f168]) ).
fof(f4821,plain,
! [X0] :
( ~ sQ41_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f163]) ).
fof(f4822,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f162]) ).
fof(f4823,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f161]) ).
fof(f4827,plain,
( ~ sQ41_spl
| product(g1,c,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1004,f63]) ).
fof(f4829,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4818]) ).
fof(f4830,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4829]) ).
fof(f4831,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4819]) ).
fof(f4832,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4831]) ).
fof(f4833,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f4820]) ).
fof(f4834,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4821]) ).
fof(f4835,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f4822]) ).
fof(f4836,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f4823]) ).
fof(f4839,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f4827]) ).
fof(f4847,plain,
( ~ sQ28_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f307,f155]) ).
fof(f4859,plain,
( ~ sQ66_spl
| b = inverse(g1,b) ),
inference(resolution,[status(thm)],[f2850,f692]) ).
fof(f4861,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f2850,f1334]) ).
fof(f4862,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f2850,f1333]) ).
fof(f4863,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f2850,f173]) ).
fof(f4864,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f2850,f172]) ).
fof(f4865,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f2850,f158]) ).
fof(f4866,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f2850,f157]) ).
fof(f4867,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,b,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2850,f146]) ).
fof(f4868,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f2850,f139]) ).
fof(f4869,plain,
! [X0] :
( ~ sQ66_spl
| X0 = b
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f2850,f75]) ).
fof(f4870,plain,
! [X0] :
( ~ sQ66_spl
| X0 = b
| ~ product(g1,b,X0,a) ),
inference(resolution,[status(thm)],[f2850,f73]) ).
fof(f4871,plain,
! [X0,X1,X2] :
( ~ sQ66_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f2850,f71]) ).
fof(f4872,plain,
! [X0,X1,X2] :
( ~ sQ66_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f2850,f69]) ).
fof(f4873,plain,
! [X0] :
( ~ sQ66_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f2850,f67]) ).
fof(f4874,plain,
( ~ sQ66_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f4859,f715,f2765]) ).
fof(f4876,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4705,f4861]) ).
fof(f4877,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f4705,f4862]) ).
fof(f4878,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4865]) ).
fof(f4879,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4705,f4878]) ).
fof(f4880,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f4705,f4866]) ).
fof(f4881,plain,
! [X0] :
( ~ sQ66_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4880]) ).
fof(f4882,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4867]) ).
fof(f4883,plain,
! [X0] :
( ~ sQ66_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4868]) ).
fof(f4889,plain,
( ~ sQ25_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,c,multiply(g1,c,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f4705,f1999]) ).
fof(f4890,plain,
( ~ sQ25_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f4705,f4889]) ).
fof(f4891,plain,
( ~ sQ25_spl
| ~ sQ16_spl
| ~ sQ18_spl
| ~ sQ72_spl
| product(g1,c,c,a) ),
inference(forward_demodulation,[status(thm)],[f3031,f4890]) ).
fof(f4892,plain,
( ~ sQ25_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,c,multiply(g1,b,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f4705,f1998]) ).
fof(f4893,plain,
( ~ sQ25_spl
| ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f4705,f4892]) ).
fof(f4896,plain,
( ~ sQ25_spl
| ~ sQ16_spl
| ~ sQ18_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f4705,f1997]) ).
fof(f4898,plain,
( ~ sQ25_spl
| ~ sQ16_spl
| ~ sQ18_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f4705,f1996]) ).
fof(f4907,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ25_spl
| ~ sQ16_spl
| product(g1,d1,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f4705,f1726]) ).
fof(f4911,plain,
( ~ sQ13_spl
| ~ sQ25_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f3681,f718,f296,f255]) ).
fof(f4912,plain,
( sQ12_spl
| ~ sQ25_spl
| ~ sQ40_spl ),
inference(split_clause,[status(thm)],[f3680,f715,f296,f252]) ).
fof(f4915,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f4790,f786,f272,f265]) ).
fof(f4916,plain,
( sQ41_spl
| ~ sQ16_spl
| ~ sQ18_spl
| c != c ),
inference(forward_demodulation,[status(thm)],[f4705,f720]) ).
fof(f4917,plain,
( sQ41_spl
| ~ sQ16_spl
| ~ sQ18_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f4916]) ).
fof(f4918,plain,
( sQ41_spl
| ~ sQ16_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f4917]) ).
fof(f4920,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ16_spl
| product(g1,a,d2,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4705,f4711]) ).
fof(f4921,plain,
! [X0] :
( ~ sQ18_spl
| ~ sQ28_spl
| ~ sQ16_spl
| product(g1,c,b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f4705,f3898]) ).
fof(f4924,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(resolution,[status(thm)],[f116,f184]) ).
fof(f4925,plain,
group_member(multiply(g1,a,d2),g1),
inference(resolution,[status(thm)],[f116,f193]) ).
fof(f4926,plain,
group_member(multiply(g1,b,d2),g1),
inference(resolution,[status(thm)],[f116,f189]) ).
fof(f4927,plain,
group_member(multiply(g1,c,d2),g1),
inference(resolution,[status(thm)],[f116,f188]) ).
fof(f4928,plain,
product(g1,b,d2,multiply(g1,b,d2)),
inference(resolution,[status(thm)],[f116,f180]) ).
fof(f4929,plain,
product(g1,c,d2,multiply(g1,c,d2)),
inference(resolution,[status(thm)],[f116,f179]) ).
fof(f4931,plain,
group_member(multiply(g1,identity_for(g1),d2),g1),
inference(resolution,[status(thm)],[f116,f192]) ).
fof(f4932,plain,
product(g1,identity_for(g1),d2,multiply(g1,identity_for(g1),d2)),
inference(resolution,[status(thm)],[f116,f183]) ).
fof(f4933,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f116,f65]) ).
fof(f4934,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f116,f64]) ).
fof(f4935,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f116,f61]) ).
fof(f4937,plain,
group_member(multiply(g1,a,d2),g1),
inference(forward_demodulation,[status(thm)],[f91,f4931]) ).
fof(f4938,plain,
product(g1,a,d2,multiply(g1,identity_for(g1),d2)),
inference(forward_demodulation,[status(thm)],[f91,f4932]) ).
fof(f4939,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(forward_demodulation,[status(thm)],[f91,f4938]) ).
fof(f4940,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f3847,f1334]) ).
fof(f4941,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f3847,f1333]) ).
fof(f4942,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f3847,f173]) ).
fof(f4943,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f3847,f172]) ).
fof(f4944,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,identity_for(g1),d2,X0) ),
inference(resolution,[status(thm)],[f3847,f158]) ).
fof(f4945,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f3847,f157]) ).
fof(f4946,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,d2,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f3847,f146]) ).
fof(f4947,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f3847,f139]) ).
fof(f4948,plain,
! [X0] :
( ~ sQ18_spl
| X0 = d1
| ~ product(g1,X0,d2,b) ),
inference(resolution,[status(thm)],[f3847,f75]) ).
fof(f4949,plain,
! [X0] :
( ~ sQ18_spl
| X0 = d2
| ~ product(g1,d1,X0,b) ),
inference(resolution,[status(thm)],[f3847,f73]) ).
fof(f4950,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f3847,f71]) ).
fof(f4951,plain,
! [X0,X1,X2] :
( ~ sQ18_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f3847,f69]) ).
fof(f4952,plain,
! [X0] :
( ~ sQ18_spl
| X0 = b
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f3847,f67]) ).
fof(f4953,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4944]) ).
fof(f4954,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4945]) ).
fof(f4955,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4946]) ).
fof(f4956,plain,
! [X0] :
( ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4947]) ).
fof(f4966,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism5(b),isomorphism5(d2),g) ),
inference(forward_demodulation,[status(thm)],[f307,f3850]) ).
fof(f4967,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,isomorphism5(d2),g) ),
inference(forward_demodulation,[status(thm)],[f110,f4966]) ).
fof(f4968,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,isomorphism5(a),g) ),
inference(forward_demodulation,[status(thm)],[f3902,f4967]) ).
fof(f4969,plain,
( sQ4_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,g,h,g) ),
inference(forward_demodulation,[status(thm)],[f109,f4968]) ).
fof(f4973,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f1250]) ).
fof(f4974,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f1249]) ).
fof(f4975,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f1248]) ).
fof(f4976,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(paramodulation,[status(thm)],[f1004,f704]) ).
fof(f4977,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f638]) ).
fof(f4978,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f1004,f556]) ).
fof(f4981,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(paramodulation,[status(thm)],[f1004,f213]) ).
fof(f4982,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f422]) ).
fof(f4983,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f1004,f420]) ).
fof(f4984,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1004,f168]) ).
fof(f4985,plain,
! [X0] :
( ~ sQ41_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f163]) ).
fof(f4986,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f162]) ).
fof(f4987,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f161]) ).
fof(f4989,plain,
( ~ sQ41_spl
| inverse(g1,b) = c ),
inference(paramodulation,[status(thm)],[f1004,f537]) ).
fof(f4991,plain,
( ~ sQ41_spl
| product(g1,c,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1004,f63]) ).
fof(f4992,plain,
( ~ sQ41_spl
| product(g1,b,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1004,f62]) ).
fof(f4993,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4982]) ).
fof(f4994,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4993]) ).
fof(f4995,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4983]) ).
fof(f4996,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4995]) ).
fof(f4997,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f4984]) ).
fof(f4998,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f4985]) ).
fof(f4999,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f4986]) ).
fof(f5000,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f4987]) ).
fof(f5003,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f4991]) ).
fof(f5004,plain,
( ~ sQ41_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f4992]) ).
fof(f5006,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism4(b),isomorphism4(d2),h) ),
inference(forward_demodulation,[status(thm)],[f307,f3852]) ).
fof(f5007,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,isomorphism4(d2),h) ),
inference(forward_demodulation,[status(thm)],[f107,f5006]) ).
fof(f5008,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,isomorphism4(a),h) ),
inference(forward_demodulation,[status(thm)],[f3902,f5007]) ).
fof(f5009,plain,
( sQ3_spl
| ~ sQ18_spl
| ~ sQ28_spl
| ~ product(g2,h,g,h) ),
inference(forward_demodulation,[status(thm)],[f106,f5008]) ).
fof(f5030,plain,
( ~ sQ28_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f307,f4723]) ).
fof(f5034,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| b = inverse(g1,c) ),
inference(resolution,[status(thm)],[f4781,f612]) ).
fof(f5035,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f4781,f1334]) ).
fof(f5036,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f4781,f1333]) ).
fof(f5037,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4781,f173]) ).
fof(f5038,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f4781,f172]) ).
fof(f5039,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f4781,f158]) ).
fof(f5040,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f4781,f157]) ).
fof(f5041,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f4781,f146]) ).
fof(f5042,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4781,f139]) ).
fof(f5043,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f4781,f75]) ).
fof(f5044,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(resolution,[status(thm)],[f4781,f73]) ).
fof(f5045,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4781,f71]) ).
fof(f5046,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f4781,f69]) ).
fof(f5047,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f4781,f67]) ).
fof(f5050,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5039]) ).
fof(f5054,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5041]) ).
fof(f5055,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5042]) ).
fof(f5056,plain,
( ~ sQ16_spl
| ~ sQ18_spl
| b = inverse(g1,c) ),
inference(resolution,[status(thm)],[f4782,f692]) ).
fof(f5060,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f4782,f173]) ).
fof(f5061,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,c,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f4782,f172]) ).
fof(f5064,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,c,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f4782,f146]) ).
fof(f5065,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f4782,f139]) ).
fof(f5066,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = b
| ~ product(g1,X0,c,a) ),
inference(resolution,[status(thm)],[f4782,f75]) ).
fof(f5067,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = c
| ~ product(g1,b,X0,a) ),
inference(resolution,[status(thm)],[f4782,f73]) ).
fof(f5068,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f4782,f71]) ).
fof(f5069,plain,
! [X0,X1,X2] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f4782,f69]) ).
fof(f5070,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| X0 = a
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f4782,f67]) ).
fof(f5077,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,b,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5064]) ).
fof(f5078,plain,
! [X0] :
( ~ sQ16_spl
| ~ sQ18_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5065]) ).
fof(f5090,plain,
( ~ sQ28_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f307,f155]) ).
fof(f5117,plain,
( ~ sQ18_spl
| ~ sQ28_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f3902,f3879]) ).
fof(f5129,plain,
( ~ sQ18_spl
| ~ sQ28_spl
| group_member(multiply(g1,c,a),g1) ),
inference(forward_demodulation,[status(thm)],[f3902,f3869]) ).
fof(f5138,plain,
product(g1,a,multiply(g1,c,b),multiply(g1,a,multiply(g1,c,b))),
inference(resolution,[status(thm)],[f1018,f184]) ).
fof(f5139,plain,
group_member(multiply(g1,a,multiply(g1,c,b)),g1),
inference(resolution,[status(thm)],[f1018,f193]) ).
fof(f5140,plain,
group_member(multiply(g1,b,multiply(g1,c,b)),g1),
inference(resolution,[status(thm)],[f1018,f189]) ).
fof(f5141,plain,
group_member(multiply(g1,c,multiply(g1,c,b)),g1),
inference(resolution,[status(thm)],[f1018,f188]) ).
fof(f5142,plain,
product(g1,b,multiply(g1,c,b),multiply(g1,b,multiply(g1,c,b))),
inference(resolution,[status(thm)],[f1018,f180]) ).
fof(f5143,plain,
product(g1,c,multiply(g1,c,b),multiply(g1,c,multiply(g1,c,b))),
inference(resolution,[status(thm)],[f1018,f179]) ).
fof(f5144,plain,
( multiply(g1,c,b) = c
| multiply(g1,c,b) = b
| multiply(g1,c,b) = a ),
inference(resolution,[status(thm)],[f1018,f89]) ).
fof(f5145,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,c,b)),g1),
inference(resolution,[status(thm)],[f1018,f192]) ).
fof(f5146,plain,
product(g1,identity_for(g1),multiply(g1,c,b),multiply(g1,identity_for(g1),multiply(g1,c,b))),
inference(resolution,[status(thm)],[f1018,f183]) ).
fof(f5147,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,c,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1018,f65]) ).
fof(f5148,plain,
! [X0] :
( product(g1,multiply(g1,c,b),X0,multiply(g1,multiply(g1,c,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1018,f64]) ).
fof(f5149,plain,
group_member(inverse(g1,multiply(g1,c,b)),g1),
inference(resolution,[status(thm)],[f1018,f61]) ).
fof(f5150,plain,
( sQ71_spl
| sQ70_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f5144,f2832,f2835,f2838]) ).
fof(f5151,plain,
group_member(multiply(g1,a,multiply(g1,c,b)),g1),
inference(forward_demodulation,[status(thm)],[f91,f5145]) ).
fof(f5152,plain,
product(g1,a,multiply(g1,c,b),multiply(g1,identity_for(g1),multiply(g1,c,b))),
inference(forward_demodulation,[status(thm)],[f91,f5146]) ).
fof(f5153,plain,
product(g1,a,multiply(g1,c,b),multiply(g1,a,multiply(g1,c,b))),
inference(forward_demodulation,[status(thm)],[f91,f5152]) ).
fof(f5154,plain,
! [X0] :
( product(g1,d1,a,X0)
| ~ product(g1,d3,inverse(g1,d2),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f202]) ).
fof(f5155,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,b,c) ),
inference(forward_demodulation,[status(thm)],[f1512,f3283]) ).
fof(f5158,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,b,c) ),
inference(forward_demodulation,[status(thm)],[f1512,f3650]) ).
fof(f5159,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| product(g1,a,b,c) ),
inference(forward_demodulation,[status(thm)],[f1512,f673]) ).
fof(f5164,plain,
( ~ sQ17_spl
| product(g1,b,c,multiply(g1,b,multiply(g1,a,c))) ),
inference(forward_demodulation,[status(thm)],[f2886,f942]) ).
fof(f5165,plain,
( ~ sQ17_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f2886,f5164]) ).
fof(f5168,plain,
( ~ sQ17_spl
| product(g1,c,c,multiply(g1,c,multiply(g1,a,c))) ),
inference(forward_demodulation,[status(thm)],[f2886,f944]) ).
fof(f5169,plain,
( ~ sQ17_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f2886,f5168]) ).
fof(f5170,plain,
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,c,c,a) ),
inference(forward_demodulation,[status(thm)],[f3031,f5169]) ).
fof(f5180,plain,
( ~ sQ17_spl
| group_member(inverse(g1,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2886,f950]) ).
fof(f5181,plain,
( ~ sQ17_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2886,f1016]) ).
fof(f5183,plain,
( ~ sQ17_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2886,f1022]) ).
fof(f5188,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f1512,f1493]) ).
fof(f5189,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f1512,f1494]) ).
fof(f5191,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| product(g1,b,c,multiply(g1,b,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f1512,f1495]) ).
fof(f5192,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f1512,f5191]) ).
fof(f5195,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| product(g1,c,c,multiply(g1,c,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f1512,f1497]) ).
fof(f5196,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f1512,f5195]) ).
fof(f5197,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| ~ sQ72_spl
| product(g1,c,c,a) ),
inference(forward_demodulation,[status(thm)],[f3031,f5196]) ).
fof(f5209,plain,
( ~ sQ17_spl
| ~ sQ56_spl
| group_member(inverse(g1,c),g1) ),
inference(forward_demodulation,[status(thm)],[f1512,f1504]) ).
fof(f5211,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,a,X0)
| ~ product(g1,a,inverse(g1,d2),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f1426]) ).
fof(f5217,plain,
( sQ47_spl
| c != c ),
inference(forward_demodulation,[status(thm)],[f2886,f959]) ).
fof(f5218,plain,
( sQ47_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f5217]) ).
fof(f5219,plain,
sQ47_spl,
inference(contradiction_clause,[status(thm)],[f5218]) ).
fof(f5220,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(resolution,[status(thm)],[f116,f184]) ).
fof(f5221,plain,
group_member(multiply(g1,a,d2),g1),
inference(resolution,[status(thm)],[f116,f193]) ).
fof(f5222,plain,
group_member(multiply(g1,b,d2),g1),
inference(resolution,[status(thm)],[f116,f189]) ).
fof(f5223,plain,
group_member(multiply(g1,c,d2),g1),
inference(resolution,[status(thm)],[f116,f188]) ).
fof(f5224,plain,
product(g1,b,d2,multiply(g1,b,d2)),
inference(resolution,[status(thm)],[f116,f180]) ).
fof(f5225,plain,
product(g1,c,d2,multiply(g1,c,d2)),
inference(resolution,[status(thm)],[f116,f179]) ).
fof(f5227,plain,
group_member(multiply(g1,identity_for(g1),d2),g1),
inference(resolution,[status(thm)],[f116,f192]) ).
fof(f5228,plain,
product(g1,identity_for(g1),d2,multiply(g1,identity_for(g1),d2)),
inference(resolution,[status(thm)],[f116,f183]) ).
fof(f5229,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f116,f65]) ).
fof(f5230,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f116,f64]) ).
fof(f5231,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f116,f61]) ).
fof(f5233,plain,
group_member(multiply(g1,a,d2),g1),
inference(forward_demodulation,[status(thm)],[f91,f5227]) ).
fof(f5234,plain,
product(g1,a,d2,multiply(g1,identity_for(g1),d2)),
inference(forward_demodulation,[status(thm)],[f91,f5228]) ).
fof(f5235,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(forward_demodulation,[status(thm)],[f91,f5234]) ).
fof(f5236,plain,
! [X0] :
( product(g1,inverse(g1,d1),d3,X0)
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f118,f1334]) ).
fof(f5237,plain,
! [X0] :
( product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),d3,X0) ),
inference(resolution,[status(thm)],[f118,f1333]) ).
fof(f5238,plain,
! [X0] :
( product(g1,a,d3,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f118,f173]) ).
fof(f5239,plain,
! [X0] :
( product(g1,d1,d2,X0)
| ~ product(g1,a,d3,X0) ),
inference(resolution,[status(thm)],[f118,f172]) ).
fof(f5240,plain,
! [X0] :
( product(g1,inverse(g1,d1),d3,X0)
| ~ product(g1,identity_for(g1),d2,X0) ),
inference(resolution,[status(thm)],[f118,f158]) ).
fof(f5241,plain,
! [X0] :
( product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,d1),d3,X0) ),
inference(resolution,[status(thm)],[f118,f157]) ).
fof(f5242,plain,
! [X0] :
( product(g1,d1,d2,X0)
| ~ product(g1,identity_for(g1),d3,X0) ),
inference(resolution,[status(thm)],[f118,f146]) ).
fof(f5243,plain,
! [X0] :
( product(g1,identity_for(g1),d3,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f118,f139]) ).
fof(f5244,plain,
! [X0] :
( X0 = d1
| ~ product(g1,X0,d2,d3) ),
inference(resolution,[status(thm)],[f118,f75]) ).
fof(f5245,plain,
! [X0] :
( X0 = d2
| ~ product(g1,d1,X0,d3) ),
inference(resolution,[status(thm)],[f118,f73]) ).
fof(f5246,plain,
! [X0,X1,X2] :
( product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f118,f71]) ).
fof(f5247,plain,
! [X0,X1,X2] :
( product(g1,d1,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f118,f69]) ).
fof(f5248,plain,
! [X0] :
( X0 = d3
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f118,f67]) ).
fof(f5249,plain,
! [X0] :
( product(g1,inverse(g1,d1),d3,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5240]) ).
fof(f5250,plain,
! [X0] :
( product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),d3,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5241]) ).
fof(f5251,plain,
! [X0] :
( product(g1,d1,d2,X0)
| ~ product(g1,a,d3,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5242]) ).
fof(f5252,plain,
! [X0] :
( product(g1,a,d3,X0)
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5243]) ).
fof(f5254,plain,
( ~ sQ25_spl
| product(g1,d1,b,d3) ),
inference(backward_demodulation,[status(thm)],[f297,f118]) ).
fof(f5257,plain,
( sQ5_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ product(g2,isomorphism6(d1),f,isomorphism6(a)) ),
inference(backward_demodulation,[status(thm)],[f270,f1754]) ).
fof(f5259,plain,
( sQ5_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ product(g2,isomorphism6(d1),f,h) ),
inference(forward_demodulation,[status(thm)],[f112,f5257]) ).
fof(f5260,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,a) ),
inference(forward_demodulation,[status(thm)],[f270,f1751]) ).
fof(f5261,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| d1 = inverse(g1,b) ),
inference(resolution,[status(thm)],[f5260,f692]) ).
fof(f5262,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| b = inverse(g1,d1) ),
inference(resolution,[status(thm)],[f5260,f612]) ).
fof(f5263,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5260,f1334]) ).
fof(f5264,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f1333]) ).
fof(f5265,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f173]) ).
fof(f5266,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f5260,f172]) ).
fof(f5267,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f5260,f158]) ).
fof(f5268,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f157]) ).
fof(f5269,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f146]) ).
fof(f5270,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f139]) ).
fof(f5271,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = d1
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f5260,f75]) ).
fof(f5272,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = b
| ~ product(g1,d1,X0,a) ),
inference(resolution,[status(thm)],[f5260,f73]) ).
fof(f5273,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5260,f71]) ).
fof(f5274,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5260,f69]) ).
fof(f5275,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f67]) ).
fof(f5276,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5267]) ).
fof(f5277,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5268]) ).
fof(f5278,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5269]) ).
fof(f5279,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5270]) ).
fof(f5280,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ25_spl
| ~ product(g2,h,isomorphism6(b),isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f1713]) ).
fof(f5281,plain,
( sQ5_spl
| ~ sQ27_spl
| ~ sQ25_spl
| ~ product(g2,h,f,isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f113,f5280]) ).
fof(f5286,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism5(d1),isomorphism5(b),isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f134]) ).
fof(f5287,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ product(g2,isomorphism5(d1),g,isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f110,f5286]) ).
fof(f5288,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ product(g2,isomorphism5(d1),g,isomorphism5(a)) ),
inference(forward_demodulation,[status(thm)],[f270,f5287]) ).
fof(f5289,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ product(g2,isomorphism5(d1),g,h) ),
inference(forward_demodulation,[status(thm)],[f109,f5288]) ).
fof(f5290,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ product(g2,isomorphism5(d1),g,isomorphism5(a)) ),
inference(forward_demodulation,[status(thm)],[f270,f1744]) ).
fof(f5291,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ product(g2,isomorphism5(d1),g,h) ),
inference(forward_demodulation,[status(thm)],[f109,f5290]) ).
fof(f5295,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(resolution,[status(thm)],[f115,f184]) ).
fof(f5296,plain,
group_member(multiply(g1,a,d1),g1),
inference(resolution,[status(thm)],[f115,f193]) ).
fof(f5297,plain,
group_member(multiply(g1,b,d1),g1),
inference(resolution,[status(thm)],[f115,f189]) ).
fof(f5298,plain,
group_member(multiply(g1,c,d1),g1),
inference(resolution,[status(thm)],[f115,f188]) ).
fof(f5299,plain,
product(g1,b,d1,multiply(g1,b,d1)),
inference(resolution,[status(thm)],[f115,f180]) ).
fof(f5300,plain,
product(g1,c,d1,multiply(g1,c,d1)),
inference(resolution,[status(thm)],[f115,f179]) ).
fof(f5302,plain,
group_member(multiply(g1,identity_for(g1),d1),g1),
inference(resolution,[status(thm)],[f115,f192]) ).
fof(f5303,plain,
product(g1,identity_for(g1),d1,multiply(g1,identity_for(g1),d1)),
inference(resolution,[status(thm)],[f115,f183]) ).
fof(f5304,plain,
! [X0] :
( group_member(multiply(g1,d1,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f115,f65]) ).
fof(f5305,plain,
! [X0] :
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f115,f64]) ).
fof(f5306,plain,
group_member(inverse(g1,d1),g1),
inference(resolution,[status(thm)],[f115,f61]) ).
fof(f5308,plain,
group_member(multiply(g1,a,d1),g1),
inference(forward_demodulation,[status(thm)],[f91,f5302]) ).
fof(f5309,plain,
product(g1,a,d1,multiply(g1,identity_for(g1),d1)),
inference(forward_demodulation,[status(thm)],[f91,f5303]) ).
fof(f5310,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(forward_demodulation,[status(thm)],[f91,f5309]) ).
fof(f5314,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,b,a) ),
inference(backward_demodulation,[status(thm)],[f307,f5260]) ).
fof(f5315,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| ~ product(g2,isomorphism5(b),g,h) ),
inference(forward_demodulation,[status(thm)],[f307,f5289]) ).
fof(f5316,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| ~ product(g2,g,g,h) ),
inference(forward_demodulation,[status(thm)],[f110,f5315]) ).
fof(f5323,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5314,f1334]) ).
fof(f5324,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f5314,f1333]) ).
fof(f5325,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f5314,f173]) ).
fof(f5326,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f5314,f172]) ).
fof(f5327,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f5314,f158]) ).
fof(f5328,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f5314,f157]) ).
fof(f5329,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f5314,f146]) ).
fof(f5330,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f5314,f139]) ).
fof(f5336,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5327]) ).
fof(f5337,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5328]) ).
fof(f5338,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5329]) ).
fof(f5339,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5330]) ).
fof(f5344,plain,
( ~ sQ25_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f4935]) ).
fof(f5345,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f5344,f184]) ).
fof(f5346,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f5344,f193]) ).
fof(f5347,plain,
( ~ sQ25_spl
| group_member(multiply(g1,b,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f5344,f189]) ).
fof(f5348,plain,
( ~ sQ25_spl
| group_member(multiply(g1,c,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f5344,f188]) ).
fof(f5349,plain,
( ~ sQ25_spl
| product(g1,b,inverse(g1,b),multiply(g1,b,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f5344,f180]) ).
fof(f5350,plain,
( ~ sQ25_spl
| product(g1,c,inverse(g1,b),multiply(g1,c,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f5344,f179]) ).
fof(f5352,plain,
( ~ sQ25_spl
| group_member(multiply(g1,identity_for(g1),inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f5344,f192]) ).
fof(f5353,plain,
( ~ sQ25_spl
| product(g1,identity_for(g1),inverse(g1,b),multiply(g1,identity_for(g1),inverse(g1,b))) ),
inference(resolution,[status(thm)],[f5344,f183]) ).
fof(f5354,plain,
! [X0] :
( ~ sQ25_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f5344,f65]) ).
fof(f5355,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f5344,f64]) ).
fof(f5358,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,inverse(g1,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f5352]) ).
fof(f5359,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,identity_for(g1),inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f5353]) ).
fof(f5360,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f5359]) ).
fof(f5370,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| inverse(g1,b) = b ),
inference(forward_demodulation,[status(thm)],[f297,f253]) ).
fof(f5371,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f5370,f1335]) ).
fof(f5372,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f5370,f1250]) ).
fof(f5373,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f5370,f1249]) ).
fof(f5374,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f5370,f1248]) ).
fof(f5375,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,X0,b,a) ),
inference(paramodulation,[status(thm)],[f5370,f704]) ).
fof(f5376,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f5370,f638]) ).
fof(f5377,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f5370,f556]) ).
fof(f5378,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,b,X0,a) ),
inference(paramodulation,[status(thm)],[f5370,f542]) ).
fof(f5379,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,a) ),
inference(paramodulation,[status(thm)],[f5370,f214]) ).
fof(f5380,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,a) ),
inference(paramodulation,[status(thm)],[f5370,f213]) ).
fof(f5381,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f5370,f422]) ).
fof(f5382,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f5370,f420]) ).
fof(f5383,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f5370,f168]) ).
fof(f5384,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = identity_for(g1)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f5370,f163]) ).
fof(f5385,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f5370,f162]) ).
fof(f5386,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f5370,f161]) ).
fof(f5387,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = identity_for(g1)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f5370,f159]) ).
fof(f5389,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,b,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f5370,f156]) ).
fof(f5390,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f5370,f63]) ).
fof(f5391,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f5370,f62]) ).
fof(f5392,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5381]) ).
fof(f5393,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5392]) ).
fof(f5394,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5382]) ).
fof(f5395,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5394]) ).
fof(f5396,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5383]) ).
fof(f5397,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5384]) ).
fof(f5398,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f5385]) ).
fof(f5399,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f5386]) ).
fof(f5400,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5387]) ).
fof(f5401,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5389]) ).
fof(f5402,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5390]) ).
fof(f5403,plain,
( ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5391]) ).
fof(f5408,plain,
( ~ sQ25_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f154]) ).
fof(f5410,plain,
( ~ sQ25_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f3877]) ).
fof(f5413,plain,
( sQ11_spl
| ~ sQ25_spl
| inverse(g1,b) != a ),
inference(forward_demodulation,[status(thm)],[f297,f251]) ).
fof(f5416,plain,
( sQ13_spl
| ~ sQ25_spl
| inverse(g1,b) != c ),
inference(forward_demodulation,[status(thm)],[f297,f257]) ).
fof(f5419,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f297,f145]) ).
fof(f5420,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ28_spl
| product(g1,d3,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f307,f5419]) ).
fof(f5421,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f5420]) ).
fof(f5423,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| product(g1,a,inverse(g1,b),X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f5421,f213]) ).
fof(f5424,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f5421,f94]) ).
fof(f5425,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| product(g1,a,inverse(g1,b),X0)
| ~ product(g1,b,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f5421,f63]) ).
fof(f5426,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f5421,f60]) ).
fof(f5428,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| product(g1,a,inverse(g1,b),X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5425]) ).
fof(f5430,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5426]) ).
fof(f5431,plain,
! [X0] :
( ~ sQ28_spl
| X0 = d3
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f307,f144]) ).
fof(f5432,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ25_spl
| X0 = d3
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f5431]) ).
fof(f5433,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f5432]) ).
fof(f5437,plain,
! [X0] :
( ~ sQ44_spl
| X0 = a
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f1335]) ).
fof(f5438,plain,
! [X0] :
( ~ sQ44_spl
| X0 = a
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f1250]) ).
fof(f5439,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f1249]) ).
fof(f5440,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f1248]) ).
fof(f5441,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,X0,c,a) ),
inference(paramodulation,[status(thm)],[f790,f704]) ).
fof(f5442,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f638]) ).
fof(f5443,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f556]) ).
fof(f5444,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,c,X0,a) ),
inference(paramodulation,[status(thm)],[f790,f542]) ).
fof(f5445,plain,
( ~ sQ44_spl
| product(g1,c,c,a) ),
inference(paramodulation,[status(thm)],[f790,f214]) ).
fof(f5446,plain,
( ~ sQ44_spl
| product(g1,c,c,a) ),
inference(paramodulation,[status(thm)],[f790,f213]) ).
fof(f5447,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f422]) ).
fof(f5448,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f420]) ).
fof(f5449,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,X0,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f790,f168]) ).
fof(f5450,plain,
! [X0] :
( ~ sQ44_spl
| X0 = identity_for(g1)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f163]) ).
fof(f5451,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f162]) ).
fof(f5452,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f790,f161]) ).
fof(f5453,plain,
! [X0] :
( ~ sQ44_spl
| X0 = identity_for(g1)
| ~ product(g1,c,c,X0) ),
inference(paramodulation,[status(thm)],[f790,f159]) ).
fof(f5455,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,c,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f790,f156]) ).
fof(f5456,plain,
( ~ sQ44_spl
| product(g1,c,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f790,f63]) ).
fof(f5457,plain,
( ~ sQ44_spl
| product(g1,c,c,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f790,f62]) ).
fof(f5458,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5447]) ).
fof(f5459,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5458]) ).
fof(f5460,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5448]) ).
fof(f5461,plain,
! [X0] :
( ~ sQ44_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5460]) ).
fof(f5462,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,X0,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5449]) ).
fof(f5463,plain,
! [X0] :
( ~ sQ44_spl
| X0 = a
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5450]) ).
fof(f5464,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f5451]) ).
fof(f5465,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f5452]) ).
fof(f5466,plain,
! [X0] :
( ~ sQ44_spl
| X0 = a
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5453]) ).
fof(f5467,plain,
! [X0] :
( ~ sQ44_spl
| X0 = c
| ~ product(g1,c,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5455]) ).
fof(f5468,plain,
( ~ sQ44_spl
| product(g1,c,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5456]) ).
fof(f5469,plain,
( ~ sQ44_spl
| product(g1,c,c,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5457]) ).
fof(f5477,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| X0 = d3
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f307,f1749]) ).
fof(f5479,plain,
! [X0] :
( ~ sQ28_spl
| X0 = d2
| ~ product(g1,b,X0,d3) ),
inference(forward_demodulation,[status(thm)],[f307,f148]) ).
fof(f5480,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ17_spl
| X0 = d2
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f270,f5479]) ).
fof(f5481,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ17_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f297,f5480]) ).
fof(f5484,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ28_spl
| product(g1,d3,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f307,f1721]) ).
fof(f5486,plain,
! [X0] :
( ~ sQ25_spl
| X0 = d1
| ~ product(g1,X0,b,d3) ),
inference(forward_demodulation,[status(thm)],[f297,f165]) ).
fof(f5487,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = d1
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f270,f5486]) ).
fof(f5488,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| X0 = b
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f307,f5487]) ).
fof(f5490,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| inverse(g1,b) = b ),
inference(resolution,[status(thm)],[f5488,f214]) ).
fof(f5491,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| product(g1,d1,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f297,f143]) ).
fof(f5492,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f5491]) ).
fof(f5493,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f307,f5492]) ).
fof(f5495,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,a,X0)
| ~ product(g1,a,inverse(g1,b),X0) ),
inference(resolution,[status(thm)],[f5493,f213]) ).
fof(f5496,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f5493,f94]) ).
fof(f5497,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,identity_for(g1),X0)
| ~ product(g1,a,inverse(g1,b),X0) ),
inference(resolution,[status(thm)],[f5493,f63]) ).
fof(f5498,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,a,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f5493,f60]) ).
fof(f5502,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5498]) ).
fof(f5503,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,b,a,c) ),
inference(resolution,[status(thm)],[f5155,f500]) ).
fof(f5504,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,X0,c,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f5155,f208]) ).
fof(f5505,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,c,X1) ),
inference(resolution,[status(thm)],[f5155,f207]) ).
fof(f5506,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| b = c ),
inference(resolution,[status(thm)],[f5155,f171]) ).
fof(f5507,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,inverse(g1,a),c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5155,f1334]) ).
fof(f5508,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,a),c,X0) ),
inference(resolution,[status(thm)],[f5155,f1333]) ).
fof(f5509,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5155,f173]) ).
fof(f5510,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f5155,f172]) ).
fof(f5511,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,inverse(g1,a),c,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f5155,f158]) ).
fof(f5512,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,a),c,X0) ),
inference(resolution,[status(thm)],[f5155,f157]) ).
fof(f5513,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f5155,f146]) ).
fof(f5514,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5155,f139]) ).
fof(f5515,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| X0 = a
| ~ product(g1,X0,b,c) ),
inference(resolution,[status(thm)],[f5155,f75]) ).
fof(f5516,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| X0 = b
| ~ product(g1,a,X0,c) ),
inference(resolution,[status(thm)],[f5155,f73]) ).
fof(f5517,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,c,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5155,f71]) ).
fof(f5518,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,X1,X2)
| ~ product(g1,c,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5155,f69]) ).
fof(f5519,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| X0 = c
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5155,f67]) ).
fof(f5520,plain,
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f5506,f235,f1511,f252,f296]) ).
fof(f5521,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f5507]) ).
fof(f5522,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f5508]) ).
fof(f5523,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,inverse(g1,a),c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5511]) ).
fof(f5524,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f5523]) ).
fof(f5525,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f5512]) ).
fof(f5526,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5525]) ).
fof(f5527,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5513]) ).
fof(f5528,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ12_spl
| ~ sQ56_spl
| product(g1,a,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5514]) ).
fof(f5531,plain,
( ~ sQ17_spl
| ~ sQ72_spl
| c = inverse(g1,c) ),
inference(resolution,[status(thm)],[f5170,f612]) ).
fof(f5532,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f5170,f1334]) ).
fof(f5533,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,a,c,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f5170,f1333]) ).
fof(f5534,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f5170,f173]) ).
fof(f5535,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,c,c,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f5170,f172]) ).
fof(f5536,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f5170,f158]) ).
fof(f5537,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f5170,f157]) ).
fof(f5538,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,c,c,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f5170,f146]) ).
fof(f5539,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f5170,f139]) ).
fof(f5540,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| X0 = c
| ~ product(g1,X0,c,a) ),
inference(resolution,[status(thm)],[f5170,f75]) ).
fof(f5541,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| X0 = c
| ~ product(g1,c,X0,a) ),
inference(resolution,[status(thm)],[f5170,f73]) ).
fof(f5542,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f5170,f71]) ).
fof(f5543,plain,
! [X0,X1,X2] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f5170,f69]) ).
fof(f5544,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| X0 = a
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f5170,f67]) ).
fof(f5547,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5536]) ).
fof(f5551,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,c,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5538]) ).
fof(f5552,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,a,a,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5539]) ).
fof(f5556,plain,
( ~ sQ28_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f307,f155]) ).
fof(f5565,plain,
( ~ sQ28_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f307,f4723]) ).
fof(f5567,plain,
( ~ sQ25_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f5231]) ).
fof(f5574,plain,
! [X0] :
( ~ sQ25_spl
| X0 = d1
| ~ product(g1,X0,b,d3) ),
inference(forward_demodulation,[status(thm)],[f297,f5244]) ).
fof(f5575,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = d1
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f270,f5574]) ).
fof(f5577,plain,
! [X0] :
( ~ sQ28_spl
| X0 = d2
| ~ product(g1,b,X0,d3) ),
inference(forward_demodulation,[status(thm)],[f307,f5245]) ).
fof(f5578,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ17_spl
| X0 = d2
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f270,f5577]) ).
fof(f5580,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f297,f5246]) ).
fof(f5581,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ28_spl
| product(g1,d3,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f307,f5580]) ).
fof(f5583,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| product(g1,d1,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f297,f5247]) ).
fof(f5584,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f5583]) ).
fof(f5587,plain,
! [X0] :
( ~ sQ28_spl
| X0 = d3
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f307,f5248]) ).
fof(f5588,plain,
! [X0] :
( ~ sQ28_spl
| ~ sQ25_spl
| X0 = d3
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f5587]) ).
fof(f5591,plain,
( ~ sQ28_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f307,f5306]) ).
fof(f5604,plain,
( ~ sQ25_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f3868]) ).
fof(f5605,plain,
( ~ sQ25_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,a,multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f5604,f184]) ).
fof(f5606,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f5604,f193]) ).
fof(f5607,plain,
( ~ sQ25_spl
| group_member(multiply(g1,b,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f5604,f189]) ).
fof(f5608,plain,
( ~ sQ25_spl
| group_member(multiply(g1,c,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f5604,f188]) ).
fof(f5609,plain,
( ~ sQ25_spl
| product(g1,b,multiply(g1,b,b),multiply(g1,b,multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f5604,f180]) ).
fof(f5610,plain,
( ~ sQ25_spl
| product(g1,c,multiply(g1,b,b),multiply(g1,c,multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f5604,f179]) ).
fof(f5611,plain,
( ~ sQ25_spl
| multiply(g1,b,b) = c
| multiply(g1,b,b) = b
| multiply(g1,b,b) = a ),
inference(resolution,[status(thm)],[f5604,f89]) ).
fof(f5612,plain,
( ~ sQ25_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f5604,f192]) ).
fof(f5613,plain,
( ~ sQ25_spl
| product(g1,identity_for(g1),multiply(g1,b,b),multiply(g1,identity_for(g1),multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f5604,f183]) ).
fof(f5614,plain,
! [X0] :
( ~ sQ25_spl
| group_member(multiply(g1,multiply(g1,b,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f5604,f65]) ).
fof(f5615,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,multiply(g1,b,b),X0,multiply(g1,multiply(g1,b,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f5604,f64]) ).
fof(f5616,plain,
( ~ sQ25_spl
| group_member(inverse(g1,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f5604,f61]) ).
fof(f5617,plain,
( ~ sQ25_spl
| sQ68_spl
| sQ67_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f5611,f2765,f2768,f2771,f296]) ).
fof(f5618,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,multiply(g1,b,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f5612]) ).
fof(f5619,plain,
( ~ sQ25_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,identity_for(g1),multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f5613]) ).
fof(f5620,plain,
( ~ sQ25_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,a,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f5619]) ).
fof(f5639,plain,
( ~ sQ72_spl
| product(g1,c,c,a) ),
inference(forward_demodulation,[status(thm)],[f3031,f869]) ).
fof(f5640,plain,
( ~ sQ76_spl
| product(g1,b,c,b) ),
inference(forward_demodulation,[status(thm)],[f3065,f912]) ).
fof(f5641,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| ~ sQ76_spl
| product(g1,b,b,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f5640,f5493]) ).
fof(f5642,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| ~ sQ76_spl
| product(g1,a,c,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f5640,f5421]) ).
fof(f5643,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f5640,f1334]) ).
fof(f5644,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,a,c,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(resolution,[status(thm)],[f5640,f1333]) ).
fof(f5645,plain,
( ~ sQ76_spl
| c = a ),
inference(resolution,[status(thm)],[f5640,f206]) ).
fof(f5646,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,a,b,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f5640,f173]) ).
fof(f5647,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,b,c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5640,f172]) ).
fof(f5648,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f5640,f158]) ).
fof(f5649,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(resolution,[status(thm)],[f5640,f157]) ).
fof(f5650,plain,
( ~ sQ76_spl
| c = identity_for(g1) ),
inference(resolution,[status(thm)],[f5640,f150]) ).
fof(f5651,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,b,c,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f5640,f146]) ).
fof(f5652,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f5640,f139]) ).
fof(f5653,plain,
! [X0] :
( ~ sQ76_spl
| X0 = b
| ~ product(g1,X0,c,b) ),
inference(resolution,[status(thm)],[f5640,f75]) ).
fof(f5654,plain,
! [X0] :
( ~ sQ76_spl
| X0 = c
| ~ product(g1,b,X0,b) ),
inference(resolution,[status(thm)],[f5640,f73]) ).
fof(f5655,plain,
! [X0,X1,X2] :
( ~ sQ76_spl
| product(g1,b,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f5640,f71]) ).
fof(f5656,plain,
! [X0,X1,X2] :
( ~ sQ76_spl
| product(g1,b,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f5640,f69]) ).
fof(f5657,plain,
! [X0] :
( ~ sQ76_spl
| X0 = b
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f5640,f67]) ).
fof(f5658,plain,
! [X0] :
( ~ sQ76_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f5370,f5643]) ).
fof(f5659,plain,
! [X0] :
( ~ sQ76_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,c,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f5370,f5644]) ).
fof(f5660,plain,
( ~ sQ76_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f5645,f232,f3064]) ).
fof(f5661,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5648]) ).
fof(f5662,plain,
! [X0] :
( ~ sQ76_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f5370,f5661]) ).
fof(f5663,plain,
! [X0] :
( ~ sQ76_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f5370,f5649]) ).
fof(f5664,plain,
! [X0] :
( ~ sQ76_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,c,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5663]) ).
fof(f5665,plain,
( ~ sQ76_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f5650,f285,f3064]) ).
fof(f5666,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,b,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5651]) ).
fof(f5667,plain,
! [X0] :
( ~ sQ76_spl
| product(g1,a,b,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5652]) ).
fof(f5668,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f3867]) ).
fof(f5670,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,d2),X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f297,f200]) ).
fof(f5674,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f3881]) ).
fof(f5675,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f5674]) ).
fof(f5677,plain,
! [X0] :
( ~ sQ25_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f297,f199]) ).
fof(f5679,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| ~ sQ77_spl
| product(g1,b,c,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f3082,f5493]) ).
fof(f5680,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ28_spl
| ~ sQ17_spl
| ~ sQ77_spl
| product(g1,a,c,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f3082,f5421]) ).
fof(f5681,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,inverse(g1,b),c,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f3082,f1334]) ).
fof(f5682,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,a,c,X0)
| ~ product(g1,inverse(g1,b),c,X0) ),
inference(resolution,[status(thm)],[f3082,f1333]) ).
fof(f5683,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,a,c,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f3082,f173]) ).
fof(f5684,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,b,c,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f3082,f172]) ).
fof(f5685,plain,
( ~ sQ77_spl
| b = a ),
inference(resolution,[status(thm)],[f3082,f170]) ).
fof(f5686,plain,
( ~ sQ77_spl
| b = identity_for(g1) ),
inference(resolution,[status(thm)],[f3082,f167]) ).
fof(f5687,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,inverse(g1,b),c,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f3082,f158]) ).
fof(f5688,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,b),c,X0) ),
inference(resolution,[status(thm)],[f3082,f157]) ).
fof(f5689,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,b,c,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f3082,f146]) ).
fof(f5690,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f3082,f139]) ).
fof(f5691,plain,
! [X0] :
( ~ sQ77_spl
| X0 = b
| ~ product(g1,X0,c,c) ),
inference(resolution,[status(thm)],[f3082,f75]) ).
fof(f5692,plain,
! [X0] :
( ~ sQ77_spl
| X0 = c
| ~ product(g1,b,X0,c) ),
inference(resolution,[status(thm)],[f3082,f73]) ).
fof(f5693,plain,
! [X0,X1,X2] :
( ~ sQ77_spl
| product(g1,c,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f3082,f71]) ).
fof(f5694,plain,
! [X0,X1,X2] :
( ~ sQ77_spl
| product(g1,b,X1,X2)
| ~ product(g1,c,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f3082,f69]) ).
fof(f5695,plain,
! [X0] :
( ~ sQ77_spl
| X0 = c
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f3082,f67]) ).
fof(f5696,plain,
! [X0] :
( ~ sQ77_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,c,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f5370,f5681]) ).
fof(f5697,plain,
! [X0] :
( ~ sQ77_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,c,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f5370,f5682]) ).
fof(f5698,plain,
( ~ sQ77_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f5685,f242,f3067]) ).
fof(f5699,plain,
( ~ sQ77_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f5686,f282,f3067]) ).
fof(f5700,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,inverse(g1,b),c,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5687]) ).
fof(f5701,plain,
! [X0] :
( ~ sQ77_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,b,c,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f5370,f5700]) ).
fof(f5702,plain,
! [X0] :
( ~ sQ77_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f5370,f5688]) ).
fof(f5703,plain,
! [X0] :
( ~ sQ77_spl
| ~ sQ12_spl
| ~ sQ25_spl
| product(g1,a,c,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5702]) ).
fof(f5704,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,b,c,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5689]) ).
fof(f5705,plain,
! [X0] :
( ~ sQ77_spl
| product(g1,a,c,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5690]) ).
fof(f5706,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f297,f5670]) ).
fof(f5707,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| product(g1,b,a,X0)
| ~ product(g1,a,inverse(g1,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5497]) ).
fof(f5708,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ28_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f5490,f715,f306,f269,f296]) ).
fof(f5714,plain,
( sQ12_spl
| ~ sQ25_spl
| inverse(g1,b) != b ),
inference(forward_demodulation,[status(thm)],[f297,f254]) ).
fof(f5715,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ72_spl
| product(g1,a,c,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5537]) ).
fof(f5716,plain,
( ~ sQ17_spl
| ~ sQ72_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f5531,f789,f3030,f269]) ).
fof(f5718,plain,
( ~ sQ13_spl
| ~ sQ25_spl
| inverse(g1,b) = c ),
inference(forward_demodulation,[status(thm)],[f297,f256]) ).
fof(f5719,plain,
! [X0] :
( ~ sQ25_spl
| X0 = d3
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f5248]) ).
fof(f5720,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f5719]) ).
fof(f5721,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f5580]) ).
fof(f5722,plain,
! [X0] :
( ~ sQ17_spl
| X0 = d2
| ~ product(g1,d1,X0,a) ),
inference(forward_demodulation,[status(thm)],[f270,f5245]) ).
fof(f5723,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,d1,X0,a) ),
inference(forward_demodulation,[status(thm)],[f297,f5722]) ).
fof(f5724,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f1721]) ).
fof(f5725,plain,
! [X0] :
( ~ sQ17_spl
| X0 = d2
| ~ product(g1,d1,X0,a) ),
inference(forward_demodulation,[status(thm)],[f270,f148]) ).
fof(f5726,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,d1,X0,a) ),
inference(forward_demodulation,[status(thm)],[f297,f5725]) ).
fof(f5727,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f1749]) ).
fof(f5728,plain,
! [X0] :
( ~ sQ25_spl
| X0 = d3
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f144]) ).
fof(f5729,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f5728]) ).
fof(f5730,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f5419]) ).
fof(f5731,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| product(g1,a,b,d3) ),
inference(forward_demodulation,[status(thm)],[f297,f407]) ).
fof(f5732,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f270,f5731]) ).
fof(f5733,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| X0 = d3
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f445]) ).
fof(f5734,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f5733]) ).
fof(f5735,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sQ25_spl
| product(g1,d3,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f297,f1709]) ).
fof(f5736,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f270,f5735]) ).
fof(f5737,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ17_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f1564]) ).
fof(f5738,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ17_spl
| ~ sQ25_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f5737]) ).
fof(f5739,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ17_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f1567]) ).
fof(f5740,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ17_spl
| ~ sQ25_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f5739]) ).
fof(f5741,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ17_spl
| X0 = d2
| ~ product(g1,a,X0,a) ),
inference(forward_demodulation,[status(thm)],[f270,f508]) ).
fof(f5742,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ17_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,a,X0,a) ),
inference(forward_demodulation,[status(thm)],[f297,f5741]) ).
fof(f5743,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ27_spl
| ~ sQ25_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f1434]) ).
fof(f5744,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ27_spl
| ~ sQ25_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f1432]) ).
fof(f5745,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ17_spl
| ~ sQ25_spl
| X0 = b
| ~ product(g1,a,X0,a) ),
inference(forward_demodulation,[status(thm)],[f297,f509]) ).
fof(f5746,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ25_spl
| ~ product(g2,h,isomorphism5(b),isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f1545]) ).
fof(f5747,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ25_spl
| ~ product(g2,h,g,isomorphism5(d3)) ),
inference(forward_demodulation,[status(thm)],[f110,f5746]) ).
fof(f5748,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ product(g2,h,g,isomorphism5(a)) ),
inference(forward_demodulation,[status(thm)],[f270,f5747]) ).
fof(f5749,plain,
( sQ4_spl
| ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ product(g2,h,g,h) ),
inference(forward_demodulation,[status(thm)],[f109,f5748]) ).
fof(f5750,plain,
! [X0] :
( product(g1,a,c,X0)
| ~ product(g1,inverse(g1,c),multiply(g1,c,c),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f2736]) ).
fof(f5751,plain,
( ~ sQ5_spl
| ~ sQ25_spl
| product(g2,isomorphism6(d1),isomorphism6(b),isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f297,f136]) ).
fof(f5752,plain,
( ~ sQ5_spl
| ~ sQ25_spl
| product(g2,isomorphism6(d1),f,isomorphism6(d3)) ),
inference(forward_demodulation,[status(thm)],[f113,f5751]) ).
fof(f5753,plain,
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g2,isomorphism6(d1),f,isomorphism6(a)) ),
inference(forward_demodulation,[status(thm)],[f270,f5752]) ).
fof(f5754,plain,
( ~ sQ5_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g2,isomorphism6(d1),f,h) ),
inference(forward_demodulation,[status(thm)],[f112,f5753]) ).
fof(f5755,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(resolution,[status(thm)],[f115,f184]) ).
fof(f5756,plain,
group_member(multiply(g1,a,d1),g1),
inference(resolution,[status(thm)],[f115,f193]) ).
fof(f5757,plain,
group_member(multiply(g1,b,d1),g1),
inference(resolution,[status(thm)],[f115,f189]) ).
fof(f5758,plain,
group_member(multiply(g1,c,d1),g1),
inference(resolution,[status(thm)],[f115,f188]) ).
fof(f5759,plain,
product(g1,b,d1,multiply(g1,b,d1)),
inference(resolution,[status(thm)],[f115,f180]) ).
fof(f5760,plain,
product(g1,c,d1,multiply(g1,c,d1)),
inference(resolution,[status(thm)],[f115,f179]) ).
fof(f5762,plain,
group_member(multiply(g1,identity_for(g1),d1),g1),
inference(resolution,[status(thm)],[f115,f192]) ).
fof(f5763,plain,
product(g1,identity_for(g1),d1,multiply(g1,identity_for(g1),d1)),
inference(resolution,[status(thm)],[f115,f183]) ).
fof(f5764,plain,
! [X0] :
( group_member(multiply(g1,d1,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f115,f65]) ).
fof(f5765,plain,
! [X0] :
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f115,f64]) ).
fof(f5766,plain,
group_member(inverse(g1,d1),g1),
inference(resolution,[status(thm)],[f115,f61]) ).
fof(f5768,plain,
group_member(multiply(g1,a,d1),g1),
inference(forward_demodulation,[status(thm)],[f91,f5762]) ).
fof(f5769,plain,
product(g1,a,d1,multiply(g1,identity_for(g1),d1)),
inference(forward_demodulation,[status(thm)],[f91,f5763]) ).
fof(f5770,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(forward_demodulation,[status(thm)],[f91,f5769]) ).
fof(f5771,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| d1 = inverse(g1,b) ),
inference(resolution,[status(thm)],[f5260,f692]) ).
fof(f5772,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| b = inverse(g1,d1) ),
inference(resolution,[status(thm)],[f5260,f612]) ).
fof(f5773,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5260,f1334]) ).
fof(f5774,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f1333]) ).
fof(f5775,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f173]) ).
fof(f5776,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f5260,f172]) ).
fof(f5777,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f5260,f158]) ).
fof(f5778,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f157]) ).
fof(f5779,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f146]) ).
fof(f5780,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f139]) ).
fof(f5781,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = d1
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f5260,f75]) ).
fof(f5782,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = b
| ~ product(g1,d1,X0,a) ),
inference(resolution,[status(thm)],[f5260,f73]) ).
fof(f5783,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5260,f71]) ).
fof(f5784,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5260,f69]) ).
fof(f5785,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f67]) ).
fof(f5786,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5777]) ).
fof(f5787,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5778]) ).
fof(f5788,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5779]) ).
fof(f5789,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5780]) ).
fof(f5790,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ27_spl
| product(g1,a,b,a) ),
inference(backward_demodulation,[status(thm)],[f304,f5260]) ).
fof(f5793,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ27_spl
| ~ product(g2,isomorphism5(a),g,h) ),
inference(backward_demodulation,[status(thm)],[f304,f5291]) ).
fof(f5794,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ27_spl
| ~ product(g2,h,g,h) ),
inference(forward_demodulation,[status(thm)],[f109,f5793]) ).
fof(f5795,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,b,a,a) ),
inference(resolution,[status(thm)],[f5732,f500]) ).
fof(f5796,plain,
! [X0,X1] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,X0,a,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f5732,f208]) ).
fof(f5797,plain,
! [X0,X1] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f5732,f207]) ).
fof(f5800,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| b = inverse(g1,a) ),
inference(resolution,[status(thm)],[f5732,f612]) ).
fof(f5801,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5732,f1334]) ).
fof(f5802,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f5732,f1333]) ).
fof(f5803,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| b = a ),
inference(resolution,[status(thm)],[f5732,f206]) ).
fof(f5804,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5732,f173]) ).
fof(f5805,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f5732,f172]) ).
fof(f5806,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f5732,f158]) ).
fof(f5807,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f5732,f157]) ).
fof(f5808,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| b = identity_for(g1) ),
inference(resolution,[status(thm)],[f5732,f150]) ).
fof(f5809,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f5732,f146]) ).
fof(f5810,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5732,f139]) ).
fof(f5811,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f5732,f75]) ).
fof(f5812,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| X0 = b
| ~ product(g1,a,X0,a) ),
inference(resolution,[status(thm)],[f5732,f73]) ).
fof(f5813,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5732,f71]) ).
fof(f5814,plain,
! [X0,X1,X2] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5732,f69]) ).
fof(f5815,plain,
! [X0] :
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5732,f67]) ).
fof(f5818,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f1572,f5800]) ).
fof(f5819,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5818,f80]) ).
fof(f5820,plain,
( ~ sQ27_spl
| ~ sQ25_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f5819]) ).
fof(f5821,plain,
! [X0,X1,X2] :
( ~ sQ29_spl
| ~ sQ25_spl
| product(g1,c,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f297,f381]) ).
fof(f5823,plain,
( ~ sQ29_spl
| ~ sQ25_spl
| product(g1,c,b,d3) ),
inference(forward_demodulation,[status(thm)],[f297,f383]) ).
fof(f5824,plain,
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f270,f5823]) ).
fof(f5825,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| d1 = inverse(g1,b) ),
inference(resolution,[status(thm)],[f5260,f692]) ).
fof(f5826,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| b = inverse(g1,d1) ),
inference(resolution,[status(thm)],[f5260,f612]) ).
fof(f5827,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5260,f1334]) ).
fof(f5828,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f1333]) ).
fof(f5829,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f173]) ).
fof(f5830,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f5260,f172]) ).
fof(f5831,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f5260,f158]) ).
fof(f5832,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f157]) ).
fof(f5833,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f5260,f146]) ).
fof(f5834,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f139]) ).
fof(f5835,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = d1
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f5260,f75]) ).
fof(f5836,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = b
| ~ product(g1,d1,X0,a) ),
inference(resolution,[status(thm)],[f5260,f73]) ).
fof(f5837,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5260,f71]) ).
fof(f5838,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f5260,f69]) ).
fof(f5839,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| X0 = a
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f5260,f67]) ).
fof(f5840,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,d1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5831]) ).
fof(f5841,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,d1),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5832]) ).
fof(f5842,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,d1,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5833]) ).
fof(f5843,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5834]) ).
fof(f5848,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| ~ product(g2,isomorphism5(c),g,h) ),
inference(forward_demodulation,[status(thm)],[f310,f5291]) ).
fof(f5849,plain,
( sQ4_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| ~ product(g2,f,g,h) ),
inference(forward_demodulation,[status(thm)],[f111,f5848]) ).
fof(f5850,plain,
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| c = inverse(g1,b) ),
inference(resolution,[status(thm)],[f5824,f692]) ).
fof(f5851,plain,
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| b = inverse(g1,c) ),
inference(resolution,[status(thm)],[f5824,f612]) ).
fof(f5852,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f5824,f1334]) ).
fof(f5853,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f5824,f1333]) ).
fof(f5856,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f5824,f158]) ).
fof(f5857,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(resolution,[status(thm)],[f5824,f157]) ).
fof(f5865,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5856]) ).
fof(f5866,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5857]) ).
fof(f5870,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f1250]) ).
fof(f5871,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f1249]) ).
fof(f5872,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f1248]) ).
fof(f5873,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(paramodulation,[status(thm)],[f1004,f704]) ).
fof(f5874,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f638]) ).
fof(f5875,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f1004,f556]) ).
fof(f5878,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(paramodulation,[status(thm)],[f1004,f213]) ).
fof(f5879,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f422]) ).
fof(f5880,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f1004,f420]) ).
fof(f5881,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1004,f168]) ).
fof(f5882,plain,
! [X0] :
( ~ sQ41_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f1004,f163]) ).
fof(f5883,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f162]) ).
fof(f5884,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f1004,f161]) ).
fof(f5888,plain,
( ~ sQ41_spl
| product(g1,c,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f1004,f63]) ).
fof(f5890,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5879]) ).
fof(f5891,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5890]) ).
fof(f5892,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5880]) ).
fof(f5893,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5892]) ).
fof(f5894,plain,
! [X0] :
( ~ sQ41_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5881]) ).
fof(f5895,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5882]) ).
fof(f5896,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f5883]) ).
fof(f5897,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f5884]) ).
fof(f5900,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5888]) ).
fof(f5902,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f5567,f184]) ).
fof(f5903,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f5567,f193]) ).
fof(f5904,plain,
( ~ sQ25_spl
| group_member(multiply(g1,b,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f5567,f189]) ).
fof(f5905,plain,
( ~ sQ25_spl
| group_member(multiply(g1,c,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f5567,f188]) ).
fof(f5906,plain,
( ~ sQ25_spl
| product(g1,b,inverse(g1,b),multiply(g1,b,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f5567,f180]) ).
fof(f5907,plain,
( ~ sQ25_spl
| product(g1,c,inverse(g1,b),multiply(g1,c,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f5567,f179]) ).
fof(f5909,plain,
( ~ sQ25_spl
| group_member(multiply(g1,identity_for(g1),inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f5567,f192]) ).
fof(f5910,plain,
( ~ sQ25_spl
| product(g1,identity_for(g1),inverse(g1,b),multiply(g1,identity_for(g1),inverse(g1,b))) ),
inference(resolution,[status(thm)],[f5567,f183]) ).
fof(f5911,plain,
! [X0] :
( ~ sQ25_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f5567,f65]) ).
fof(f5912,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f5567,f64]) ).
fof(f5915,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,inverse(g1,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f91,f5909]) ).
fof(f5916,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,identity_for(g1),inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f5910]) ).
fof(f5917,plain,
( ~ sQ25_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f91,f5916]) ).
fof(f5922,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f4989,f1335]) ).
fof(f5924,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f4989,f1249]) ).
fof(f5925,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f4989,f1248]) ).
fof(f5927,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f4989,f638]) ).
fof(f5928,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f4989,f556]) ).
fof(f5929,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(paramodulation,[status(thm)],[f4989,f542]) ).
fof(f5930,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(paramodulation,[status(thm)],[f4989,f214]) ).
fof(f5932,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(paramodulation,[status(thm)],[f4989,f422]) ).
fof(f5933,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f4989,f420]) ).
fof(f5936,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f4989,f162]) ).
fof(f5937,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f4989,f161]) ).
fof(f5938,plain,
! [X0] :
( ~ sQ41_spl
| X0 = identity_for(g1)
| ~ product(g1,c,b,X0) ),
inference(paramodulation,[status(thm)],[f4989,f159]) ).
fof(f5940,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,c,X0,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f4989,f156]) ).
fof(f5942,plain,
( ~ sQ41_spl
| product(g1,c,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f4989,f62]) ).
fof(f5943,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5932]) ).
fof(f5944,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5943]) ).
fof(f5945,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5933]) ).
fof(f5946,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5945]) ).
fof(f5949,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f5936]) ).
fof(f5950,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f91,f5937]) ).
fof(f5951,plain,
! [X0] :
( ~ sQ41_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5938]) ).
fof(f5952,plain,
! [X0] :
( ~ sQ41_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5940]) ).
fof(f5954,plain,
( ~ sQ41_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f91,f5942]) ).
fof(f5965,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5275]) ).
fof(f5967,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f310,f5274]) ).
fof(f5968,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,a,X0)
| ~ product(g1,a,inverse(g1,b),X0) ),
inference(resolution,[status(thm)],[f5967,f213]) ).
fof(f5970,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,identity_for(g1),X0)
| ~ product(g1,a,inverse(g1,b),X0) ),
inference(resolution,[status(thm)],[f5967,f63]) ).
fof(f5976,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| b = inverse(g1,c) ),
inference(forward_demodulation,[status(thm)],[f310,f5262]) ).
fof(f5977,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f310,f5273]) ).
fof(f5978,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,inverse(g1,b),X0)
| ~ product(g1,c,a,X0) ),
inference(resolution,[status(thm)],[f5977,f213]) ).
fof(f5980,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,inverse(g1,b),X0)
| ~ product(g1,c,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f5977,f63]) ).
fof(f5983,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,inverse(g1,b),X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f5980]) ).
fof(f5986,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| c = inverse(g1,b) ),
inference(forward_demodulation,[status(thm)],[f310,f5261]) ).
fof(f5987,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| c = inverse(g1,b) ),
inference(forward_demodulation,[status(thm)],[f310,f5771]) ).
fof(f5988,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(forward_demodulation,[status(thm)],[f310,f5272]) ).
fof(f5990,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| inverse(g1,c) = b ),
inference(resolution,[status(thm)],[f5988,f213]) ).
fof(f5991,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f310,f5271]) ).
fof(f5993,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| inverse(g1,b) = c ),
inference(resolution,[status(thm)],[f5991,f214]) ).
fof(f5995,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| b = inverse(g1,c) ),
inference(forward_demodulation,[status(thm)],[f310,f5772]) ).
fof(f5996,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| c = inverse(g1,b) ),
inference(forward_demodulation,[status(thm)],[f310,f5825]) ).
fof(f5997,plain,
( ~ sQ29_spl
| group_member(inverse(g1,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f5306]) ).
fof(f6001,plain,
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| b = inverse(g1,c) ),
inference(forward_demodulation,[status(thm)],[f310,f5826]) ).
fof(f6011,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f5004,f173]) ).
fof(f6012,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,b,c,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f5004,f172]) ).
fof(f6015,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,b,c,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f5004,f146]) ).
fof(f6016,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f5004,f139]) ).
fof(f6019,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f5004,f71]) ).
fof(f6020,plain,
! [X0,X1,X2] :
( ~ sQ41_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(resolution,[status(thm)],[f5004,f69]) ).
fof(f6028,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,b,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6015]) ).
fof(f6029,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6016]) ).
fof(f6030,plain,
( ~ sQ29_spl
| group_member(inverse(g1,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f4723]) ).
fof(f6036,plain,
( ~ sQ29_spl
| group_member(inverse(g1,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f155]) ).
fof(f6051,plain,
( ~ sQ29_spl
| group_member(inverse(g1,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f5766]) ).
fof(f6070,plain,
( ~ sQ87_spl
| product(g2,g,g,f) ),
inference(forward_demodulation,[status(thm)],[f3359,f1118]) ).
fof(f6071,plain,
( ~ sQ29_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f4714]) ).
fof(f6073,plain,
( ~ sQ25_spl
| product(g1,c,b,multiply(g1,c,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f3871]) ).
fof(f6074,plain,
( ~ sQ25_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6073]) ).
fof(f6075,plain,
( ~ sQ25_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f6074]) ).
fof(f6076,plain,
( ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f3870]) ).
fof(f6077,plain,
( ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6076]) ).
fof(f6078,plain,
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,b,b,b) ),
inference(forward_demodulation,[status(thm)],[f2769,f6077]) ).
fof(f6079,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| ~ sQ67_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f6078,f5977]) ).
fof(f6080,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| ~ sQ67_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6078,f5967]) ).
fof(f6081,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6078,f1334]) ).
fof(f6082,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(resolution,[status(thm)],[f6078,f1333]) ).
fof(f6083,plain,
( ~ sQ25_spl
| ~ sQ67_spl
| b = a ),
inference(resolution,[status(thm)],[f6078,f206]) ).
fof(f6084,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,a,b,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f6078,f173]) ).
fof(f6085,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,b,b,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6078,f172]) ).
fof(f6087,plain,
( ~ sQ25_spl
| ~ sQ67_spl
| b = identity_for(g1) ),
inference(resolution,[status(thm)],[f6078,f167]) ).
fof(f6088,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f6078,f158]) ).
fof(f6089,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(resolution,[status(thm)],[f6078,f157]) ).
fof(f6091,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,b,b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f6078,f146]) ).
fof(f6092,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f6078,f139]) ).
fof(f6093,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| X0 = b
| ~ product(g1,X0,b,b) ),
inference(resolution,[status(thm)],[f6078,f75]) ).
fof(f6094,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| X0 = b
| ~ product(g1,b,X0,b) ),
inference(resolution,[status(thm)],[f6078,f73]) ).
fof(f6095,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,b,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f6078,f71]) ).
fof(f6096,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,b,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f6078,f69]) ).
fof(f6097,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| X0 = b
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f6078,f67]) ).
fof(f6098,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| ~ sQ41_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6081]) ).
fof(f6099,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| ~ sQ41_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6082]) ).
fof(f6100,plain,
( ~ sQ25_spl
| ~ sQ67_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f6083,f242,f2768,f296]) ).
fof(f6102,plain,
( ~ sQ25_spl
| ~ sQ67_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f6087,f282,f2768,f296]) ).
fof(f6103,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6088]) ).
fof(f6104,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| ~ sQ41_spl
| product(g1,c,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6103]) ).
fof(f6105,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| ~ sQ41_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6089]) ).
fof(f6106,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| ~ sQ41_spl
| product(g1,a,b,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6105]) ).
fof(f6108,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,b,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6091]) ).
fof(f6109,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ67_spl
| product(g1,a,b,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6092]) ).
fof(f6110,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f3866]) ).
fof(f6111,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6110]) ).
fof(f6112,plain,
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f1506,f6111]) ).
fof(f6113,plain,
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,b,a,a) ),
inference(resolution,[status(thm)],[f6112,f500]) ).
fof(f6114,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,X0,a,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f6112,f208]) ).
fof(f6115,plain,
! [X0,X1] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f6112,f207]) ).
fof(f6119,plain,
( ~ sQ25_spl
| ~ sQ54_spl
| b = inverse(g1,a) ),
inference(resolution,[status(thm)],[f6112,f612]) ).
fof(f6120,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6112,f1334]) ).
fof(f6121,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f6112,f1333]) ).
fof(f6122,plain,
( ~ sQ25_spl
| ~ sQ54_spl
| b = a ),
inference(resolution,[status(thm)],[f6112,f206]) ).
fof(f6123,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6112,f173]) ).
fof(f6124,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f6112,f172]) ).
fof(f6125,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f6112,f158]) ).
fof(f6126,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f6112,f157]) ).
fof(f6127,plain,
( ~ sQ25_spl
| ~ sQ54_spl
| b = identity_for(g1) ),
inference(resolution,[status(thm)],[f6112,f150]) ).
fof(f6128,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f6112,f146]) ).
fof(f6129,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6112,f139]) ).
fof(f6130,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| X0 = a
| ~ product(g1,X0,b,a) ),
inference(resolution,[status(thm)],[f6112,f75]) ).
fof(f6131,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| X0 = b
| ~ product(g1,a,X0,a) ),
inference(resolution,[status(thm)],[f6112,f73]) ).
fof(f6132,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f6112,f71]) ).
fof(f6133,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ54_spl
| product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f6112,f69]) ).
fof(f6134,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ54_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6112,f67]) ).
fof(f6138,plain,
( ~ sQ25_spl
| ~ sQ54_spl
| b = a ),
inference(forward_demodulation,[status(thm)],[f1572,f6119]) ).
fof(f6139,plain,
( ~ sQ25_spl
| ~ sQ54_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6138,f80]) ).
fof(f6140,plain,
( ~ sQ25_spl
| ~ sQ54_spl ),
inference(contradiction_clause,[status(thm)],[f6139]) ).
fof(f6144,plain,
( ~ sQ93_spl
| product(g2,h,h,f) ),
inference(forward_demodulation,[status(thm)],[f3490,f1197]) ).
fof(f6152,plain,
product(g1,b,a,multiply(g1,a,b)),
inference(resolution,[status(thm)],[f1895,f500]) ).
fof(f6153,plain,
! [X0,X1] :
( product(g1,X0,multiply(g1,a,b),X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f1895,f208]) ).
fof(f6154,plain,
! [X0,X1] :
( product(g1,X0,b,X1)
| ~ product(g1,X0,multiply(g1,a,b),X1) ),
inference(resolution,[status(thm)],[f1895,f207]) ).
fof(f6155,plain,
b = multiply(g1,a,b),
inference(resolution,[status(thm)],[f1895,f171]) ).
fof(f6156,plain,
! [X0] :
( product(g1,inverse(g1,a),multiply(g1,a,b),X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1895,f1334]) ).
fof(f6157,plain,
! [X0] :
( product(g1,a,b,X0)
| ~ product(g1,inverse(g1,a),multiply(g1,a,b),X0) ),
inference(resolution,[status(thm)],[f1895,f1333]) ).
fof(f6158,plain,
! [X0] :
( product(g1,a,multiply(g1,a,b),X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1895,f173]) ).
fof(f6159,plain,
! [X0] :
( product(g1,a,b,X0)
| ~ product(g1,a,multiply(g1,a,b),X0) ),
inference(resolution,[status(thm)],[f1895,f172]) ).
fof(f6160,plain,
! [X0] :
( product(g1,inverse(g1,a),multiply(g1,a,b),X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1895,f158]) ).
fof(f6161,plain,
! [X0] :
( product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,a),multiply(g1,a,b),X0) ),
inference(resolution,[status(thm)],[f1895,f157]) ).
fof(f6162,plain,
! [X0] :
( product(g1,a,b,X0)
| ~ product(g1,identity_for(g1),multiply(g1,a,b),X0) ),
inference(resolution,[status(thm)],[f1895,f146]) ).
fof(f6163,plain,
! [X0] :
( product(g1,identity_for(g1),multiply(g1,a,b),X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1895,f139]) ).
fof(f6164,plain,
! [X0] :
( X0 = a
| ~ product(g1,X0,b,multiply(g1,a,b)) ),
inference(resolution,[status(thm)],[f1895,f75]) ).
fof(f6165,plain,
! [X0] :
( X0 = b
| ~ product(g1,a,X0,multiply(g1,a,b)) ),
inference(resolution,[status(thm)],[f1895,f73]) ).
fof(f6166,plain,
! [X0,X1,X2] :
( product(g1,multiply(g1,a,b),X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1895,f71]) ).
fof(f6167,plain,
! [X0,X1,X2] :
( product(g1,a,X1,X2)
| ~ product(g1,multiply(g1,a,b),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1895,f69]) ).
fof(f6168,plain,
! [X0] :
( X0 = multiply(g1,a,b)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1895,f67]) ).
fof(f6169,plain,
! [X0] :
( product(g1,a,multiply(g1,a,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f6156]) ).
fof(f6170,plain,
! [X0] :
( product(g1,a,b,X0)
| ~ product(g1,a,multiply(g1,a,b),X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f6157]) ).
fof(f6171,plain,
! [X0] :
( product(g1,inverse(g1,a),multiply(g1,a,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6160]) ).
fof(f6172,plain,
! [X0] :
( product(g1,a,multiply(g1,a,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f6171]) ).
fof(f6173,plain,
! [X0] :
( product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,multiply(g1,a,b),X0) ),
inference(forward_demodulation,[status(thm)],[f1572,f6161]) ).
fof(f6174,plain,
! [X0] :
( product(g1,a,b,X0)
| ~ product(g1,a,multiply(g1,a,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6173]) ).
fof(f6175,plain,
! [X0] :
( product(g1,a,b,X0)
| ~ product(g1,a,multiply(g1,a,b),X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6162]) ).
fof(f6176,plain,
! [X0] :
( product(g1,a,multiply(g1,a,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6163]) ).
fof(f6177,plain,
( ~ sQ29_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f4715]) ).
fof(f6184,plain,
( ~ sQ53_spl
| product(g2,g,h,multiply(g2,g,inverse(g2,h))) ),
inference(forward_demodulation,[status(thm)],[f1222,f1205]) ).
fof(f6185,plain,
( ~ sQ53_spl
| product(g2,g,h,multiply(g2,g,h)) ),
inference(forward_demodulation,[status(thm)],[f1222,f6184]) ).
fof(f6186,plain,
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,g,h,g) ),
inference(forward_demodulation,[status(thm)],[f3265,f6185]) ).
fof(f6187,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,inverse(g2,g),g,X0)
| ~ product(g2,f,h,X0) ),
inference(resolution,[status(thm)],[f6186,f1408]) ).
fof(f6188,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,f,h,X0)
| ~ product(g2,inverse(g2,g),g,X0) ),
inference(resolution,[status(thm)],[f6186,f1407]) ).
fof(f6189,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,f,g,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f6186,f379]) ).
fof(f6190,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,g,h,X0)
| ~ product(g2,f,g,X0) ),
inference(resolution,[status(thm)],[f6186,f378]) ).
fof(f6191,plain,
( ~ sQ53_spl
| ~ sQ85_spl
| h = f ),
inference(resolution,[status(thm)],[f6186,f392]) ).
fof(f6192,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,inverse(g2,g),g,X0)
| ~ product(g2,identity_for(g2),h,X0) ),
inference(resolution,[status(thm)],[f6186,f158]) ).
fof(f6193,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,inverse(g2,g),g,X0) ),
inference(resolution,[status(thm)],[f6186,f157]) ).
fof(f6194,plain,
( ~ sQ53_spl
| ~ sQ85_spl
| h = identity_for(g2) ),
inference(resolution,[status(thm)],[f6186,f150]) ).
fof(f6195,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,g,h,X0)
| ~ product(g2,identity_for(g2),g,X0) ),
inference(resolution,[status(thm)],[f6186,f146]) ).
fof(f6196,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f6186,f139]) ).
fof(f6197,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| X0 = g
| ~ product(g2,X0,h,g) ),
inference(resolution,[status(thm)],[f6186,f75]) ).
fof(f6198,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| X0 = h
| ~ product(g2,g,X0,g) ),
inference(resolution,[status(thm)],[f6186,f73]) ).
fof(f6199,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,g,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f6186,f71]) ).
fof(f6200,plain,
! [X0,X1,X2] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,g,X1,X2)
| ~ product(g2,g,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f6186,f69]) ).
fof(f6201,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| X0 = g
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f6186,f67]) ).
fof(f6202,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| ~ sQ49_spl
| product(g2,g,g,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1084,f6187]) ).
fof(f6203,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| ~ sQ49_spl
| product(g2,f,h,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1084,f6188]) ).
fof(f6204,plain,
( ~ sQ53_spl
| ~ sQ85_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f6191,f331,f3264,f1221]) ).
fof(f6205,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,inverse(g2,g),g,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6192]) ).
fof(f6206,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| ~ sQ49_spl
| product(g2,g,g,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1084,f6205]) ).
fof(f6207,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| ~ sQ49_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1084,f6193]) ).
fof(f6208,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| ~ sQ49_spl
| product(g2,f,h,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6207]) ).
fof(f6209,plain,
( ~ sQ53_spl
| ~ sQ85_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f6194,f358,f3264,f1221]) ).
fof(f6210,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,g,h,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6195]) ).
fof(f6211,plain,
! [X0] :
( ~ sQ53_spl
| ~ sQ85_spl
| product(g2,f,g,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6196]) ).
fof(f6214,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ93_spl
| product(g2,g,f,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3490,f3572]) ).
fof(f6215,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ93_spl
| product(g2,f,h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f3490,f3574]) ).
fof(f6216,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,h,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f3628,f3641]) ).
fof(f6217,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3628,f3643]) ).
fof(f6218,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,f,h,X0)
| ~ product(g2,inverse(g2,g),f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f4117]) ).
fof(f6221,plain,
( ~ sQ29_spl
| product(g1,b,c,multiply(g1,b,d1)) ),
inference(forward_demodulation,[status(thm)],[f310,f4716]) ).
fof(f6222,plain,
( ~ sQ29_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f310,f6221]) ).
fof(f6223,plain,
( ~ sQ29_spl
| ~ sQ75_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f6222]) ).
fof(f6224,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1100,f1409]) ).
fof(f6225,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1100,f1374]) ).
fof(f6228,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(paramodulation,[status(thm)],[f1100,f703]) ).
fof(f6230,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1100,f554]) ).
fof(f6231,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(paramodulation,[status(thm)],[f1100,f541]) ).
fof(f6235,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1100,f420]) ).
fof(f6236,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1100,f168]) ).
fof(f6237,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1100,f163]) ).
fof(f6240,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1100,f159]) ).
fof(f6242,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1100,f156]) ).
fof(f6247,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,identity_for(g2),X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6235]) ).
fof(f6248,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6247]) ).
fof(f6249,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(forward_demodulation,[status(thm)],[f92,f6236]) ).
fof(f6250,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6237]) ).
fof(f6253,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6240]) ).
fof(f6254,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(forward_demodulation,[status(thm)],[f92,f6242]) ).
fof(f6257,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1278,f1409]) ).
fof(f6258,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1278,f1374]) ).
fof(f6259,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1278,f1373]) ).
fof(f6260,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1278,f1372]) ).
fof(f6261,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,f) ),
inference(paramodulation,[status(thm)],[f1278,f703]) ).
fof(f6262,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1278,f637]) ).
fof(f6267,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1278,f422]) ).
fof(f6269,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f1278,f168]) ).
fof(f6270,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,g,h,X0) ),
inference(paramodulation,[status(thm)],[f1278,f163]) ).
fof(f6271,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1278,f162]) ).
fof(f6272,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(paramodulation,[status(thm)],[f1278,f161]) ).
fof(f6273,plain,
! [X0] :
( ~ sQ50_spl
| X0 = identity_for(g2)
| ~ product(g2,h,g,X0) ),
inference(paramodulation,[status(thm)],[f1278,f159]) ).
fof(f6278,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,identity_for(g2),X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6267]) ).
fof(f6279,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6278]) ).
fof(f6282,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,f) ),
inference(forward_demodulation,[status(thm)],[f92,f6269]) ).
fof(f6283,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6270]) ).
fof(f6284,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f6271]) ).
fof(f6285,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f92,f6272]) ).
fof(f6286,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6273]) ).
fof(f6290,plain,
( ~ sQ29_spl
| product(g1,c,c,multiply(g1,c,d1)) ),
inference(forward_demodulation,[status(thm)],[f310,f4717]) ).
fof(f6291,plain,
( ~ sQ29_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f310,f6290]) ).
fof(f6292,plain,
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,c,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f6291]) ).
fof(f6293,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,inverse(g1,c),b,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f6292,f1334]) ).
fof(f6294,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,a,c,X0)
| ~ product(g1,inverse(g1,c),b,X0) ),
inference(resolution,[status(thm)],[f6292,f1333]) ).
fof(f6295,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,a,b,X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f6292,f173]) ).
fof(f6296,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,c,c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6292,f172]) ).
fof(f6297,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,inverse(g1,c),b,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f6292,f158]) ).
fof(f6298,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,inverse(g1,c),b,X0) ),
inference(resolution,[status(thm)],[f6292,f157]) ).
fof(f6301,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| X0 = c
| ~ product(g1,X0,c,b) ),
inference(resolution,[status(thm)],[f6292,f75]) ).
fof(f6302,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| X0 = c
| ~ product(g1,c,X0,b) ),
inference(resolution,[status(thm)],[f6292,f73]) ).
fof(f6305,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| X0 = b
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f6292,f67]) ).
fof(f6306,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| ~ sQ41_spl
| product(g1,b,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f6293]) ).
fof(f6307,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| ~ sQ41_spl
| product(g1,a,c,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f6294]) ).
fof(f6308,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,inverse(g1,c),b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6297]) ).
fof(f6338,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f4925]) ).
fof(f6340,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f4924]) ).
fof(f6341,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6340]) ).
fof(f6343,plain,
( ~ sQ25_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f4926]) ).
fof(f6345,plain,
( ~ sQ25_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f4927]) ).
fof(f6349,plain,
( ~ sQ50_spl
| product(g2,h,g,multiply(g2,h,inverse(g2,h))) ),
inference(forward_demodulation,[status(thm)],[f1100,f1203]) ).
fof(f6350,plain,
( ~ sQ50_spl
| product(g2,h,g,multiply(g2,h,g)) ),
inference(forward_demodulation,[status(thm)],[f1100,f6349]) ).
fof(f6359,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,multiply(g2,h,g)) ),
inference(resolution,[status(thm)],[f6350,f75]) ).
fof(f6363,plain,
! [X0] :
( ~ sQ50_spl
| X0 = multiply(g2,h,g)
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f6350,f67]) ).
fof(f6374,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f4937]) ).
fof(f6376,plain,
( ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f4928]) ).
fof(f6377,plain,
( ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6376]) ).
fof(f6378,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,b,c) ),
inference(forward_demodulation,[status(thm)],[f2772,f6377]) ).
fof(f6379,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| ~ sQ68_spl
| product(g1,a,b,X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f6378,f5977]) ).
fof(f6380,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| ~ sQ68_spl
| product(g1,c,c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6378,f5967]) ).
fof(f6381,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,inverse(g1,b),c,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f6378,f1334]) ).
fof(f6382,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,b),c,X0) ),
inference(resolution,[status(thm)],[f6378,f1333]) ).
fof(f6383,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,a,c,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f6378,f173]) ).
fof(f6384,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,b,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f6378,f172]) ).
fof(f6385,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,inverse(g1,b),c,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f6378,f158]) ).
fof(f6386,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,b),c,X0) ),
inference(resolution,[status(thm)],[f6378,f157]) ).
fof(f6387,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,b,X0)
| ~ product(g1,identity_for(g1),c,X0) ),
inference(resolution,[status(thm)],[f6378,f146]) ).
fof(f6388,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,identity_for(g1),c,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f6378,f139]) ).
fof(f6389,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| X0 = b
| ~ product(g1,X0,b,c) ),
inference(resolution,[status(thm)],[f6378,f75]) ).
fof(f6390,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| X0 = b
| ~ product(g1,b,X0,c) ),
inference(resolution,[status(thm)],[f6378,f73]) ).
fof(f6391,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f6378,f71]) ).
fof(f6392,plain,
! [X0,X1,X2] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,X1,X2)
| ~ product(g1,c,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f6378,f69]) ).
fof(f6393,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| X0 = c
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f6378,f67]) ).
fof(f6394,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ41_spl
| product(g1,c,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6381]) ).
fof(f6395,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ41_spl
| product(g1,a,b,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6382]) ).
fof(f6396,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,inverse(g1,b),c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6385]) ).
fof(f6397,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ41_spl
| product(g1,c,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6396]) ).
fof(f6398,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ41_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6386]) ).
fof(f6399,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ41_spl
| product(g1,a,b,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6398]) ).
fof(f6400,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6387]) ).
fof(f6401,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,a,c,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f6388]) ).
fof(f6412,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(resolution,[status(thm)],[f1149,f75]) ).
fof(f6416,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f1149,f67]) ).
fof(f6429,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f1150,f379]) ).
fof(f6430,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,h,X0)
| ~ product(g2,f,f,X0) ),
inference(resolution,[status(thm)],[f1150,f378]) ).
fof(f6433,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,h,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f1150,f146]) ).
fof(f6434,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f1150,f139]) ).
fof(f6435,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,h,f) ),
inference(resolution,[status(thm)],[f1150,f75]) ).
fof(f6436,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,g,X0,f) ),
inference(resolution,[status(thm)],[f1150,f73]) ).
fof(f6437,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,f,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f1150,f71]) ).
fof(f6438,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f1150,f69]) ).
fof(f6439,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f1150,f67]) ).
fof(f6446,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,h,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6433]) ).
fof(f6447,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6434]) ).
fof(f6448,plain,
( ~ sQ25_spl
| product(g1,c,b,multiply(g1,c,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f4929]) ).
fof(f6449,plain,
( ~ sQ25_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6448]) ).
fof(f6450,plain,
( ~ sQ25_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f6449]) ).
fof(f6451,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f4939]) ).
fof(f6452,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6451]) ).
fof(f6460,plain,
( ~ sQ25_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f3869]) ).
fof(f6462,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f3879]) ).
fof(f6469,plain,
( ~ sQ93_spl
| h = inverse(g2,h) ),
inference(resolution,[status(thm)],[f6144,f691]) ).
fof(f6471,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,inverse(g2,h),f,X0)
| ~ product(g2,f,h,X0) ),
inference(resolution,[status(thm)],[f6144,f1408]) ).
fof(f6472,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,f,h,X0)
| ~ product(g2,inverse(g2,h),f,X0) ),
inference(resolution,[status(thm)],[f6144,f1407]) ).
fof(f6473,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f6144,f379]) ).
fof(f6474,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,h,h,X0)
| ~ product(g2,f,f,X0) ),
inference(resolution,[status(thm)],[f6144,f378]) ).
fof(f6475,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,inverse(g2,h),f,X0)
| ~ product(g2,identity_for(g2),h,X0) ),
inference(resolution,[status(thm)],[f6144,f158]) ).
fof(f6476,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,inverse(g2,h),f,X0) ),
inference(resolution,[status(thm)],[f6144,f157]) ).
fof(f6477,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,h,h,X0)
| ~ product(g2,identity_for(g2),f,X0) ),
inference(resolution,[status(thm)],[f6144,f146]) ).
fof(f6478,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,identity_for(g2),f,X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f6144,f139]) ).
fof(f6479,plain,
! [X0] :
( ~ sQ93_spl
| X0 = h
| ~ product(g2,X0,h,f) ),
inference(resolution,[status(thm)],[f6144,f75]) ).
fof(f6480,plain,
! [X0] :
( ~ sQ93_spl
| X0 = h
| ~ product(g2,h,X0,f) ),
inference(resolution,[status(thm)],[f6144,f73]) ).
fof(f6481,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| product(g2,f,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f6144,f71]) ).
fof(f6482,plain,
! [X0,X1,X2] :
( ~ sQ93_spl
| product(g2,h,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(resolution,[status(thm)],[f6144,f69]) ).
fof(f6483,plain,
! [X0] :
( ~ sQ93_spl
| X0 = f
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f6144,f67]) ).
fof(f6484,plain,
( ~ sQ93_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f6469,f1221,f3489]) ).
fof(f6486,plain,
! [X0] :
( ~ sQ93_spl
| ~ sQ50_spl
| product(g2,g,f,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f6471]) ).
fof(f6487,plain,
! [X0] :
( ~ sQ93_spl
| ~ sQ50_spl
| product(g2,f,h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f6472]) ).
fof(f6488,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,inverse(g2,h),f,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6475]) ).
fof(f6489,plain,
! [X0] :
( ~ sQ93_spl
| ~ sQ50_spl
| product(g2,g,f,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f6488]) ).
fof(f6490,plain,
! [X0] :
( ~ sQ93_spl
| ~ sQ50_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f6476]) ).
fof(f6491,plain,
! [X0] :
( ~ sQ93_spl
| ~ sQ50_spl
| product(g2,f,h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6490]) ).
fof(f6492,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,h,h,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6477]) ).
fof(f6493,plain,
! [X0] :
( ~ sQ93_spl
| product(g2,f,f,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6478]) ).
fof(f6512,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,inverse(g2,h))) ),
inference(forward_demodulation,[status(thm)],[f1100,f3755]) ).
fof(f6513,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,g)) ),
inference(forward_demodulation,[status(thm)],[f1100,f6512]) ).
fof(f6514,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,inverse(g2,g),multiply(g2,g,g),X0)
| ~ product(g2,f,g,X0) ),
inference(resolution,[status(thm)],[f6513,f1408]) ).
fof(f6515,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,g,X0)
| ~ product(g2,inverse(g2,g),multiply(g2,g,g),X0) ),
inference(resolution,[status(thm)],[f6513,f1407]) ).
fof(f6516,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,multiply(g2,g,g),X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f6513,f379]) ).
fof(f6517,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,g,X0)
| ~ product(g2,f,multiply(g2,g,g),X0) ),
inference(resolution,[status(thm)],[f6513,f378]) ).
fof(f6518,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,inverse(g2,g),multiply(g2,g,g),X0)
| ~ product(g2,identity_for(g2),g,X0) ),
inference(resolution,[status(thm)],[f6513,f158]) ).
fof(f6519,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,inverse(g2,g),multiply(g2,g,g),X0) ),
inference(resolution,[status(thm)],[f6513,f157]) ).
fof(f6520,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,g,X0)
| ~ product(g2,identity_for(g2),multiply(g2,g,g),X0) ),
inference(resolution,[status(thm)],[f6513,f146]) ).
fof(f6521,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),multiply(g2,g,g),X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f6513,f139]) ).
fof(f6522,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,X0,g,multiply(g2,g,g)) ),
inference(resolution,[status(thm)],[f6513,f75]) ).
fof(f6523,plain,
! [X0] :
( ~ sQ50_spl
| X0 = g
| ~ product(g2,g,X0,multiply(g2,g,g)) ),
inference(resolution,[status(thm)],[f6513,f73]) ).
fof(f6524,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,multiply(g2,g,g),X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f6513,f71]) ).
fof(f6525,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,g,X1,X2)
| ~ product(g2,multiply(g2,g,g),X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(resolution,[status(thm)],[f6513,f69]) ).
fof(f6526,plain,
! [X0] :
( ~ sQ50_spl
| X0 = multiply(g2,g,g)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f6513,f67]) ).
fof(f6527,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,h,multiply(g2,g,g),X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f6514]) ).
fof(f6528,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,g,X0)
| ~ product(g2,h,multiply(g2,g,g),X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f6515]) ).
fof(f6529,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,inverse(g2,g),multiply(g2,g,g),X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6518]) ).
fof(f6530,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,h,multiply(g2,g,g),X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f6529]) ).
fof(f6531,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,h,multiply(g2,g,g),X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f6519]) ).
fof(f6532,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,g,X0)
| ~ product(g2,h,multiply(g2,g,g),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6531]) ).
fof(f6533,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,g,X0)
| ~ product(g2,f,multiply(g2,g,g),X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6520]) ).
fof(f6534,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,multiply(g2,g,g),X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6521]) ).
fof(f6535,plain,
( ~ sQ50_spl
| group_member(multiply(g2,g,g),g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3756]) ).
fof(f6536,plain,
( ~ sQ50_spl
| product(g2,h,multiply(g2,g,g),multiply(g2,h,multiply(g2,g,g))) ),
inference(resolution,[status(thm)],[f6535,f211]) ).
fof(f6537,plain,
( ~ sQ50_spl
| group_member(multiply(g2,h,multiply(g2,g,g)),g2) ),
inference(resolution,[status(thm)],[f6535,f210]) ).
fof(f6538,plain,
( ~ sQ50_spl
| product(g2,g,multiply(g2,g,g),multiply(g2,g,multiply(g2,g,g))) ),
inference(resolution,[status(thm)],[f6535,f197]) ).
fof(f6539,plain,
( ~ sQ50_spl
| group_member(multiply(g2,g,multiply(g2,g,g)),g2) ),
inference(resolution,[status(thm)],[f6535,f196]) ).
fof(f6540,plain,
( ~ sQ50_spl
| group_member(multiply(g2,f,multiply(g2,g,g)),g2) ),
inference(resolution,[status(thm)],[f6535,f187]) ).
fof(f6541,plain,
( ~ sQ50_spl
| product(g2,f,multiply(g2,g,g),multiply(g2,f,multiply(g2,g,g))) ),
inference(resolution,[status(thm)],[f6535,f178]) ).
fof(f6543,plain,
( ~ sQ50_spl
| group_member(multiply(g2,identity_for(g2),multiply(g2,g,g)),g2) ),
inference(resolution,[status(thm)],[f6535,f192]) ).
fof(f6544,plain,
( ~ sQ50_spl
| product(g2,identity_for(g2),multiply(g2,g,g),multiply(g2,identity_for(g2),multiply(g2,g,g))) ),
inference(resolution,[status(thm)],[f6535,f183]) ).
fof(f6545,plain,
! [X0] :
( ~ sQ50_spl
| group_member(multiply(g2,multiply(g2,g,g),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f6535,f65]) ).
fof(f6546,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,multiply(g2,g,g),X0,multiply(g2,multiply(g2,g,g),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f6535,f64]) ).
fof(f6547,plain,
( ~ sQ50_spl
| group_member(inverse(g2,multiply(g2,g,g)),g2) ),
inference(resolution,[status(thm)],[f6535,f61]) ).
fof(f6549,plain,
( ~ sQ50_spl
| group_member(multiply(g2,f,multiply(g2,g,g)),g2) ),
inference(forward_demodulation,[status(thm)],[f92,f6543]) ).
fof(f6550,plain,
( ~ sQ50_spl
| product(g2,f,multiply(g2,g,g),multiply(g2,identity_for(g2),multiply(g2,g,g))) ),
inference(forward_demodulation,[status(thm)],[f92,f6544]) ).
fof(f6551,plain,
( ~ sQ50_spl
| product(g2,f,multiply(g2,g,g),multiply(g2,f,multiply(g2,g,g))) ),
inference(forward_demodulation,[status(thm)],[f92,f6550]) ).
fof(f6552,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f5221]) ).
fof(f6554,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f4989,f1996]) ).
fof(f6556,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f4989,f1997]) ).
fof(f6561,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,h) ),
inference(backward_demodulation,[status(thm)],[f3365,f6513]) ).
fof(f6572,plain,
( ~ sQ25_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f5222]) ).
fof(f6574,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,b,c,multiply(g1,b,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f4989,f1998]) ).
fof(f6575,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f4989,f6574]) ).
fof(f6577,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,c,c,multiply(g1,c,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f4989,f1999]) ).
fof(f6578,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f4989,f6577]) ).
fof(f6579,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| ~ sQ73_spl
| product(g1,c,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f6578]) ).
fof(f6590,plain,
( ~ sQ25_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f5223]) ).
fof(f6594,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,inverse(g2,g),h,X0)
| ~ product(g2,f,g,X0) ),
inference(resolution,[status(thm)],[f6561,f1408]) ).
fof(f6595,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,g,X0)
| ~ product(g2,inverse(g2,g),h,X0) ),
inference(resolution,[status(thm)],[f6561,f1407]) ).
fof(f6596,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,h,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f6561,f379]) ).
fof(f6597,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,X0)
| ~ product(g2,f,h,X0) ),
inference(resolution,[status(thm)],[f6561,f378]) ).
fof(f6598,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,inverse(g2,g),h,X0)
| ~ product(g2,identity_for(g2),g,X0) ),
inference(resolution,[status(thm)],[f6561,f158]) ).
fof(f6599,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,inverse(g2,g),h,X0) ),
inference(resolution,[status(thm)],[f6561,f157]) ).
fof(f6600,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,X0)
| ~ product(g2,identity_for(g2),h,X0) ),
inference(resolution,[status(thm)],[f6561,f146]) ).
fof(f6601,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,identity_for(g2),h,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f6561,f139]) ).
fof(f6602,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| X0 = g
| ~ product(g2,X0,g,h) ),
inference(resolution,[status(thm)],[f6561,f75]) ).
fof(f6603,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| X0 = g
| ~ product(g2,g,X0,h) ),
inference(resolution,[status(thm)],[f6561,f73]) ).
fof(f6606,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| X0 = h
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f6561,f67]) ).
fof(f6607,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f6594]) ).
fof(f6608,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,g,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f6595]) ).
fof(f6609,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,inverse(g2,g),h,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6598]) ).
fof(f6610,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f6609]) ).
fof(f6611,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,identity_for(g2),g,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f6599]) ).
fof(f6612,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,g,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6611]) ).
fof(f6613,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6600]) ).
fof(f6614,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,h,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f6601]) ).
fof(f6615,plain,
( ~ sQ25_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f297,f5233]) ).
fof(f6626,plain,
( ~ sQ50_spl
| product(g2,h,h,multiply(g2,h,inverse(g2,g))) ),
inference(forward_demodulation,[status(thm)],[f1278,f3775]) ).
fof(f6627,plain,
( ~ sQ50_spl
| product(g2,h,h,multiply(g2,h,h)) ),
inference(forward_demodulation,[status(thm)],[f1278,f6626]) ).
fof(f6628,plain,
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,h,h,g) ),
inference(forward_demodulation,[status(thm)],[f3493,f6627]) ).
fof(f6637,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| X0 = h
| ~ product(g2,X0,h,g) ),
inference(resolution,[status(thm)],[f6628,f75]) ).
fof(f6638,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| X0 = h
| ~ product(g2,h,X0,g) ),
inference(resolution,[status(thm)],[f6628,f73]) ).
fof(f6641,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| X0 = g
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f6628,f67]) ).
fof(f6650,plain,
( ~ sQ50_spl
| group_member(multiply(g2,h,h),g2) ),
inference(forward_demodulation,[status(thm)],[f1278,f3776]) ).
fof(f6652,plain,
( ~ sQ50_spl
| product(g2,g,h,multiply(g2,g,inverse(g2,g))) ),
inference(forward_demodulation,[status(thm)],[f1278,f3777]) ).
fof(f6653,plain,
( ~ sQ50_spl
| product(g2,g,h,multiply(g2,g,h)) ),
inference(forward_demodulation,[status(thm)],[f1278,f6652]) ).
fof(f6657,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f204]) ).
fof(f6658,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f6657]) ).
fof(f6659,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ29_spl
| ~ sQ25_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f6658]) ).
fof(f6662,plain,
( ~ sQ29_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f5297]) ).
fof(f6664,plain,
( ~ sQ29_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f5298]) ).
fof(f6666,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f1566]) ).
fof(f6667,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f6666]) ).
fof(f6669,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,a,X0)
| ~ product(g1,a,inverse(g1,d2),X0) ),
inference(forward_demodulation,[status(thm)],[f270,f5154]) ).
fof(f6670,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ25_spl
| product(g1,d1,a,X0)
| ~ product(g1,a,inverse(g1,b),X0) ),
inference(forward_demodulation,[status(thm)],[f297,f6669]) ).
fof(f6671,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ41_spl
| product(g1,d1,a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6670]) ).
fof(f6677,plain,
( ~ sQ50_spl
| group_member(multiply(g2,g,h),g2) ),
inference(forward_demodulation,[status(thm)],[f1278,f3778]) ).
fof(f6691,plain,
( ~ sQ17_spl
| ~ sQ41_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,c))) ),
inference(forward_demodulation,[status(thm)],[f1004,f778]) ).
fof(f6692,plain,
( ~ sQ17_spl
| ~ sQ41_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1004,f6691]) ).
fof(f6694,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f1433]) ).
fof(f6703,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f1431]) ).
fof(f6705,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ25_spl
| product(g1,d1,a,X0)
| ~ product(g1,a,inverse(g1,b),X0) ),
inference(forward_demodulation,[status(thm)],[f297,f5211]) ).
fof(f6706,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ25_spl
| ~ sQ41_spl
| product(g1,d1,a,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f6705]) ).
fof(f6712,plain,
( ~ sQ84_spl
| product(g2,g,h,f) ),
inference(forward_demodulation,[status(thm)],[f3262,f1117]) ).
fof(f6716,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f5220]) ).
fof(f6717,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6716]) ).
fof(f6721,plain,
( ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f5224]) ).
fof(f6722,plain,
( ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6721]) ).
fof(f6724,plain,
( ~ sQ25_spl
| product(g1,c,b,multiply(g1,c,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f5225]) ).
fof(f6725,plain,
( ~ sQ25_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6724]) ).
fof(f6726,plain,
( ~ sQ25_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f6725]) ).
fof(f6728,plain,
( ~ sQ41_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,c))) ),
inference(forward_demodulation,[status(thm)],[f1004,f1966]) ).
fof(f6729,plain,
( ~ sQ41_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1004,f6728]) ).
fof(f6731,plain,
( ~ sQ41_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1004,f1964]) ).
fof(f6735,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f297,f5235]) ).
fof(f6736,plain,
( ~ sQ25_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f297,f6735]) ).
fof(f6738,plain,
! [X0] :
( ~ sQ29_spl
| product(g1,a,d3,X0)
| ~ product(g1,c,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5238]) ).
fof(f6739,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| product(g1,a,d3,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f6738]) ).
fof(f6740,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f6739]) ).
fof(f6742,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f5239]) ).
fof(f6743,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f6742]) ).
fof(f6745,plain,
( ~ sQ41_spl
| product(g1,c,b,multiply(g1,c,inverse(g1,c))) ),
inference(forward_demodulation,[status(thm)],[f1004,f1956]) ).
fof(f6746,plain,
( ~ sQ41_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f1004,f6745]) ).
fof(f6747,plain,
( ~ sQ41_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f6746]) ).
fof(f6748,plain,
( ~ sQ41_spl
| product(g1,b,b,multiply(g1,b,inverse(g1,c))) ),
inference(forward_demodulation,[status(thm)],[f1004,f1955]) ).
fof(f6749,plain,
( ~ sQ41_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f1004,f6748]) ).
fof(f6750,plain,
( ~ sQ41_spl
| ~ sQ68_spl
| product(g1,b,b,c) ),
inference(forward_demodulation,[status(thm)],[f2772,f6749]) ).
fof(f6751,plain,
( ~ sQ41_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1004,f1954]) ).
fof(f6753,plain,
( ~ sQ29_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f5757]) ).
fof(f6755,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,d1),d3,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f5249]) ).
fof(f6756,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ29_spl
| product(g1,inverse(g1,c),d3,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f6755]) ).
fof(f6757,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ29_spl
| ~ sQ41_spl
| product(g1,b,d3,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f6756]) ).
fof(f6759,plain,
! [X0] :
( ~ sQ29_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,c),d3,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5250]) ).
fof(f6760,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ41_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,d3,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f6759]) ).
fof(f6761,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ41_spl
| ~ sQ17_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f6760]) ).
fof(f6763,plain,
! [X0] :
( ~ sQ17_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f5251]) ).
fof(f6764,plain,
! [X0] :
( ~ sQ17_spl
| ~ sQ29_spl
| product(g1,c,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f6763]) ).
fof(f6766,plain,
( ~ sQ41_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1004,f1953]) ).
fof(f6771,plain,
( ~ sQ29_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f310,f5758]) ).
fof(f6773,plain,
! [X0] :
( ~ sQ29_spl
| product(g1,a,d3,X0)
| ~ product(g1,c,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5252]) ).
fof(f6774,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| product(g1,a,d3,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f6773]) ).
fof(f6778,plain,
( ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f870]) ).
fof(f6779,plain,
( ~ sQ68_spl
| product(g1,b,b,c) ),
inference(forward_demodulation,[status(thm)],[f2772,f913]) ).
fof(f6780,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5276]) ).
fof(f6784,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5277]) ).
fof(f6793,plain,
( ~ sQ29_spl
| product(g1,b,c,multiply(g1,b,d1)) ),
inference(forward_demodulation,[status(thm)],[f310,f5299]) ).
fof(f6794,plain,
( ~ sQ29_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f310,f6793]) ).
fof(f6795,plain,
( ~ sQ29_spl
| ~ sQ75_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f6794]) ).
fof(f6796,plain,
( ~ sQ29_spl
| product(g1,c,c,multiply(g1,c,d1)) ),
inference(forward_demodulation,[status(thm)],[f310,f5300]) ).
fof(f6797,plain,
( ~ sQ29_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f310,f6796]) ).
fof(f6808,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f4989,f5347]) ).
fof(f6810,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f4989,f5348]) ).
fof(f6812,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,b,c,multiply(g1,b,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f4989,f5349]) ).
fof(f6813,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f4989,f6812]) ).
fof(f6816,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,c,c,multiply(g1,c,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f4989,f5350]) ).
fof(f6817,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f4989,f6816]) ).
fof(f6818,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| ~ sQ73_spl
| product(g1,c,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f6817]) ).
fof(f6832,plain,
( ~ sQ41_spl
| product(g1,a,b,multiply(g1,a,inverse(g1,c))) ),
inference(forward_demodulation,[status(thm)],[f1004,f1951]) ).
fof(f6833,plain,
( ~ sQ41_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1004,f6832]) ).
fof(f6835,plain,
( ~ sQ75_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f912]) ).
fof(f6836,plain,
( ~ sQ41_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1004,f1952]) ).
fof(f6843,plain,
( ~ sQ29_spl
| product(g1,b,c,multiply(g1,b,d1)) ),
inference(forward_demodulation,[status(thm)],[f310,f5759]) ).
fof(f6844,plain,
( ~ sQ29_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f310,f6843]) ).
fof(f6845,plain,
( ~ sQ29_spl
| ~ sQ75_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f6844]) ).
fof(f6846,plain,
( ~ sQ29_spl
| product(g1,c,c,multiply(g1,c,d1)) ),
inference(forward_demodulation,[status(thm)],[f310,f5760]) ).
fof(f6847,plain,
( ~ sQ29_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f310,f6846]) ).
fof(f6851,plain,
( ~ sQ52_spl
| inverse(g2,g) = h ),
inference(resolution,[status(thm)],[f1446,f219]) ).
fof(f6852,plain,
( ~ sQ73_spl
| product(g1,c,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f869]) ).
fof(f6861,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5786]) ).
fof(f6863,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5787]) ).
fof(f6866,plain,
( ~ sQ52_spl
| inverse(g2,g) = h ),
inference(resolution,[status(thm)],[f1452,f218]) ).
fof(f6868,plain,
( ~ sQ84_spl
| inverse(g2,h) = g ),
inference(resolution,[status(thm)],[f4120,f219]) ).
fof(f6874,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5840]) ).
fof(f6876,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5841]) ).
fof(f6882,plain,
( ~ sQ17_spl
| ~ sQ75_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f5165]) ).
fof(f6888,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f1504]) ).
fof(f6892,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f4989,f5904]) ).
fof(f6894,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f4989,f5905]) ).
fof(f6896,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,b,c,multiply(g1,b,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f4989,f5906]) ).
fof(f6897,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f4989,f6896]) ).
fof(f6899,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,c,c,multiply(g1,c,inverse(g1,b))) ),
inference(forward_demodulation,[status(thm)],[f4989,f5907]) ).
fof(f6900,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f4989,f6899]) ).
fof(f6901,plain,
( ~ sQ25_spl
| ~ sQ41_spl
| ~ sQ73_spl
| product(g1,c,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f6900]) ).
fof(f6904,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| group_member(inverse(g1,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2772,f5616]) ).
fof(f6912,plain,
( ~ sQ17_spl
| ~ sQ73_spl
| product(g1,c,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f5169]) ).
fof(f6915,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,inverse(g2,h))) ),
inference(forward_demodulation,[status(thm)],[f1100,f1205]) ).
fof(f6916,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,g)) ),
inference(forward_demodulation,[status(thm)],[f1100,f6915]) ).
fof(f6923,plain,
! [X0] :
( ~ sQ25_spl
| product(g1,inverse(g1,d1),d3,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f297,f5236]) ).
fof(f6924,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ29_spl
| product(g1,inverse(g1,c),d3,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f6923]) ).
fof(f6925,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ29_spl
| ~ sQ41_spl
| product(g1,b,d3,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f6924]) ).
fof(f6940,plain,
! [X0] :
( ~ sQ29_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,c),d3,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5237]) ).
fof(f6941,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ41_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,d3,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f6940]) ).
fof(f6942,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ41_spl
| ~ sQ17_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f270,f6941]) ).
fof(f6946,plain,
( ~ sQ50_spl
| group_member(multiply(g2,g,g),g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f1206]) ).
fof(f6950,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f1494]) ).
fof(f6952,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5263]) ).
fof(f6960,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f1493]) ).
fof(f6962,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5264]) ).
fof(f6969,plain,
( ~ sQ50_spl
| group_member(multiply(g2,g,h),g2) ),
inference(forward_demodulation,[status(thm)],[f1278,f1479]) ).
fof(f6975,plain,
( ~ sQ50_spl
| product(g2,g,h,multiply(g2,g,inverse(g2,g))) ),
inference(forward_demodulation,[status(thm)],[f1278,f1478]) ).
fof(f6976,plain,
( ~ sQ50_spl
| product(g2,g,h,multiply(g2,g,h)) ),
inference(forward_demodulation,[status(thm)],[f1278,f6975]) ).
fof(f6978,plain,
( ~ sQ50_spl
| group_member(multiply(g2,h,h),g2) ),
inference(forward_demodulation,[status(thm)],[f1278,f1477]) ).
fof(f6980,plain,
( ~ sQ50_spl
| product(g2,h,h,multiply(g2,h,inverse(g2,g))) ),
inference(forward_demodulation,[status(thm)],[f1278,f1476]) ).
fof(f6981,plain,
( ~ sQ50_spl
| product(g2,h,h,multiply(g2,h,h)) ),
inference(forward_demodulation,[status(thm)],[f1278,f6980]) ).
fof(f6983,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2772,f5607]) ).
fof(f6990,plain,
( ~ sQ89_spl
| product(g2,g,g,h) ),
inference(forward_demodulation,[status(thm)],[f3365,f1118]) ).
fof(f6991,plain,
( ~ sQ94_spl
| product(g2,h,h,g) ),
inference(forward_demodulation,[status(thm)],[f3493,f1197]) ).
fof(f6992,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2772,f5608]) ).
fof(f7000,plain,
( ~ sQ104_spl
| ~ sQ50_spl
| multiply(g2,g,g) = h ),
inference(forward_demodulation,[status(thm)],[f1100,f3811]) ).
fof(f7011,plain,
( ~ sQ59_spl
| group_member(inverse(g1,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2453,f2445]) ).
fof(f7013,plain,
( ~ sQ59_spl
| group_member(multiply(g1,b,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2453,f2436]) ).
fof(f7015,plain,
( ~ sQ59_spl
| group_member(multiply(g1,c,c),g1) ),
inference(forward_demodulation,[status(thm)],[f2453,f2437]) ).
fof(f7017,plain,
( ~ sQ89_spl
| ~ sQ103_spl
| ~ sQ50_spl
| g = h ),
inference(backward_demodulation,[status(thm)],[f7018,f3365]) ).
fof(f7018,plain,
( ~ sQ103_spl
| ~ sQ50_spl
| multiply(g2,g,g) = g ),
inference(forward_demodulation,[status(thm)],[f1100,f3808]) ).
fof(f7019,plain,
( ~ sQ89_spl
| ~ sQ103_spl
| ~ sQ50_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f7017,f334,f1086,f3807,f3364]) ).
fof(f7020,plain,
( sQ103_spl
| ~ sQ50_spl
| multiply(g2,g,g) != g ),
inference(forward_demodulation,[status(thm)],[f1100,f3809]) ).
fof(f7022,plain,
( ~ sQ59_spl
| product(g1,b,c,multiply(g1,b,multiply(g1,c,a))) ),
inference(forward_demodulation,[status(thm)],[f2453,f2438]) ).
fof(f7023,plain,
( ~ sQ59_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f2453,f7022]) ).
fof(f7024,plain,
( ~ sQ59_spl
| ~ sQ75_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f7023]) ).
fof(f7025,plain,
( ~ sQ59_spl
| product(g1,c,c,multiply(g1,c,multiply(g1,c,a))) ),
inference(forward_demodulation,[status(thm)],[f2453,f2439]) ).
fof(f7026,plain,
( ~ sQ59_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f2453,f7025]) ).
fof(f7027,plain,
( ~ sQ59_spl
| ~ sQ73_spl
| product(g1,c,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f7026]) ).
fof(f7030,plain,
( ~ sQ29_spl
| ~ sQ73_spl
| ~ sQ41_spl
| product(g1,b,b,c) ),
inference(resolution,[status(thm)],[f6306,f93]) ).
fof(f7031,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| product(g1,c,b,multiply(g1,c,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f1509,f1497]) ).
fof(f7032,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f1509,f7031]) ).
fof(f7033,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f7032]) ).
fof(f7034,plain,
( ~ sQ61_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2519,f2514]) ).
fof(f7042,plain,
( ~ sQ89_spl
| ~ sQ102_spl
| ~ sQ50_spl
| f = h ),
inference(backward_demodulation,[status(thm)],[f7043,f3365]) ).
fof(f7043,plain,
( ~ sQ102_spl
| ~ sQ50_spl
| multiply(g2,g,g) = f ),
inference(forward_demodulation,[status(thm)],[f1100,f3805]) ).
fof(f7044,plain,
( ~ sQ89_spl
| ~ sQ102_spl
| ~ sQ50_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f7042,f331,f1086,f3804,f3364]) ).
fof(f7045,plain,
( sQ102_spl
| ~ sQ50_spl
| multiply(g2,g,g) != f ),
inference(forward_demodulation,[status(thm)],[f1100,f3806]) ).
fof(f7049,plain,
( ~ sQ61_spl
| product(g1,a,b,multiply(g1,a,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f2519,f2503]) ).
fof(f7050,plain,
( ~ sQ61_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f2519,f7049]) ).
fof(f7052,plain,
( ~ sQ61_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2519,f2504]) ).
fof(f7055,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| product(g1,b,b,multiply(g1,b,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f1509,f1495]) ).
fof(f7056,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f1509,f7055]) ).
fof(f7057,plain,
( ~ sQ17_spl
| ~ sQ55_spl
| ~ sQ68_spl
| product(g1,b,b,c) ),
inference(forward_demodulation,[status(thm)],[f2772,f7056]) ).
fof(f7060,plain,
( ~ sQ61_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2519,f2505]) ).
fof(f7062,plain,
( ~ sQ61_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2519,f2506]) ).
fof(f7064,plain,
( ~ sQ107_spl
| ~ sQ50_spl
| multiply(g2,f,g) = h ),
inference(forward_demodulation,[status(thm)],[f1100,f3836]) ).
fof(f7065,plain,
( ~ sQ107_spl
| ~ sQ50_spl
| g = h ),
inference(forward_demodulation,[status(thm)],[f2667,f7064]) ).
fof(f7066,plain,
( ~ sQ107_spl
| ~ sQ50_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7065,f88]) ).
fof(f7067,plain,
( ~ sQ107_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f7066]) ).
fof(f7071,plain,
( ~ sQ105_spl
| ~ sQ50_spl
| g = f ),
inference(backward_demodulation,[status(thm)],[f7072,f2667]) ).
fof(f7072,plain,
( ~ sQ105_spl
| ~ sQ50_spl
| multiply(g2,f,g) = f ),
inference(forward_demodulation,[status(thm)],[f1100,f3830]) ).
fof(f7073,plain,
( ~ sQ105_spl
| ~ sQ50_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f7071,f341,f1086,f3829]) ).
fof(f7075,plain,
( ~ sQ61_spl
| product(g1,b,b,multiply(g1,b,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f2519,f2507]) ).
fof(f7076,plain,
( ~ sQ61_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f2519,f7075]) ).
fof(f7077,plain,
( ~ sQ61_spl
| ~ sQ68_spl
| product(g1,b,b,c) ),
inference(forward_demodulation,[status(thm)],[f2772,f7076]) ).
fof(f7078,plain,
( ~ sQ61_spl
| product(g1,c,b,multiply(g1,c,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f2519,f2508]) ).
fof(f7079,plain,
( ~ sQ61_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f2519,f7078]) ).
fof(f7080,plain,
( ~ sQ61_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f7079]) ).
fof(f7081,plain,
( ~ sQ61_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f2519,f2525]) ).
fof(f7088,plain,
( ~ sQ61_spl
| product(g1,a,b,multiply(g1,a,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f2519,f2527]) ).
fof(f7089,plain,
( ~ sQ61_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f2519,f7088]) ).
fof(f7095,plain,
( ~ sQ73_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f3034,f3029]) ).
fof(f7105,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,c,multiply(g1,b,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f2772,f5609]) ).
fof(f7106,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,c,multiply(g1,b,c)) ),
inference(forward_demodulation,[status(thm)],[f2772,f7105]) ).
fof(f7107,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ75_spl
| product(g1,b,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f7106]) ).
fof(f7110,plain,
( ~ sQ63_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2547,f2536]) ).
fof(f7112,plain,
( ~ sQ63_spl
| group_member(multiply(g1,c,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2547,f2537]) ).
fof(f7118,plain,
( ~ sQ89_spl
| group_member(inverse(g2,h),g2) ),
inference(forward_demodulation,[status(thm)],[f3365,f3357]) ).
fof(f7120,plain,
( ~ sQ63_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f2547,f2538]) ).
fof(f7121,plain,
( ~ sQ63_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f2547,f7120]) ).
fof(f7123,plain,
( ~ sQ63_spl
| product(g1,c,a,multiply(g1,c,multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f2547,f2539]) ).
fof(f7124,plain,
( ~ sQ63_spl
| product(g1,c,a,multiply(g1,c,a)) ),
inference(forward_demodulation,[status(thm)],[f2547,f7123]) ).
fof(f7128,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,c,multiply(g1,c,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f2772,f5610]) ).
fof(f7129,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,c,multiply(g1,c,c)) ),
inference(forward_demodulation,[status(thm)],[f2772,f7128]) ).
fof(f7130,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ73_spl
| product(g1,c,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f7129]) ).
fof(f7137,plain,
group_member(inverse(g2,g),g2),
inference(forward_demodulation,[status(thm)],[f3453,f3385]) ).
fof(f7139,plain,
( ~ sQ94_spl
| group_member(inverse(g2,g),g2) ),
inference(forward_demodulation,[status(thm)],[f3493,f3488]) ).
fof(f7148,plain,
( ~ sQ55_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f4041]) ).
fof(f7151,plain,
group_member(inverse(g2,h),g2),
inference(forward_demodulation,[status(thm)],[f3628,f3538]) ).
fof(f7174,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5773]) ).
fof(f7179,plain,
! [X0] :
( ~ sQ73_spl
| X0 = c
| ~ product(g1,X0,c,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f2739]) ).
fof(f7180,plain,
! [X0] :
( ~ sQ73_spl
| X0 = c
| ~ product(g1,c,X0,b) ),
inference(forward_demodulation,[status(thm)],[f3034,f2740]) ).
fof(f7183,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5774]) ).
fof(f7185,plain,
! [X0] :
( ~ sQ73_spl
| X0 = b
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f3034,f2743]) ).
fof(f7186,plain,
! [X0] :
( ~ sQ69_spl
| X0 = c
| ~ product(g1,X0,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f2788]) ).
fof(f7187,plain,
! [X0] :
( ~ sQ69_spl
| X0 = b
| ~ product(g1,c,X0,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f2789]) ).
fof(f7188,plain,
! [X0] :
( ~ sQ69_spl
| X0 = a
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f2833,f2792]) ).
fof(f7189,plain,
! [X0] :
( ~ sQ75_spl
| X0 = b
| ~ product(g1,X0,c,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f2806]) ).
fof(f7190,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,inverse(g1,c),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5827]) ).
fof(f7192,plain,
! [X0] :
( ~ sQ75_spl
| X0 = c
| ~ product(g1,b,X0,a) ),
inference(forward_demodulation,[status(thm)],[f3062,f2807]) ).
fof(f7193,plain,
! [X0] :
( ~ sQ75_spl
| X0 = a
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f3062,f2810]) ).
fof(f7199,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,a,b,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f3034,f2733]) ).
fof(f7200,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ29_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,c),a,X0) ),
inference(forward_demodulation,[status(thm)],[f310,f5828]) ).
fof(f7202,plain,
( ~ sQ73_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f3034,f3019]) ).
fof(f7204,plain,
( ~ sQ75_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f3062,f3050]) ).
fof(f7206,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,c,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f3034,f2734]) ).
fof(f7207,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,c,c,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f3034,f2748]) ).
fof(f7208,plain,
( ~ sQ73_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f3034,f3020]) ).
fof(f7210,plain,
( ~ sQ73_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f3034,f3021]) ).
fof(f7212,plain,
( ~ sQ73_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f3034,f3040]) ).
fof(f7214,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,a,b,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f3034,f2749]) ).
fof(f7215,plain,
! [X0,X1,X2] :
( ~ sQ73_spl
| product(g1,b,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3034,f2741]) ).
fof(f7216,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,b,c,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f7215,f6292]) ).
fof(f7217,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ73_spl
| product(g1,b,b,X0)
| ~ product(g1,c,a,X0) ),
inference(resolution,[status(thm)],[f7215,f5824]) ).
fof(f7218,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,b,inverse(g1,c),X0)
| ~ product(g1,c,a,X0) ),
inference(resolution,[status(thm)],[f7215,f213]) ).
fof(f7219,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,b,a,X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f7215,f94]) ).
fof(f7220,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,b,inverse(g1,c),X0)
| ~ product(g1,c,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f7215,f63]) ).
fof(f7221,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,b,identity_for(g1),X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f7215,f60]) ).
fof(f7222,plain,
! [X0] :
( ~ sQ73_spl
| ~ sQ41_spl
| product(g1,b,b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f7218]) ).
fof(f7223,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,b,inverse(g1,c),X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f7220]) ).
fof(f7224,plain,
! [X0] :
( ~ sQ73_spl
| ~ sQ41_spl
| product(g1,b,b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f7223]) ).
fof(f7225,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,b,a,X0)
| ~ product(g1,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f7221]) ).
fof(f7226,plain,
! [X0,X1,X2] :
( ~ sQ73_spl
| product(g1,c,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3034,f2742]) ).
fof(f7227,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| product(g1,c,b,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f7226,f6292]) ).
fof(f7228,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ73_spl
| product(g1,c,a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f7226,f5824]) ).
fof(f7229,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,c,a,X0)
| ~ product(g1,b,inverse(g1,c),X0) ),
inference(resolution,[status(thm)],[f7226,f213]) ).
fof(f7230,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,c,c,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f7226,f94]) ).
fof(f7231,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,c,identity_for(g1),X0)
| ~ product(g1,b,inverse(g1,c),X0) ),
inference(resolution,[status(thm)],[f7226,f63]) ).
fof(f7232,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,c,c,X0)
| ~ product(g1,b,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f7226,f60]) ).
fof(f7233,plain,
! [X0] :
( ~ sQ73_spl
| ~ sQ41_spl
| product(g1,c,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f7229]) ).
fof(f7234,plain,
! [X0] :
( ~ sQ73_spl
| ~ sQ41_spl
| product(g1,c,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f7231]) ).
fof(f7235,plain,
! [X0] :
( ~ sQ73_spl
| ~ sQ41_spl
| product(g1,c,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f7234]) ).
fof(f7236,plain,
! [X0] :
( ~ sQ73_spl
| product(g1,c,c,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f7232]) ).
fof(f7240,plain,
! [X0] :
( ~ sQ69_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f2833,f2782]) ).
fof(f7241,plain,
! [X0] :
( ~ sQ69_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f2833,f2783]) ).
fof(f7242,plain,
( ~ sQ75_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f3062,f3051]) ).
fof(f7244,plain,
( ~ sQ75_spl
| group_member(multiply(g1,c,a),g1) ),
inference(forward_demodulation,[status(thm)],[f3062,f3052]) ).
fof(f7246,plain,
( ~ sQ75_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f3062,f3071]) ).
fof(f7248,plain,
! [X0] :
( ~ sQ69_spl
| product(g1,c,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f2833,f2797]) ).
fof(f7249,plain,
! [X0] :
( ~ sQ69_spl
| product(g1,a,a,X0)
| ~ product(g1,c,b,X0) ),
inference(forward_demodulation,[status(thm)],[f2833,f2798]) ).
fof(f7250,plain,
! [X0,X1,X2] :
( ~ sQ69_spl
| product(g1,a,X0,X2)
| ~ product(g1,c,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f2833,f2790]) ).
fof(f7253,plain,
! [X0] :
( ~ sQ94_spl
| X0 = h
| ~ product(g2,X0,h,g) ),
inference(forward_demodulation,[status(thm)],[f3493,f3566]) ).
fof(f7254,plain,
! [X0,X1,X2] :
( ~ sQ69_spl
| product(g1,c,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f2833,f2791]) ).
fof(f7255,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,a,a,X0)
| ~ product(g1,b,c,X0) ),
inference(forward_demodulation,[status(thm)],[f3062,f2800]) ).
fof(f7263,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,b,c,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f3062,f2801]) ).
fof(f7264,plain,
( ~ sQ75_spl
| product(g1,b,c,a) ),
inference(resolution,[status(thm)],[f7263,f93]) ).
fof(f7265,plain,
( ~ sQ75_spl
| product(g1,b,c,a) ),
inference(resolution,[status(thm)],[f7263,f94]) ).
fof(f7268,plain,
! [X0] :
( ~ sQ94_spl
| X0 = h
| ~ product(g2,h,X0,g) ),
inference(forward_demodulation,[status(thm)],[f3493,f3567]) ).
fof(f7269,plain,
! [X0] :
( ~ sQ94_spl
| X0 = g
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3493,f3570]) ).
fof(f7270,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3062,f2808]) ).
fof(f7271,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| ~ sQ75_spl
| product(g1,a,c,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f7270,f6292]) ).
fof(f7273,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,a,inverse(g1,c),X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f7270,f213]) ).
fof(f7275,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,a,inverse(g1,c),X0)
| ~ product(g1,b,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f7270,f63]) ).
fof(f7278,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,a,inverse(g1,c),X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f7275]) ).
fof(f7281,plain,
! [X0,X1,X2] :
( ~ sQ75_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3062,f2809]) ).
fof(f7282,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ73_spl
| ~ sQ75_spl
| product(g1,b,b,X0)
| ~ product(g1,a,c,X0) ),
inference(resolution,[status(thm)],[f7281,f6292]) ).
fof(f7284,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,b,a,X0)
| ~ product(g1,a,inverse(g1,c),X0) ),
inference(resolution,[status(thm)],[f7281,f213]) ).
fof(f7286,plain,
! [X0] :
( ~ sQ75_spl
| product(g1,b,identity_for(g1),X0)
| ~ product(g1,a,inverse(g1,c),X0) ),
inference(resolution,[status(thm)],[f7281,f63]) ).
fof(f7296,plain,
( ~ sQ89_spl
| group_member(multiply(g2,h,h),g2) ),
inference(forward_demodulation,[status(thm)],[f3365,f3347]) ).
fof(f7298,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(forward_demodulation,[status(thm)],[f3577,f3584]) ).
fof(f7300,plain,
( ~ sQ89_spl
| group_member(multiply(g2,g,h),g2) ),
inference(forward_demodulation,[status(thm)],[f3365,f3349]) ).
fof(f7306,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3577,f3588]) ).
fof(f7310,plain,
group_member(multiply(g2,h,g),g2),
inference(forward_demodulation,[status(thm)],[f3453,f3375]) ).
fof(f7312,plain,
group_member(multiply(g2,g,g),g2),
inference(forward_demodulation,[status(thm)],[f3453,f3377]) ).
fof(f7316,plain,
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ73_spl
| product(g1,b,c,a) ),
inference(resolution,[status(thm)],[f7216,f5824]) ).
fof(f7317,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,b,X0)
| ~ product(g1,b,c,X0) ),
inference(resolution,[status(thm)],[f6391,f6378]) ).
fof(f7319,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,inverse(g1,b),X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f6391,f213]) ).
fof(f7320,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f6391,f94]) ).
fof(f7321,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,inverse(g1,b),X0)
| ~ product(g1,b,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f6391,f63]) ).
fof(f7322,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f6391,f60]) ).
fof(f7323,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ41_spl
| product(g1,c,c,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f7319]) ).
fof(f7324,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,inverse(g1,b),X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f7321]) ).
fof(f7326,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,c,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f7322]) ).
fof(f7331,plain,
( ~ sQ94_spl
| group_member(multiply(g2,h,g),g2) ),
inference(forward_demodulation,[status(thm)],[f3493,f3478]) ).
fof(f7333,plain,
( ~ sQ94_spl
| group_member(multiply(g2,g,g),g2) ),
inference(forward_demodulation,[status(thm)],[f3493,f3480]) ).
fof(f7337,plain,
( ~ sQ29_spl
| ~ sQ25_spl
| ~ sQ17_spl
| ~ sQ73_spl
| product(g1,b,b,c) ),
inference(resolution,[status(thm)],[f7217,f94]) ).
fof(f7338,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,c,X0)
| ~ product(g1,c,b,X0) ),
inference(resolution,[status(thm)],[f6392,f6378]) ).
fof(f7339,plain,
! [X0] :
( ~ sQ41_spl
| ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,a,X0)
| ~ product(g1,c,c,X0) ),
inference(resolution,[status(thm)],[f6392,f5004]) ).
fof(f7340,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,a,X0)
| ~ product(g1,c,inverse(g1,b),X0) ),
inference(resolution,[status(thm)],[f6392,f213]) ).
fof(f7341,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,b,X0)
| ~ product(g1,c,a,X0) ),
inference(resolution,[status(thm)],[f6392,f94]) ).
fof(f7342,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,identity_for(g1),X0)
| ~ product(g1,c,inverse(g1,b),X0) ),
inference(resolution,[status(thm)],[f6392,f63]) ).
fof(f7343,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,b,X0)
| ~ product(g1,c,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f6392,f60]) ).
fof(f7347,plain,
! [X0] :
( ~ sQ25_spl
| ~ sQ68_spl
| product(g1,b,b,X0)
| ~ product(g1,c,a,X0) ),
inference(forward_demodulation,[status(thm)],[f91,f7343]) ).
fof(f7350,plain,
( ~ sQ55_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f4032]) ).
fof(f7361,plain,
( ~ sQ73_spl
| product(g1,a,b,multiply(g1,a,multiply(g1,c,c))) ),
inference(forward_demodulation,[status(thm)],[f3034,f3018]) ).
fof(f7362,plain,
( ~ sQ73_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f3034,f7361]) ).
fof(f7364,plain,
( ~ sQ73_spl
| product(g1,b,b,multiply(g1,b,multiply(g1,c,c))) ),
inference(forward_demodulation,[status(thm)],[f3034,f3022]) ).
fof(f7365,plain,
( ~ sQ73_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f3034,f7364]) ).
fof(f7366,plain,
( ~ sQ73_spl
| ~ sQ68_spl
| product(g1,b,b,c) ),
inference(forward_demodulation,[status(thm)],[f2772,f7365]) ).
fof(f7367,plain,
( ~ sQ41_spl
| ~ sQ29_spl
| ~ sQ73_spl
| product(g1,c,b,a) ),
inference(resolution,[status(thm)],[f7227,f5004]) ).
fof(f7369,plain,
( ~ sQ55_spl
| group_member(multiply(g1,c,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1509,f4033]) ).
fof(f7373,plain,
( ~ sQ75_spl
| product(g1,a,a,multiply(g1,a,multiply(g1,b,c))) ),
inference(forward_demodulation,[status(thm)],[f3062,f3049]) ).
fof(f7374,plain,
( ~ sQ75_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f3062,f7373]) ).
fof(f7382,plain,
( ~ sQ73_spl
| product(g1,c,b,multiply(g1,c,multiply(g1,c,c))) ),
inference(forward_demodulation,[status(thm)],[f3034,f3023]) ).
fof(f7383,plain,
( ~ sQ73_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f3034,f7382]) ).
fof(f7384,plain,
( ~ sQ73_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f7383]) ).
fof(f7385,plain,
( ~ sQ73_spl
| product(g1,a,b,multiply(g1,a,multiply(g1,c,c))) ),
inference(forward_demodulation,[status(thm)],[f3034,f3042]) ).
fof(f7386,plain,
( ~ sQ73_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f3034,f7385]) ).
fof(f7389,plain,
( ~ sQ25_spl
| ~ sQ68_spl
| ~ sQ41_spl
| product(g1,c,c,b) ),
inference(resolution,[status(thm)],[f7323,f94]) ).
fof(f7390,plain,
( ~ sQ69_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2833,f5139]) ).
fof(f7393,plain,
group_member(multiply(g2,h,h),g2),
inference(forward_demodulation,[status(thm)],[f3628,f3528]) ).
fof(f7395,plain,
group_member(multiply(g2,g,h),g2),
inference(forward_demodulation,[status(thm)],[f3628,f3530]) ).
fof(f7401,plain,
( ~ sQ75_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,b,c))) ),
inference(forward_demodulation,[status(thm)],[f3062,f3053]) ).
fof(f7402,plain,
( ~ sQ75_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f3062,f7401]) ).
fof(f7404,plain,
( ~ sQ75_spl
| product(g1,c,a,multiply(g1,c,multiply(g1,b,c))) ),
inference(forward_demodulation,[status(thm)],[f3062,f3054]) ).
fof(f7405,plain,
( ~ sQ75_spl
| product(g1,c,a,multiply(g1,c,a)) ),
inference(forward_demodulation,[status(thm)],[f3062,f7404]) ).
fof(f7411,plain,
( ~ sQ69_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2833,f5140]) ).
fof(f7413,plain,
( ~ sQ69_spl
| group_member(multiply(g1,c,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2833,f5141]) ).
fof(f7415,plain,
( ~ sQ75_spl
| product(g1,a,a,multiply(g1,a,multiply(g1,b,c))) ),
inference(forward_demodulation,[status(thm)],[f3062,f3073]) ).
fof(f7416,plain,
( ~ sQ75_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f3062,f7415]) ).
fof(f7423,plain,
( ~ sQ69_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f2833,f5151]) ).
fof(f7433,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,f,g,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3493,f3560]) ).
fof(f7444,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,h,h,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3493,f3561]) ).
fof(f7445,plain,
( ~ sQ94_spl
| product(g2,h,h,g) ),
inference(resolution,[status(thm)],[f7444,f95]) ).
fof(f7454,plain,
! [X0,X1,X2] :
( ~ sQ94_spl
| product(g2,g,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3493,f3568]) ).
fof(f7455,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,g,h,X0)
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f7454,f6628]) ).
fof(f7456,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,g,g,X0)
| ~ product(g2,h,f,X0) ),
inference(resolution,[status(thm)],[f7454,f1149]) ).
fof(f7457,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,g,inverse(g2,h),X0)
| ~ product(g2,h,f,X0) ),
inference(resolution,[status(thm)],[f7454,f218]) ).
fof(f7458,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,g,f,X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f7454,f96]) ).
fof(f7459,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,g,inverse(g2,h),X0)
| ~ product(g2,h,identity_for(g2),X0) ),
inference(resolution,[status(thm)],[f7454,f63]) ).
fof(f7462,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,g,inverse(g2,h),X0)
| ~ product(g2,h,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f7459]) ).
fof(f7465,plain,
! [X0,X1,X2] :
( ~ sQ94_spl
| product(g2,h,X1,X2)
| ~ product(g2,g,X0,X2)
| ~ product(g2,h,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3493,f3569]) ).
fof(f7466,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,h,g,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f7465,f6628]) ).
fof(f7467,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,h,f,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f7465,f1149]) ).
fof(f7468,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,h,f,X0)
| ~ product(g2,g,inverse(g2,h),X0) ),
inference(resolution,[status(thm)],[f7465,f218]) ).
fof(f7469,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,h,h,X0)
| ~ product(g2,g,f,X0) ),
inference(resolution,[status(thm)],[f7465,f96]) ).
fof(f7470,plain,
! [X0] :
( ~ sQ94_spl
| product(g2,h,identity_for(g2),X0)
| ~ product(g2,g,inverse(g2,h),X0) ),
inference(resolution,[status(thm)],[f7465,f63]) ).
fof(f7476,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3577,f3578]) ).
fof(f7481,plain,
( ~ sQ89_spl
| product(g2,h,h,multiply(g2,h,multiply(g2,g,g))) ),
inference(forward_demodulation,[status(thm)],[f3365,f3346]) ).
fof(f7482,plain,
( ~ sQ89_spl
| product(g2,h,h,multiply(g2,h,h)) ),
inference(forward_demodulation,[status(thm)],[f3365,f7481]) ).
fof(f7483,plain,
( ~ sQ89_spl
| ~ sQ94_spl
| product(g2,h,h,g) ),
inference(forward_demodulation,[status(thm)],[f3493,f7482]) ).
fof(f7484,plain,
( ~ sQ89_spl
| product(g2,g,h,multiply(g2,g,multiply(g2,g,g))) ),
inference(forward_demodulation,[status(thm)],[f3365,f3348]) ).
fof(f7485,plain,
( ~ sQ89_spl
| product(g2,g,h,multiply(g2,g,h)) ),
inference(forward_demodulation,[status(thm)],[f3365,f7484]) ).
fof(f7486,plain,
( ~ sQ89_spl
| ~ sQ84_spl
| product(g2,g,h,f) ),
inference(forward_demodulation,[status(thm)],[f3262,f7485]) ).
fof(f7491,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,h,g,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f3577,f3579]) ).
fof(f7494,plain,
( ~ sQ84_spl
| product(g2,g,h,f) ),
inference(resolution,[status(thm)],[f4115,f95]) ).
fof(f7495,plain,
( ~ sQ84_spl
| product(g2,g,h,f) ),
inference(resolution,[status(thm)],[f4115,f96]) ).
fof(f7504,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,f,X0,X2)
| ~ product(g2,h,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3577,f3586]) ).
fof(f7505,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,g,X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f7504,f6561]) ).
fof(f7515,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| product(g2,h,X1,X2)
| ~ product(g2,f,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3577,f3587]) ).
fof(f7516,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,X0)
| ~ product(g2,f,g,X0) ),
inference(resolution,[status(thm)],[f7515,f6561]) ).
fof(f7527,plain,
product(g2,h,g,multiply(g2,h,multiply(g2,g,f))),
inference(forward_demodulation,[status(thm)],[f3453,f3374]) ).
fof(f7528,plain,
product(g2,h,g,multiply(g2,h,g)),
inference(forward_demodulation,[status(thm)],[f3453,f7527]) ).
fof(f7530,plain,
product(g2,g,g,multiply(g2,g,multiply(g2,g,f))),
inference(forward_demodulation,[status(thm)],[f3453,f3376]) ).
fof(f7531,plain,
product(g2,g,g,multiply(g2,g,g)),
inference(forward_demodulation,[status(thm)],[f3453,f7530]) ).
fof(f7532,plain,
( ~ sQ89_spl
| product(g2,g,g,h) ),
inference(forward_demodulation,[status(thm)],[f3365,f7531]) ).
fof(f7547,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,multiply(g2,h,f),X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f3746]) ).
fof(f7548,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,f,X0)
| ~ product(g2,g,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3628,f7547]) ).
fof(f7549,plain,
( ~ sQ94_spl
| product(g2,h,g,multiply(g2,h,multiply(g2,h,h))) ),
inference(forward_demodulation,[status(thm)],[f3493,f3477]) ).
fof(f7550,plain,
( ~ sQ94_spl
| product(g2,h,g,multiply(g2,h,g)) ),
inference(forward_demodulation,[status(thm)],[f3493,f7549]) ).
fof(f7552,plain,
( ~ sQ94_spl
| product(g2,g,g,multiply(g2,g,multiply(g2,h,h))) ),
inference(forward_demodulation,[status(thm)],[f3493,f3479]) ).
fof(f7553,plain,
( ~ sQ94_spl
| product(g2,g,g,multiply(g2,g,g)) ),
inference(forward_demodulation,[status(thm)],[f3493,f7552]) ).
fof(f7554,plain,
( ~ sQ94_spl
| ~ sQ89_spl
| product(g2,g,g,h) ),
inference(forward_demodulation,[status(thm)],[f3365,f7553]) ).
fof(f7558,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,multiply(g2,h,f),X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f3640]) ).
fof(f7559,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,h,X0)
| ~ product(g2,f,f,X0) ),
inference(forward_demodulation,[status(thm)],[f3628,f7558]) ).
fof(f7570,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,f,h,X0)
| ~ product(g2,g,multiply(g2,h,h),X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f3748]) ).
fof(f7571,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,f,h,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3493,f7570]) ).
fof(f7575,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,g,multiply(g2,h,h),X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1100,f3571]) ).
fof(f7576,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,g,g,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3493,f7575]) ).
fof(f7577,plain,
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,g,g,h) ),
inference(resolution,[status(thm)],[f7576,f95]) ).
fof(f7596,plain,
! [X0] :
( ~ sQ50_spl
| X0 = h
| ~ product(g2,X0,g,f) ),
inference(forward_demodulation,[status(thm)],[f3577,f6359]) ).
fof(f7597,plain,
( ~ sQ55_spl
| product(g1,b,b,multiply(g1,b,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f1509,f4034]) ).
fof(f7598,plain,
( ~ sQ55_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f1509,f7597]) ).
fof(f7599,plain,
( ~ sQ55_spl
| ~ sQ68_spl
| product(g1,b,b,c) ),
inference(forward_demodulation,[status(thm)],[f2772,f7598]) ).
fof(f7601,plain,
! [X0] :
( ~ sQ50_spl
| X0 = f
| ~ product(g2,h,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3577,f6363]) ).
fof(f7602,plain,
( ~ sQ55_spl
| product(g1,c,b,multiply(g1,c,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f1509,f4035]) ).
fof(f7603,plain,
( ~ sQ55_spl
| product(g1,c,b,multiply(g1,c,b)) ),
inference(forward_demodulation,[status(thm)],[f1509,f7602]) ).
fof(f7604,plain,
( ~ sQ55_spl
| ~ sQ69_spl
| product(g1,c,b,a) ),
inference(forward_demodulation,[status(thm)],[f2833,f7603]) ).
fof(f7618,plain,
product(g2,h,h,multiply(g2,h,multiply(g2,h,f))),
inference(forward_demodulation,[status(thm)],[f3628,f3527]) ).
fof(f7619,plain,
product(g2,h,h,multiply(g2,h,h)),
inference(forward_demodulation,[status(thm)],[f3628,f7618]) ).
fof(f7620,plain,
( ~ sQ94_spl
| product(g2,h,h,g) ),
inference(forward_demodulation,[status(thm)],[f3493,f7619]) ).
fof(f7621,plain,
product(g2,g,h,multiply(g2,g,multiply(g2,h,f))),
inference(forward_demodulation,[status(thm)],[f3628,f3529]) ).
fof(f7622,plain,
product(g2,g,h,multiply(g2,g,h)),
inference(forward_demodulation,[status(thm)],[f3628,f7621]) ).
fof(f7623,plain,
( ~ sQ84_spl
| product(g2,g,h,f) ),
inference(forward_demodulation,[status(thm)],[f3262,f7622]) ).
fof(f7629,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| group_member(multiply(g2,h,h),g2) ),
inference(forward_demodulation,[status(thm)],[f3365,f6537]) ).
fof(f7631,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,c,X0)
| ~ product(g1,c,multiply(g1,b,c),X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f4699]) ).
fof(f7633,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,c,multiply(g1,b,c),X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f4989,f2811]) ).
fof(f7635,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| group_member(multiply(g2,g,h),g2) ),
inference(forward_demodulation,[status(thm)],[f3365,f6539]) ).
fof(f7647,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,b,X0)
| ~ product(g1,b,multiply(g1,c,b),X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f4701]) ).
fof(f7649,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,b,multiply(g1,c,b),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f2793]) ).
fof(f7651,plain,
( ~ sQ69_spl
| product(g1,a,a,multiply(g1,a,multiply(g1,c,b))) ),
inference(forward_demodulation,[status(thm)],[f2833,f5138]) ).
fof(f7652,plain,
( ~ sQ69_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f2833,f7651]) ).
fof(f7654,plain,
( ~ sQ50_spl
| product(g2,h,multiply(g2,g,g),multiply(g2,h,multiply(g2,g,inverse(g2,h)))) ),
inference(forward_demodulation,[status(thm)],[f1100,f3792]) ).
fof(f7655,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,multiply(g2,h,multiply(g2,g,inverse(g2,h)))) ),
inference(forward_demodulation,[status(thm)],[f3365,f7654]) ).
fof(f7656,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,multiply(g2,h,multiply(g2,g,g))) ),
inference(forward_demodulation,[status(thm)],[f1100,f7655]) ).
fof(f7657,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,multiply(g2,h,h)) ),
inference(forward_demodulation,[status(thm)],[f3365,f7656]) ).
fof(f7659,plain,
( ~ sQ50_spl
| group_member(multiply(g2,h,multiply(g2,g,g)),g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3793]) ).
fof(f7660,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| group_member(multiply(g2,h,h),g2) ),
inference(forward_demodulation,[status(thm)],[f3365,f7659]) ).
fof(f7662,plain,
( ~ sQ50_spl
| product(g2,g,multiply(g2,g,g),multiply(g2,g,multiply(g2,g,inverse(g2,h)))) ),
inference(forward_demodulation,[status(thm)],[f1100,f3794]) ).
fof(f7663,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,h,multiply(g2,g,multiply(g2,g,inverse(g2,h)))) ),
inference(forward_demodulation,[status(thm)],[f3365,f7662]) ).
fof(f7664,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,h,multiply(g2,g,multiply(g2,g,g))) ),
inference(forward_demodulation,[status(thm)],[f1100,f7663]) ).
fof(f7665,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,h,multiply(g2,g,h)) ),
inference(forward_demodulation,[status(thm)],[f3365,f7664]) ).
fof(f7667,plain,
( ~ sQ50_spl
| group_member(multiply(g2,g,multiply(g2,g,g)),g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3795]) ).
fof(f7668,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| group_member(multiply(g2,g,h),g2) ),
inference(forward_demodulation,[status(thm)],[f3365,f7667]) ).
fof(f7670,plain,
( ~ sQ50_spl
| group_member(multiply(g2,f,multiply(g2,g,g)),g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3796]) ).
fof(f7673,plain,
( ~ sQ50_spl
| product(g2,f,multiply(g2,g,g),multiply(g2,f,multiply(g2,g,inverse(g2,h)))) ),
inference(forward_demodulation,[status(thm)],[f1100,f3797]) ).
fof(f7678,plain,
( ~ sQ50_spl
| group_member(multiply(g2,f,multiply(g2,g,g)),g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3814]) ).
fof(f7681,plain,
( ~ sQ50_spl
| product(g2,f,multiply(g2,g,g),multiply(g2,f,multiply(g2,g,inverse(g2,h)))) ),
inference(forward_demodulation,[status(thm)],[f1100,f3816]) ).
fof(f7686,plain,
! [X0] :
( ~ sQ50_spl
| group_member(multiply(g2,multiply(g2,g,g),X0),g2)
| ~ group_member(X0,g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3801]) ).
fof(f7689,plain,
! [X0] :
( ~ sQ50_spl
| product(g2,multiply(g2,g,g),X0,multiply(g2,multiply(g2,g,inverse(g2,h)),X0))
| ~ group_member(X0,g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3802]) ).
fof(f7693,plain,
( ~ sQ50_spl
| group_member(inverse(g2,multiply(g2,g,g)),g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3803]) ).
fof(f7703,plain,
( ~ sQ50_spl
| ~ sQ94_spl
| product(g2,g,g,h) ),
inference(resolution,[status(thm)],[f7456,f96]) ).
fof(f7704,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,b,multiply(g1,c,c),X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f2744]) ).
fof(f7705,plain,
! [X0] :
( ~ sQ41_spl
| ~ sQ73_spl
| product(g1,b,b,X0)
| ~ product(g1,a,c,X0) ),
inference(forward_demodulation,[status(thm)],[f3034,f7704]) ).
fof(f7706,plain,
! [X0] :
( ~ sQ41_spl
| product(g1,a,c,X0)
| ~ product(g1,b,multiply(g1,c,c),X0) ),
inference(forward_demodulation,[status(thm)],[f1004,f5750]) ).
fof(f7707,plain,
! [X0] :
( ~ sQ41_spl
| ~ sQ73_spl
| product(g1,a,c,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f3034,f7706]) ).
fof(f7712,plain,
( ~ sQ50_spl
| product(g2,g,multiply(g2,f,g),multiply(g2,g,multiply(g2,f,inverse(g2,h)))) ),
inference(forward_demodulation,[status(thm)],[f1100,f3819]) ).
fof(f7713,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,multiply(g2,f,inverse(g2,h)))) ),
inference(forward_demodulation,[status(thm)],[f2667,f7712]) ).
fof(f7714,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,multiply(g2,f,g))) ),
inference(forward_demodulation,[status(thm)],[f1100,f7713]) ).
fof(f7715,plain,
( ~ sQ50_spl
| product(g2,g,g,multiply(g2,g,g)) ),
inference(forward_demodulation,[status(thm)],[f2667,f7714]) ).
fof(f7717,plain,
( ~ sQ50_spl
| group_member(multiply(g2,g,multiply(g2,f,g)),g2) ),
inference(forward_demodulation,[status(thm)],[f1100,f3820]) ).
fof(f7718,plain,
( ~ sQ50_spl
| group_member(multiply(g2,g,g),g2) ),
inference(forward_demodulation,[status(thm)],[f2667,f7717]) ).
fof(f7722,plain,
( ~ sQ94_spl
| product(g2,h,h,g) ),
inference(resolution,[status(thm)],[f7469,f96]) ).
fof(f7753,plain,
( ~ sQ69_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,c,b))) ),
inference(forward_demodulation,[status(thm)],[f2833,f5142]) ).
fof(f7754,plain,
( ~ sQ69_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f2833,f7753]) ).
fof(f7756,plain,
( ~ sQ69_spl
| product(g1,c,a,multiply(g1,c,multiply(g1,c,b))) ),
inference(forward_demodulation,[status(thm)],[f2833,f5143]) ).
fof(f7757,plain,
( ~ sQ69_spl
| product(g1,c,a,multiply(g1,c,a)) ),
inference(forward_demodulation,[status(thm)],[f2833,f7756]) ).
fof(f7759,plain,
( ~ sQ69_spl
| product(g1,a,a,multiply(g1,a,multiply(g1,c,b))) ),
inference(forward_demodulation,[status(thm)],[f2833,f5153]) ).
fof(f7760,plain,
( ~ sQ69_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f2833,f7759]) ).
fof(f7768,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,f,inverse(g2,h),X0)
| ~ product(g2,g,f,X0) ),
inference(resolution,[status(thm)],[f4122,f218]) ).
fof(f7770,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,f,inverse(g2,h),X0)
| ~ product(g2,g,identity_for(g2),X0) ),
inference(resolution,[status(thm)],[f4122,f63]) ).
fof(f7773,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,f,inverse(g2,h),X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f7770]) ).
fof(f7778,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,g,f,X0)
| ~ product(g2,f,inverse(g2,h),X0) ),
inference(resolution,[status(thm)],[f4123,f218]) ).
fof(f7780,plain,
! [X0] :
( ~ sQ84_spl
| product(g2,g,identity_for(g2),X0)
| ~ product(g2,f,inverse(g2,h),X0) ),
inference(resolution,[status(thm)],[f4123,f63]) ).
fof(f7814,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3365,f6527]) ).
fof(f7815,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,g,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3365,f6528]) ).
fof(f7816,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,h,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3365,f6516]) ).
fof(f7817,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3365,f6517]) ).
fof(f7818,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,X0)
| ~ product(g2,f,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3365,f6530]) ).
fof(f7819,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,g,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3365,f6532]) ).
fof(f7820,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,X0)
| ~ product(g2,f,h,X0) ),
inference(forward_demodulation,[status(thm)],[f3365,f6533]) ).
fof(f7821,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,f,h,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f3365,f6534]) ).
fof(f7822,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,X0,X2)
| ~ product(g2,g,X1,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3365,f6524]) ).
fof(f7823,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,g,X0)
| ~ product(g2,g,h,X0) ),
inference(resolution,[status(thm)],[f7822,f6561]) ).
fof(f7824,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,X0)
| ~ product(g2,g,f,X0) ),
inference(resolution,[status(thm)],[f7822,f1150]) ).
fof(f7825,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,inverse(g2,g),X0)
| ~ product(g2,g,f,X0) ),
inference(resolution,[status(thm)],[f7822,f218]) ).
fof(f7826,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,f,X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f7822,f96]) ).
fof(f7827,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,inverse(g2,g),X0)
| ~ product(g2,g,identity_for(g2),X0) ),
inference(resolution,[status(thm)],[f7822,f63]) ).
fof(f7828,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,identity_for(g2),X0)
| ~ product(g2,g,g,X0) ),
inference(resolution,[status(thm)],[f7822,f60]) ).
fof(f7829,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f7825]) ).
fof(f7830,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,inverse(g2,g),X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f7827]) ).
fof(f7831,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,X0)
| ~ product(g2,g,f,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f7830]) ).
fof(f7832,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,f,X0)
| ~ product(g2,g,g,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f7828]) ).
fof(f7833,plain,
! [X0,X1,X2] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,X1,X2)
| ~ product(g2,h,X0,X2)
| ~ product(g2,g,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f3365,f6525]) ).
fof(f7834,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,h,X0)
| ~ product(g2,h,g,X0) ),
inference(resolution,[status(thm)],[f7833,f6561]) ).
fof(f7835,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,f,X0)
| ~ product(g2,h,h,X0) ),
inference(resolution,[status(thm)],[f7833,f1150]) ).
fof(f7836,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,f,X0)
| ~ product(g2,h,inverse(g2,g),X0) ),
inference(resolution,[status(thm)],[f7833,f218]) ).
fof(f7837,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,X0)
| ~ product(g2,h,f,X0) ),
inference(resolution,[status(thm)],[f7833,f96]) ).
fof(f7838,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,identity_for(g2),X0)
| ~ product(g2,h,inverse(g2,g),X0) ),
inference(resolution,[status(thm)],[f7833,f63]) ).
fof(f7839,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,X0)
| ~ product(g2,h,identity_for(g2),X0) ),
inference(resolution,[status(thm)],[f7833,f60]) ).
fof(f7840,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,f,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f7836]) ).
fof(f7841,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,identity_for(g2),X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f1278,f7838]) ).
fof(f7842,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,f,X0)
| ~ product(g2,h,h,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f7841]) ).
fof(f7843,plain,
! [X0] :
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,g,X0)
| ~ product(g2,h,f,X0) ),
inference(forward_demodulation,[status(thm)],[f92,f7839]) ).
fof(f7844,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,multiply(g2,h,multiply(g2,g,g))) ),
inference(forward_demodulation,[status(thm)],[f3365,f6536]) ).
fof(f7845,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,h,h,multiply(g2,h,h)) ),
inference(forward_demodulation,[status(thm)],[f3365,f7844]) ).
fof(f7847,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,h,multiply(g2,g,multiply(g2,g,g))) ),
inference(forward_demodulation,[status(thm)],[f3365,f6538]) ).
fof(f7848,plain,
( ~ sQ50_spl
| ~ sQ89_spl
| product(g2,g,h,multiply(g2,g,h)) ),
inference(forward_demodulation,[status(thm)],[f3365,f7847]) ).
fof(model,axiom,
( ~ sQ4_spl
| ~ sQ6_spl
| ~ sQ7_spl
| sQ8_spl
| ~ sQ9_spl
| sQ10_spl
| ~ sQ11_spl
| ~ sQ12_spl
| sQ13_spl
| sQ14_spl
| ~ sQ15_spl
| sQ17_spl
| ~ sQ18_spl
| sQ20_spl
| ~ sQ21_spl
| ~ sQ22_spl
| sQ23_spl
| ~ sQ24_spl
| sQ25_spl
| ~ sQ26_spl
| ~ sQ27_spl
| ~ sQ28_spl
| sQ29_spl
| ~ sQ30_spl
| ~ sQ31_spl
| sQ32_spl
| ~ sQ33_spl
| sQ34_spl
| sQ35_spl
| sQ36_spl
| ~ sQ37_spl
| ~ sQ38_spl
| ~ sQ39_spl
| ~ sQ40_spl
| sQ41_spl
| ~ sQ42_spl
| sQ43_spl
| ~ sQ44_spl
| ~ sQ45_spl
| ~ sQ46_spl
| sQ47_spl
| ~ sQ48_spl
| ~ sQ49_spl
| sQ50_spl
| ~ sQ51_spl
| sQ52_spl
| ~ sQ53_spl
| ~ sQ54_spl
| sQ55_spl
| ~ sQ56_spl
| ~ sQ57_spl
| ~ sQ58_spl
| sQ59_spl
| ~ sQ60_spl
| sQ61_spl
| ~ sQ62_spl
| sQ63_spl
| ~ sQ64_spl
| ~ sQ66_spl
| ~ sQ67_spl
| sQ68_spl
| sQ69_spl
| ~ sQ70_spl
| ~ sQ71_spl
| ~ sQ72_spl
| sQ73_spl
| ~ sQ74_spl
| sQ75_spl
| ~ sQ76_spl
| ~ sQ77_spl
| sQ78_spl
| ~ sQ79_spl
| ~ sQ80_spl
| sQ81_spl
| ~ sQ82_spl
| ~ sQ83_spl
| sQ84_spl
| ~ sQ85_spl
| ~ sQ87_spl
| ~ sQ88_spl
| sQ89_spl
| ~ sQ90_spl
| sQ91_spl
| ~ sQ92_spl
| ~ sQ93_spl
| sQ94_spl
| ~ sQ95_spl
| sQ96_spl
| ~ sQ97_spl
| ~ sQ99_spl
| ~ sQ100_spl
| sQ101_spl
| ~ sQ102_spl
| ~ sQ103_spl
| sQ104_spl
| ~ sQ105_spl
| sQ106_spl
| ~ sQ107_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP026-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.33 % Computer : n003.cluster.edu
% 0.08/0.33 % Model : x86_64 x86_64
% 0.08/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.33 % Memory : 8046.5625MB
% 0.08/0.33 % OS : Linux 6.8.0-71-generic
% 0.08/0.33 % CPULimit : 300
% 0.08/0.33 % WCLimit : 300
% 0.08/0.33 % DateTime : Sun Sep 20 19:56:45 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 4.90/1.04 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 4.90/1.04 % SZS output start Saturation for theBenchmark
% See solution above
% 0.47/1.11 % Elapsed time: 0.766094 seconds
% 0.47/1.11 % CPU time: 5.222293 seconds
% 0.47/1.11 % Total memory used: 167.969 MB
% 0.47/1.11 % Net memory used: 160.521 MB
%------------------------------------------------------------------------------