%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : GRP025-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n005.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 12:35:27 PM UTC 2026
% Result : Satisfiable 1.45s 0.65s
% Output : Saturation 1.45s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [Xg] : group_member(identity_for(Xg),Xg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [Xg,X] : product(Xg,identity_for(Xg),X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [Xg,X] : product(Xg,X,identity_for(Xg),X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Xg] :
( group_member(inverse(Xg,X),Xg)
| ~ group_member(X,Xg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [Xg,X] : product(Xg,inverse(Xg,X),X,identity_for(Xg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [Xg,X] : product(Xg,X,inverse(Xg,X),identity_for(Xg)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,hypothesis,
g1 != g2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,hypothesis,
group_member(a,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,hypothesis,
group_member(b,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,hypothesis,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,hypothesis,
group_member(c,g2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,hypothesis,
group_member(d,g2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,hypothesis,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,hypothesis,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,hypothesis,
a != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,hypothesis,
b != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,hypothesis,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,hypothesis,
! [X] :
( X = b
| X = a
| ~ group_member(X,g1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,hypothesis,
! [X] :
( X = d
| X = c
| ~ group_member(X,g2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,hypothesis,
identity_for(g1) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,hypothesis,
identity_for(g2) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,hypothesis,
! [X] : product(g1,a,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,hypothesis,
! [X] : product(g1,X,a,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,hypothesis,
! [X] : product(g2,c,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,hypothesis,
! [X] : product(g2,X,c,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,hypothesis,
isomorphism1(a) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,hypothesis,
isomorphism1(b) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,hypothesis,
isomorphism2(a) = d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,hypothesis,
isomorphism2(b) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,negated_conjecture,
group_member(d1,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,negated_conjecture,
group_member(d2,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
group_member(d3,g1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,negated_conjecture,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,negated_conjecture,
( ~ product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3))
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [X0] : group_member(identity_for(X0),X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f41,plain,
! [X0,X1] : product(X0,identity_for(X0),X1,X1),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f42,plain,
! [X0,X1] : product(X0,X1,identity_for(X0),X1),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f43,plain,
! [X0,X1] :
( group_member(inverse(X1,X0),X1)
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f44,plain,
! [X0,X1] : product(X0,inverse(X0,X1),X1,identity_for(X0)),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f45,plain,
! [X0,X1] : product(X0,X1,inverse(X0,X1),identity_for(X0)),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f46,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(f47,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(f48,plain,
! [Z,W] :
( W = Z
| ! [Xg,X,Y] :
( ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f49,plain,
! [X0,X1,X2,X3,X4] :
( X4 = X3
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,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(f51,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)],[f50]) ).
fof(f52,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(f53,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)],[f52]) ).
fof(f54,plain,
g1 != g2,
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f55,plain,
group_member(a,g1),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f56,plain,
group_member(b,g1),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f57,plain,
a != b,
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f58,plain,
group_member(c,g2),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f59,plain,
group_member(d,g2),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f60,plain,
c != d,
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f61,plain,
a != c,
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f62,plain,
a != d,
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f63,plain,
b != c,
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f64,plain,
b != d,
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f65,plain,
! [X0] :
( X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f66,plain,
! [X0] :
( X0 = d
| X0 = c
| ~ group_member(X0,g2) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f67,plain,
identity_for(g1) = a,
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f68,plain,
identity_for(g2) = c,
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f69,plain,
! [X0] : product(g1,a,X0,X0),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f70,plain,
! [X0] : product(g1,X0,a,X0),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f71,plain,
! [X0] : product(g2,c,X0,X0),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f72,plain,
! [X0] : product(g2,X0,c,X0),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f73,plain,
isomorphism1(a) = c,
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f74,plain,
isomorphism1(b) = d,
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f75,plain,
isomorphism2(a) = d,
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f76,plain,
isomorphism2(b) = c,
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f77,plain,
group_member(d1,g1),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f78,plain,
group_member(d2,g1),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f79,plain,
group_member(d3,g1),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f80,plain,
product(g1,d1,d2,d3),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f81,plain,
( ~ product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3))
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f82,definition,
( sQ0_spl
<=> product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f83,plain,
( ~ sQ0_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( sQ0_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(d3)) ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,definition,
( sQ1_spl
<=> product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( ~ sQ1_spl
| product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3)) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f87,plain,
( sQ1_spl
| ~ product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(d3)) ),
inference(component_clause,[status(thm)],[f85]) ).
fof(f88,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f81,f82,f85]) ).
fof(f89,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)],[f41,f51]) ).
fof(f90,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(resolution,[status(thm)],[f41,f49]) ).
fof(f91,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)],[f42,f51]) ).
fof(f92,plain,
! [X0,X1,X2] :
( X2 = X1
| ~ product(X0,X1,identity_for(X0),X2) ),
inference(resolution,[status(thm)],[f42,f49]) ).
fof(f93,plain,
! [X0,X1,X2] :
( product(g1,d1,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f80,f51]) ).
fof(f94,plain,
! [X0] :
( X0 = d3
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f80,f49]) ).
fof(f95,plain,
! [X0,X1,X2] :
( product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f53,f80]) ).
fof(f96,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)],[f53,f41]) ).
fof(f97,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)],[f53,f42]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( product(g2,X0,X1,X3)
| ~ product(g2,c,X2,X3)
| ~ product(g2,X0,X1,X2) ),
inference(resolution,[status(thm)],[f71,f53]) ).
fof(f99,plain,
! [X0,X1,X2,X3] :
( product(g2,c,X2,X3)
| ~ product(g2,X0,X1,X3)
| ~ product(g2,X0,X1,X2) ),
inference(resolution,[status(thm)],[f71,f51]) ).
fof(f100,plain,
! [X0,X1] :
( X1 = X0
| ~ product(g2,c,X0,X1) ),
inference(resolution,[status(thm)],[f71,f49]) ).
fof(f101,plain,
group_member(inverse(g1,d3),g1),
inference(resolution,[status(thm)],[f43,f79]) ).
fof(f104,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f43,f78]) ).
fof(f105,plain,
group_member(inverse(g1,d1),g1),
inference(resolution,[status(thm)],[f43,f77]) ).
fof(f106,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)],[f44,f53]) ).
fof(f107,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)],[f44,f51]) ).
fof(f108,plain,
! [X0,X1,X2] :
( X2 = identity_for(X0)
| ~ product(X0,inverse(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f44,f49]) ).
fof(f109,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)],[f45,f53]) ).
fof(f110,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)],[f45,f51]) ).
fof(f111,plain,
! [X0,X1,X2] :
( X2 = identity_for(X0)
| ~ product(X0,X1,inverse(X0,X1),X2) ),
inference(resolution,[status(thm)],[f45,f49]) ).
fof(f112,plain,
group_member(inverse(g1,inverse(g1,d3)),g1),
inference(resolution,[status(thm)],[f101,f43]) ).
fof(f113,plain,
! [X0,X1,X2,X3] :
( product(g2,X2,X0,X3)
| ~ product(g2,X2,X1,X3)
| ~ product(g2,c,X0,X1) ),
inference(resolution,[status(thm)],[f72,f53]) ).
fof(f114,plain,
! [X0,X1,X2,X3] :
( product(g2,X2,X1,X3)
| ~ product(g2,X2,X0,X3)
| ~ product(g2,c,X0,X1) ),
inference(resolution,[status(thm)],[f72,f51]) ).
fof(f115,plain,
! [X0,X1] :
( X1 = X0
| ~ product(g2,X0,c,X1) ),
inference(resolution,[status(thm)],[f72,f49]) ).
fof(f117,plain,
! [X0,X1] :
( product(g2,identity_for(g2),X0,X1)
| ~ product(g2,X0,c,X1) ),
inference(resolution,[status(thm)],[f89,f72]) ).
fof(f118,plain,
! [X0] :
( product(g1,identity_for(g1),d3,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f89,f80]) ).
fof(f119,plain,
! [X0,X1,X2] :
( product(X0,identity_for(X0),identity_for(X0),X2)
| ~ product(X0,inverse(X0,X1),X1,X2) ),
inference(resolution,[status(thm)],[f89,f44]) ).
fof(f121,plain,
! [X0,X1,X2] :
( product(X0,identity_for(X0),identity_for(X0),X2)
| ~ product(X0,X1,inverse(X0,X1),X2) ),
inference(resolution,[status(thm)],[f89,f45]) ).
fof(f122,plain,
! [X0,X1,X2] :
( product(X0,identity_for(X0),X1,X2)
| ~ product(X0,X1,identity_for(X0),X2) ),
inference(resolution,[status(thm)],[f89,f42]) ).
fof(f124,plain,
group_member(inverse(g1,b),g1),
inference(resolution,[status(thm)],[f56,f43]) ).
fof(f125,plain,
group_member(inverse(g2,d),g2),
inference(resolution,[status(thm)],[f59,f43]) ).
fof(f126,plain,
! [X0] :
( product(g2,d,X0,multiply(g2,d,X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f46,f59]) ).
fof(f127,plain,
! [X0] :
( product(g1,b,X0,multiply(g1,b,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f46,f56]) ).
fof(f128,plain,
! [X0] :
( product(g1,a,X0,multiply(g1,a,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f46,f55]) ).
fof(f129,plain,
! [X0] :
( product(g1,inverse(g1,d3),X0,multiply(g1,inverse(g1,d3),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f46,f101]) ).
fof(f130,plain,
! [X0] :
( product(g1,d3,X0,multiply(g1,d3,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f46,f79]) ).
fof(f131,plain,
! [X0,X1] :
( product(X1,identity_for(X1),X0,multiply(X1,identity_for(X1),X0))
| ~ group_member(X0,X1) ),
inference(resolution,[status(thm)],[f46,f40]) ).
fof(f132,plain,
! [X0] :
( product(g2,c,X0,multiply(g2,c,X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f46,f58]) ).
fof(f133,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f46,f78]) ).
fof(f134,plain,
! [X0] :
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f46,f77]) ).
fof(f135,plain,
! [X0] :
( group_member(multiply(g2,d,X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f47,f59]) ).
fof(f136,plain,
! [X0] :
( group_member(multiply(g1,b,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f47,f56]) ).
fof(f137,plain,
! [X0] :
( group_member(multiply(g1,a,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f47,f55]) ).
fof(f138,plain,
! [X0] :
( group_member(multiply(g1,inverse(g1,d3),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f47,f101]) ).
fof(f139,plain,
! [X0] :
( group_member(multiply(g1,d3,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f47,f79]) ).
fof(f140,plain,
! [X0,X1] :
( group_member(multiply(X1,identity_for(X1),X0),X1)
| ~ group_member(X0,X1) ),
inference(resolution,[status(thm)],[f47,f40]) ).
fof(f141,plain,
! [X0] :
( group_member(multiply(g2,c,X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f47,f58]) ).
fof(f142,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f47,f78]) ).
fof(f143,plain,
! [X0] :
( group_member(multiply(g1,d1,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f47,f77]) ).
fof(f144,plain,
( b = b
| b = a ),
inference(resolution,[status(thm)],[f65,f56]) ).
fof(f145,plain,
( a = b
| a = a ),
inference(resolution,[status(thm)],[f65,f55]) ).
fof(f146,plain,
( inverse(g1,d3) = b
| inverse(g1,d3) = a ),
inference(resolution,[status(thm)],[f65,f101]) ).
fof(f147,plain,
( d3 = b
| d3 = a ),
inference(resolution,[status(thm)],[f65,f79]) ).
fof(f148,plain,
( identity_for(g1) = b
| identity_for(g1) = a ),
inference(resolution,[status(thm)],[f65,f40]) ).
fof(f149,plain,
( d2 = b
| d2 = a ),
inference(resolution,[status(thm)],[f65,f78]) ).
fof(f150,plain,
( d1 = b
| d1 = a ),
inference(resolution,[status(thm)],[f65,f77]) ).
fof(f151,definition,
( sQ2_spl
<=> b = a ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( ~ sQ2_spl
| b = a ),
inference(component_clause,[status(thm)],[f151]) ).
fof(f154,definition,
( sQ3_spl
<=> b = b ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f157,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f144,f151,f154]) ).
fof(f158,definition,
( sQ4_spl
<=> a = a ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f161,plain,
( sQ2_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f145,f158,f151]) ).
fof(f162,definition,
( sQ5_spl
<=> inverse(g1,d3) = a ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f163,plain,
( ~ sQ5_spl
| inverse(g1,d3) = a ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f164,plain,
( sQ5_spl
| inverse(g1,d3) != a ),
inference(component_clause,[status(thm)],[f162]) ).
fof(f165,definition,
( sQ6_spl
<=> inverse(g1,d3) = b ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( ~ sQ6_spl
| inverse(g1,d3) = b ),
inference(component_clause,[status(thm)],[f165]) ).
fof(f168,plain,
( sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f146,f162,f165]) ).
fof(f169,definition,
( sQ7_spl
<=> d3 = a ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f170,plain,
( ~ sQ7_spl
| d3 = a ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f171,plain,
( sQ7_spl
| d3 != a ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f172,definition,
( sQ8_spl
<=> d3 = b ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f173,plain,
( ~ sQ8_spl
| d3 = b ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f174,plain,
( sQ8_spl
| d3 != b ),
inference(component_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f147,f169,f172]) ).
fof(f176,definition,
( sQ9_spl
<=> identity_for(g1) = a ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f179,definition,
( sQ10_spl
<=> identity_for(g1) = b ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f180,plain,
( ~ sQ10_spl
| identity_for(g1) = b ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f148,f176,f179]) ).
fof(f183,definition,
( sQ11_spl
<=> d2 = a ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f184,plain,
( ~ sQ11_spl
| d2 = a ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f185,plain,
( sQ11_spl
| d2 != a ),
inference(component_clause,[status(thm)],[f183]) ).
fof(f186,definition,
( sQ12_spl
<=> d2 = b ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f187,plain,
( ~ sQ12_spl
| d2 = b ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f188,plain,
( sQ12_spl
| d2 != b ),
inference(component_clause,[status(thm)],[f186]) ).
fof(f189,plain,
( sQ12_spl
| sQ11_spl ),
inference(split_clause,[status(thm)],[f149,f183,f186]) ).
fof(f190,definition,
( sQ13_spl
<=> d1 = a ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f191,plain,
( ~ sQ13_spl
| d1 = a ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f192,plain,
( sQ13_spl
| d1 != a ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,definition,
( sQ14_spl
<=> d1 = b ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f194,plain,
( ~ sQ14_spl
| d1 = b ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f195,plain,
( sQ14_spl
| d1 != b ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( sQ14_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f150,f190,f193]) ).
fof(f197,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f57]) ).
fof(f198,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f197]) ).
fof(f199,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ product(g2,isomorphism1(a),isomorphism1(d2),isomorphism1(d3)) ),
inference(backward_demodulation,[status(thm)],[f191,f84]) ).
fof(f200,plain,
( ~ sQ13_spl
| product(g1,a,d2,d3) ),
inference(backward_demodulation,[status(thm)],[f191,f80]) ).
fof(f202,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ product(g2,c,isomorphism1(d2),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f73,f199]) ).
fof(f203,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ product(g2,c,isomorphism1(a),isomorphism1(d3)) ),
inference(backward_demodulation,[status(thm)],[f184,f202]) ).
fof(f205,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ product(g2,c,c,isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f73,f203]) ).
fof(f208,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| product(g1,a,a,d3) ),
inference(forward_demodulation,[status(thm)],[f184,f200]) ).
fof(f214,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ product(g2,c,c,isomorphism1(a)) ),
inference(forward_demodulation,[status(thm)],[f170,f205]) ).
fof(f215,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ7_spl
| ~ product(g2,c,c,c) ),
inference(forward_demodulation,[status(thm)],[f73,f214]) ).
fof(f216,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f215,f71]) ).
fof(f217,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f216]) ).
fof(f218,plain,
( d = d
| d = c ),
inference(resolution,[status(thm)],[f66,f59]) ).
fof(f219,plain,
( identity_for(g2) = d
| identity_for(g2) = c ),
inference(resolution,[status(thm)],[f66,f40]) ).
fof(f220,plain,
( c = d
| c = c ),
inference(resolution,[status(thm)],[f66,f58]) ).
fof(f221,definition,
( sQ15_spl
<=> d = c ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f222,plain,
( ~ sQ15_spl
| d = c ),
inference(component_clause,[status(thm)],[f221]) ).
fof(f224,definition,
( sQ16_spl
<=> d = d ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f227,plain,
( sQ16_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f218,f221,f224]) ).
fof(f228,definition,
( sQ17_spl
<=> identity_for(g2) = c ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f231,definition,
( sQ18_spl
<=> identity_for(g2) = d ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f232,plain,
( ~ sQ18_spl
| identity_for(g2) = d ),
inference(component_clause,[status(thm)],[f231]) ).
fof(f234,plain,
( sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f219,f228,f231]) ).
fof(f235,definition,
( sQ19_spl
<=> c = c ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f238,plain,
( sQ15_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f220,f235,f221]) ).
fof(f239,plain,
( ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f222,f60]) ).
fof(f240,plain,
~ sQ15_spl,
inference(contradiction_clause,[status(thm)],[f239]) ).
fof(f241,plain,
! [X0] : product(g1,X0,inverse(g1,X0),a),
inference(paramodulation,[status(thm)],[f67,f45]) ).
fof(f242,plain,
! [X0] : product(g1,inverse(g1,X0),X0,a),
inference(paramodulation,[status(thm)],[f67,f44]) ).
fof(f246,plain,
! [X0] : product(g2,X0,inverse(g2,X0),c),
inference(paramodulation,[status(thm)],[f68,f45]) ).
fof(f247,plain,
! [X0] : product(g2,inverse(g2,X0),X0,c),
inference(paramodulation,[status(thm)],[f68,f44]) ).
fof(f252,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ product(g2,isomorphism2(b),isomorphism2(d2),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f194,f87]) ).
fof(f253,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ product(g2,c,isomorphism2(d2),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f76,f252]) ).
fof(f254,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ product(g2,c,isomorphism2(b),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f187,f253]) ).
fof(f255,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ product(g2,c,c,isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f76,f254]) ).
fof(f256,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ product(g2,c,c,isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f255]) ).
fof(f257,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ8_spl
| ~ product(g2,c,c,c) ),
inference(forward_demodulation,[status(thm)],[f76,f256]) ).
fof(f258,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f257,f71]) ).
fof(f259,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ12_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f258]) ).
fof(f260,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ product(g2,c,c,isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f205]) ).
fof(f261,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ product(g2,c,c,d) ),
inference(forward_demodulation,[status(thm)],[f74,f260]) ).
fof(f264,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ product(g2,c,isomorphism1(d2),isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f202]) ).
fof(f265,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ product(g2,c,isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f74,f264]) ).
fof(f267,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f84]) ).
fof(f268,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f74,f267]) ).
fof(f269,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f86]) ).
fof(f270,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| product(g2,isomorphism2(d1),isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f76,f269]) ).
fof(f271,plain,
( ~ sQ13_spl
| product(g1,a,d2,d3) ),
inference(forward_demodulation,[status(thm)],[f191,f80]) ).
fof(f272,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| product(g1,a,a,d3) ),
inference(forward_demodulation,[status(thm)],[f184,f271]) ).
fof(f273,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| product(g1,a,a,b) ),
inference(forward_demodulation,[status(thm)],[f173,f272]) ).
fof(f274,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f273,f89]) ).
fof(f275,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f273,f53]) ).
fof(f276,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| product(g1,a,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f273,f51]) ).
fof(f277,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| X0 = b
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f273,f49]) ).
fof(f278,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f274]) ).
fof(f280,plain,
( ~ sQ10_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f67,f180]) ).
fof(f281,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f280,f57]) ).
fof(f282,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f281]) ).
fof(f286,plain,
! [X0,X1,X2,X3] :
( product(g1,X0,X1,X3)
| ~ product(g1,a,X2,X3)
| ~ product(g1,X0,X1,X2) ),
inference(resolution,[status(thm)],[f69,f53]) ).
fof(f287,plain,
! [X0,X1,X2,X3] :
( product(g1,a,X2,X3)
| ~ product(g1,X0,X1,X3)
| ~ product(g1,X0,X1,X2) ),
inference(resolution,[status(thm)],[f69,f51]) ).
fof(f288,plain,
! [X0,X1] :
( X1 = X0
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f69,f49]) ).
fof(f289,plain,
! [X0,X1] :
( product(g1,identity_for(g1),X0,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f70,f89]) ).
fof(f290,plain,
! [X0,X1,X2,X3] :
( product(g1,X2,X0,X3)
| ~ product(g1,X2,X1,X3)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f70,f53]) ).
fof(f291,plain,
! [X0,X1,X2,X3] :
( product(g1,X2,X1,X3)
| ~ product(g1,X2,X0,X3)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f70,f51]) ).
fof(f292,plain,
! [X0,X1] :
( X1 = X0
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f70,f49]) ).
fof(f293,plain,
! [X0,X1] :
( product(g1,a,X0,X1)
| ~ product(g1,X0,a,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f289]) ).
fof(f295,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| inverse(g1,b) = a ),
inference(forward_demodulation,[status(thm)],[f173,f163]) ).
fof(f296,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| product(g1,b,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f295,f45]) ).
fof(f297,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| product(g1,a,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f295,f44]) ).
fof(f298,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f67,f296]) ).
fof(f299,plain,
( ~ sQ5_spl
| ~ sQ8_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f67,f297]) ).
fof(f300,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| inverse(g1,b) = b ),
inference(forward_demodulation,[status(thm)],[f173,f166]) ).
fof(f301,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ5_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f295,f300]) ).
fof(f302,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f301,f57]) ).
fof(f303,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f302]) ).
fof(f304,plain,
( sQ5_spl
| ~ sQ8_spl
| inverse(g1,b) != a ),
inference(forward_demodulation,[status(thm)],[f173,f164]) ).
fof(f308,plain,
( ~ sQ18_spl
| c = d ),
inference(forward_demodulation,[status(thm)],[f68,f232]) ).
fof(f309,plain,
( ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f308,f60]) ).
fof(f310,plain,
~ sQ18_spl,
inference(contradiction_clause,[status(thm)],[f309]) ).
fof(f312,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ product(g2,isomorphism1(a),isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f191,f268]) ).
fof(f313,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ product(g2,c,isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f73,f312]) ).
fof(f316,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g2,isomorphism2(a),isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f191,f270]) ).
fof(f317,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g2,d,isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f75,f316]) ).
fof(f318,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ11_spl
| product(g2,d,isomorphism2(a),c) ),
inference(forward_demodulation,[status(thm)],[f184,f317]) ).
fof(f319,plain,
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ11_spl
| product(g2,d,d,c) ),
inference(forward_demodulation,[status(thm)],[f75,f318]) ).
fof(f320,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ11_spl
| product(g2,identity_for(g2),c,X0)
| ~ product(g2,d,d,X0) ),
inference(resolution,[status(thm)],[f319,f89]) ).
fof(f321,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ11_spl
| product(g2,c,X0,X2)
| ~ product(g2,d,X1,X2)
| ~ product(g2,d,X0,X1) ),
inference(resolution,[status(thm)],[f319,f53]) ).
fof(f322,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ11_spl
| product(g2,d,X1,X2)
| ~ product(g2,c,X0,X2)
| ~ product(g2,d,X0,X1) ),
inference(resolution,[status(thm)],[f319,f51]) ).
fof(f323,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ11_spl
| X0 = c
| ~ product(g2,d,d,X0) ),
inference(resolution,[status(thm)],[f319,f49]) ).
fof(f324,plain,
! [X0] :
( ~ sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ sQ11_spl
| product(g2,c,c,X0)
| ~ product(g2,d,d,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f320]) ).
fof(f328,plain,
! [X0] : identity_for(X0) = inverse(X0,identity_for(X0)),
inference(resolution,[status(thm)],[f90,f45]) ).
fof(f332,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f300,f45]) ).
fof(f333,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f300,f44]) ).
fof(f334,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f67,f332]) ).
fof(f335,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f67,f333]) ).
fof(f336,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f93]) ).
fof(f337,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ8_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f336]) ).
fof(f338,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f191,f337]) ).
fof(f339,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f338,f273]) ).
fof(f340,plain,
! [X0,X1] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,X0,X1)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f338,f69]) ).
fof(f341,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,a,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f338,f70]) ).
fof(f342,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,inverse(g1,a),X0) ),
inference(resolution,[status(thm)],[f338,f45]) ).
fof(f343,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,a,X0)
| ~ product(g1,b,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f338,f42]) ).
fof(f344,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,a,X0)
| ~ product(g1,b,inverse(g1,a),X0) ),
inference(forward_demodulation,[status(thm)],[f67,f342]) ).
fof(f345,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,a,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f343]) ).
fof(f347,plain,
identity_for(g2) = inverse(g2,c),
inference(paramodulation,[status(thm)],[f68,f328]) ).
fof(f348,plain,
identity_for(g1) = inverse(g1,a),
inference(paramodulation,[status(thm)],[f67,f328]) ).
fof(f351,plain,
c = inverse(g2,c),
inference(forward_demodulation,[status(thm)],[f68,f347]) ).
fof(f352,plain,
a = inverse(g1,a),
inference(forward_demodulation,[status(thm)],[f67,f348]) ).
fof(f375,plain,
! [X0] :
( ~ sQ13_spl
| X0 = d3
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f191,f94]) ).
fof(f376,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| X0 = d3
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f375]) ).
fof(f377,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| X0 = b
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f173,f376]) ).
fof(f379,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| a = b ),
inference(resolution,[status(thm)],[f377,f69]) ).
fof(f381,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f379,f151,f172,f183,f190]) ).
fof(f383,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ product(g2,isomorphism1(a),isomorphism1(d2),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f191,f84]) ).
fof(f384,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ product(g2,c,isomorphism1(d2),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f73,f383]) ).
fof(f385,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| product(g1,a,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f191,f93]) ).
fof(f388,plain,
! [X0] :
( group_member(multiply(g1,d3,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f79,f47]) ).
fof(f389,plain,
! [X0] :
( product(g1,d3,X0,multiply(g1,d3,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f79,f46]) ).
fof(f390,plain,
group_member(inverse(g1,d3),g1),
inference(resolution,[status(thm)],[f79,f43]) ).
fof(f393,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ product(g2,c,isomorphism1(d2),isomorphism1(a)) ),
inference(backward_demodulation,[status(thm)],[f170,f384]) ).
fof(f395,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ product(g2,c,isomorphism1(d2),c) ),
inference(forward_demodulation,[status(thm)],[f73,f393]) ).
fof(f396,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,d2,a) ),
inference(forward_demodulation,[status(thm)],[f170,f200]) ).
fof(f397,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f396,f89]) ).
fof(f398,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f396,f53]) ).
fof(f399,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f396,f51]) ).
fof(f400,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| X0 = a
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f396,f49]) ).
fof(f401,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,a,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f397]) ).
fof(f403,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f404,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f46]) ).
fof(f405,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f78,f43]) ).
fof(f412,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| product(g1,a,b,d3) ),
inference(forward_demodulation,[status(thm)],[f187,f271]) ).
fof(f413,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f170,f412]) ).
fof(f414,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f413,f89]) ).
fof(f415,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f413,f53]) ).
fof(f416,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f413,f51]) ).
fof(f417,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f413,f49]) ).
fof(f418,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f414]) ).
fof(f419,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ product(g2,c,isomorphism1(b),c) ),
inference(forward_demodulation,[status(thm)],[f187,f395]) ).
fof(f420,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ12_spl
| ~ product(g2,c,d,c) ),
inference(forward_demodulation,[status(thm)],[f74,f419]) ).
fof(f421,plain,
( ~ sQ12_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f104]) ).
fof(f423,plain,
! [X0] :
( ~ sQ12_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f421,f47]) ).
fof(f424,plain,
! [X0] :
( ~ sQ12_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f421,f46]) ).
fof(f425,plain,
( ~ sQ12_spl
| group_member(inverse(g1,inverse(g1,b)),g1) ),
inference(resolution,[status(thm)],[f421,f43]) ).
fof(f426,definition,
( sQ20_spl
<=> inverse(g1,b) = a ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f427,plain,
( ~ sQ20_spl
| inverse(g1,b) = a ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f428,plain,
( sQ20_spl
| inverse(g1,b) != a ),
inference(component_clause,[status(thm)],[f426]) ).
fof(f429,definition,
( sQ21_spl
<=> inverse(g1,b) = b ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f430,plain,
( ~ sQ21_spl
| inverse(g1,b) = b ),
inference(component_clause,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f187,f95]) ).
fof(f434,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ13_spl
| product(g1,d3,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f191,f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f170,f434]) ).
fof(f436,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f435,f70]) ).
fof(f437,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,inverse(g1,b),X0)
| ~ product(g1,a,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f435,f45]) ).
fof(f438,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f435,f42]) ).
fof(f439,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,inverse(g1,b),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f437]) ).
fof(f440,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f438]) ).
fof(f442,plain,
( ~ sQ20_spl
| product(g1,b,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f427,f45]) ).
fof(f443,plain,
( ~ sQ20_spl
| product(g1,a,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f427,f44]) ).
fof(f444,plain,
( ~ sQ20_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f67,f442]) ).
fof(f445,plain,
( ~ sQ20_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f67,f443]) ).
fof(f451,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,a,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f96,f413]) ).
fof(f453,plain,
! [X0,X1] :
( product(g1,X0,a,X1)
| ~ product(g1,identity_for(g1),X0,X1) ),
inference(resolution,[status(thm)],[f96,f70]) ).
fof(f455,plain,
! [X0,X1] :
( product(g2,X0,c,X1)
| ~ product(g2,identity_for(g2),X0,X1) ),
inference(resolution,[status(thm)],[f96,f72]) ).
fof(f456,plain,
! [X0,X1,X2] :
( product(X0,inverse(X0,X2),X2,X1)
| ~ product(X0,identity_for(X0),identity_for(X0),X1) ),
inference(resolution,[status(thm)],[f96,f44]) ).
fof(f458,plain,
! [X0,X1,X2] :
( product(X0,X2,inverse(X0,X2),X1)
| ~ product(X0,identity_for(X0),identity_for(X0),X1) ),
inference(resolution,[status(thm)],[f96,f45]) ).
fof(f459,plain,
! [X0,X1,X2] :
( product(X0,X1,identity_for(X0),X2)
| ~ product(X0,identity_for(X0),X1,X2) ),
inference(resolution,[status(thm)],[f96,f42]) ).
fof(f460,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f451]) ).
fof(f461,plain,
! [X0,X1] :
( product(g1,X0,a,X1)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f453]) ).
fof(f462,plain,
! [X0,X1] :
( product(g2,X0,c,X1)
| ~ product(g2,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f68,f455]) ).
fof(f480,plain,
! [X0,X1] :
( product(g2,inverse(g2,X1),X1,X0)
| ~ product(g2,c,identity_for(g2),X0) ),
inference(resolution,[status(thm)],[f98,f44]) ).
fof(f482,plain,
! [X0,X1] :
( product(g2,X1,inverse(g2,X1),X0)
| ~ product(g2,c,identity_for(g2),X0) ),
inference(resolution,[status(thm)],[f98,f45]) ).
fof(f484,plain,
! [X0,X1] :
( product(g2,inverse(g2,X1),X1,X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f480]) ).
fof(f485,plain,
! [X0,X1] :
( product(g2,X1,inverse(g2,X1),X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f482]) ).
fof(f489,plain,
! [X0,X1] :
( product(g2,c,identity_for(g2),X1)
| ~ product(g2,inverse(g2,X0),X0,X1) ),
inference(resolution,[status(thm)],[f99,f44]) ).
fof(f491,plain,
! [X0,X1] :
( product(g2,c,identity_for(g2),X1)
| ~ product(g2,X0,inverse(g2,X0),X1) ),
inference(resolution,[status(thm)],[f99,f45]) ).
fof(f493,plain,
! [X0,X1] :
( product(g2,c,c,X1)
| ~ product(g2,inverse(g2,X0),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f68,f489]) ).
fof(f494,plain,
! [X0,X1] :
( product(g2,c,c,X1)
| ~ product(g2,X0,inverse(g2,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f68,f491]) ).
fof(f496,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f106,f413]) ).
fof(f498,plain,
! [X0,X1] :
( product(g1,identity_for(g1),a,X1)
| ~ product(g1,inverse(g1,X0),X0,X1) ),
inference(resolution,[status(thm)],[f106,f70]) ).
fof(f501,plain,
! [X0,X1,X2] :
( product(X0,identity_for(X0),X1,X2)
| ~ product(X0,inverse(X0,inverse(X0,X1)),identity_for(X0),X2) ),
inference(resolution,[status(thm)],[f106,f44]) ).
fof(f505,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f352,f496]) ).
fof(f506,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f505]) ).
fof(f508,plain,
! [X0,X1] :
( product(g1,a,a,X1)
| ~ product(g1,inverse(g1,X0),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f498]) ).
fof(f513,plain,
! [X0] :
( ~ sQ7_spl
| product(g1,a,X0,multiply(g1,d3,X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f170,f130]) ).
fof(f514,plain,
! [X0] :
( ~ sQ7_spl
| product(g1,a,X0,multiply(g1,a,X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f170,f513]) ).
fof(f515,plain,
( ~ sQ7_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(resolution,[status(thm)],[f514,f56]) ).
fof(f516,plain,
( ~ sQ7_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(resolution,[status(thm)],[f514,f55]) ).
fof(f517,plain,
( ~ sQ7_spl
| product(g1,a,identity_for(g1),multiply(g1,a,identity_for(g1))) ),
inference(resolution,[status(thm)],[f514,f40]) ).
fof(f518,plain,
( ~ sQ7_spl
| product(g1,a,a,multiply(g1,a,identity_for(g1))) ),
inference(forward_demodulation,[status(thm)],[f67,f517]) ).
fof(f519,plain,
( ~ sQ7_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f67,f518]) ).
fof(f520,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| a = b ),
inference(resolution,[status(thm)],[f288,f413]) ).
fof(f525,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ7_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f520,f151,f169,f186,f190]) ).
fof(f527,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| product(g1,d3,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f191,f95]) ).
fof(f528,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f170,f527]) ).
fof(f529,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,d2,a) ),
inference(forward_demodulation,[status(thm)],[f170,f271]) ).
fof(f531,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ7_spl
| product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f170,f336]) ).
fof(f535,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| product(g2,isomorphism1(a),isomorphism1(d2),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f191,f83]) ).
fof(f536,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| product(g2,c,isomorphism1(d2),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f73,f535]) ).
fof(f537,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ7_spl
| product(g2,c,isomorphism1(d2),isomorphism1(a)) ),
inference(forward_demodulation,[status(thm)],[f170,f536]) ).
fof(f538,plain,
( ~ sQ0_spl
| ~ sQ13_spl
| ~ sQ7_spl
| product(g2,c,isomorphism1(d2),c) ),
inference(forward_demodulation,[status(thm)],[f73,f537]) ).
fof(f539,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ product(g2,isomorphism2(a),isomorphism2(d2),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f191,f87]) ).
fof(f540,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ product(g2,d,isomorphism2(d2),isomorphism2(d3)) ),
inference(forward_demodulation,[status(thm)],[f75,f539]) ).
fof(f541,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ product(g2,d,isomorphism2(d2),isomorphism2(a)) ),
inference(forward_demodulation,[status(thm)],[f170,f540]) ).
fof(f542,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ product(g2,d,isomorphism2(d2),d) ),
inference(forward_demodulation,[status(thm)],[f75,f541]) ).
fof(f543,plain,
( ~ sQ13_spl
| ~ sQ7_spl
| a = d2 ),
inference(resolution,[status(thm)],[f529,f288]) ).
fof(f544,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f529,f106]) ).
fof(f545,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,d2,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f529,f96]) ).
fof(f546,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f529,f89]) ).
fof(f547,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f529,f53]) ).
fof(f548,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f529,f51]) ).
fof(f549,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| X0 = a
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f529,f49]) ).
fof(f550,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f352,f544]) ).
fof(f551,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f550]) ).
fof(f552,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f545]) ).
fof(f553,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ7_spl
| product(g1,a,a,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f546]) ).
fof(f554,plain,
( ~ sQ7_spl
| product(g1,a,d2,multiply(g1,a,d2)) ),
inference(resolution,[status(thm)],[f78,f514]) ).
fof(f556,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f557,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f46]) ).
fof(f558,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f78,f43]) ).
fof(f567,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ product(g2,d,isomorphism2(a),d) ),
inference(forward_demodulation,[status(thm)],[f184,f542]) ).
fof(f568,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ7_spl
| ~ sQ11_spl
| ~ product(g2,d,d,d) ),
inference(forward_demodulation,[status(thm)],[f75,f567]) ).
fof(f579,plain,
! [X0,X1] :
( product(g1,inverse(g1,X1),X1,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f107,f70]) ).
fof(f587,plain,
! [X0,X1] :
( product(g1,inverse(g1,X1),X1,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f579]) ).
fof(f601,plain,
( ~ sQ7_spl
| product(g1,a,inverse(g1,b),multiply(g1,a,inverse(g1,b))) ),
inference(resolution,[status(thm)],[f124,f514]) ).
fof(f602,plain,
( inverse(g1,b) = b
| inverse(g1,b) = a ),
inference(resolution,[status(thm)],[f124,f65]) ).
fof(f603,plain,
! [X0] :
( group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f124,f47]) ).
fof(f604,plain,
! [X0] :
( product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f124,f46]) ).
fof(f605,plain,
group_member(inverse(g1,inverse(g1,b)),g1),
inference(resolution,[status(thm)],[f124,f43]) ).
fof(f606,plain,
( sQ21_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f602,f426,f429]) ).
fof(f608,plain,
! [X0] :
( ~ sQ20_spl
| X0 = identity_for(g1)
| ~ product(g1,a,b,X0) ),
inference(paramodulation,[status(thm)],[f427,f108]) ).
fof(f609,plain,
( ~ sQ20_spl
| product(g1,b,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f427,f45]) ).
fof(f610,plain,
( ~ sQ20_spl
| product(g1,a,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f427,f44]) ).
fof(f611,plain,
! [X0] :
( ~ sQ20_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f608]) ).
fof(f612,plain,
( ~ sQ20_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f67,f609]) ).
fof(f613,plain,
( ~ sQ20_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f67,f610]) ).
fof(f614,plain,
( inverse(g2,d) = d
| inverse(g2,d) = c ),
inference(resolution,[status(thm)],[f125,f66]) ).
fof(f615,plain,
! [X0] :
( group_member(multiply(g2,inverse(g2,d),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f125,f47]) ).
fof(f616,plain,
! [X0] :
( product(g2,inverse(g2,d),X0,multiply(g2,inverse(g2,d),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f125,f46]) ).
fof(f617,plain,
group_member(inverse(g2,inverse(g2,d)),g2),
inference(resolution,[status(thm)],[f125,f43]) ).
fof(f618,definition,
( sQ22_spl
<=> inverse(g2,d) = c ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f619,plain,
( ~ sQ22_spl
| inverse(g2,d) = c ),
inference(component_clause,[status(thm)],[f618]) ).
fof(f620,plain,
( sQ22_spl
| inverse(g2,d) != c ),
inference(component_clause,[status(thm)],[f618]) ).
fof(f621,definition,
( sQ23_spl
<=> inverse(g2,d) = d ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f622,plain,
( ~ sQ23_spl
| inverse(g2,d) = d ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,plain,
( sQ23_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f614,f618,f621]) ).
fof(f625,plain,
! [X0,X1] :
( product(g1,identity_for(g1),a,X1)
| ~ product(g1,X0,inverse(g1,X0),X1) ),
inference(resolution,[status(thm)],[f109,f70]) ).
fof(f631,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f427,f109]) ).
fof(f634,plain,
! [X0,X1] :
( product(g1,a,a,X1)
| ~ product(g1,X0,inverse(g1,X0),X1) ),
inference(forward_demodulation,[status(thm)],[f67,f625]) ).
fof(f637,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f631]) ).
fof(f639,plain,
! [X0,X1] :
( product(g1,X1,inverse(g1,X1),X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f110,f70]) ).
fof(f645,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f427,f110]) ).
fof(f648,plain,
! [X0,X1] :
( product(g1,X1,inverse(g1,X1),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f639]) ).
fof(f651,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f645]) ).
fof(f658,plain,
! [X0] :
( ~ sQ20_spl
| X0 = identity_for(g1)
| ~ product(g1,b,a,X0) ),
inference(paramodulation,[status(thm)],[f427,f111]) ).
fof(f664,plain,
! [X0] :
( ~ sQ20_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f658]) ).
fof(f681,plain,
! [X0] :
( ~ sQ22_spl
| X0 = identity_for(g2)
| ~ product(g2,d,c,X0) ),
inference(paramodulation,[status(thm)],[f619,f111]) ).
fof(f682,plain,
! [X0,X1,X2] :
( ~ sQ22_spl
| product(g2,d,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f619,f110]) ).
fof(f683,plain,
! [X0,X1,X2] :
( ~ sQ22_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,d,X1,X2)
| ~ product(g2,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f619,f109]) ).
fof(f684,plain,
! [X0] :
( ~ sQ22_spl
| X0 = identity_for(g2)
| ~ product(g2,c,d,X0) ),
inference(paramodulation,[status(thm)],[f619,f108]) ).
fof(f685,plain,
( ~ sQ22_spl
| product(g2,d,c,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f619,f45]) ).
fof(f686,plain,
( ~ sQ22_spl
| product(g2,c,d,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f619,f44]) ).
fof(f687,plain,
! [X0] :
( ~ sQ22_spl
| X0 = c
| ~ product(g2,d,c,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f681]) ).
fof(f688,plain,
! [X0,X1,X2] :
( ~ sQ22_spl
| product(g2,d,X1,X2)
| ~ product(g2,c,X0,X2)
| ~ product(g2,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f68,f682]) ).
fof(f689,plain,
! [X0,X1,X2] :
( ~ sQ22_spl
| product(g2,c,X0,X2)
| ~ product(g2,d,X1,X2)
| ~ product(g2,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f68,f683]) ).
fof(f690,plain,
! [X0] :
( ~ sQ22_spl
| X0 = c
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f684]) ).
fof(f691,plain,
( ~ sQ22_spl
| product(g2,d,c,c) ),
inference(forward_demodulation,[status(thm)],[f68,f685]) ).
fof(f692,plain,
( ~ sQ22_spl
| product(g2,c,d,c) ),
inference(forward_demodulation,[status(thm)],[f68,f686]) ).
fof(f695,plain,
product(g2,d,d,multiply(g2,d,d)),
inference(resolution,[status(thm)],[f126,f59]) ).
fof(f696,plain,
product(g2,d,identity_for(g2),multiply(g2,d,identity_for(g2))),
inference(resolution,[status(thm)],[f126,f40]) ).
fof(f697,plain,
product(g2,d,c,multiply(g2,d,c)),
inference(resolution,[status(thm)],[f126,f58]) ).
fof(f698,plain,
product(g2,d,c,multiply(g2,d,identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f68,f696]) ).
fof(f699,plain,
product(g2,d,c,multiply(g2,d,c)),
inference(forward_demodulation,[status(thm)],[f68,f698]) ).
fof(f700,plain,
product(g1,b,b,multiply(g1,b,b)),
inference(resolution,[status(thm)],[f127,f56]) ).
fof(f701,plain,
product(g1,b,a,multiply(g1,b,a)),
inference(resolution,[status(thm)],[f127,f55]) ).
fof(f702,plain,
product(g1,b,identity_for(g1),multiply(g1,b,identity_for(g1))),
inference(resolution,[status(thm)],[f127,f40]) ).
fof(f703,plain,
product(g1,b,a,multiply(g1,b,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f67,f702]) ).
fof(f704,plain,
product(g1,b,a,multiply(g1,b,a)),
inference(forward_demodulation,[status(thm)],[f67,f703]) ).
fof(f707,plain,
! [X0] :
( ~ sQ7_spl
| group_member(multiply(g1,a,X0),g1)
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f170,f139]) ).
fof(f708,plain,
( ~ sQ7_spl
| group_member(multiply(g1,a,b),g1) ),
inference(resolution,[status(thm)],[f707,f56]) ).
fof(f709,plain,
( ~ sQ7_spl
| group_member(multiply(g1,a,a),g1) ),
inference(resolution,[status(thm)],[f707,f55]) ).
fof(f710,plain,
( ~ sQ7_spl
| group_member(multiply(g1,a,identity_for(g1)),g1) ),
inference(resolution,[status(thm)],[f707,f40]) ).
fof(f711,plain,
( ~ sQ7_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f67,f710]) ).
fof(f712,plain,
( ~ sQ20_spl
| a = b ),
inference(resolution,[status(thm)],[f444,f292]) ).
fof(f715,plain,
! [X0] :
( ~ sQ20_spl
| product(g1,b,a,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f444,f96]) ).
fof(f716,plain,
! [X0] :
( ~ sQ20_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f444,f89]) ).
fof(f717,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f444,f53]) ).
fof(f718,plain,
! [X0,X1,X2] :
( ~ sQ20_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f444,f51]) ).
fof(f719,plain,
! [X0] :
( ~ sQ20_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f444,f49]) ).
fof(f720,plain,
( ~ sQ20_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f712,f151,f426]) ).
fof(f723,plain,
! [X0] :
( ~ sQ20_spl
| product(g1,b,a,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f715]) ).
fof(f724,plain,
! [X0] :
( ~ sQ20_spl
| product(g1,a,a,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f716]) ).
fof(f725,plain,
! [X0] :
( ~ sQ21_spl
| X0 = identity_for(g1)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f430,f111]) ).
fof(f726,plain,
! [X0,X1,X2] :
( ~ sQ21_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f430,f110]) ).
fof(f727,plain,
! [X0,X1,X2] :
( ~ sQ21_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(paramodulation,[status(thm)],[f430,f109]) ).
fof(f729,plain,
( ~ sQ21_spl
| product(g1,b,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f430,f45]) ).
fof(f731,plain,
! [X0] :
( ~ sQ21_spl
| X0 = a
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f725]) ).
fof(f732,plain,
! [X0,X1,X2] :
( ~ sQ21_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f726]) ).
fof(f733,plain,
! [X0,X1,X2] :
( ~ sQ21_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f727]) ).
fof(f735,plain,
( ~ sQ21_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f67,f729]) ).
fof(f737,plain,
product(g2,c,d,multiply(g2,c,d)),
inference(resolution,[status(thm)],[f132,f59]) ).
fof(f738,plain,
product(g2,c,identity_for(g2),multiply(g2,c,identity_for(g2))),
inference(resolution,[status(thm)],[f132,f40]) ).
fof(f739,plain,
product(g2,c,c,multiply(g2,c,c)),
inference(resolution,[status(thm)],[f132,f58]) ).
fof(f740,plain,
product(g2,c,c,multiply(g2,c,identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f68,f738]) ).
fof(f741,plain,
product(g2,c,c,multiply(g2,c,c)),
inference(forward_demodulation,[status(thm)],[f68,f740]) ).
fof(f742,plain,
group_member(multiply(g2,c,d),g2),
inference(resolution,[status(thm)],[f141,f59]) ).
fof(f743,plain,
group_member(multiply(g2,c,identity_for(g2)),g2),
inference(resolution,[status(thm)],[f141,f40]) ).
fof(f744,plain,
group_member(multiply(g2,c,c),g2),
inference(resolution,[status(thm)],[f141,f58]) ).
fof(f745,plain,
group_member(multiply(g2,c,c),g2),
inference(forward_demodulation,[status(thm)],[f68,f743]) ).
fof(f747,plain,
( ~ sQ22_spl
| c = d ),
inference(resolution,[status(thm)],[f691,f115]) ).
fof(f748,plain,
! [X0] :
( ~ sQ22_spl
| product(g2,c,c,X0)
| ~ product(g2,d,c,X0) ),
inference(resolution,[status(thm)],[f691,f99]) ).
fof(f749,plain,
! [X0] :
( ~ sQ22_spl
| product(g2,d,c,X0)
| ~ product(g2,c,c,X0) ),
inference(resolution,[status(thm)],[f691,f98]) ).
fof(f752,plain,
! [X0] :
( ~ sQ22_spl
| product(g2,d,c,X0)
| ~ product(g2,identity_for(g2),c,X0) ),
inference(resolution,[status(thm)],[f691,f96]) ).
fof(f753,plain,
! [X0] :
( ~ sQ22_spl
| product(g2,identity_for(g2),c,X0)
| ~ product(g2,d,c,X0) ),
inference(resolution,[status(thm)],[f691,f89]) ).
fof(f754,plain,
! [X0,X1,X2] :
( ~ sQ22_spl
| product(g2,c,X0,X2)
| ~ product(g2,d,X1,X2)
| ~ product(g2,c,X0,X1) ),
inference(resolution,[status(thm)],[f691,f53]) ).
fof(f755,plain,
! [X0,X1,X2] :
( ~ sQ22_spl
| product(g2,d,X1,X2)
| ~ product(g2,c,X0,X2)
| ~ product(g2,c,X0,X1) ),
inference(resolution,[status(thm)],[f691,f51]) ).
fof(f756,plain,
! [X0] :
( ~ sQ22_spl
| X0 = c
| ~ product(g2,d,c,X0) ),
inference(resolution,[status(thm)],[f691,f49]) ).
fof(f757,plain,
( ~ sQ22_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f747,f221,f618]) ).
fof(f760,plain,
! [X0] :
( ~ sQ22_spl
| product(g2,d,c,X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f752]) ).
fof(f761,plain,
! [X0] :
( ~ sQ22_spl
| product(g2,c,c,X0)
| ~ product(g2,d,c,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f753]) ).
fof(f762,plain,
! [X0] :
( ~ sQ23_spl
| X0 = identity_for(g2)
| ~ product(g2,d,d,X0) ),
inference(paramodulation,[status(thm)],[f622,f111]) ).
fof(f763,plain,
! [X0,X1,X2] :
( ~ sQ23_spl
| product(g2,d,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,d,X0,X1) ),
inference(paramodulation,[status(thm)],[f622,f110]) ).
fof(f764,plain,
! [X0,X1,X2] :
( ~ sQ23_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,d,X1,X2)
| ~ product(g2,d,X0,X1) ),
inference(paramodulation,[status(thm)],[f622,f109]) ).
fof(f766,plain,
( ~ sQ23_spl
| product(g2,d,d,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f622,f45]) ).
fof(f768,plain,
! [X0] :
( ~ sQ23_spl
| X0 = c
| ~ product(g2,d,d,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f762]) ).
fof(f769,plain,
! [X0,X1,X2] :
( ~ sQ23_spl
| product(g2,d,X1,X2)
| ~ product(g2,c,X0,X2)
| ~ product(g2,d,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f68,f763]) ).
fof(f770,plain,
! [X0,X1,X2] :
( ~ sQ23_spl
| product(g2,c,X0,X2)
| ~ product(g2,d,X1,X2)
| ~ product(g2,d,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f68,f764]) ).
fof(f772,plain,
( ~ sQ23_spl
| product(g2,d,d,c) ),
inference(forward_demodulation,[status(thm)],[f68,f766]) ).
fof(f774,plain,
product(g2,identity_for(g2),d,multiply(g2,identity_for(g2),d)),
inference(resolution,[status(thm)],[f131,f59]) ).
fof(f775,plain,
product(g1,identity_for(g1),b,multiply(g1,identity_for(g1),b)),
inference(resolution,[status(thm)],[f131,f56]) ).
fof(f776,plain,
product(g1,identity_for(g1),a,multiply(g1,identity_for(g1),a)),
inference(resolution,[status(thm)],[f131,f55]) ).
fof(f777,plain,
! [X0] : product(X0,identity_for(X0),identity_for(X0),multiply(X0,identity_for(X0),identity_for(X0))),
inference(resolution,[status(thm)],[f131,f40]) ).
fof(f778,plain,
product(g2,identity_for(g2),c,multiply(g2,identity_for(g2),c)),
inference(resolution,[status(thm)],[f131,f58]) ).
fof(f779,plain,
product(g2,c,d,multiply(g2,identity_for(g2),d)),
inference(forward_demodulation,[status(thm)],[f68,f774]) ).
fof(f780,plain,
product(g2,c,d,multiply(g2,c,d)),
inference(forward_demodulation,[status(thm)],[f68,f779]) ).
fof(f781,plain,
product(g1,a,b,multiply(g1,identity_for(g1),b)),
inference(forward_demodulation,[status(thm)],[f67,f775]) ).
fof(f782,plain,
product(g1,a,b,multiply(g1,a,b)),
inference(forward_demodulation,[status(thm)],[f67,f781]) ).
fof(f783,plain,
product(g1,a,a,multiply(g1,identity_for(g1),a)),
inference(forward_demodulation,[status(thm)],[f67,f776]) ).
fof(f784,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f67,f783]) ).
fof(f785,plain,
product(g2,c,c,multiply(g2,identity_for(g2),c)),
inference(forward_demodulation,[status(thm)],[f68,f778]) ).
fof(f786,plain,
product(g2,c,c,multiply(g2,c,c)),
inference(forward_demodulation,[status(thm)],[f68,f785]) ).
fof(f787,plain,
group_member(multiply(g2,d,d),g2),
inference(resolution,[status(thm)],[f135,f59]) ).
fof(f788,plain,
group_member(multiply(g2,d,identity_for(g2)),g2),
inference(resolution,[status(thm)],[f135,f40]) ).
fof(f789,plain,
group_member(multiply(g2,d,c),g2),
inference(resolution,[status(thm)],[f135,f58]) ).
fof(f790,plain,
group_member(multiply(g2,d,c),g2),
inference(forward_demodulation,[status(thm)],[f68,f788]) ).
fof(f791,plain,
group_member(multiply(g1,b,b),g1),
inference(resolution,[status(thm)],[f136,f56]) ).
fof(f792,plain,
group_member(multiply(g1,b,a),g1),
inference(resolution,[status(thm)],[f136,f55]) ).
fof(f793,plain,
group_member(multiply(g1,b,identity_for(g1)),g1),
inference(resolution,[status(thm)],[f136,f40]) ).
fof(f794,plain,
group_member(multiply(g1,b,a),g1),
inference(forward_demodulation,[status(thm)],[f67,f793]) ).
fof(f797,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,b,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f735,f96]) ).
fof(f798,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f735,f89]) ).
fof(f806,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f797]) ).
fof(f807,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f798]) ).
fof(f809,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| X0 = d3
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f375]) ).
fof(f812,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f286,f735]) ).
fof(f825,plain,
group_member(multiply(g2,identity_for(g2),d),g2),
inference(resolution,[status(thm)],[f140,f59]) ).
fof(f826,plain,
group_member(multiply(g1,identity_for(g1),b),g1),
inference(resolution,[status(thm)],[f140,f56]) ).
fof(f827,plain,
group_member(multiply(g1,identity_for(g1),a),g1),
inference(resolution,[status(thm)],[f140,f55]) ).
fof(f828,plain,
! [X0] : group_member(multiply(X0,identity_for(X0),identity_for(X0)),X0),
inference(resolution,[status(thm)],[f140,f40]) ).
fof(f829,plain,
group_member(multiply(g2,identity_for(g2),c),g2),
inference(resolution,[status(thm)],[f140,f58]) ).
fof(f830,plain,
group_member(multiply(g2,c,d),g2),
inference(forward_demodulation,[status(thm)],[f68,f825]) ).
fof(f831,plain,
group_member(multiply(g1,a,b),g1),
inference(forward_demodulation,[status(thm)],[f67,f826]) ).
fof(f832,plain,
group_member(multiply(g1,a,a),g1),
inference(forward_demodulation,[status(thm)],[f67,f827]) ).
fof(f833,plain,
group_member(multiply(g2,c,c),g2),
inference(forward_demodulation,[status(thm)],[f68,f829]) ).
fof(f846,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)],[f241,f53]) ).
fof(f847,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)],[f241,f51]) ).
fof(f848,plain,
! [X0,X1] :
( X1 = a
| ~ product(g1,X0,inverse(g1,X0),X1) ),
inference(resolution,[status(thm)],[f241,f49]) ).
fof(f864,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ11_spl
| product(g1,a,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f385]) ).
fof(f873,plain,
( ~ sQ7_spl
| group_member(multiply(g1,b,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f708,f136]) ).
fof(f874,plain,
( ~ sQ7_spl
| group_member(multiply(g1,a,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f708,f707]) ).
fof(f875,plain,
( ~ sQ7_spl
| product(g1,b,multiply(g1,a,b),multiply(g1,b,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f708,f127]) ).
fof(f876,plain,
( ~ sQ7_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f708,f514]) ).
fof(f877,plain,
( ~ sQ7_spl
| multiply(g1,a,b) = b
| multiply(g1,a,b) = a ),
inference(resolution,[status(thm)],[f708,f65]) ).
fof(f878,plain,
( ~ sQ7_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f708,f140]) ).
fof(f879,plain,
( ~ sQ7_spl
| product(g1,identity_for(g1),multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f708,f131]) ).
fof(f880,plain,
! [X0] :
( ~ sQ7_spl
| group_member(multiply(g1,multiply(g1,a,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f708,f47]) ).
fof(f881,plain,
! [X0] :
( ~ sQ7_spl
| product(g1,multiply(g1,a,b),X0,multiply(g1,multiply(g1,a,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f708,f46]) ).
fof(f882,plain,
( ~ sQ7_spl
| group_member(inverse(g1,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f708,f43]) ).
fof(f883,definition,
( sQ24_spl
<=> multiply(g1,a,b) = a ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f884,plain,
( ~ sQ24_spl
| multiply(g1,a,b) = a ),
inference(component_clause,[status(thm)],[f883]) ).
fof(f886,definition,
( sQ25_spl
<=> multiply(g1,a,b) = b ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f887,plain,
( ~ sQ25_spl
| multiply(g1,a,b) = b ),
inference(component_clause,[status(thm)],[f886]) ).
fof(f889,plain,
( ~ sQ7_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f877,f883,f886,f169]) ).
fof(f890,plain,
( ~ sQ7_spl
| group_member(multiply(g1,a,multiply(g1,a,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f67,f878]) ).
fof(f891,plain,
( ~ sQ7_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f67,f879]) ).
fof(f892,plain,
( ~ sQ7_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f67,f891]) ).
fof(f893,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f287,f735]) ).
fof(f910,plain,
! [X0] :
( ~ sQ23_spl
| product(g2,c,c,X0)
| ~ product(g2,d,d,X0) ),
inference(resolution,[status(thm)],[f772,f99]) ).
fof(f911,plain,
! [X0] :
( ~ sQ23_spl
| product(g2,d,d,X0)
| ~ product(g2,c,c,X0) ),
inference(resolution,[status(thm)],[f772,f98]) ).
fof(f937,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)],[f242,f53]) ).
fof(f938,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)],[f242,f51]) ).
fof(f939,plain,
! [X0,X1] :
( X1 = a
| ~ product(g1,inverse(g1,X0),X0,X1) ),
inference(resolution,[status(thm)],[f242,f49]) ).
fof(f967,plain,
! [X0,X1,X2,X3] :
( product(g2,c,X1,X3)
| ~ product(g2,X0,X2,X3)
| ~ product(g2,inverse(g2,X0),X1,X2) ),
inference(resolution,[status(thm)],[f246,f53]) ).
fof(f968,plain,
! [X0,X1,X2,X3] :
( product(g2,X0,X2,X3)
| ~ product(g2,c,X1,X3)
| ~ product(g2,inverse(g2,X0),X1,X2) ),
inference(resolution,[status(thm)],[f246,f51]) ).
fof(f969,plain,
! [X0,X1] :
( X1 = c
| ~ product(g2,X0,inverse(g2,X0),X1) ),
inference(resolution,[status(thm)],[f246,f49]) ).
fof(f995,plain,
! [X0,X1,X2,X3] :
( product(g2,c,X1,X3)
| ~ product(g2,inverse(g2,X0),X2,X3)
| ~ product(g2,X0,X1,X2) ),
inference(resolution,[status(thm)],[f247,f53]) ).
fof(f996,plain,
! [X0,X1,X2,X3] :
( product(g2,inverse(g2,X0),X2,X3)
| ~ product(g2,c,X1,X3)
| ~ product(g2,X0,X1,X2) ),
inference(resolution,[status(thm)],[f247,f51]) ).
fof(f997,plain,
! [X0,X1] :
( X1 = c
| ~ product(g2,inverse(g2,X0),X0,X1) ),
inference(resolution,[status(thm)],[f247,f49]) ).
fof(f1010,plain,
( ~ sQ7_spl
| group_member(multiply(g1,b,multiply(g1,a,a)),g1) ),
inference(resolution,[status(thm)],[f709,f136]) ).
fof(f1011,plain,
( ~ sQ7_spl
| group_member(multiply(g1,a,multiply(g1,a,a)),g1) ),
inference(resolution,[status(thm)],[f709,f707]) ).
fof(f1012,plain,
( ~ sQ7_spl
| product(g1,b,multiply(g1,a,a),multiply(g1,b,multiply(g1,a,a))) ),
inference(resolution,[status(thm)],[f709,f127]) ).
fof(f1013,plain,
( ~ sQ7_spl
| product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,a,a))) ),
inference(resolution,[status(thm)],[f709,f514]) ).
fof(f1015,plain,
( ~ sQ7_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,a,a)),g1) ),
inference(resolution,[status(thm)],[f709,f140]) ).
fof(f1016,plain,
( ~ sQ7_spl
| product(g1,identity_for(g1),multiply(g1,a,a),multiply(g1,identity_for(g1),multiply(g1,a,a))) ),
inference(resolution,[status(thm)],[f709,f131]) ).
fof(f1017,plain,
! [X0] :
( ~ sQ7_spl
| group_member(multiply(g1,multiply(g1,a,a),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f709,f47]) ).
fof(f1018,plain,
! [X0] :
( ~ sQ7_spl
| product(g1,multiply(g1,a,a),X0,multiply(g1,multiply(g1,a,a),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f709,f46]) ).
fof(f1019,plain,
( ~ sQ7_spl
| group_member(inverse(g1,multiply(g1,a,a)),g1) ),
inference(resolution,[status(thm)],[f709,f43]) ).
fof(f1020,definition,
( sQ26_spl
<=> multiply(g1,a,a) = a ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f1021,plain,
( ~ sQ26_spl
| multiply(g1,a,a) = a ),
inference(component_clause,[status(thm)],[f1020]) ).
fof(f1022,plain,
( sQ26_spl
| multiply(g1,a,a) != a ),
inference(component_clause,[status(thm)],[f1020]) ).
fof(f1023,definition,
( sQ27_spl
<=> multiply(g1,a,a) = b ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f1024,plain,
( ~ sQ27_spl
| multiply(g1,a,a) = b ),
inference(component_clause,[status(thm)],[f1023]) ).
fof(f1025,plain,
( sQ27_spl
| multiply(g1,a,a) != b ),
inference(component_clause,[status(thm)],[f1023]) ).
fof(f1027,plain,
( ~ sQ7_spl
| group_member(multiply(g1,a,multiply(g1,a,a)),g1) ),
inference(forward_demodulation,[status(thm)],[f67,f1015]) ).
fof(f1028,plain,
( ~ sQ7_spl
| product(g1,a,multiply(g1,a,a),multiply(g1,identity_for(g1),multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f67,f1016]) ).
fof(f1029,plain,
( ~ sQ7_spl
| product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f67,f1028]) ).
fof(f1042,plain,
group_member(multiply(g2,d,multiply(g2,c,d)),g2),
inference(resolution,[status(thm)],[f742,f135]) ).
fof(f1043,plain,
group_member(multiply(g2,c,multiply(g2,c,d)),g2),
inference(resolution,[status(thm)],[f742,f141]) ).
fof(f1044,plain,
product(g2,c,multiply(g2,c,d),multiply(g2,c,multiply(g2,c,d))),
inference(resolution,[status(thm)],[f742,f132]) ).
fof(f1045,plain,
product(g2,d,multiply(g2,c,d),multiply(g2,d,multiply(g2,c,d))),
inference(resolution,[status(thm)],[f742,f126]) ).
fof(f1046,plain,
( multiply(g2,c,d) = d
| multiply(g2,c,d) = c ),
inference(resolution,[status(thm)],[f742,f66]) ).
fof(f1047,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,c,d)),g2),
inference(resolution,[status(thm)],[f742,f140]) ).
fof(f1048,plain,
product(g2,identity_for(g2),multiply(g2,c,d),multiply(g2,identity_for(g2),multiply(g2,c,d))),
inference(resolution,[status(thm)],[f742,f131]) ).
fof(f1049,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,c,d),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f742,f47]) ).
fof(f1050,plain,
! [X0] :
( product(g2,multiply(g2,c,d),X0,multiply(g2,multiply(g2,c,d),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f742,f46]) ).
fof(f1051,plain,
group_member(inverse(g2,multiply(g2,c,d)),g2),
inference(resolution,[status(thm)],[f742,f43]) ).
fof(f1052,definition,
( sQ28_spl
<=> multiply(g2,c,d) = c ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f1053,plain,
( ~ sQ28_spl
| multiply(g2,c,d) = c ),
inference(component_clause,[status(thm)],[f1052]) ).
fof(f1055,definition,
( sQ29_spl
<=> multiply(g2,c,d) = d ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( ~ sQ29_spl
| multiply(g2,c,d) = d ),
inference(component_clause,[status(thm)],[f1055]) ).
fof(f1058,plain,
( sQ29_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f1046,f1052,f1055]) ).
fof(f1059,plain,
group_member(multiply(g2,c,multiply(g2,c,d)),g2),
inference(forward_demodulation,[status(thm)],[f68,f1047]) ).
fof(f1060,plain,
product(g2,c,multiply(g2,c,d),multiply(g2,identity_for(g2),multiply(g2,c,d))),
inference(forward_demodulation,[status(thm)],[f68,f1048]) ).
fof(f1061,plain,
product(g2,c,multiply(g2,c,d),multiply(g2,c,multiply(g2,c,d))),
inference(forward_demodulation,[status(thm)],[f68,f1060]) ).
fof(f1068,plain,
group_member(multiply(g2,d,multiply(g2,c,c)),g2),
inference(resolution,[status(thm)],[f745,f135]) ).
fof(f1069,plain,
group_member(multiply(g2,c,multiply(g2,c,c)),g2),
inference(resolution,[status(thm)],[f745,f141]) ).
fof(f1070,plain,
product(g2,c,multiply(g2,c,c),multiply(g2,c,multiply(g2,c,c))),
inference(resolution,[status(thm)],[f745,f132]) ).
fof(f1071,plain,
product(g2,d,multiply(g2,c,c),multiply(g2,d,multiply(g2,c,c))),
inference(resolution,[status(thm)],[f745,f126]) ).
fof(f1072,plain,
( multiply(g2,c,c) = d
| multiply(g2,c,c) = c ),
inference(resolution,[status(thm)],[f745,f66]) ).
fof(f1073,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,c,c)),g2),
inference(resolution,[status(thm)],[f745,f140]) ).
fof(f1074,plain,
product(g2,identity_for(g2),multiply(g2,c,c),multiply(g2,identity_for(g2),multiply(g2,c,c))),
inference(resolution,[status(thm)],[f745,f131]) ).
fof(f1075,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,c,c),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f745,f47]) ).
fof(f1076,plain,
! [X0] :
( product(g2,multiply(g2,c,c),X0,multiply(g2,multiply(g2,c,c),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f745,f46]) ).
fof(f1077,plain,
group_member(inverse(g2,multiply(g2,c,c)),g2),
inference(resolution,[status(thm)],[f745,f43]) ).
fof(f1078,definition,
( sQ30_spl
<=> multiply(g2,c,c) = c ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f1079,plain,
( ~ sQ30_spl
| multiply(g2,c,c) = c ),
inference(component_clause,[status(thm)],[f1078]) ).
fof(f1080,plain,
( sQ30_spl
| multiply(g2,c,c) != c ),
inference(component_clause,[status(thm)],[f1078]) ).
fof(f1081,definition,
( sQ31_spl
<=> multiply(g2,c,c) = d ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f1082,plain,
( ~ sQ31_spl
| multiply(g2,c,c) = d ),
inference(component_clause,[status(thm)],[f1081]) ).
fof(f1083,plain,
( sQ31_spl
| multiply(g2,c,c) != d ),
inference(component_clause,[status(thm)],[f1081]) ).
fof(f1084,plain,
( sQ31_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f1072,f1078,f1081]) ).
fof(f1085,plain,
group_member(multiply(g2,c,multiply(g2,c,c)),g2),
inference(forward_demodulation,[status(thm)],[f68,f1073]) ).
fof(f1086,plain,
product(g2,c,multiply(g2,c,c),multiply(g2,identity_for(g2),multiply(g2,c,c))),
inference(forward_demodulation,[status(thm)],[f68,f1074]) ).
fof(f1087,plain,
product(g2,c,multiply(g2,c,c),multiply(g2,c,multiply(g2,c,c))),
inference(forward_demodulation,[status(thm)],[f68,f1086]) ).
fof(f1097,plain,
group_member(multiply(g2,d,multiply(g2,d,c)),g2),
inference(resolution,[status(thm)],[f789,f135]) ).
fof(f1098,plain,
group_member(multiply(g2,c,multiply(g2,d,c)),g2),
inference(resolution,[status(thm)],[f789,f141]) ).
fof(f1099,plain,
product(g2,c,multiply(g2,d,c),multiply(g2,c,multiply(g2,d,c))),
inference(resolution,[status(thm)],[f789,f132]) ).
fof(f1100,plain,
product(g2,d,multiply(g2,d,c),multiply(g2,d,multiply(g2,d,c))),
inference(resolution,[status(thm)],[f789,f126]) ).
fof(f1101,plain,
( multiply(g2,d,c) = d
| multiply(g2,d,c) = c ),
inference(resolution,[status(thm)],[f789,f66]) ).
fof(f1102,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,d,c)),g2),
inference(resolution,[status(thm)],[f789,f140]) ).
fof(f1103,plain,
product(g2,identity_for(g2),multiply(g2,d,c),multiply(g2,identity_for(g2),multiply(g2,d,c))),
inference(resolution,[status(thm)],[f789,f131]) ).
fof(f1104,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,d,c),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f789,f47]) ).
fof(f1105,plain,
! [X0] :
( product(g2,multiply(g2,d,c),X0,multiply(g2,multiply(g2,d,c),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f789,f46]) ).
fof(f1106,plain,
group_member(inverse(g2,multiply(g2,d,c)),g2),
inference(resolution,[status(thm)],[f789,f43]) ).
fof(f1107,definition,
( sQ32_spl
<=> multiply(g2,d,c) = c ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f1108,plain,
( ~ sQ32_spl
| multiply(g2,d,c) = c ),
inference(component_clause,[status(thm)],[f1107]) ).
fof(f1109,plain,
( sQ32_spl
| multiply(g2,d,c) != c ),
inference(component_clause,[status(thm)],[f1107]) ).
fof(f1110,definition,
( sQ33_spl
<=> multiply(g2,d,c) = d ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f1111,plain,
( ~ sQ33_spl
| multiply(g2,d,c) = d ),
inference(component_clause,[status(thm)],[f1110]) ).
fof(f1113,plain,
( sQ33_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f1101,f1107,f1110]) ).
fof(f1114,plain,
group_member(multiply(g2,c,multiply(g2,d,c)),g2),
inference(forward_demodulation,[status(thm)],[f68,f1102]) ).
fof(f1115,plain,
product(g2,c,multiply(g2,d,c),multiply(g2,identity_for(g2),multiply(g2,d,c))),
inference(forward_demodulation,[status(thm)],[f68,f1103]) ).
fof(f1116,plain,
product(g2,c,multiply(g2,d,c),multiply(g2,c,multiply(g2,d,c))),
inference(forward_demodulation,[status(thm)],[f68,f1115]) ).
fof(f1121,plain,
group_member(multiply(g2,d,multiply(g2,d,d)),g2),
inference(resolution,[status(thm)],[f787,f135]) ).
fof(f1122,plain,
group_member(multiply(g2,c,multiply(g2,d,d)),g2),
inference(resolution,[status(thm)],[f787,f141]) ).
fof(f1123,plain,
product(g2,c,multiply(g2,d,d),multiply(g2,c,multiply(g2,d,d))),
inference(resolution,[status(thm)],[f787,f132]) ).
fof(f1124,plain,
product(g2,d,multiply(g2,d,d),multiply(g2,d,multiply(g2,d,d))),
inference(resolution,[status(thm)],[f787,f126]) ).
fof(f1125,plain,
( multiply(g2,d,d) = d
| multiply(g2,d,d) = c ),
inference(resolution,[status(thm)],[f787,f66]) ).
fof(f1126,plain,
group_member(multiply(g2,identity_for(g2),multiply(g2,d,d)),g2),
inference(resolution,[status(thm)],[f787,f140]) ).
fof(f1127,plain,
product(g2,identity_for(g2),multiply(g2,d,d),multiply(g2,identity_for(g2),multiply(g2,d,d))),
inference(resolution,[status(thm)],[f787,f131]) ).
fof(f1128,plain,
! [X0] :
( group_member(multiply(g2,multiply(g2,d,d),X0),g2)
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f787,f47]) ).
fof(f1129,plain,
! [X0] :
( product(g2,multiply(g2,d,d),X0,multiply(g2,multiply(g2,d,d),X0))
| ~ group_member(X0,g2) ),
inference(resolution,[status(thm)],[f787,f46]) ).
fof(f1130,plain,
group_member(inverse(g2,multiply(g2,d,d)),g2),
inference(resolution,[status(thm)],[f787,f43]) ).
fof(f1131,definition,
( sQ34_spl
<=> multiply(g2,d,d) = c ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f1132,plain,
( ~ sQ34_spl
| multiply(g2,d,d) = c ),
inference(component_clause,[status(thm)],[f1131]) ).
fof(f1134,definition,
( sQ35_spl
<=> multiply(g2,d,d) = d ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f1137,plain,
( sQ35_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f1125,f1131,f1134]) ).
fof(f1138,plain,
group_member(multiply(g2,c,multiply(g2,d,d)),g2),
inference(forward_demodulation,[status(thm)],[f68,f1126]) ).
fof(f1139,plain,
product(g2,c,multiply(g2,d,d),multiply(g2,identity_for(g2),multiply(g2,d,d))),
inference(forward_demodulation,[status(thm)],[f68,f1127]) ).
fof(f1140,plain,
product(g2,c,multiply(g2,d,d),multiply(g2,c,multiply(g2,d,d))),
inference(forward_demodulation,[status(thm)],[f68,f1139]) ).
fof(f1142,plain,
! [X0,X1] :
( product(g2,c,X0,X1)
| ~ product(g2,X0,c,X1) ),
inference(forward_demodulation,[status(thm)],[f68,f117]) ).
fof(f1152,plain,
! [X0] :
( ~ sQ13_spl
| product(g1,identity_for(g1),d3,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f191,f118]) ).
fof(f1153,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| product(g1,identity_for(g1),d3,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f1152]) ).
fof(f1154,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ11_spl
| product(g1,a,d3,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1153]) ).
fof(f1155,plain,
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f884,f515]) ).
fof(f1156,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,X0,a,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f1155,f291]) ).
fof(f1157,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f1155,f290]) ).
fof(f1158,plain,
( ~ sQ7_spl
| ~ sQ24_spl
| a = b ),
inference(resolution,[status(thm)],[f1155,f288]) ).
fof(f1159,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1155,f287]) ).
fof(f1160,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f1155,f286]) ).
fof(f1161,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1155,f107]) ).
fof(f1162,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,a),a,X0) ),
inference(resolution,[status(thm)],[f1155,f106]) ).
fof(f1163,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f1155,f96]) ).
fof(f1164,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1155,f89]) ).
fof(f1165,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1155,f53]) ).
fof(f1166,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1155,f51]) ).
fof(f1167,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1155,f49]) ).
fof(f1168,plain,
( ~ sQ7_spl
| ~ sQ24_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1158,f151,f883,f169]) ).
fof(f1169,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,inverse(g1,a),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1161]) ).
fof(f1170,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f352,f1169]) ).
fof(f1171,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f352,f1162]) ).
fof(f1172,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1171]) ).
fof(f1173,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1163]) ).
fof(f1174,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ24_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1164]) ).
fof(f1176,plain,
! [X0] :
( ~ sQ11_spl
| product(g1,identity_for(g1),d3,X0)
| ~ product(g1,d1,a,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f118]) ).
fof(f1177,plain,
! [X0] :
( ~ sQ11_spl
| product(g1,a,d3,X0)
| ~ product(g1,d1,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1176]) ).
fof(f1178,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| product(g1,d3,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f95]) ).
fof(f1179,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,d3,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f93]) ).
fof(f1180,plain,
( sQ0_spl
| ~ sQ11_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(a),isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f184,f84]) ).
fof(f1181,plain,
( sQ0_spl
| ~ sQ11_spl
| ~ product(g2,isomorphism1(d1),c,isomorphism1(d3)) ),
inference(forward_demodulation,[status(thm)],[f73,f1180]) ).
fof(f1182,plain,
! [X0] :
( ~ sQ11_spl
| X0 = d3
| ~ product(g1,d1,a,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f94]) ).
fof(f1185,plain,
( ~ sQ11_spl
| product(g1,d1,a,d3) ),
inference(forward_demodulation,[status(thm)],[f184,f80]) ).
fof(f1186,plain,
group_member(multiply(g1,b,d3),g1),
inference(resolution,[status(thm)],[f79,f136]) ).
fof(f1187,plain,
product(g1,b,d3,multiply(g1,b,d3)),
inference(resolution,[status(thm)],[f79,f127]) ).
fof(f1189,plain,
group_member(multiply(g1,identity_for(g1),d3),g1),
inference(resolution,[status(thm)],[f79,f140]) ).
fof(f1190,plain,
product(g1,identity_for(g1),d3,multiply(g1,identity_for(g1),d3)),
inference(resolution,[status(thm)],[f79,f131]) ).
fof(f1191,plain,
! [X0] :
( group_member(multiply(g1,d3,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f79,f47]) ).
fof(f1192,plain,
! [X0] :
( product(g1,d3,X0,multiply(g1,d3,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f79,f46]) ).
fof(f1193,plain,
group_member(inverse(g1,d3),g1),
inference(resolution,[status(thm)],[f79,f43]) ).
fof(f1195,plain,
group_member(multiply(g1,a,d3),g1),
inference(forward_demodulation,[status(thm)],[f67,f1189]) ).
fof(f1196,plain,
product(g1,a,d3,multiply(g1,identity_for(g1),d3)),
inference(forward_demodulation,[status(thm)],[f67,f1190]) ).
fof(f1197,plain,
product(g1,a,d3,multiply(g1,a,d3)),
inference(forward_demodulation,[status(thm)],[f67,f1196]) ).
fof(f1200,plain,
( sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ product(g2,isomorphism1(d1),c,isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f1181]) ).
fof(f1201,plain,
( sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ product(g2,isomorphism1(d1),c,d) ),
inference(forward_demodulation,[status(thm)],[f74,f1200]) ).
fof(f1203,plain,
( sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ product(g2,isomorphism1(b),c,d) ),
inference(backward_demodulation,[status(thm)],[f194,f1201]) ).
fof(f1204,plain,
( sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ product(g2,d,c,d) ),
inference(forward_demodulation,[status(thm)],[f74,f1203]) ).
fof(f1205,plain,
( sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1204,f72]) ).
fof(f1206,plain,
( sQ0_spl
| ~ sQ11_spl
| ~ sQ8_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1205]) ).
fof(f1207,plain,
( ~ sQ8_spl
| product(g1,d1,d2,b) ),
inference(forward_demodulation,[status(thm)],[f173,f80]) ).
fof(f1208,plain,
! [X0] :
( ~ sQ8_spl
| X0 = b
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f173,f94]) ).
fof(f1209,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f84]) ).
fof(f1210,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f74,f1209]) ).
fof(f1211,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f93]) ).
fof(f1212,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f95]) ).
fof(f1213,plain,
! [X0] :
( product(g1,a,d3,X0)
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f118]) ).
fof(f1214,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f173,f1213]) ).
fof(f1215,plain,
! [X0] :
( ~ sQ13_spl
| product(g1,a,d3,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1152]) ).
fof(f1216,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f173,f1215]) ).
fof(f1217,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f385]) ).
fof(f1218,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| X0 = b
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f173,f375]) ).
fof(f1226,plain,
! [X0,X1,X2] :
( ~ sQ12_spl
| ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f433]) ).
fof(f1228,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,d2,b) ),
inference(forward_demodulation,[status(thm)],[f173,f271]) ).
fof(f1229,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f527]) ).
fof(f1231,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ product(g2,c,isomorphism1(d2),isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f384]) ).
fof(f1232,plain,
( sQ0_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ product(g2,c,isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f74,f1231]) ).
fof(f1233,plain,
group_member(multiply(g1,b,d1),g1),
inference(resolution,[status(thm)],[f77,f136]) ).
fof(f1234,plain,
product(g1,b,d1,multiply(g1,b,d1)),
inference(resolution,[status(thm)],[f77,f127]) ).
fof(f1236,plain,
group_member(multiply(g1,identity_for(g1),d1),g1),
inference(resolution,[status(thm)],[f77,f140]) ).
fof(f1237,plain,
product(g1,identity_for(g1),d1,multiply(g1,identity_for(g1),d1)),
inference(resolution,[status(thm)],[f77,f131]) ).
fof(f1238,plain,
! [X0] :
( group_member(multiply(g1,d1,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f77,f47]) ).
fof(f1239,plain,
! [X0] :
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f77,f46]) ).
fof(f1240,plain,
group_member(inverse(g1,d1),g1),
inference(resolution,[status(thm)],[f77,f43]) ).
fof(f1242,plain,
group_member(multiply(g1,a,d1),g1),
inference(forward_demodulation,[status(thm)],[f67,f1236]) ).
fof(f1243,plain,
product(g1,a,d1,multiply(g1,identity_for(g1),d1)),
inference(forward_demodulation,[status(thm)],[f67,f1237]) ).
fof(f1244,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(forward_demodulation,[status(thm)],[f67,f1243]) ).
fof(f1245,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f287]) ).
fof(f1246,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1207,f286]) ).
fof(f1247,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,identity_for(g1),d2,X0) ),
inference(resolution,[status(thm)],[f1207,f107]) ).
fof(f1248,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f1207,f106]) ).
fof(f1249,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1207,f96]) ).
fof(f1250,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f89]) ).
fof(f1251,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f1207,f53]) ).
fof(f1252,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f1207,f51]) ).
fof(f1253,plain,
! [X0] :
( ~ sQ8_spl
| X0 = b
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f49]) ).
fof(f1254,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1247]) ).
fof(f1255,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1248]) ).
fof(f1256,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1249]) ).
fof(f1257,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1250]) ).
fof(f1258,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(b),d) ),
inference(backward_demodulation,[status(thm)],[f187,f268]) ).
fof(f1259,plain,
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,d1,b,b) ),
inference(backward_demodulation,[status(thm)],[f187,f1207]) ).
fof(f1261,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ product(g2,isomorphism1(d1),d,d) ),
inference(forward_demodulation,[status(thm)],[f74,f1258]) ).
fof(f1262,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ product(g2,isomorphism1(d1),isomorphism1(b),d) ),
inference(forward_demodulation,[status(thm)],[f187,f1210]) ).
fof(f1263,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ product(g2,isomorphism1(d1),d,d) ),
inference(forward_demodulation,[status(thm)],[f74,f1262]) ).
fof(f1264,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ product(g2,isomorphism1(a),d,d) ),
inference(backward_demodulation,[status(thm)],[f191,f1263]) ).
fof(f1266,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ13_spl
| ~ product(g2,c,d,d) ),
inference(forward_demodulation,[status(thm)],[f73,f1264]) ).
fof(f1267,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1266,f71]) ).
fof(f1268,plain,
( sQ0_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f1267]) ).
fof(f1269,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ8_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f336]) ).
fof(f1270,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,a,X0) ),
inference(forward_demodulation,[status(thm)],[f173,f1177]) ).
fof(f1271,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f1178]) ).
fof(f1272,plain,
! [X0,X1,X2] :
( ~ sQ11_spl
| ~ sQ8_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f173,f1179]) ).
fof(f1273,plain,
! [X0] :
( ~ sQ11_spl
| ~ sQ8_spl
| X0 = b
| ~ product(g1,d1,a,X0) ),
inference(forward_demodulation,[status(thm)],[f173,f1182]) ).
fof(f1274,plain,
( ~ sQ11_spl
| ~ sQ8_spl
| product(g1,d1,a,b) ),
inference(forward_demodulation,[status(thm)],[f173,f1185]) ).
fof(f1275,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),isomorphism1(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f83]) ).
fof(f1276,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f74,f1275]) ).
fof(f1277,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ product(g2,c,isomorphism2(d2),isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f253]) ).
fof(f1278,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ product(g2,c,isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f76,f1277]) ).
fof(f1279,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ product(g2,isomorphism2(d1),isomorphism2(d2),isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f87]) ).
fof(f1280,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ product(g2,isomorphism2(d1),isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f76,f1279]) ).
fof(f1281,plain,
group_member(multiply(g1,b,d2),g1),
inference(resolution,[status(thm)],[f78,f136]) ).
fof(f1282,plain,
product(g1,b,d2,multiply(g1,b,d2)),
inference(resolution,[status(thm)],[f78,f127]) ).
fof(f1284,plain,
group_member(multiply(g1,identity_for(g1),d2),g1),
inference(resolution,[status(thm)],[f78,f140]) ).
fof(f1285,plain,
product(g1,identity_for(g1),d2,multiply(g1,identity_for(g1),d2)),
inference(resolution,[status(thm)],[f78,f131]) ).
fof(f1286,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f1287,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f46]) ).
fof(f1288,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f78,f43]) ).
fof(f1290,plain,
group_member(multiply(g1,a,d2),g1),
inference(forward_demodulation,[status(thm)],[f67,f1284]) ).
fof(f1291,plain,
product(g1,a,d2,multiply(g1,identity_for(g1),d2)),
inference(forward_demodulation,[status(thm)],[f67,f1285]) ).
fof(f1292,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(forward_demodulation,[status(thm)],[f67,f1291]) ).
fof(f1293,plain,
group_member(multiply(g1,b,d1),g1),
inference(resolution,[status(thm)],[f77,f136]) ).
fof(f1294,plain,
product(g1,b,d1,multiply(g1,b,d1)),
inference(resolution,[status(thm)],[f77,f127]) ).
fof(f1296,plain,
group_member(multiply(g1,identity_for(g1),d1),g1),
inference(resolution,[status(thm)],[f77,f140]) ).
fof(f1297,plain,
product(g1,identity_for(g1),d1,multiply(g1,identity_for(g1),d1)),
inference(resolution,[status(thm)],[f77,f131]) ).
fof(f1298,plain,
! [X0] :
( group_member(multiply(g1,d1,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f77,f47]) ).
fof(f1299,plain,
! [X0] :
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f77,f46]) ).
fof(f1300,plain,
group_member(inverse(g1,d1),g1),
inference(resolution,[status(thm)],[f77,f43]) ).
fof(f1302,plain,
group_member(multiply(g1,a,d1),g1),
inference(forward_demodulation,[status(thm)],[f67,f1296]) ).
fof(f1303,plain,
product(g1,a,d1,multiply(g1,identity_for(g1),d1)),
inference(forward_demodulation,[status(thm)],[f67,f1297]) ).
fof(f1304,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(forward_demodulation,[status(thm)],[f67,f1303]) ).
fof(f1309,plain,
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,b,d2,b) ),
inference(forward_demodulation,[status(thm)],[f194,f1207]) ).
fof(f1312,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,isomorphism1(b),isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f194,f1276]) ).
fof(f1313,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,d,isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f74,f1312]) ).
fof(f1316,plain,
( sQ5_spl
| ~ sQ8_spl
| inverse(g1,b) != a ),
inference(forward_demodulation,[status(thm)],[f173,f164]) ).
fof(f1318,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ product(g2,c,isomorphism2(a),c) ),
inference(forward_demodulation,[status(thm)],[f184,f1278]) ).
fof(f1319,plain,
( sQ1_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ product(g2,c,d,c) ),
inference(forward_demodulation,[status(thm)],[f75,f1318]) ).
fof(f1320,plain,
( ~ sQ6_spl
| ~ sQ8_spl
| inverse(g1,b) = b ),
inference(forward_demodulation,[status(thm)],[f173,f166]) ).
fof(f1321,plain,
( ~ sQ8_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f173,f390]) ).
fof(f1323,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ product(g2,isomorphism2(b),isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f194,f1280]) ).
fof(f1324,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ product(g2,c,isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f76,f1323]) ).
fof(f1329,plain,
( ~ sQ8_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f173,f101]) ).
fof(f1331,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f105]) ).
fof(f1333,plain,
( ~ sQ8_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f173,f1193]) ).
fof(f1336,plain,
group_member(multiply(g1,a,b),g1),
inference(resolution,[status(thm)],[f137,f56]) ).
fof(f1337,plain,
group_member(multiply(g1,a,a),g1),
inference(resolution,[status(thm)],[f137,f55]) ).
fof(f1338,plain,
group_member(multiply(g1,a,identity_for(g1)),g1),
inference(resolution,[status(thm)],[f137,f40]) ).
fof(f1339,plain,
group_member(multiply(g1,a,a),g1),
inference(forward_demodulation,[status(thm)],[f67,f1338]) ).
fof(f1352,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1240]) ).
fof(f1356,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1300]) ).
fof(f1358,plain,
product(g1,a,b,multiply(g1,a,b)),
inference(resolution,[status(thm)],[f128,f56]) ).
fof(f1359,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(resolution,[status(thm)],[f128,f55]) ).
fof(f1360,plain,
product(g1,a,identity_for(g1),multiply(g1,a,identity_for(g1))),
inference(resolution,[status(thm)],[f128,f40]) ).
fof(f1361,plain,
product(g1,a,a,multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f67,f1360]) ).
fof(f1362,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f67,f1361]) ).
fof(f1366,plain,
( ~ sQ8_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f173,f1186]) ).
fof(f1367,plain,
( ~ sQ8_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,a,multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f1366,f128]) ).
fof(f1368,plain,
( ~ sQ8_spl
| group_member(multiply(g1,a,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f1366,f137]) ).
fof(f1369,plain,
( ~ sQ8_spl
| group_member(multiply(g1,b,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f1366,f136]) ).
fof(f1370,plain,
( ~ sQ8_spl
| product(g1,b,multiply(g1,b,b),multiply(g1,b,multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f1366,f127]) ).
fof(f1371,plain,
( ~ sQ8_spl
| multiply(g1,b,b) = b
| multiply(g1,b,b) = a ),
inference(resolution,[status(thm)],[f1366,f65]) ).
fof(f1372,plain,
( ~ sQ8_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f1366,f140]) ).
fof(f1373,plain,
( ~ sQ8_spl
| product(g1,identity_for(g1),multiply(g1,b,b),multiply(g1,identity_for(g1),multiply(g1,b,b))) ),
inference(resolution,[status(thm)],[f1366,f131]) ).
fof(f1374,plain,
! [X0] :
( ~ sQ8_spl
| group_member(multiply(g1,multiply(g1,b,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1366,f47]) ).
fof(f1375,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,multiply(g1,b,b),X0,multiply(g1,multiply(g1,b,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1366,f46]) ).
fof(f1376,plain,
( ~ sQ8_spl
| group_member(inverse(g1,multiply(g1,b,b)),g1) ),
inference(resolution,[status(thm)],[f1366,f43]) ).
fof(f1377,definition,
( sQ36_spl
<=> multiply(g1,b,b) = a ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f1378,plain,
( ~ sQ36_spl
| multiply(g1,b,b) = a ),
inference(component_clause,[status(thm)],[f1377]) ).
fof(f1380,definition,
( sQ37_spl
<=> multiply(g1,b,b) = b ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f1383,plain,
( ~ sQ8_spl
| sQ37_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f1371,f1377,f1380,f172]) ).
fof(f1384,plain,
( ~ sQ8_spl
| group_member(multiply(g1,a,multiply(g1,b,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f67,f1372]) ).
fof(f1385,plain,
( ~ sQ8_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,identity_for(g1),multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f67,f1373]) ).
fof(f1386,plain,
( ~ sQ8_spl
| product(g1,a,multiply(g1,b,b),multiply(g1,a,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f67,f1385]) ).
fof(f1387,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1208]) ).
fof(f1391,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1211]) ).
fof(f1393,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1212]) ).
fof(f1397,plain,
product(g1,a,multiply(g1,b,a),multiply(g1,a,multiply(g1,b,a))),
inference(resolution,[status(thm)],[f792,f128]) ).
fof(f1398,plain,
group_member(multiply(g1,a,multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f792,f137]) ).
fof(f1399,plain,
group_member(multiply(g1,b,multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f792,f136]) ).
fof(f1400,plain,
product(g1,b,multiply(g1,b,a),multiply(g1,b,multiply(g1,b,a))),
inference(resolution,[status(thm)],[f792,f127]) ).
fof(f1401,plain,
( multiply(g1,b,a) = b
| multiply(g1,b,a) = a ),
inference(resolution,[status(thm)],[f792,f65]) ).
fof(f1402,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f792,f140]) ).
fof(f1403,plain,
product(g1,identity_for(g1),multiply(g1,b,a),multiply(g1,identity_for(g1),multiply(g1,b,a))),
inference(resolution,[status(thm)],[f792,f131]) ).
fof(f1404,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,b,a),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f792,f47]) ).
fof(f1405,plain,
! [X0] :
( product(g1,multiply(g1,b,a),X0,multiply(g1,multiply(g1,b,a),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f792,f46]) ).
fof(f1406,plain,
group_member(inverse(g1,multiply(g1,b,a)),g1),
inference(resolution,[status(thm)],[f792,f43]) ).
fof(f1407,definition,
( sQ38_spl
<=> multiply(g1,b,a) = a ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1408,plain,
( ~ sQ38_spl
| multiply(g1,b,a) = a ),
inference(component_clause,[status(thm)],[f1407]) ).
fof(f1409,plain,
( sQ38_spl
| multiply(g1,b,a) != a ),
inference(component_clause,[status(thm)],[f1407]) ).
fof(f1410,definition,
( sQ39_spl
<=> multiply(g1,b,a) = b ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1411,plain,
( ~ sQ39_spl
| multiply(g1,b,a) = b ),
inference(component_clause,[status(thm)],[f1410]) ).
fof(f1413,plain,
( sQ39_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f1401,f1407,f1410]) ).
fof(f1414,plain,
group_member(multiply(g1,a,multiply(g1,b,a)),g1),
inference(forward_demodulation,[status(thm)],[f67,f1402]) ).
fof(f1415,plain,
product(g1,a,multiply(g1,b,a),multiply(g1,identity_for(g1),multiply(g1,b,a))),
inference(forward_demodulation,[status(thm)],[f67,f1403]) ).
fof(f1416,plain,
product(g1,a,multiply(g1,b,a),multiply(g1,a,multiply(g1,b,a))),
inference(forward_demodulation,[status(thm)],[f67,f1415]) ).
fof(f1422,plain,
( ~ sQ8_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f173,f1195]) ).
fof(f1423,plain,
( ~ sQ8_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f1422,f128]) ).
fof(f1424,plain,
( ~ sQ8_spl
| group_member(multiply(g1,a,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f1422,f137]) ).
fof(f1425,plain,
( ~ sQ8_spl
| group_member(multiply(g1,b,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f1422,f136]) ).
fof(f1426,plain,
( ~ sQ8_spl
| product(g1,b,multiply(g1,a,b),multiply(g1,b,multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f1422,f127]) ).
fof(f1427,plain,
( ~ sQ8_spl
| multiply(g1,a,b) = b
| multiply(g1,a,b) = a ),
inference(resolution,[status(thm)],[f1422,f65]) ).
fof(f1428,plain,
( ~ sQ8_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f1422,f140]) ).
fof(f1429,plain,
( ~ sQ8_spl
| product(g1,identity_for(g1),multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))) ),
inference(resolution,[status(thm)],[f1422,f131]) ).
fof(f1430,plain,
! [X0] :
( ~ sQ8_spl
| group_member(multiply(g1,multiply(g1,a,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1422,f47]) ).
fof(f1431,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,multiply(g1,a,b),X0,multiply(g1,multiply(g1,a,b),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1422,f46]) ).
fof(f1432,plain,
( ~ sQ8_spl
| group_member(inverse(g1,multiply(g1,a,b)),g1) ),
inference(resolution,[status(thm)],[f1422,f43]) ).
fof(f1433,plain,
( ~ sQ8_spl
| sQ25_spl
| sQ24_spl ),
inference(split_clause,[status(thm)],[f1427,f883,f886,f172]) ).
fof(f1434,plain,
( ~ sQ8_spl
| group_member(multiply(g1,a,multiply(g1,a,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f67,f1428]) ).
fof(f1435,plain,
( ~ sQ8_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,identity_for(g1),multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f67,f1429]) ).
fof(f1436,plain,
( ~ sQ8_spl
| product(g1,a,multiply(g1,a,b),multiply(g1,a,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f67,f1435]) ).
fof(f1448,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1251]) ).
fof(f1450,plain,
( ~ sQ14_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1233]) ).
fof(f1452,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1252]) ).
fof(f1454,plain,
( ~ sQ14_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1242]) ).
fof(f1456,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1253]) ).
fof(f1459,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,a,a))),
inference(resolution,[status(thm)],[f832,f128]) ).
fof(f1460,plain,
group_member(multiply(g1,a,multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f832,f137]) ).
fof(f1461,plain,
group_member(multiply(g1,b,multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f832,f136]) ).
fof(f1462,plain,
product(g1,b,multiply(g1,a,a),multiply(g1,b,multiply(g1,a,a))),
inference(resolution,[status(thm)],[f832,f127]) ).
fof(f1463,plain,
( multiply(g1,a,a) = b
| multiply(g1,a,a) = a ),
inference(resolution,[status(thm)],[f832,f65]) ).
fof(f1464,plain,
group_member(multiply(g1,identity_for(g1),multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f832,f140]) ).
fof(f1465,plain,
product(g1,identity_for(g1),multiply(g1,a,a),multiply(g1,identity_for(g1),multiply(g1,a,a))),
inference(resolution,[status(thm)],[f832,f131]) ).
fof(f1466,plain,
! [X0] :
( group_member(multiply(g1,multiply(g1,a,a),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f832,f47]) ).
fof(f1467,plain,
! [X0] :
( product(g1,multiply(g1,a,a),X0,multiply(g1,multiply(g1,a,a),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f832,f46]) ).
fof(f1468,plain,
group_member(inverse(g1,multiply(g1,a,a)),g1),
inference(resolution,[status(thm)],[f832,f43]) ).
fof(f1469,plain,
( sQ27_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1463,f1020,f1023]) ).
fof(f1470,plain,
group_member(multiply(g1,a,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f67,f1464]) ).
fof(f1471,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,identity_for(g1),multiply(g1,a,a))),
inference(forward_demodulation,[status(thm)],[f67,f1465]) ).
fof(f1472,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,a,a))),
inference(forward_demodulation,[status(thm)],[f67,f1471]) ).
fof(f1475,plain,
( ~ sQ11_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1281]) ).
fof(f1477,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1290]) ).
fof(f1481,plain,
group_member(multiply(g2,d,multiply(g2,identity_for(g2),identity_for(g2))),g2),
inference(resolution,[status(thm)],[f828,f135]) ).
fof(f1482,plain,
group_member(multiply(g2,c,multiply(g2,identity_for(g2),identity_for(g2))),g2),
inference(resolution,[status(thm)],[f828,f141]) ).
fof(f1483,plain,
product(g2,c,multiply(g2,identity_for(g2),identity_for(g2)),multiply(g2,c,multiply(g2,identity_for(g2),identity_for(g2)))),
inference(resolution,[status(thm)],[f828,f132]) ).
fof(f1484,plain,
product(g2,d,multiply(g2,identity_for(g2),identity_for(g2)),multiply(g2,d,multiply(g2,identity_for(g2),identity_for(g2)))),
inference(resolution,[status(thm)],[f828,f126]) ).
fof(f1485,plain,
( multiply(g2,identity_for(g2),identity_for(g2)) = d
| multiply(g2,identity_for(g2),identity_for(g2)) = c ),
inference(resolution,[status(thm)],[f828,f66]) ).
fof(f1486,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)],[f828,f128]) ).
fof(f1487,plain,
group_member(multiply(g1,a,multiply(g1,identity_for(g1),identity_for(g1))),g1),
inference(resolution,[status(thm)],[f828,f137]) ).
fof(f1488,plain,
group_member(multiply(g1,b,multiply(g1,identity_for(g1),identity_for(g1))),g1),
inference(resolution,[status(thm)],[f828,f136]) ).
fof(f1489,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)],[f828,f127]) ).
fof(f1490,plain,
( multiply(g1,identity_for(g1),identity_for(g1)) = b
| multiply(g1,identity_for(g1),identity_for(g1)) = a ),
inference(resolution,[status(thm)],[f828,f65]) ).
fof(f1495,plain,
! [X0] : group_member(inverse(X0,multiply(X0,identity_for(X0),identity_for(X0))),X0),
inference(resolution,[status(thm)],[f828,f43]) ).
fof(f1496,plain,
group_member(multiply(g2,c,identity_for(g2)),g2),
inference(paramodulation,[status(thm)],[f68,f828]) ).
fof(f1497,plain,
group_member(multiply(g1,a,identity_for(g1)),g1),
inference(paramodulation,[status(thm)],[f67,f828]) ).
fof(f1498,plain,
group_member(multiply(g2,identity_for(g2),c),g2),
inference(paramodulation,[status(thm)],[f68,f828]) ).
fof(f1499,plain,
group_member(multiply(g1,identity_for(g1),a),g1),
inference(paramodulation,[status(thm)],[f67,f828]) ).
fof(f1500,plain,
group_member(multiply(g2,d,multiply(g2,c,identity_for(g2))),g2),
inference(forward_demodulation,[status(thm)],[f68,f1481]) ).
fof(f1501,plain,
group_member(multiply(g2,d,multiply(g2,c,c)),g2),
inference(forward_demodulation,[status(thm)],[f68,f1500]) ).
fof(f1502,plain,
( ~ sQ30_spl
| group_member(multiply(g2,d,c),g2) ),
inference(forward_demodulation,[status(thm)],[f1079,f1501]) ).
fof(f1504,plain,
group_member(multiply(g2,c,multiply(g2,c,identity_for(g2))),g2),
inference(forward_demodulation,[status(thm)],[f68,f1482]) ).
fof(f1505,plain,
group_member(multiply(g2,c,multiply(g2,c,c)),g2),
inference(forward_demodulation,[status(thm)],[f68,f1504]) ).
fof(f1508,plain,
product(g2,c,multiply(g2,c,identity_for(g2)),multiply(g2,c,multiply(g2,identity_for(g2),identity_for(g2)))),
inference(forward_demodulation,[status(thm)],[f68,f1483]) ).
fof(f1509,plain,
product(g2,c,multiply(g2,c,c),multiply(g2,c,multiply(g2,identity_for(g2),identity_for(g2)))),
inference(forward_demodulation,[status(thm)],[f68,f1508]) ).
fof(f1515,plain,
product(g2,d,multiply(g2,c,identity_for(g2)),multiply(g2,d,multiply(g2,identity_for(g2),identity_for(g2)))),
inference(forward_demodulation,[status(thm)],[f68,f1484]) ).
fof(f1516,plain,
product(g2,d,multiply(g2,c,c),multiply(g2,d,multiply(g2,identity_for(g2),identity_for(g2)))),
inference(forward_demodulation,[status(thm)],[f68,f1515]) ).
fof(f1517,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,multiply(g2,identity_for(g2),identity_for(g2)))) ),
inference(forward_demodulation,[status(thm)],[f1079,f1516]) ).
fof(f1518,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,multiply(g2,c,identity_for(g2)))) ),
inference(forward_demodulation,[status(thm)],[f68,f1517]) ).
fof(f1519,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,multiply(g2,c,c))) ),
inference(forward_demodulation,[status(thm)],[f68,f1518]) ).
fof(f1520,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,c)) ),
inference(forward_demodulation,[status(thm)],[f1079,f1519]) ).
fof(f1521,plain,
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,d,c,c) ),
inference(forward_demodulation,[status(thm)],[f1108,f1520]) ).
fof(f1522,definition,
( sQ40_spl
<=> multiply(g2,identity_for(g2),identity_for(g2)) = c ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1523,plain,
( ~ sQ40_spl
| multiply(g2,identity_for(g2),identity_for(g2)) = c ),
inference(component_clause,[status(thm)],[f1522]) ).
fof(f1524,plain,
( sQ40_spl
| multiply(g2,identity_for(g2),identity_for(g2)) != c ),
inference(component_clause,[status(thm)],[f1522]) ).
fof(f1525,definition,
( sQ41_spl
<=> multiply(g2,identity_for(g2),identity_for(g2)) = d ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1526,plain,
( ~ sQ41_spl
| multiply(g2,identity_for(g2),identity_for(g2)) = d ),
inference(component_clause,[status(thm)],[f1525]) ).
fof(f1527,plain,
( sQ41_spl
| multiply(g2,identity_for(g2),identity_for(g2)) != d ),
inference(component_clause,[status(thm)],[f1525]) ).
fof(f1528,plain,
( sQ41_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f1485,f1522,f1525]) ).
fof(f1529,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)],[f67,f1486]) ).
fof(f1530,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f67,f1529]) ).
fof(f1536,plain,
group_member(multiply(g1,a,multiply(g1,a,identity_for(g1))),g1),
inference(forward_demodulation,[status(thm)],[f67,f1487]) ).
fof(f1537,plain,
group_member(multiply(g1,a,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f67,f1536]) ).
fof(f1540,plain,
group_member(multiply(g1,b,multiply(g1,a,identity_for(g1))),g1),
inference(forward_demodulation,[status(thm)],[f67,f1488]) ).
fof(f1541,plain,
group_member(multiply(g1,b,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f67,f1540]) ).
fof(f1542,plain,
( ~ sQ26_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f1021,f1541]) ).
fof(f1544,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)],[f67,f1489]) ).
fof(f1545,plain,
product(g1,b,multiply(g1,a,a),multiply(g1,b,multiply(g1,identity_for(g1),identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f67,f1544]) ).
fof(f1546,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,identity_for(g1),identity_for(g1)))) ),
inference(forward_demodulation,[status(thm)],[f1021,f1545]) ).
fof(f1547,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,a,identity_for(g1)))) ),
inference(forward_demodulation,[status(thm)],[f67,f1546]) ).
fof(f1548,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f67,f1547]) ).
fof(f1549,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f1021,f1548]) ).
fof(f1550,plain,
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f1408,f1549]) ).
fof(f1551,definition,
( sQ42_spl
<=> multiply(g1,identity_for(g1),identity_for(g1)) = a ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1552,plain,
( ~ sQ42_spl
| multiply(g1,identity_for(g1),identity_for(g1)) = a ),
inference(component_clause,[status(thm)],[f1551]) ).
fof(f1553,plain,
( sQ42_spl
| multiply(g1,identity_for(g1),identity_for(g1)) != a ),
inference(component_clause,[status(thm)],[f1551]) ).
fof(f1554,definition,
( sQ43_spl
<=> multiply(g1,identity_for(g1),identity_for(g1)) = b ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1555,plain,
( ~ sQ43_spl
| multiply(g1,identity_for(g1),identity_for(g1)) = b ),
inference(component_clause,[status(thm)],[f1554]) ).
fof(f1556,plain,
( sQ43_spl
| multiply(g1,identity_for(g1),identity_for(g1)) != b ),
inference(component_clause,[status(thm)],[f1554]) ).
fof(f1557,plain,
( sQ43_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1490,f1551,f1554]) ).
fof(f1558,plain,
group_member(multiply(g2,c,c),g2),
inference(forward_demodulation,[status(thm)],[f68,f1496]) ).
fof(f1560,plain,
group_member(multiply(g1,a,a),g1),
inference(forward_demodulation,[status(thm)],[f67,f1497]) ).
fof(f1562,plain,
group_member(multiply(g2,c,c),g2),
inference(forward_demodulation,[status(thm)],[f68,f1498]) ).
fof(f1564,plain,
group_member(multiply(g1,a,a),g1),
inference(forward_demodulation,[status(thm)],[f67,f1499]) ).
fof(f1566,plain,
( ~ sQ42_spl
| multiply(g1,a,identity_for(g1)) = a ),
inference(forward_demodulation,[status(thm)],[f67,f1552]) ).
fof(f1567,plain,
( ~ sQ42_spl
| multiply(g1,a,a) = a ),
inference(forward_demodulation,[status(thm)],[f67,f1566]) ).
fof(f1568,plain,
( ~ sQ40_spl
| multiply(g2,c,identity_for(g2)) = c ),
inference(forward_demodulation,[status(thm)],[f68,f1523]) ).
fof(f1569,plain,
( ~ sQ40_spl
| multiply(g2,c,c) = c ),
inference(forward_demodulation,[status(thm)],[f68,f1568]) ).
fof(f1570,plain,
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,c,d,c) ),
inference(resolution,[status(thm)],[f1521,f1142]) ).
fof(f1571,plain,
( ~ sQ30_spl
| ~ sQ32_spl
| c = d ),
inference(resolution,[status(thm)],[f1521,f115]) ).
fof(f1572,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,c,c,X0)
| ~ product(g2,d,c,X0) ),
inference(resolution,[status(thm)],[f1521,f99]) ).
fof(f1573,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,d,c,X0)
| ~ product(g2,c,c,X0) ),
inference(resolution,[status(thm)],[f1521,f98]) ).
fof(f1574,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,inverse(g2,d),c,X0)
| ~ product(g2,identity_for(g2),c,X0) ),
inference(resolution,[status(thm)],[f1521,f107]) ).
fof(f1575,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,identity_for(g2),c,X0)
| ~ product(g2,inverse(g2,d),c,X0) ),
inference(resolution,[status(thm)],[f1521,f106]) ).
fof(f1576,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,d,c,X0)
| ~ product(g2,identity_for(g2),c,X0) ),
inference(resolution,[status(thm)],[f1521,f96]) ).
fof(f1577,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,identity_for(g2),c,X0)
| ~ product(g2,d,c,X0) ),
inference(resolution,[status(thm)],[f1521,f89]) ).
fof(f1578,plain,
! [X0,X1,X2] :
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,c,X0,X2)
| ~ product(g2,d,X1,X2)
| ~ product(g2,c,X0,X1) ),
inference(resolution,[status(thm)],[f1521,f53]) ).
fof(f1579,plain,
! [X0,X1,X2] :
( ~ sQ30_spl
| ~ sQ32_spl
| product(g2,d,X1,X2)
| ~ product(g2,c,X0,X2)
| ~ product(g2,c,X0,X1) ),
inference(resolution,[status(thm)],[f1521,f51]) ).
fof(f1580,plain,
! [X0] :
( ~ sQ30_spl
| ~ sQ32_spl
| X0 = c
| ~ product(g2,d,c,X0) ),
inference(resolution,[status(thm)],[f1521,f49]) ).
fof(f1581,plain,
( ~ sQ30_spl
| ~ sQ32_spl
| sQ1_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1570,f1319]) ).
fof(f1582,plain,
( ~ sQ30_spl
| ~ sQ32_spl
| sQ1_spl
| ~ sQ14_spl
| ~ sQ8_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f1581]) ).
fof(f1583,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ product(g2,d,isomorphism2(d2),isomorphism2(b)) ),
inference(forward_demodulation,[status(thm)],[f173,f540]) ).
fof(f1584,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ product(g2,d,isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f76,f1583]) ).
fof(f1587,plain,
product(g2,d,multiply(g2,c,c),multiply(g2,d,multiply(g2,c,identity_for(g2)))),
inference(forward_demodulation,[status(thm)],[f68,f1516]) ).
fof(f1588,plain,
product(g2,d,multiply(g2,c,c),multiply(g2,d,multiply(g2,c,c))),
inference(forward_demodulation,[status(thm)],[f68,f1587]) ).
fof(f1589,plain,
product(g2,c,multiply(g2,c,c),multiply(g2,c,multiply(g2,c,identity_for(g2)))),
inference(forward_demodulation,[status(thm)],[f68,f1509]) ).
fof(f1590,plain,
product(g2,c,multiply(g2,c,c),multiply(g2,c,multiply(g2,c,c))),
inference(forward_demodulation,[status(thm)],[f68,f1589]) ).
fof(f1591,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(resolution,[status(thm)],[f78,f128]) ).
fof(f1592,plain,
group_member(multiply(g1,a,d2),g1),
inference(resolution,[status(thm)],[f78,f137]) ).
fof(f1593,plain,
group_member(multiply(g1,b,d2),g1),
inference(resolution,[status(thm)],[f78,f136]) ).
fof(f1594,plain,
product(g1,b,d2,multiply(g1,b,d2)),
inference(resolution,[status(thm)],[f78,f127]) ).
fof(f1596,plain,
group_member(multiply(g1,identity_for(g1),d2),g1),
inference(resolution,[status(thm)],[f78,f140]) ).
fof(f1597,plain,
product(g1,identity_for(g1),d2,multiply(g1,identity_for(g1),d2)),
inference(resolution,[status(thm)],[f78,f131]) ).
fof(f1598,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f1599,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f46]) ).
fof(f1600,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f78,f43]) ).
fof(f1602,plain,
group_member(multiply(g1,a,d2),g1),
inference(forward_demodulation,[status(thm)],[f67,f1596]) ).
fof(f1603,plain,
product(g1,a,d2,multiply(g1,identity_for(g1),d2)),
inference(forward_demodulation,[status(thm)],[f67,f1597]) ).
fof(f1604,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(forward_demodulation,[status(thm)],[f67,f1603]) ).
fof(f1605,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f1259,f287]) ).
fof(f1606,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,d1,b,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1259,f286]) ).
fof(f1607,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1259,f107]) ).
fof(f1608,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f1259,f106]) ).
fof(f1609,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,d1,b,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1259,f96]) ).
fof(f1610,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f1259,f89]) ).
fof(f1611,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1259,f53]) ).
fof(f1612,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(resolution,[status(thm)],[f1259,f51]) ).
fof(f1613,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| X0 = b
| ~ product(g1,d1,b,X0) ),
inference(resolution,[status(thm)],[f1259,f49]) ).
fof(f1614,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1607]) ).
fof(f1615,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,a,b,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1608]) ).
fof(f1616,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,d1,b,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1609]) ).
fof(f1617,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1610]) ).
fof(f1618,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,d2,X1) ),
inference(resolution,[status(thm)],[f1228,f291]) ).
fof(f1619,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,X0,d2,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f1228,f290]) ).
fof(f1620,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| b = d2 ),
inference(resolution,[status(thm)],[f1228,f288]) ).
fof(f1621,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f1228,f287]) ).
fof(f1622,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1228,f286]) ).
fof(f1623,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,inverse(g1,a),b,X0)
| ~ product(g1,identity_for(g1),d2,X0) ),
inference(resolution,[status(thm)],[f1228,f107]) ).
fof(f1624,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,a),b,X0) ),
inference(resolution,[status(thm)],[f1228,f106]) ).
fof(f1625,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,d2,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1228,f96]) ).
fof(f1626,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f1228,f89]) ).
fof(f1627,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f1228,f53]) ).
fof(f1628,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f1228,f51]) ).
fof(f1629,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| X0 = b
| ~ product(g1,a,d2,X0) ),
inference(resolution,[status(thm)],[f1228,f49]) ).
fof(f1630,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,inverse(g1,a),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1623]) ).
fof(f1631,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f352,f1630]) ).
fof(f1632,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f352,f1624]) ).
fof(f1633,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1632]) ).
fof(f1634,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1625]) ).
fof(f1635,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1626]) ).
fof(f1643,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ product(g2,d,isomorphism2(b),c) ),
inference(forward_demodulation,[status(thm)],[f187,f1584]) ).
fof(f1644,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ12_spl
| ~ product(g2,d,c,c) ),
inference(forward_demodulation,[status(thm)],[f76,f1643]) ).
fof(f1646,plain,
( ~ sQ26_spl
| ~ sQ38_spl
| a = b ),
inference(resolution,[status(thm)],[f1550,f292]) ).
fof(f1647,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,a,a,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f1550,f287]) ).
fof(f1648,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,b,a,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f1550,f286]) ).
fof(f1649,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f1550,f107]) ).
fof(f1650,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,inverse(g1,b),a,X0) ),
inference(resolution,[status(thm)],[f1550,f106]) ).
fof(f1651,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,b,a,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f1550,f96]) ).
fof(f1652,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f1550,f89]) ).
fof(f1653,plain,
! [X0,X1,X2] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f1550,f53]) ).
fof(f1654,plain,
! [X0,X1,X2] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f1550,f51]) ).
fof(f1655,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(resolution,[status(thm)],[f1550,f49]) ).
fof(f1656,plain,
( ~ sQ26_spl
| ~ sQ38_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1646,f151,f1407,f1020]) ).
fof(f1657,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,inverse(g1,b),a,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1649]) ).
fof(f1658,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| ~ sQ21_spl
| product(g1,b,a,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f430,f1657]) ).
fof(f1659,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| ~ sQ21_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f430,f1650]) ).
fof(f1660,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1659]) ).
fof(f1661,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,b,a,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1651]) ).
fof(f1662,plain,
! [X0] :
( ~ sQ26_spl
| ~ sQ38_spl
| product(g1,a,a,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1652]) ).
fof(f1663,plain,
( ~ sQ42_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f1567,f1020,f1551]) ).
fof(f1664,plain,
product(g1,b,multiply(g1,a,a),multiply(g1,b,multiply(g1,a,identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f67,f1545]) ).
fof(f1665,plain,
product(g1,b,multiply(g1,a,a),multiply(g1,b,multiply(g1,a,a))),
inference(forward_demodulation,[status(thm)],[f67,f1664]) ).
fof(f1666,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,a,identity_for(g1)))),
inference(forward_demodulation,[status(thm)],[f67,f1530]) ).
fof(f1667,plain,
product(g1,a,multiply(g1,a,a),multiply(g1,a,multiply(g1,a,a))),
inference(forward_demodulation,[status(thm)],[f67,f1666]) ).
fof(f1668,plain,
( ~ sQ43_spl
| multiply(g1,a,identity_for(g1)) = b ),
inference(forward_demodulation,[status(thm)],[f67,f1555]) ).
fof(f1669,plain,
( ~ sQ43_spl
| multiply(g1,a,a) = b ),
inference(forward_demodulation,[status(thm)],[f67,f1668]) ).
fof(f1670,plain,
( sQ42_spl
| multiply(g1,a,identity_for(g1)) != a ),
inference(forward_demodulation,[status(thm)],[f67,f1553]) ).
fof(f1671,plain,
( sQ42_spl
| multiply(g1,a,a) != a ),
inference(forward_demodulation,[status(thm)],[f67,f1670]) ).
fof(f1674,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ product(g2,isomorphism2(a),isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f191,f1280]) ).
fof(f1675,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ product(g2,d,isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f75,f1674]) ).
fof(f1682,plain,
( ~ sQ12_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f1288]) ).
fof(f1689,plain,
( ~ sQ12_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f405]) ).
fof(f1691,plain,
( ~ sQ12_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f104]) ).
fof(f1693,plain,
( ~ sQ12_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f558]) ).
fof(f1698,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f187,f1252]) ).
fof(f1702,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f187,f1251]) ).
fof(f1711,plain,
( ~ sQ31_spl
| ~ sQ40_spl
| c = d ),
inference(backward_demodulation,[status(thm)],[f1569,f1082]) ).
fof(f1712,plain,
( ~ sQ31_spl
| ~ sQ40_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f1711,f221,f1522,f1081]) ).
fof(f1713,plain,
( ~ sQ41_spl
| multiply(g2,c,identity_for(g2)) = d ),
inference(forward_demodulation,[status(thm)],[f68,f1526]) ).
fof(f1714,plain,
( ~ sQ41_spl
| multiply(g2,c,c) = d ),
inference(forward_demodulation,[status(thm)],[f68,f1713]) ).
fof(f1715,plain,
( sQ40_spl
| multiply(g2,c,identity_for(g2)) != c ),
inference(forward_demodulation,[status(thm)],[f68,f1524]) ).
fof(f1716,plain,
( sQ40_spl
| multiply(g2,c,c) != c ),
inference(forward_demodulation,[status(thm)],[f68,f1715]) ).
fof(f1719,plain,
( ~ sQ12_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f1600]) ).
fof(f1728,plain,
( ~ sQ13_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f191,f1293]) ).
fof(f1729,plain,
( ~ sQ13_spl
| product(g1,a,multiply(g1,b,a),multiply(g1,a,multiply(g1,b,a))) ),
inference(resolution,[status(thm)],[f1728,f128]) ).
fof(f1730,plain,
( ~ sQ13_spl
| group_member(multiply(g1,a,multiply(g1,b,a)),g1) ),
inference(resolution,[status(thm)],[f1728,f137]) ).
fof(f1731,plain,
( ~ sQ13_spl
| group_member(multiply(g1,b,multiply(g1,b,a)),g1) ),
inference(resolution,[status(thm)],[f1728,f136]) ).
fof(f1732,plain,
( ~ sQ13_spl
| product(g1,b,multiply(g1,b,a),multiply(g1,b,multiply(g1,b,a))) ),
inference(resolution,[status(thm)],[f1728,f127]) ).
fof(f1734,plain,
( ~ sQ13_spl
| group_member(multiply(g1,identity_for(g1),multiply(g1,b,a)),g1) ),
inference(resolution,[status(thm)],[f1728,f140]) ).
fof(f1735,plain,
( ~ sQ13_spl
| product(g1,identity_for(g1),multiply(g1,b,a),multiply(g1,identity_for(g1),multiply(g1,b,a))) ),
inference(resolution,[status(thm)],[f1728,f131]) ).
fof(f1736,plain,
! [X0] :
( ~ sQ13_spl
| group_member(multiply(g1,multiply(g1,b,a),X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1728,f47]) ).
fof(f1737,plain,
! [X0] :
( ~ sQ13_spl
| product(g1,multiply(g1,b,a),X0,multiply(g1,multiply(g1,b,a),X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f1728,f46]) ).
fof(f1738,plain,
( ~ sQ13_spl
| group_member(inverse(g1,multiply(g1,b,a)),g1) ),
inference(resolution,[status(thm)],[f1728,f43]) ).
fof(f1740,plain,
( ~ sQ13_spl
| group_member(multiply(g1,a,multiply(g1,b,a)),g1) ),
inference(forward_demodulation,[status(thm)],[f67,f1734]) ).
fof(f1741,plain,
( ~ sQ13_spl
| product(g1,a,multiply(g1,b,a),multiply(g1,identity_for(g1),multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f67,f1735]) ).
fof(f1742,plain,
( ~ sQ13_spl
| product(g1,a,multiply(g1,b,a),multiply(g1,a,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f67,f1741]) ).
fof(f1743,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f187,f1212]) ).
fof(f1745,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ12_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,b,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f187,f1211]) ).
fof(f1752,plain,
( ~ sQ13_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f191,f1302]) ).
fof(f1755,plain,
( ~ sQ12_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f1290]) ).
fof(f1757,plain,
( ~ sQ12_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f1281]) ).
fof(f1759,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ13_spl
| X0 = b
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f191,f1253]) ).
fof(f1763,plain,
( ~ sQ41_spl
| ~ sQ30_spl
| c = d ),
inference(forward_demodulation,[status(thm)],[f1079,f1714]) ).
fof(f1764,plain,
( ~ sQ41_spl
| ~ sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1763,f60]) ).
fof(f1765,plain,
( ~ sQ41_spl
| ~ sQ30_spl ),
inference(contradiction_clause,[status(thm)],[f1764]) ).
fof(f1768,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ13_spl
| X0 = b
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f191,f1208]) ).
fof(f1772,plain,
( ~ sQ13_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f191,f1242]) ).
fof(f1785,plain,
( ~ sQ13_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f191,f1233]) ).
fof(f1803,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f430,f119]) ).
fof(f1820,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1803]) ).
fof(f1821,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1820]) ).
fof(f1831,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f430,f121]) ).
fof(f1848,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1831]) ).
fof(f1849,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f1848]) ).
fof(f1873,plain,
( ~ sQ12_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f1592]) ).
fof(f1875,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,inverse(g1,b),X0,multiply(g1,inverse(g1,d3),X0))
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f173,f129]) ).
fof(f1880,plain,
( ~ sQ12_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f1593]) ).
fof(f1882,plain,
! [X0] :
( ~ sQ8_spl
| group_member(multiply(g1,inverse(g1,b),X0),g1)
| ~ group_member(X0,g1) ),
inference(forward_demodulation,[status(thm)],[f173,f138]) ).
fof(f1894,plain,
( ~ sQ12_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f187,f1602]) ).
fof(f1906,plain,
( ~ sQ8_spl
| group_member(inverse(g1,inverse(g1,b)),g1) ),
inference(forward_demodulation,[status(thm)],[f173,f112]) ).
fof(f1909,plain,
( ~ sQ8_spl
| product(g1,b,b,multiply(g1,b,d3)) ),
inference(forward_demodulation,[status(thm)],[f173,f1187]) ).
fof(f1910,plain,
( ~ sQ8_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f173,f1909]) ).
fof(f1911,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f1378,f1910]) ).
fof(f1986,plain,
( ~ sQ8_spl
| product(g1,a,b,multiply(g1,a,d3)) ),
inference(forward_demodulation,[status(thm)],[f173,f1197]) ).
fof(f1987,plain,
( ~ sQ8_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f173,f1986]) ).
fof(f1989,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f191,f1214]) ).
fof(f2019,plain,
( ~ sQ13_spl
| product(g1,b,a,multiply(g1,b,d1)) ),
inference(forward_demodulation,[status(thm)],[f191,f1234]) ).
fof(f2020,plain,
( ~ sQ13_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f191,f2019]) ).
fof(f2022,plain,
( ~ sQ13_spl
| product(g1,a,a,multiply(g1,a,d1)) ),
inference(forward_demodulation,[status(thm)],[f191,f1244]) ).
fof(f2023,plain,
( ~ sQ13_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f191,f2022]) ).
fof(f2024,plain,
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,a,b) ),
inference(forward_demodulation,[status(thm)],[f1024,f2023]) ).
fof(f2026,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,X0,b,X1)
| ~ product(g1,X0,a,X1) ),
inference(resolution,[status(thm)],[f2024,f291]) ).
fof(f2027,plain,
! [X0,X1] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,X0,a,X1)
| ~ product(g1,X0,b,X1) ),
inference(resolution,[status(thm)],[f2024,f290]) ).
fof(f2028,plain,
( ~ sQ13_spl
| ~ sQ27_spl
| b = a ),
inference(resolution,[status(thm)],[f2024,f288]) ).
fof(f2031,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f2024,f287]) ).
fof(f2032,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f2024,f286]) ).
fof(f2033,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,inverse(g1,a),b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2024,f107]) ).
fof(f2034,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,inverse(g1,a),b,X0) ),
inference(resolution,[status(thm)],[f2024,f106]) ).
fof(f2035,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f2024,f96]) ).
fof(f2036,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f2024,f89]) ).
fof(f2037,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,b,X0,X2)
| ~ product(g1,a,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2024,f53]) ).
fof(f2038,plain,
! [X0,X1,X2] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2024,f51]) ).
fof(f2039,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| X0 = b
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f2024,f49]) ).
fof(f2040,plain,
( ~ sQ13_spl
| ~ sQ27_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2028,f151,f1023,f190]) ).
fof(f2042,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,inverse(g1,a),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2033]) ).
fof(f2043,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f352,f2042]) ).
fof(f2044,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f352,f2034]) ).
fof(f2045,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2044]) ).
fof(f2046,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2035]) ).
fof(f2047,plain,
! [X0] :
( ~ sQ13_spl
| ~ sQ27_spl
| product(g1,a,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2036]) ).
fof(f2050,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f287]) ).
fof(f2051,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1207,f286]) ).
fof(f2052,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,identity_for(g1),d2,X0) ),
inference(resolution,[status(thm)],[f1207,f107]) ).
fof(f2053,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f1207,f106]) ).
fof(f2054,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1207,f96]) ).
fof(f2055,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f89]) ).
fof(f2056,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f1207,f53]) ).
fof(f2057,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f1207,f51]) ).
fof(f2058,plain,
! [X0] :
( ~ sQ8_spl
| X0 = b
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f49]) ).
fof(f2059,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2052]) ).
fof(f2060,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2053]) ).
fof(f2061,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2054]) ).
fof(f2062,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2055]) ).
fof(f2063,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,c,d,X0)
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),X0) ),
inference(resolution,[status(thm)],[f1276,f99]) ).
fof(f2064,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(resolution,[status(thm)],[f1276,f98]) ).
fof(f2065,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,inverse(g2,isomorphism1(d1)),d,X0)
| ~ product(g2,identity_for(g2),isomorphism1(d2),X0) ),
inference(resolution,[status(thm)],[f1276,f107]) ).
fof(f2066,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,identity_for(g2),isomorphism1(d2),X0)
| ~ product(g2,inverse(g2,isomorphism1(d1)),d,X0) ),
inference(resolution,[status(thm)],[f1276,f106]) ).
fof(f2067,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),X0)
| ~ product(g2,identity_for(g2),d,X0) ),
inference(resolution,[status(thm)],[f1276,f96]) ).
fof(f2068,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,identity_for(g2),d,X0)
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),X0) ),
inference(resolution,[status(thm)],[f1276,f89]) ).
fof(f2069,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,isomorphism1(d2),X0,X1) ),
inference(resolution,[status(thm)],[f1276,f53]) ).
fof(f2070,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(d2),X0,X1) ),
inference(resolution,[status(thm)],[f1276,f51]) ).
fof(f2071,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| X0 = d
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),X0) ),
inference(resolution,[status(thm)],[f1276,f49]) ).
fof(f2072,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,inverse(g2,isomorphism1(d1)),d,X0)
| ~ product(g2,c,isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2065]) ).
fof(f2073,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,c,isomorphism1(d2),X0)
| ~ product(g2,inverse(g2,isomorphism1(d1)),d,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2066]) ).
fof(f2074,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2067]) ).
fof(f2075,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,c,d,X0)
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2068]) ).
fof(f2076,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,isomorphism1(d1),isomorphism1(a),d) ),
inference(backward_demodulation,[status(thm)],[f184,f1276]) ).
fof(f2077,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,a,b) ),
inference(backward_demodulation,[status(thm)],[f184,f1207]) ).
fof(f2079,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,isomorphism1(d1),c,d) ),
inference(forward_demodulation,[status(thm)],[f73,f2076]) ).
fof(f2082,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ product(g2,isomorphism2(b),isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f194,f1280]) ).
fof(f2083,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ product(g2,c,isomorphism2(d2),c) ),
inference(forward_demodulation,[status(thm)],[f76,f2082]) ).
fof(f2084,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ product(g2,c,isomorphism2(a),c) ),
inference(forward_demodulation,[status(thm)],[f184,f2083]) ).
fof(f2085,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ11_spl
| ~ product(g2,c,d,c) ),
inference(forward_demodulation,[status(thm)],[f75,f2084]) ).
fof(f2087,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f105]) ).
fof(f2090,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1240]) ).
fof(f2092,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1300]) ).
fof(f2114,plain,
( ~ sQ14_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1233]) ).
fof(f2119,plain,
( ~ sQ14_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1242]) ).
fof(f2121,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1208]) ).
fof(f2123,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1253]) ).
fof(f2130,plain,
( ~ sQ14_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1302]) ).
fof(f2133,plain,
( ~ sQ14_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1293]) ).
fof(f2135,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1602]) ).
fof(f2140,plain,
( ~ sQ11_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1593]) ).
fof(f2142,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1592]) ).
fof(f2144,plain,
( ~ sQ11_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1281]) ).
fof(f2146,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1211]) ).
fof(f2148,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1212]) ).
fof(f2152,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1290]) ).
fof(f2161,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2058]) ).
fof(f2163,plain,
group_member(multiply(g2,d,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2)))),g2),
inference(resolution,[status(thm)],[f1495,f135]) ).
fof(f2164,plain,
group_member(multiply(g2,c,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2)))),g2),
inference(resolution,[status(thm)],[f1495,f141]) ).
fof(f2165,plain,
product(g2,c,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))),multiply(g2,c,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))),
inference(resolution,[status(thm)],[f1495,f132]) ).
fof(f2166,plain,
product(g2,d,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))),multiply(g2,d,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))),
inference(resolution,[status(thm)],[f1495,f126]) ).
fof(f2167,plain,
( inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))) = d
| inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))) = c ),
inference(resolution,[status(thm)],[f1495,f66]) ).
fof(f2168,plain,
product(g1,a,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))),multiply(g1,a,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))))),
inference(resolution,[status(thm)],[f1495,f128]) ).
fof(f2169,plain,
group_member(multiply(g1,a,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1)))),g1),
inference(resolution,[status(thm)],[f1495,f137]) ).
fof(f2170,plain,
group_member(multiply(g1,b,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1)))),g1),
inference(resolution,[status(thm)],[f1495,f136]) ).
fof(f2171,plain,
product(g1,b,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))),multiply(g1,b,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))))),
inference(resolution,[status(thm)],[f1495,f127]) ).
fof(f2172,plain,
( inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))) = b
| inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))) = a ),
inference(resolution,[status(thm)],[f1495,f65]) ).
fof(f2178,plain,
group_member(inverse(g2,multiply(g2,c,identity_for(g2))),g2),
inference(paramodulation,[status(thm)],[f68,f1495]) ).
fof(f2179,plain,
group_member(inverse(g1,multiply(g1,a,identity_for(g1))),g1),
inference(paramodulation,[status(thm)],[f67,f1495]) ).
fof(f2180,plain,
group_member(inverse(g2,multiply(g2,identity_for(g2),c)),g2),
inference(paramodulation,[status(thm)],[f68,f1495]) ).
fof(f2181,plain,
group_member(inverse(g1,multiply(g1,identity_for(g1),a)),g1),
inference(paramodulation,[status(thm)],[f67,f1495]) ).
fof(f2182,plain,
group_member(multiply(g2,d,inverse(g2,multiply(g2,c,identity_for(g2)))),g2),
inference(forward_demodulation,[status(thm)],[f68,f2163]) ).
fof(f2183,plain,
group_member(multiply(g2,d,inverse(g2,multiply(g2,c,c))),g2),
inference(forward_demodulation,[status(thm)],[f68,f2182]) ).
fof(f2184,plain,
( ~ sQ41_spl
| group_member(multiply(g2,d,inverse(g2,d)),g2) ),
inference(forward_demodulation,[status(thm)],[f1714,f2183]) ).
fof(f2185,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| group_member(multiply(g2,d,d),g2) ),
inference(forward_demodulation,[status(thm)],[f622,f2184]) ).
fof(f2187,plain,
group_member(multiply(g2,c,inverse(g2,multiply(g2,c,identity_for(g2)))),g2),
inference(forward_demodulation,[status(thm)],[f68,f2164]) ).
fof(f2188,plain,
group_member(multiply(g2,c,inverse(g2,multiply(g2,c,c))),g2),
inference(forward_demodulation,[status(thm)],[f68,f2187]) ).
fof(f2189,plain,
( ~ sQ41_spl
| group_member(multiply(g2,c,inverse(g2,d)),g2) ),
inference(forward_demodulation,[status(thm)],[f1714,f2188]) ).
fof(f2190,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| group_member(multiply(g2,c,d),g2) ),
inference(forward_demodulation,[status(thm)],[f622,f2189]) ).
fof(f2192,plain,
product(g2,c,inverse(g2,multiply(g2,c,identity_for(g2))),multiply(g2,c,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))),
inference(forward_demodulation,[status(thm)],[f68,f2165]) ).
fof(f2193,plain,
product(g2,c,inverse(g2,multiply(g2,c,c)),multiply(g2,c,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))),
inference(forward_demodulation,[status(thm)],[f68,f2192]) ).
fof(f2194,plain,
( ~ sQ41_spl
| product(g2,c,inverse(g2,d),multiply(g2,c,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))) ),
inference(forward_demodulation,[status(thm)],[f1714,f2193]) ).
fof(f2195,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,c,d,multiply(g2,c,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))) ),
inference(forward_demodulation,[status(thm)],[f622,f2194]) ).
fof(f2196,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,c,d,multiply(g2,c,inverse(g2,multiply(g2,c,identity_for(g2))))) ),
inference(forward_demodulation,[status(thm)],[f68,f2195]) ).
fof(f2197,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,c,d,multiply(g2,c,inverse(g2,multiply(g2,c,c)))) ),
inference(forward_demodulation,[status(thm)],[f68,f2196]) ).
fof(f2198,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,c,d,multiply(g2,c,inverse(g2,d))) ),
inference(forward_demodulation,[status(thm)],[f1714,f2197]) ).
fof(f2199,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,c,d,multiply(g2,c,d)) ),
inference(forward_demodulation,[status(thm)],[f622,f2198]) ).
fof(f2200,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| ~ sQ28_spl
| product(g2,c,d,c) ),
inference(forward_demodulation,[status(thm)],[f1053,f2199]) ).
fof(f2201,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| ~ sQ28_spl
| sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2200,f2085]) ).
fof(f2202,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| ~ sQ28_spl
| sQ1_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f2201]) ).
fof(f2203,plain,
product(g2,d,inverse(g2,multiply(g2,c,identity_for(g2))),multiply(g2,d,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))),
inference(forward_demodulation,[status(thm)],[f68,f2166]) ).
fof(f2204,plain,
product(g2,d,inverse(g2,multiply(g2,c,c)),multiply(g2,d,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))),
inference(forward_demodulation,[status(thm)],[f68,f2203]) ).
fof(f2205,plain,
( ~ sQ41_spl
| product(g2,d,inverse(g2,d),multiply(g2,d,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))) ),
inference(forward_demodulation,[status(thm)],[f1714,f2204]) ).
fof(f2206,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,d,d,multiply(g2,d,inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))))) ),
inference(forward_demodulation,[status(thm)],[f622,f2205]) ).
fof(f2207,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,d,d,multiply(g2,d,inverse(g2,multiply(g2,c,identity_for(g2))))) ),
inference(forward_demodulation,[status(thm)],[f68,f2206]) ).
fof(f2208,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,d,d,multiply(g2,d,inverse(g2,multiply(g2,c,c)))) ),
inference(forward_demodulation,[status(thm)],[f68,f2207]) ).
fof(f2209,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,d,d,multiply(g2,d,inverse(g2,d))) ),
inference(forward_demodulation,[status(thm)],[f1714,f2208]) ).
fof(f2210,plain,
( ~ sQ41_spl
| ~ sQ23_spl
| product(g2,d,d,multiply(g2,d,d)) ),
inference(forward_demodulation,[status(thm)],[f622,f2209]) ).
fof(f2212,definition,
( sQ44_spl
<=> inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))) = c ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f2213,plain,
( ~ sQ44_spl
| inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))) = c ),
inference(component_clause,[status(thm)],[f2212]) ).
fof(f2215,definition,
( sQ45_spl
<=> inverse(g2,multiply(g2,identity_for(g2),identity_for(g2))) = d ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f2218,plain,
( sQ45_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f2167,f2212,f2215]) ).
fof(f2219,plain,
product(g1,a,inverse(g1,multiply(g1,a,identity_for(g1))),multiply(g1,a,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))))),
inference(forward_demodulation,[status(thm)],[f67,f2168]) ).
fof(f2220,plain,
product(g1,a,inverse(g1,multiply(g1,a,a)),multiply(g1,a,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))))),
inference(forward_demodulation,[status(thm)],[f67,f2219]) ).
fof(f2221,plain,
product(g1,a,inverse(g1,multiply(g1,a,a)),multiply(g1,a,inverse(g1,multiply(g1,a,identity_for(g1))))),
inference(forward_demodulation,[status(thm)],[f67,f2220]) ).
fof(f2222,plain,
product(g1,a,inverse(g1,multiply(g1,a,a)),multiply(g1,a,inverse(g1,multiply(g1,a,a)))),
inference(forward_demodulation,[status(thm)],[f67,f2221]) ).
fof(f2223,plain,
group_member(multiply(g1,a,inverse(g1,multiply(g1,a,identity_for(g1)))),g1),
inference(forward_demodulation,[status(thm)],[f67,f2169]) ).
fof(f2224,plain,
group_member(multiply(g1,a,inverse(g1,multiply(g1,a,a))),g1),
inference(forward_demodulation,[status(thm)],[f67,f2223]) ).
fof(f2225,plain,
group_member(multiply(g1,b,inverse(g1,multiply(g1,a,identity_for(g1)))),g1),
inference(forward_demodulation,[status(thm)],[f67,f2170]) ).
fof(f2226,plain,
group_member(multiply(g1,b,inverse(g1,multiply(g1,a,a))),g1),
inference(forward_demodulation,[status(thm)],[f67,f2225]) ).
fof(f2227,plain,
product(g1,b,inverse(g1,multiply(g1,a,identity_for(g1))),multiply(g1,b,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))))),
inference(forward_demodulation,[status(thm)],[f67,f2171]) ).
fof(f2228,plain,
product(g1,b,inverse(g1,multiply(g1,a,a)),multiply(g1,b,inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))))),
inference(forward_demodulation,[status(thm)],[f67,f2227]) ).
fof(f2229,plain,
product(g1,b,inverse(g1,multiply(g1,a,a)),multiply(g1,b,inverse(g1,multiply(g1,a,identity_for(g1))))),
inference(forward_demodulation,[status(thm)],[f67,f2228]) ).
fof(f2230,plain,
product(g1,b,inverse(g1,multiply(g1,a,a)),multiply(g1,b,inverse(g1,multiply(g1,a,a)))),
inference(forward_demodulation,[status(thm)],[f67,f2229]) ).
fof(f2231,definition,
( sQ46_spl
<=> inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))) = a ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f2232,plain,
( ~ sQ46_spl
| inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))) = a ),
inference(component_clause,[status(thm)],[f2231]) ).
fof(f2234,definition,
( sQ47_spl
<=> inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))) = b ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f2235,plain,
( ~ sQ47_spl
| inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))) = b ),
inference(component_clause,[status(thm)],[f2234]) ).
fof(f2236,plain,
( sQ47_spl
| inverse(g1,multiply(g1,identity_for(g1),identity_for(g1))) != b ),
inference(component_clause,[status(thm)],[f2234]) ).
fof(f2237,plain,
( sQ47_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f2172,f2231,f2234]) ).
fof(f2238,plain,
group_member(inverse(g2,multiply(g2,c,c)),g2),
inference(forward_demodulation,[status(thm)],[f68,f2178]) ).
fof(f2239,plain,
( ~ sQ41_spl
| group_member(inverse(g2,d),g2) ),
inference(forward_demodulation,[status(thm)],[f1714,f2238]) ).
fof(f2241,plain,
group_member(inverse(g1,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f67,f2179]) ).
fof(f2242,plain,
group_member(inverse(g2,multiply(g2,c,c)),g2),
inference(forward_demodulation,[status(thm)],[f68,f2180]) ).
fof(f2243,plain,
( ~ sQ41_spl
| group_member(inverse(g2,d),g2) ),
inference(forward_demodulation,[status(thm)],[f1714,f2242]) ).
fof(f2245,plain,
group_member(inverse(g1,multiply(g1,a,a)),g1),
inference(forward_demodulation,[status(thm)],[f67,f2181]) ).
fof(f2246,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| product(g1,a,b,multiply(g1,a,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f1411,f1729]) ).
fof(f2247,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1411,f2246]) ).
fof(f2249,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1411,f1730]) ).
fof(f2251,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1411,f1731]) ).
fof(f2253,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| product(g1,b,b,multiply(g1,b,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f1411,f1732]) ).
fof(f2254,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f1411,f2253]) ).
fof(f2255,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| ~ sQ36_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f1378,f2254]) ).
fof(f2256,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1411,f1740]) ).
fof(f2258,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| product(g1,a,b,multiply(g1,a,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f1411,f1742]) ).
fof(f2259,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1411,f2258]) ).
fof(f2264,plain,
( ~ sQ13_spl
| ~ sQ39_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1411,f1738]) ).
fof(f2268,plain,
( ~ sQ43_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f1669,f1023,f1554]) ).
fof(f2270,plain,
( ~ sQ46_spl
| inverse(g1,multiply(g1,a,identity_for(g1))) = a ),
inference(forward_demodulation,[status(thm)],[f67,f2232]) ).
fof(f2271,plain,
( ~ sQ46_spl
| inverse(g1,multiply(g1,a,a)) = a ),
inference(forward_demodulation,[status(thm)],[f67,f2270]) ).
fof(f2272,plain,
( ~ sQ44_spl
| inverse(g2,multiply(g2,c,identity_for(g2))) = c ),
inference(forward_demodulation,[status(thm)],[f68,f2213]) ).
fof(f2273,plain,
( ~ sQ44_spl
| inverse(g2,multiply(g2,c,c)) = c ),
inference(forward_demodulation,[status(thm)],[f68,f2272]) ).
fof(f2274,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| inverse(g2,d) = c ),
inference(forward_demodulation,[status(thm)],[f1714,f2273]) ).
fof(f2275,plain,
( sQ43_spl
| multiply(g1,a,identity_for(g1)) != b ),
inference(forward_demodulation,[status(thm)],[f67,f1556]) ).
fof(f2276,plain,
( sQ43_spl
| multiply(g1,a,a) != b ),
inference(forward_demodulation,[status(thm)],[f67,f2275]) ).
fof(f2277,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(resolution,[status(thm)],[f78,f128]) ).
fof(f2278,plain,
group_member(multiply(g1,a,d2),g1),
inference(resolution,[status(thm)],[f78,f137]) ).
fof(f2279,plain,
group_member(multiply(g1,b,d2),g1),
inference(resolution,[status(thm)],[f78,f136]) ).
fof(f2280,plain,
product(g1,b,d2,multiply(g1,b,d2)),
inference(resolution,[status(thm)],[f78,f127]) ).
fof(f2282,plain,
group_member(multiply(g1,identity_for(g1),d2),g1),
inference(resolution,[status(thm)],[f78,f140]) ).
fof(f2283,plain,
product(g1,identity_for(g1),d2,multiply(g1,identity_for(g1),d2)),
inference(resolution,[status(thm)],[f78,f131]) ).
fof(f2284,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f2285,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f46]) ).
fof(f2286,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f78,f43]) ).
fof(f2288,plain,
group_member(multiply(g1,a,d2),g1),
inference(forward_demodulation,[status(thm)],[f67,f2282]) ).
fof(f2289,plain,
product(g1,a,d2,multiply(g1,identity_for(g1),d2)),
inference(forward_demodulation,[status(thm)],[f67,f2283]) ).
fof(f2290,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(forward_demodulation,[status(thm)],[f67,f2289]) ).
fof(f2291,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,c,d,X0)
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),X0) ),
inference(resolution,[status(thm)],[f1276,f99]) ).
fof(f2292,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(resolution,[status(thm)],[f1276,f98]) ).
fof(f2293,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,inverse(g2,isomorphism1(d1)),d,X0)
| ~ product(g2,identity_for(g2),isomorphism1(d2),X0) ),
inference(resolution,[status(thm)],[f1276,f107]) ).
fof(f2294,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,identity_for(g2),isomorphism1(d2),X0)
| ~ product(g2,inverse(g2,isomorphism1(d1)),d,X0) ),
inference(resolution,[status(thm)],[f1276,f106]) ).
fof(f2295,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),X0)
| ~ product(g2,identity_for(g2),d,X0) ),
inference(resolution,[status(thm)],[f1276,f96]) ).
fof(f2296,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,identity_for(g2),d,X0)
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),X0) ),
inference(resolution,[status(thm)],[f1276,f89]) ).
fof(f2297,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,isomorphism1(d2),X0,X1) ),
inference(resolution,[status(thm)],[f1276,f53]) ).
fof(f2298,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(d2),X0,X1) ),
inference(resolution,[status(thm)],[f1276,f51]) ).
fof(f2299,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| X0 = d
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),X0) ),
inference(resolution,[status(thm)],[f1276,f49]) ).
fof(f2300,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,inverse(g2,isomorphism1(d1)),d,X0)
| ~ product(g2,c,isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2293]) ).
fof(f2301,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,c,isomorphism1(d2),X0)
| ~ product(g2,inverse(g2,isomorphism1(d1)),d,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2294]) ).
fof(f2302,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,isomorphism1(d1),isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2295]) ).
fof(f2303,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| product(g2,c,d,X0)
| ~ product(g2,isomorphism1(d1),isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2296]) ).
fof(f2304,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f287]) ).
fof(f2305,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f1207,f286]) ).
fof(f2306,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,identity_for(g1),d2,X0) ),
inference(resolution,[status(thm)],[f1207,f107]) ).
fof(f2307,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,identity_for(g1),d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f1207,f106]) ).
fof(f2308,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f1207,f96]) ).
fof(f2309,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f89]) ).
fof(f2310,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f1207,f53]) ).
fof(f2311,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,d2,X0,X1) ),
inference(resolution,[status(thm)],[f1207,f51]) ).
fof(f2312,plain,
! [X0] :
( ~ sQ8_spl
| X0 = b
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[f1207,f49]) ).
fof(f2313,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2306]) ).
fof(f2314,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2307]) ).
fof(f2315,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,d1,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2308]) ).
fof(f2316,plain,
! [X0] :
( ~ sQ8_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2309]) ).
fof(f2317,plain,
( ~ sQ8_spl
| ~ sQ13_spl
| product(g1,a,d2,b) ),
inference(backward_demodulation,[status(thm)],[f191,f1207]) ).
fof(f2318,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g2,isomorphism1(a),isomorphism1(d2),d) ),
inference(backward_demodulation,[status(thm)],[f191,f1276]) ).
fof(f2319,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ13_spl
| product(g2,c,isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f73,f2318]) ).
fof(f2327,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ product(g2,d,isomorphism2(b),c) ),
inference(forward_demodulation,[status(thm)],[f1620,f1675]) ).
fof(f2328,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ13_spl
| ~ product(g2,d,c,c) ),
inference(forward_demodulation,[status(thm)],[f76,f2327]) ).
fof(f2331,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ product(g2,d,isomorphism2(b),c) ),
inference(forward_demodulation,[status(thm)],[f1620,f1584]) ).
fof(f2332,plain,
( sQ1_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ product(g2,d,c,c) ),
inference(forward_demodulation,[status(thm)],[f76,f2331]) ).
fof(f2333,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1620,f1288]) ).
fof(f2336,plain,
( ~ sQ13_spl
| ~ sQ8_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1620,f405]) ).
fof(f2340,plain,
( ~ sQ23_spl
| ~ sQ44_spl
| ~ sQ41_spl
| c = d ),
inference(backward_demodulation,[status(thm)],[f2274,f622]) ).
fof(f2341,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ41_spl
| X0 = c
| ~ product(g2,c,d,X0) ),
inference(paramodulation,[status(thm)],[f2274,f997]) ).
fof(f2342,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ41_spl
| X0 = c
| ~ product(g2,d,c,X0) ),
inference(paramodulation,[status(thm)],[f2274,f969]) ).
fof(f2343,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| product(g2,c,d,c) ),
inference(paramodulation,[status(thm)],[f2274,f247]) ).
fof(f2344,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| product(g2,d,c,c) ),
inference(paramodulation,[status(thm)],[f2274,f246]) ).
fof(f2345,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ41_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,d,c,X0) ),
inference(paramodulation,[status(thm)],[f2274,f121]) ).
fof(f2346,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ41_spl
| product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,c,d,X0) ),
inference(paramodulation,[status(thm)],[f2274,f119]) ).
fof(f2347,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ41_spl
| X0 = identity_for(g2)
| ~ product(g2,d,c,X0) ),
inference(paramodulation,[status(thm)],[f2274,f111]) ).
fof(f2348,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| ~ sQ41_spl
| product(g2,d,X1,X2)
| ~ product(g2,identity_for(g2),X0,X2)
| ~ product(g2,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f2274,f110]) ).
fof(f2349,plain,
! [X0,X1,X2] :
( ~ sQ44_spl
| ~ sQ41_spl
| product(g2,identity_for(g2),X0,X2)
| ~ product(g2,d,X1,X2)
| ~ product(g2,c,X0,X1) ),
inference(paramodulation,[status(thm)],[f2274,f109]) ).
fof(f2350,plain,
! [X0] :
( ~ sQ44_spl
| ~ sQ41_spl
| X0 = identity_for(g2)
| ~ product(g2,c,d,X0) ),
inference(paramodulation,[status(thm)],[f2274,f108]) ).
fof(f2351,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| product(g2,d,c,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f2274,f45]) ).
fof(f2352,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| product(g2,c,d,identity_for(g2)) ),
inference(paramodulation,[status(thm)],[f2274,f44]) ).
fof(f2353,plain,
( ~ sQ23_spl
| ~ sQ44_spl
| ~ sQ41_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f2340,f221,f1525,f2212,f621]) ).
fof(f2354,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| sQ1_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2344,f1644]) ).
fof(f2355,plain,
( ~ sQ44_spl
| ~ sQ41_spl
| sQ1_spl
| ~ sQ13_spl
| ~ sQ8_spl
| ~ sQ12_spl ),
inference(contradiction_clause,[status(thm)],[f2354]) ).
fof(f2356,plain,
product(g2,d,inverse(g2,multiply(g2,c,c)),multiply(g2,d,inverse(g2,multiply(g2,c,identity_for(g2))))),
inference(forward_demodulation,[status(thm)],[f68,f2204]) ).
fof(f2357,plain,
product(g2,d,inverse(g2,multiply(g2,c,c)),multiply(g2,d,inverse(g2,multiply(g2,c,c)))),
inference(forward_demodulation,[status(thm)],[f68,f2356]) ).
fof(f2358,plain,
product(g2,c,inverse(g2,multiply(g2,c,c)),multiply(g2,c,inverse(g2,multiply(g2,c,identity_for(g2))))),
inference(forward_demodulation,[status(thm)],[f68,f2193]) ).
fof(f2359,plain,
product(g2,c,inverse(g2,multiply(g2,c,c)),multiply(g2,c,inverse(g2,multiply(g2,c,c)))),
inference(forward_demodulation,[status(thm)],[f68,f2358]) ).
fof(f2360,plain,
( sQ41_spl
| multiply(g2,c,identity_for(g2)) != d ),
inference(forward_demodulation,[status(thm)],[f68,f1527]) ).
fof(f2361,plain,
( sQ41_spl
| multiply(g2,c,c) != d ),
inference(forward_demodulation,[status(thm)],[f68,f2360]) ).
fof(f2363,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(resolution,[status(thm)],[f77,f128]) ).
fof(f2364,plain,
group_member(multiply(g1,a,d1),g1),
inference(resolution,[status(thm)],[f77,f137]) ).
fof(f2365,plain,
group_member(multiply(g1,b,d1),g1),
inference(resolution,[status(thm)],[f77,f136]) ).
fof(f2366,plain,
product(g1,b,d1,multiply(g1,b,d1)),
inference(resolution,[status(thm)],[f77,f127]) ).
fof(f2368,plain,
group_member(multiply(g1,identity_for(g1),d1),g1),
inference(resolution,[status(thm)],[f77,f140]) ).
fof(f2369,plain,
product(g1,identity_for(g1),d1,multiply(g1,identity_for(g1),d1)),
inference(resolution,[status(thm)],[f77,f131]) ).
fof(f2370,plain,
! [X0] :
( group_member(multiply(g1,d1,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f77,f47]) ).
fof(f2371,plain,
! [X0] :
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f77,f46]) ).
fof(f2372,plain,
group_member(inverse(g1,d1),g1),
inference(resolution,[status(thm)],[f77,f43]) ).
fof(f2374,plain,
group_member(multiply(g1,a,d1),g1),
inference(forward_demodulation,[status(thm)],[f67,f2368]) ).
fof(f2375,plain,
product(g1,a,d1,multiply(g1,identity_for(g1),d1)),
inference(forward_demodulation,[status(thm)],[f67,f2369]) ).
fof(f2376,plain,
product(g1,a,d1,multiply(g1,a,d1)),
inference(forward_demodulation,[status(thm)],[f67,f2375]) ).
fof(f2377,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(resolution,[status(thm)],[f78,f128]) ).
fof(f2378,plain,
group_member(multiply(g1,a,d2),g1),
inference(resolution,[status(thm)],[f78,f137]) ).
fof(f2379,plain,
group_member(multiply(g1,b,d2),g1),
inference(resolution,[status(thm)],[f78,f136]) ).
fof(f2380,plain,
product(g1,b,d2,multiply(g1,b,d2)),
inference(resolution,[status(thm)],[f78,f127]) ).
fof(f2382,plain,
group_member(multiply(g1,identity_for(g1),d2),g1),
inference(resolution,[status(thm)],[f78,f140]) ).
fof(f2383,plain,
product(g1,identity_for(g1),d2,multiply(g1,identity_for(g1),d2)),
inference(resolution,[status(thm)],[f78,f131]) ).
fof(f2384,plain,
! [X0] :
( group_member(multiply(g1,d2,X0),g1)
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f47]) ).
fof(f2385,plain,
! [X0] :
( product(g1,d2,X0,multiply(g1,d2,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[f78,f46]) ).
fof(f2386,plain,
group_member(inverse(g1,d2),g1),
inference(resolution,[status(thm)],[f78,f43]) ).
fof(f2388,plain,
group_member(multiply(g1,a,d2),g1),
inference(forward_demodulation,[status(thm)],[f67,f2382]) ).
fof(f2389,plain,
product(g1,a,d2,multiply(g1,identity_for(g1),d2)),
inference(forward_demodulation,[status(thm)],[f67,f2383]) ).
fof(f2390,plain,
product(g1,a,d2,multiply(g1,a,d2)),
inference(forward_demodulation,[status(thm)],[f67,f2389]) ).
fof(f2392,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ product(g2,isomorphism2(d1),isomorphism2(a),c) ),
inference(backward_demodulation,[status(thm)],[f184,f1280]) ).
fof(f2394,plain,
( sQ1_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ product(g2,isomorphism2(d1),d,c) ),
inference(forward_demodulation,[status(thm)],[f75,f2392]) ).
fof(f2395,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,a,b) ),
inference(forward_demodulation,[status(thm)],[f184,f1207]) ).
fof(f2396,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,a,d1,b) ),
inference(resolution,[status(thm)],[f2395,f293]) ).
fof(f2397,plain,
( ~ sQ8_spl
| ~ sQ11_spl
| b = d1 ),
inference(resolution,[status(thm)],[f2395,f292]) ).
fof(f2398,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,a,X0) ),
inference(resolution,[status(thm)],[f2395,f287]) ).
fof(f2399,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,a,X0)
| ~ product(g1,a,b,X0) ),
inference(resolution,[status(thm)],[f2395,f286]) ).
fof(f2400,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,identity_for(g1),a,X0) ),
inference(resolution,[status(thm)],[f2395,f107]) ).
fof(f2401,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,identity_for(g1),a,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(resolution,[status(thm)],[f2395,f106]) ).
fof(f2402,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,a,X0)
| ~ product(g1,identity_for(g1),b,X0) ),
inference(resolution,[status(thm)],[f2395,f96]) ).
fof(f2403,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,identity_for(g1),b,X0)
| ~ product(g1,d1,a,X0) ),
inference(resolution,[status(thm)],[f2395,f89]) ).
fof(f2404,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2395,f53]) ).
fof(f2405,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(resolution,[status(thm)],[f2395,f51]) ).
fof(f2406,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| X0 = b
| ~ product(g1,d1,a,X0) ),
inference(resolution,[status(thm)],[f2395,f49]) ).
fof(f2407,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2400]) ).
fof(f2408,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,a,a,X0)
| ~ product(g1,inverse(g1,d1),b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2401]) ).
fof(f2409,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2402]) ).
fof(f2410,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,a,b,X0)
| ~ product(g1,d1,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2403]) ).
fof(f2414,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,isomorphism1(b),isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f194,f1276]) ).
fof(f2415,plain,
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,d,isomorphism1(d2),d) ),
inference(forward_demodulation,[status(thm)],[f74,f2414]) ).
fof(f2451,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1300]) ).
fof(f2453,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1240]) ).
fof(f2459,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f105]) ).
fof(f2477,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1251]) ).
fof(f2480,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1252]) ).
fof(f2485,plain,
( ~ sQ14_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f2372]) ).
fof(f2487,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f2056]) ).
fof(f2492,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f2057]) ).
fof(f2494,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,isomorphism1(a),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f2069]) ).
fof(f2495,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f73,f2494]) ).
fof(f2500,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1290]) ).
fof(f2502,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(a),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f2070]) ).
fof(f2503,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,d,X0,X2)
| ~ product(g2,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f73,f2502]) ).
fof(f2506,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| X0 = d
| ~ product(g2,isomorphism1(b),isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2071]) ).
fof(f2507,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| X0 = d
| ~ product(g2,d,isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f74,f2506]) ).
fof(f2511,plain,
( ~ sQ11_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1281]) ).
fof(f2515,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1592]) ).
fof(f2517,plain,
( ~ sQ11_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1593]) ).
fof(f2522,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f1602]) ).
fof(f2524,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2058]) ).
fof(f2526,plain,
( ~ sQ14_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1293]) ).
fof(f2528,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1212]) ).
fof(f2530,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f1211]) ).
fof(f2533,plain,
( ~ sQ14_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1302]) ).
fof(f2537,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1253]) ).
fof(f2539,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1208]) ).
fof(f2544,plain,
( ~ sQ14_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1242]) ).
fof(f2546,plain,
( ~ sQ14_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f1233]) ).
fof(f2554,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f2278]) ).
fof(f2558,plain,
( ~ sQ11_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f2279]) ).
fof(f2566,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,isomorphism1(a),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f2297]) ).
fof(f2567,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f73,f2566]) ).
fof(f2570,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,d,X0,X2)
| ~ product(g2,isomorphism1(a),X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f2298]) ).
fof(f2571,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,isomorphism1(d1),X1,X2)
| ~ product(g2,d,X0,X2)
| ~ product(g2,c,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f73,f2570]) ).
fof(f2574,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| X0 = d
| ~ product(g2,isomorphism1(b),isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2299]) ).
fof(f2575,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| X0 = d
| ~ product(g2,d,isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f74,f2574]) ).
fof(f2578,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f2288]) ).
fof(f2580,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,b,X0,X2)
| ~ product(g1,d1,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f2310]) ).
fof(f2582,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| X0 = b
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2312]) ).
fof(f2585,plain,
! [X0,X1,X2] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,d1,X1,X2)
| ~ product(g1,b,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f184,f2311]) ).
fof(f2613,plain,
( ~ sQ14_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f2364]) ).
fof(f2615,plain,
( ~ sQ14_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f2365]) ).
fof(f2621,plain,
( ~ sQ14_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f194,f2374]) ).
fof(f2625,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f2378]) ).
fof(f2627,plain,
( ~ sQ11_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f2379]) ).
fof(f2631,plain,
( ~ sQ11_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f184,f2388]) ).
fof(f2634,plain,
( ~ sQ21_spl
| ~ sQ46_spl
| ~ sQ27_spl
| a = b ),
inference(backward_demodulation,[status(thm)],[f2635,f430]) ).
fof(f2635,plain,
( ~ sQ46_spl
| ~ sQ27_spl
| inverse(g1,b) = a ),
inference(forward_demodulation,[status(thm)],[f1024,f2271]) ).
fof(f2636,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(paramodulation,[status(thm)],[f2635,f939]) ).
fof(f2637,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(paramodulation,[status(thm)],[f2635,f848]) ).
fof(f2638,plain,
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,a,b,a) ),
inference(paramodulation,[status(thm)],[f2635,f242]) ).
fof(f2639,plain,
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,b,a,a) ),
inference(paramodulation,[status(thm)],[f2635,f241]) ).
fof(f2640,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,a,X0) ),
inference(paramodulation,[status(thm)],[f2635,f121]) ).
fof(f2641,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,a,b,X0) ),
inference(paramodulation,[status(thm)],[f2635,f119]) ).
fof(f2642,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| X0 = identity_for(g1)
| ~ product(g1,b,a,X0) ),
inference(paramodulation,[status(thm)],[f2635,f111]) ).
fof(f2643,plain,
! [X0,X1,X2] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,b,X1,X2)
| ~ product(g1,identity_for(g1),X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f2635,f110]) ).
fof(f2644,plain,
! [X0,X1,X2] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,identity_for(g1),X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(paramodulation,[status(thm)],[f2635,f109]) ).
fof(f2645,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| X0 = identity_for(g1)
| ~ product(g1,a,b,X0) ),
inference(paramodulation,[status(thm)],[f2635,f108]) ).
fof(f2646,plain,
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,b,a,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f2635,f45]) ).
fof(f2647,plain,
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,a,b,identity_for(g1)) ),
inference(paramodulation,[status(thm)],[f2635,f44]) ).
fof(f2648,plain,
( ~ sQ21_spl
| ~ sQ46_spl
| ~ sQ27_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f2634,f151,f1023,f2231,f429]) ).
fof(f2649,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2640]) ).
fof(f2650,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2649]) ).
fof(f2651,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2641]) ).
fof(f2652,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,a,a,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2651]) ).
fof(f2653,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| X0 = a
| ~ product(g1,b,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2642]) ).
fof(f2654,plain,
! [X0,X1,X2] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,b,X1,X2)
| ~ product(g1,a,X0,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f2643]) ).
fof(f2655,plain,
! [X0,X1,X2] :
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,a,X0,X2)
| ~ product(g1,b,X1,X2)
| ~ product(g1,a,X0,X1) ),
inference(forward_demodulation,[status(thm)],[f67,f2644]) ).
fof(f2656,plain,
! [X0] :
( ~ sQ46_spl
| ~ sQ27_spl
| X0 = a
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2645]) ).
fof(f2657,plain,
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,b,a,a) ),
inference(forward_demodulation,[status(thm)],[f67,f2646]) ).
fof(f2658,plain,
( ~ sQ46_spl
| ~ sQ27_spl
| product(g1,a,b,a) ),
inference(forward_demodulation,[status(thm)],[f67,f2647]) ).
fof(f2659,plain,
( ~ sQ47_spl
| inverse(g1,multiply(g1,a,identity_for(g1))) = b ),
inference(forward_demodulation,[status(thm)],[f67,f2235]) ).
fof(f2660,plain,
( ~ sQ47_spl
| inverse(g1,multiply(g1,a,a)) = b ),
inference(forward_demodulation,[status(thm)],[f67,f2659]) ).
fof(f2689,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f430,f121]) ).
fof(f2690,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f430,f119]) ).
fof(f2697,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2689]) ).
fof(f2698,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2697]) ).
fof(f2699,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2690]) ).
fof(f2700,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f2699]) ).
fof(f2707,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1245]) ).
fof(f2714,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f430,f508]) ).
fof(f2725,plain,
! [X0,X1] : product(X0,identity_for(X0),X1,inverse(X0,inverse(X0,X1))),
inference(resolution,[status(thm)],[f501,f42]) ).
fof(f2746,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,b,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1246]) ).
fof(f2790,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f1254]) ).
fof(f2791,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2790]) ).
fof(f2792,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| ~ sQ21_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f430,f2791]) ).
fof(f2801,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(paramodulation,[status(thm)],[f430,f634]) ).
fof(f2817,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1255]) ).
fof(f2818,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ21_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f430,f2817]) ).
fof(f2819,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ21_spl
| ~ sQ11_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f2818]) ).
fof(f2839,plain,
! [X0,X1] : inverse(X0,inverse(X0,X1)) = X1,
inference(resolution,[status(thm)],[f2725,f90]) ).
fof(f2940,plain,
( ~ sQ47_spl
| ~ sQ26_spl
| inverse(g1,a) = b ),
inference(forward_demodulation,[status(thm)],[f1021,f2660]) ).
fof(f2941,plain,
( ~ sQ47_spl
| ~ sQ26_spl
| a = b ),
inference(forward_demodulation,[status(thm)],[f352,f2940]) ).
fof(f2942,plain,
( ~ sQ47_spl
| ~ sQ26_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2941,f57]) ).
fof(f2943,plain,
( ~ sQ47_spl
| ~ sQ26_spl ),
inference(contradiction_clause,[status(thm)],[f2942]) ).
fof(f2944,plain,
( sQ47_spl
| inverse(g1,multiply(g1,a,identity_for(g1))) != b ),
inference(forward_demodulation,[status(thm)],[f67,f2236]) ).
fof(f2945,plain,
( sQ47_spl
| inverse(g1,multiply(g1,a,a)) != b ),
inference(forward_demodulation,[status(thm)],[f67,f2944]) ).
fof(f2952,plain,
( ~ sQ11_spl
| product(g1,b,a,multiply(g1,b,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f1282]) ).
fof(f2953,plain,
( ~ sQ11_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f2952]) ).
fof(f2955,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,b,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1256]) ).
fof(f2961,plain,
( ~ sQ34_spl
| product(g2,d,d,c) ),
inference(forward_demodulation,[status(thm)],[f1132,f695]) ).
fof(f2965,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f1292]) ).
fof(f2966,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f2965]) ).
fof(f2968,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1257]) ).
fof(f2974,plain,
( ~ sQ36_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f1378,f700]) ).
fof(f2980,plain,
( ~ sQ14_spl
| product(g1,b,b,multiply(g1,b,d1)) ),
inference(forward_demodulation,[status(thm)],[f194,f1294]) ).
fof(f2981,plain,
( ~ sQ14_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f194,f2980]) ).
fof(f2982,plain,
( ~ sQ14_spl
| ~ sQ36_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f1378,f2981]) ).
fof(f2983,plain,
( ~ sQ14_spl
| product(g1,a,b,multiply(g1,a,d1)) ),
inference(forward_demodulation,[status(thm)],[f194,f1304]) ).
fof(f2984,plain,
( ~ sQ14_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f194,f2983]) ).
fof(f2986,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)],[f777,f287]) ).
fof(f2987,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)],[f777,f286]) ).
fof(f2988,plain,
! [X0] :
( product(g2,c,multiply(g2,identity_for(g2),identity_for(g2)),X0)
| ~ product(g2,identity_for(g2),identity_for(g2),X0) ),
inference(resolution,[status(thm)],[f777,f99]) ).
fof(f2989,plain,
! [X0] :
( product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,c,multiply(g2,identity_for(g2),identity_for(g2)),X0) ),
inference(resolution,[status(thm)],[f777,f98]) ).
fof(f2995,plain,
! [X0] : multiply(X0,identity_for(X0),identity_for(X0)) = identity_for(X0),
inference(resolution,[status(thm)],[f777,f90]) ).
fof(f3005,plain,
product(g2,c,identity_for(g2),multiply(g2,identity_for(g2),identity_for(g2))),
inference(paramodulation,[status(thm)],[f68,f777]) ).
fof(f3006,plain,
product(g1,a,identity_for(g1),multiply(g1,identity_for(g1),identity_for(g1))),
inference(paramodulation,[status(thm)],[f67,f777]) ).
fof(f3007,plain,
product(g2,identity_for(g2),c,multiply(g2,identity_for(g2),identity_for(g2))),
inference(paramodulation,[status(thm)],[f68,f777]) ).
fof(f3008,plain,
product(g1,identity_for(g1),a,multiply(g1,identity_for(g1),identity_for(g1))),
inference(paramodulation,[status(thm)],[f67,f777]) ).
fof(f3009,plain,
product(g2,identity_for(g2),identity_for(g2),multiply(g2,c,identity_for(g2))),
inference(paramodulation,[status(thm)],[f68,f777]) ).
fof(f3010,plain,
product(g1,identity_for(g1),identity_for(g1),multiply(g1,a,identity_for(g1))),
inference(paramodulation,[status(thm)],[f67,f777]) ).
fof(f3011,plain,
product(g2,identity_for(g2),identity_for(g2),multiply(g2,identity_for(g2),c)),
inference(paramodulation,[status(thm)],[f68,f777]) ).
fof(f3012,plain,
product(g1,identity_for(g1),identity_for(g1),multiply(g1,identity_for(g1),a)),
inference(paramodulation,[status(thm)],[f67,f777]) ).
fof(f3013,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)],[f67,f2986]) ).
fof(f3014,plain,
! [X0] :
( product(g1,a,multiply(g1,identity_for(g1),identity_for(g1)),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f3013]) ).
fof(f3015,plain,
! [X0] :
( product(g1,a,multiply(g1,a,identity_for(g1)),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f3014]) ).
fof(f3016,plain,
! [X0] :
( product(g1,a,multiply(g1,a,a),X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f3015]) ).
fof(f3017,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)],[f67,f2987]) ).
fof(f3018,plain,
! [X0] :
( product(g1,identity_for(g1),identity_for(g1),X0)
| ~ product(g1,a,multiply(g1,a,a),X0) ),
inference(forward_demodulation,[status(thm)],[f67,f3017]) ).
fof(f3021,plain,
! [X0] :
( product(g2,c,multiply(g2,identity_for(g2),identity_for(g2)),X0)
| ~ product(g2,c,identity_for(g2),X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2988]) ).
fof(f3022,plain,
! [X0] :
( product(g2,c,multiply(g2,identity_for(g2),identity_for(g2)),X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f3021]) ).
fof(f3023,plain,
! [X0] :
( product(g2,c,multiply(g2,c,identity_for(g2)),X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f3022]) ).
fof(f3024,plain,
! [X0] :
( product(g2,c,multiply(g2,c,c),X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f68,f3023]) ).
fof(f3025,plain,
! [X0] :
( product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,c,multiply(g2,c,identity_for(g2)),X0) ),
inference(forward_demodulation,[status(thm)],[f68,f2989]) ).
fof(f3026,plain,
! [X0] :
( product(g2,identity_for(g2),identity_for(g2),X0)
| ~ product(g2,c,multiply(g2,c,c),X0) ),
inference(forward_demodulation,[status(thm)],[f68,f3025]) ).
fof(f3031,plain,
product(g2,c,c,multiply(g2,identity_for(g2),identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f68,f3005]) ).
fof(f3032,plain,
product(g2,c,c,multiply(g2,c,identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f68,f3031]) ).
fof(f3033,plain,
product(g2,c,c,multiply(g2,c,c)),
inference(forward_demodulation,[status(thm)],[f68,f3032]) ).
fof(f3035,plain,
product(g1,a,a,multiply(g1,identity_for(g1),identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f67,f3006]) ).
fof(f3036,plain,
product(g1,a,a,multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f67,f3035]) ).
fof(f3037,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f67,f3036]) ).
fof(f3039,plain,
product(g2,c,c,multiply(g2,identity_for(g2),identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f68,f3007]) ).
fof(f3040,plain,
product(g2,c,c,multiply(g2,c,identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f68,f3039]) ).
fof(f3041,plain,
product(g2,c,c,multiply(g2,c,c)),
inference(forward_demodulation,[status(thm)],[f68,f3040]) ).
fof(f3043,plain,
product(g1,a,a,multiply(g1,identity_for(g1),identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f67,f3008]) ).
fof(f3044,plain,
product(g1,a,a,multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f67,f3043]) ).
fof(f3045,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f67,f3044]) ).
fof(f3047,plain,
product(g2,c,identity_for(g2),multiply(g2,c,identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f68,f3009]) ).
fof(f3048,plain,
product(g2,c,c,multiply(g2,c,identity_for(g2))),
inference(forward_demodulation,[status(thm)],[f68,f3047]) ).
fof(f3049,plain,
product(g2,c,c,multiply(g2,c,c)),
inference(forward_demodulation,[status(thm)],[f68,f3048]) ).
fof(f3051,plain,
product(g1,a,identity_for(g1),multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f67,f3010]) ).
fof(f3052,plain,
product(g1,a,a,multiply(g1,a,identity_for(g1))),
inference(forward_demodulation,[status(thm)],[f67,f3051]) ).
fof(f3053,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f67,f3052]) ).
fof(f3055,plain,
product(g2,c,identity_for(g2),multiply(g2,identity_for(g2),c)),
inference(forward_demodulation,[status(thm)],[f68,f3011]) ).
fof(f3056,plain,
product(g2,c,c,multiply(g2,identity_for(g2),c)),
inference(forward_demodulation,[status(thm)],[f68,f3055]) ).
fof(f3057,plain,
product(g2,c,c,multiply(g2,c,c)),
inference(forward_demodulation,[status(thm)],[f68,f3056]) ).
fof(f3059,plain,
product(g1,a,identity_for(g1),multiply(g1,identity_for(g1),a)),
inference(forward_demodulation,[status(thm)],[f67,f3012]) ).
fof(f3060,plain,
product(g1,a,a,multiply(g1,identity_for(g1),a)),
inference(forward_demodulation,[status(thm)],[f67,f3059]) ).
fof(f3061,plain,
product(g1,a,a,multiply(g1,a,a)),
inference(forward_demodulation,[status(thm)],[f67,f3060]) ).
fof(f3066,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f1591]) ).
fof(f3067,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3066]) ).
fof(f3072,plain,
multiply(g2,c,identity_for(g2)) = identity_for(g2),
inference(paramodulation,[status(thm)],[f68,f2995]) ).
fof(f3073,plain,
multiply(g1,a,identity_for(g1)) = identity_for(g1),
inference(paramodulation,[status(thm)],[f67,f2995]) ).
fof(f3074,plain,
multiply(g2,identity_for(g2),c) = identity_for(g2),
inference(paramodulation,[status(thm)],[f68,f2995]) ).
fof(f3075,plain,
multiply(g1,identity_for(g1),a) = identity_for(g1),
inference(paramodulation,[status(thm)],[f67,f2995]) ).
fof(f3077,plain,
multiply(g2,c,c) = identity_for(g2),
inference(forward_demodulation,[status(thm)],[f68,f3072]) ).
fof(f3079,plain,
multiply(g1,a,a) = identity_for(g1),
inference(forward_demodulation,[status(thm)],[f67,f3073]) ).
fof(f3081,plain,
multiply(g2,c,c) = identity_for(g2),
inference(forward_demodulation,[status(thm)],[f68,f3074]) ).
fof(f3083,plain,
multiply(g1,a,a) = identity_for(g1),
inference(forward_demodulation,[status(thm)],[f67,f3075]) ).
fof(f3086,plain,
( ~ sQ8_spl
| ~ sQ25_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f887,f1432]) ).
fof(f3088,plain,
( ~ sQ11_spl
| product(g1,b,a,multiply(g1,b,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f1594]) ).
fof(f3089,plain,
( ~ sQ11_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3088]) ).
fof(f3091,plain,
( ~ sQ29_spl
| group_member(inverse(g2,d),g2) ),
inference(forward_demodulation,[status(thm)],[f1056,f1051]) ).
fof(f3129,plain,
( ~ sQ33_spl
| group_member(inverse(g2,d),g2) ),
inference(forward_demodulation,[status(thm)],[f1111,f1106]) ).
fof(f3134,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f1604]) ).
fof(f3135,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3134]) ).
fof(f3137,plain,
( ~ sQ14_spl
| product(g1,a,b,multiply(g1,a,d1)) ),
inference(forward_demodulation,[status(thm)],[f194,f1244]) ).
fof(f3138,plain,
( ~ sQ14_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f194,f3137]) ).
fof(f3140,plain,
( ~ sQ14_spl
| product(g1,b,b,multiply(g1,b,d1)) ),
inference(forward_demodulation,[status(thm)],[f194,f1234]) ).
fof(f3141,plain,
( ~ sQ14_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f194,f3140]) ).
fof(f3142,plain,
( ~ sQ14_spl
| ~ sQ36_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f1378,f3141]) ).
fof(f3145,plain,
( ~ sQ39_spl
| group_member(inverse(g1,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1411,f1406]) ).
fof(f3149,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f2277]) ).
fof(f3150,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3149]) ).
fof(f3152,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f1214]) ).
fof(f3154,plain,
( ~ sQ11_spl
| product(g1,b,a,multiply(g1,b,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f2280]) ).
fof(f3155,plain,
( ~ sQ11_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3154]) ).
fof(f3157,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f2290]) ).
fof(f3158,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3157]) ).
fof(f3198,plain,
( ~ sQ14_spl
| product(g1,a,b,multiply(g1,a,d1)) ),
inference(forward_demodulation,[status(thm)],[f194,f2363]) ).
fof(f3199,plain,
( ~ sQ14_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f194,f3198]) ).
fof(f3201,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2050]) ).
fof(f3203,plain,
( ~ sQ14_spl
| product(g1,b,b,multiply(g1,b,d1)) ),
inference(forward_demodulation,[status(thm)],[f194,f2366]) ).
fof(f3204,plain,
( ~ sQ14_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f194,f3203]) ).
fof(f3205,plain,
( ~ sQ14_spl
| ~ sQ36_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f1378,f3204]) ).
fof(f3206,plain,
( ~ sQ14_spl
| product(g1,a,b,multiply(g1,a,d1)) ),
inference(forward_demodulation,[status(thm)],[f194,f2376]) ).
fof(f3207,plain,
( ~ sQ14_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f194,f3206]) ).
fof(f3215,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f2377]) ).
fof(f3216,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3215]) ).
fof(f3218,plain,
( ~ sQ11_spl
| product(g1,b,a,multiply(g1,b,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f2380]) ).
fof(f3219,plain,
( ~ sQ11_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3218]) ).
fof(f3221,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,b,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2051]) ).
fof(f3223,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,d2)) ),
inference(forward_demodulation,[status(thm)],[f184,f2390]) ).
fof(f3224,plain,
( ~ sQ11_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f184,f3223]) ).
fof(f3264,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f2059]) ).
fof(f3265,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f3264]) ).
fof(f3286,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2060]) ).
fof(f3287,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ21_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f430,f3286]) ).
fof(f3308,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,b,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2061]) ).
fof(f3310,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2062]) ).
fof(f3312,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,d,X0)
| ~ product(g2,isomorphism1(b),isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2063]) ).
fof(f3313,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,d,X0)
| ~ product(g2,d,isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3312]) ).
fof(f3316,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,isomorphism1(b),isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2064]) ).
fof(f3317,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,d,isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3316]) ).
fof(f3320,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f1378,f1368]) ).
fof(f3322,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,inverse(g2,isomorphism1(d1)),d,X0)
| ~ product(g2,c,isomorphism1(a),X0) ),
inference(forward_demodulation,[status(thm)],[f184,f2072]) ).
fof(f3323,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,inverse(g2,isomorphism1(d1)),d,X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f73,f3322]) ).
fof(f3324,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g2,inverse(g2,isomorphism1(b)),d,X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f3323]) ).
fof(f3325,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g2,inverse(g2,d),d,X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3324]) ).
fof(f3327,plain,
( ~ sQ29_spl
| group_member(multiply(g2,d,d),g2) ),
inference(forward_demodulation,[status(thm)],[f1056,f1042]) ).
fof(f3329,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,isomorphism1(d2),X0)
| ~ product(g2,inverse(g2,isomorphism1(b)),d,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2073]) ).
fof(f3330,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,isomorphism1(d2),X0)
| ~ product(g2,inverse(g2,d),d,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3329]) ).
fof(f3331,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ23_spl
| product(g2,c,isomorphism1(d2),X0)
| ~ product(g2,d,d,X0) ),
inference(forward_demodulation,[status(thm)],[f622,f3330]) ).
fof(f3334,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,isomorphism1(b),isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2074]) ).
fof(f3335,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,d,isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3334]) ).
fof(f3342,plain,
( ~ sQ30_spl
| group_member(multiply(g2,d,c),g2) ),
inference(forward_demodulation,[status(thm)],[f1079,f1068]) ).
fof(f3344,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,d,X0)
| ~ product(g2,isomorphism1(b),isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2075]) ).
fof(f3345,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,d,X0)
| ~ product(g2,d,isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3344]) ).
fof(f3348,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,d,X0)
| ~ product(g2,isomorphism1(b),isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2291]) ).
fof(f3349,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,d,X0)
| ~ product(g2,d,isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3348]) ).
fof(f3352,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,isomorphism1(b),isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2292]) ).
fof(f3353,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,d,isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3352]) ).
fof(f3356,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f1378,f1369]) ).
fof(f3358,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,inverse(g2,isomorphism1(d1)),d,X0)
| ~ product(g2,c,isomorphism1(a),X0) ),
inference(forward_demodulation,[status(thm)],[f184,f2300]) ).
fof(f3359,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| product(g2,inverse(g2,isomorphism1(d1)),d,X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f73,f3358]) ).
fof(f3360,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g2,inverse(g2,isomorphism1(b)),d,X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f3359]) ).
fof(f3361,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g2,inverse(g2,d),d,X0)
| ~ product(g2,c,c,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3360]) ).
fof(f3367,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,isomorphism1(d2),X0)
| ~ product(g2,inverse(g2,isomorphism1(b)),d,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2301]) ).
fof(f3368,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,isomorphism1(d2),X0)
| ~ product(g2,inverse(g2,d),d,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3367]) ).
fof(f3369,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ23_spl
| product(g2,c,isomorphism1(d2),X0)
| ~ product(g2,d,d,X0) ),
inference(forward_demodulation,[status(thm)],[f622,f3368]) ).
fof(f3372,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,isomorphism1(b),isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2302]) ).
fof(f3373,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,d,isomorphism1(d2),X0)
| ~ product(g2,c,d,X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3372]) ).
fof(f3376,plain,
( ~ sQ33_spl
| group_member(multiply(g2,d,d),g2) ),
inference(forward_demodulation,[status(thm)],[f1111,f1097]) ).
fof(f3378,plain,
( ~ sQ33_spl
| group_member(multiply(g2,c,d),g2) ),
inference(forward_demodulation,[status(thm)],[f1111,f1098]) ).
fof(f3380,plain,
( ~ sQ33_spl
| group_member(multiply(g2,c,d),g2) ),
inference(forward_demodulation,[status(thm)],[f1111,f1114]) ).
fof(f3382,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,d,X0)
| ~ product(g2,isomorphism1(b),isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2303]) ).
fof(f3383,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ8_spl
| ~ sQ14_spl
| product(g2,c,d,X0)
| ~ product(g2,d,isomorphism1(d2),X0) ),
inference(forward_demodulation,[status(thm)],[f74,f3382]) ).
fof(f3386,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2304]) ).
fof(f3388,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,b,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2305]) ).
fof(f3390,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| group_member(multiply(g1,a,a),g1) ),
inference(forward_demodulation,[status(thm)],[f1378,f1384]) ).
fof(f3392,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| product(g1,inverse(g1,d1),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f184,f2313]) ).
fof(f3393,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f3392]) ).
fof(f3395,plain,
( ~ sQ34_spl
| group_member(multiply(g2,c,c),g2) ),
inference(forward_demodulation,[status(thm)],[f1132,f1122]) ).
fof(f3399,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,d2,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2314]) ).
fof(f3400,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| ~ sQ21_spl
| product(g1,a,d2,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f430,f3399]) ).
fof(f3402,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,b,d2,X0)
| ~ product(g1,a,b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2315]) ).
fof(f3404,plain,
( ~ sQ34_spl
| group_member(multiply(g2,d,c),g2) ),
inference(forward_demodulation,[status(thm)],[f1132,f1121]) ).
fof(f3406,plain,
( ~ sQ34_spl
| group_member(multiply(g2,c,c),g2) ),
inference(forward_demodulation,[status(thm)],[f1132,f1138]) ).
fof(f3408,plain,
( ~ sQ39_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1411,f1398]) ).
fof(f3410,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ14_spl
| product(g1,a,b,X0)
| ~ product(g1,b,d2,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2316]) ).
fof(f3414,plain,
( ~ sQ8_spl
| ~ sQ25_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f887,f1425]) ).
fof(f3421,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g1,inverse(g1,b),b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2407]) ).
fof(f3423,plain,
! [X0] :
( ~ sQ8_spl
| ~ sQ11_spl
| ~ sQ14_spl
| product(g1,a,a,X0)
| ~ product(g1,inverse(g1,b),b,X0) ),
inference(forward_demodulation,[status(thm)],[f194,f2408]) ).
fof(f3425,plain,
( ~ sQ39_spl
| group_member(multiply(g1,b,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1411,f1399]) ).
fof(f3427,plain,
( ~ sQ39_spl
| group_member(multiply(g1,a,b),g1) ),
inference(forward_demodulation,[status(thm)],[f1411,f1414]) ).
fof(f3435,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[f732,f70]) ).
fof(f3437,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,b,b,X0)
| ~ product(g1,a,identity_for(g1),X0) ),
inference(resolution,[status(thm)],[f732,f42]) ).
fof(f3441,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,b,b,X0)
| ~ product(g1,a,a,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f3437]) ).
fof(f3444,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f733,f70]) ).
fof(f3446,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,identity_for(g1),X0)
| ~ product(g1,b,b,X0) ),
inference(resolution,[status(thm)],[f733,f42]) ).
fof(f3450,plain,
! [X0] :
( ~ sQ21_spl
| product(g1,a,a,X0)
| ~ product(g1,b,b,X0) ),
inference(forward_demodulation,[status(thm)],[f67,f3446]) ).
fof(f3469,plain,
( ~ sQ26_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f1021,f1461]) ).
fof(f3478,plain,
( ~ sQ29_spl
| product(g2,d,d,multiply(g2,d,multiply(g2,c,d))) ),
inference(forward_demodulation,[status(thm)],[f1056,f1045]) ).
fof(f3479,plain,
( ~ sQ29_spl
| product(g2,d,d,multiply(g2,d,d)) ),
inference(forward_demodulation,[status(thm)],[f1056,f3478]) ).
fof(f3480,plain,
( ~ sQ29_spl
| ~ sQ34_spl
| product(g2,d,d,c) ),
inference(forward_demodulation,[status(thm)],[f1132,f3479]) ).
fof(f3484,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| product(g1,a,a,multiply(g1,a,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f1378,f1367]) ).
fof(f3485,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f1378,f3484]) ).
fof(f3490,plain,
( ~ sQ30_spl
| group_member(multiply(g2,d,c),g2) ),
inference(forward_demodulation,[status(thm)],[f1079,f1501]) ).
fof(f3492,plain,
( ~ sQ26_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f1021,f1541]) ).
fof(f3499,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,multiply(g2,c,c))) ),
inference(forward_demodulation,[status(thm)],[f1079,f1071]) ).
fof(f3500,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,c)) ),
inference(forward_demodulation,[status(thm)],[f1079,f3499]) ).
fof(f3505,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f1378,f1370]) ).
fof(f3506,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f1378,f3505]) ).
fof(f3513,plain,
( ~ sQ33_spl
| product(g2,c,d,multiply(g2,c,multiply(g2,d,c))) ),
inference(forward_demodulation,[status(thm)],[f1111,f1099]) ).
fof(f3514,plain,
( ~ sQ33_spl
| product(g2,c,d,multiply(g2,c,d)) ),
inference(forward_demodulation,[status(thm)],[f1111,f3513]) ).
fof(f3516,plain,
( ~ sQ33_spl
| product(g2,d,d,multiply(g2,d,multiply(g2,d,c))) ),
inference(forward_demodulation,[status(thm)],[f1111,f1100]) ).
fof(f3517,plain,
( ~ sQ33_spl
| product(g2,d,d,multiply(g2,d,d)) ),
inference(forward_demodulation,[status(thm)],[f1111,f3516]) ).
fof(f3518,plain,
( ~ sQ33_spl
| ~ sQ34_spl
| product(g2,d,d,c) ),
inference(forward_demodulation,[status(thm)],[f1132,f3517]) ).
fof(f3519,plain,
( ~ sQ33_spl
| product(g2,c,d,multiply(g2,c,multiply(g2,d,c))) ),
inference(forward_demodulation,[status(thm)],[f1111,f1116]) ).
fof(f3520,plain,
( ~ sQ33_spl
| product(g2,c,d,multiply(g2,c,d)) ),
inference(forward_demodulation,[status(thm)],[f1111,f3519]) ).
fof(f3522,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| product(g1,a,a,multiply(g1,a,multiply(g1,b,b))) ),
inference(forward_demodulation,[status(thm)],[f1378,f1386]) ).
fof(f3523,plain,
( ~ sQ8_spl
| ~ sQ36_spl
| product(g1,a,a,multiply(g1,a,a)) ),
inference(forward_demodulation,[status(thm)],[f1378,f3522]) ).
fof(f3529,plain,
( ~ sQ34_spl
| product(g2,c,c,multiply(g2,c,multiply(g2,d,d))) ),
inference(forward_demodulation,[status(thm)],[f1132,f1123]) ).
fof(f3530,plain,
( ~ sQ34_spl
| product(g2,c,c,multiply(g2,c,c)) ),
inference(forward_demodulation,[status(thm)],[f1132,f3529]) ).
fof(f3532,plain,
( ~ sQ34_spl
| product(g2,d,c,multiply(g2,d,multiply(g2,d,d))) ),
inference(forward_demodulation,[status(thm)],[f1132,f1124]) ).
fof(f3533,plain,
( ~ sQ34_spl
| product(g2,d,c,multiply(g2,d,c)) ),
inference(forward_demodulation,[status(thm)],[f1132,f3532]) ).
fof(f3535,plain,
( ~ sQ34_spl
| product(g2,c,c,multiply(g2,c,multiply(g2,d,d))) ),
inference(forward_demodulation,[status(thm)],[f1132,f1140]) ).
fof(f3536,plain,
( ~ sQ34_spl
| product(g2,c,c,multiply(g2,c,c)) ),
inference(forward_demodulation,[status(thm)],[f1132,f3535]) ).
fof(f3544,plain,
( ~ sQ8_spl
| ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,multiply(g1,a,b))) ),
inference(forward_demodulation,[status(thm)],[f887,f1426]) ).
fof(f3545,plain,
( ~ sQ8_spl
| ~ sQ25_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f887,f3544]) ).
fof(f3546,plain,
( ~ sQ8_spl
| ~ sQ25_spl
| ~ sQ36_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f1378,f3545]) ).
fof(f3550,plain,
( ~ sQ39_spl
| product(g1,a,b,multiply(g1,a,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f1411,f1397]) ).
fof(f3551,plain,
( ~ sQ39_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1411,f3550]) ).
fof(f3568,plain,
( ~ sQ39_spl
| product(g1,b,b,multiply(g1,b,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f1411,f1400]) ).
fof(f3569,plain,
( ~ sQ39_spl
| product(g1,b,b,multiply(g1,b,b)) ),
inference(forward_demodulation,[status(thm)],[f1411,f3568]) ).
fof(f3570,plain,
( ~ sQ39_spl
| ~ sQ36_spl
| product(g1,b,b,a) ),
inference(forward_demodulation,[status(thm)],[f1378,f3569]) ).
fof(f3571,plain,
( ~ sQ39_spl
| product(g1,a,b,multiply(g1,a,multiply(g1,b,a))) ),
inference(forward_demodulation,[status(thm)],[f1411,f1416]) ).
fof(f3572,plain,
( ~ sQ39_spl
| product(g1,a,b,multiply(g1,a,b)) ),
inference(forward_demodulation,[status(thm)],[f1411,f3571]) ).
fof(f3582,plain,
( ~ sQ26_spl
| group_member(multiply(g1,b,inverse(g1,a)),g1) ),
inference(forward_demodulation,[status(thm)],[f1021,f2226]) ).
fof(f3583,plain,
( ~ sQ26_spl
| group_member(multiply(g1,b,a),g1) ),
inference(forward_demodulation,[status(thm)],[f352,f3582]) ).
fof(f3585,plain,
( ~ sQ30_spl
| group_member(multiply(g2,d,inverse(g2,c)),g2) ),
inference(forward_demodulation,[status(thm)],[f1079,f2183]) ).
fof(f3586,plain,
( ~ sQ30_spl
| group_member(multiply(g2,d,c),g2) ),
inference(forward_demodulation,[status(thm)],[f351,f3585]) ).
fof(f3591,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f1021,f1462]) ).
fof(f3592,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f1021,f3591]) ).
fof(f3610,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,multiply(g2,c,c))) ),
inference(forward_demodulation,[status(thm)],[f1079,f1588]) ).
fof(f3611,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,c)) ),
inference(forward_demodulation,[status(thm)],[f1079,f3610]) ).
fof(f3613,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,multiply(g1,a,a))) ),
inference(forward_demodulation,[status(thm)],[f1021,f1665]) ).
fof(f3614,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f1021,f3613]) ).
fof(f3633,plain,
( ~ sQ26_spl
| product(g1,b,inverse(g1,a),multiply(g1,b,inverse(g1,multiply(g1,a,a)))) ),
inference(forward_demodulation,[status(thm)],[f1021,f2230]) ).
fof(f3634,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,inverse(g1,multiply(g1,a,a)))) ),
inference(forward_demodulation,[status(thm)],[f352,f3633]) ).
fof(f3635,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,inverse(g1,a))) ),
inference(forward_demodulation,[status(thm)],[f1021,f3634]) ).
fof(f3636,plain,
( ~ sQ26_spl
| product(g1,b,a,multiply(g1,b,a)) ),
inference(forward_demodulation,[status(thm)],[f352,f3635]) ).
fof(f3647,plain,
( ~ sQ30_spl
| product(g2,d,inverse(g2,c),multiply(g2,d,inverse(g2,multiply(g2,c,c)))) ),
inference(forward_demodulation,[status(thm)],[f1079,f2357]) ).
fof(f3648,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,inverse(g2,multiply(g2,c,c)))) ),
inference(forward_demodulation,[status(thm)],[f351,f3647]) ).
fof(f3649,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,inverse(g2,c))) ),
inference(forward_demodulation,[status(thm)],[f1079,f3648]) ).
fof(f3650,plain,
( ~ sQ30_spl
| product(g2,d,c,multiply(g2,d,c)) ),
inference(forward_demodulation,[status(thm)],[f351,f3649]) ).
fof(model,axiom,
( sQ0_spl
| ~ sQ1_spl
| ~ sQ2_spl
| sQ3_spl
| sQ4_spl
| ~ sQ5_spl
| sQ6_spl
| ~ sQ7_spl
| sQ8_spl
| sQ9_spl
| ~ sQ10_spl
| sQ11_spl
| ~ sQ12_spl
| ~ sQ13_spl
| sQ14_spl
| ~ sQ15_spl
| sQ16_spl
| sQ17_spl
| ~ sQ18_spl
| sQ19_spl
| ~ sQ20_spl
| sQ21_spl
| ~ sQ22_spl
| sQ23_spl
| sQ25_spl
| sQ26_spl
| ~ sQ27_spl
| sQ29_spl
| sQ30_spl
| ~ sQ31_spl
| ~ sQ32_spl
| sQ33_spl
| sQ34_spl
| sQ36_spl
| ~ sQ38_spl
| sQ39_spl
| sQ40_spl
| ~ sQ41_spl
| sQ42_spl
| ~ sQ43_spl
| sQ44_spl
| sQ46_spl
| ~ sQ47_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP025-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.34 % Computer : n005.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.34 % CPULimit : 300
% 0.10/0.34 % WCLimit : 300
% 0.10/0.34 % DateTime : Sun Sep 20 19:54:03 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.36 % Drodi V4.1.1
% 1.45/0.65 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 1.45/0.65 % SZS output start Saturation for theBenchmark
% See solution above
% 0.31/0.70 % Elapsed time: 0.338940 seconds
% 0.31/0.70 % CPU time: 2.115532 seconds
% 0.31/0.70 % Total memory used: 120.237 MB
% 0.31/0.70 % Net memory used: 117.693 MB
%------------------------------------------------------------------------------