%------------------------------------------------------------------------------
% File : Drodi-SAT---4.1.1
% Problem : KLE182+1 : TPTP v9.3.1. Released v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 12:58:32 PM UTC 2026
% Result : Satisfiable 4.12s 1.03s
% Output : Saturation 4.12s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] : addition(one,multiplication(star(A),A)) = star(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,C),B),C)
=> leq(multiplication(star(A),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] : strong_iteration(A) = addition(star(A),multiplication(strong_iteration(A),zero)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f28,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f29,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f30,plain,
! [X0] : addition(one,multiplication(star(X0),X0)) = star(X0),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f31,plain,
! [A,B,C] :
( leq(multiplication(star(A),B),C)
| ~ leq(addition(multiplication(A,C),B),C) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f32,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [A,B,C] :
( leq(multiplication(B,star(A)),C)
| ~ leq(addition(multiplication(C,A),B),C) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f34,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f36,plain,
! [A,B,C] :
( leq(C,multiplication(strong_iteration(A),B))
| ~ leq(C,addition(multiplication(A,C),B)) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f37,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),X2))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0] : strong_iteration(X0) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f39,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f18]) ).
fof(f40,plain,
( ! [A,B] :
( addition(A,B) != B
| leq(A,B) )
& ! [A,B] :
( addition(A,B) = B
| ~ leq(A,B) ) ),
inference(miniscoping,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( addition(X0,X1) = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f49,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f21,f19]) ).
fof(f58,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f63,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f65,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f82,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f42,f22]) ).
fof(f83,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f42,f49]) ).
fof(f85,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f20,f42]) ).
fof(f87,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(X0,X1) ),
inference(paramodulation,[status(thm)],[f19,f42]) ).
fof(f104,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f110,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f114,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f115,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f26,f42]) ).
fof(f116,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f26,f20]) ).
fof(f135,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f26,f87]) ).
fof(f137,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f20,f87]) ).
fof(f145,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f65,f42]) ).
fof(f147,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f20,f65]) ).
fof(f150,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f20,f65]) ).
fof(f153,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f65]) ).
fof(f157,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f65,f20]) ).
fof(f158,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f65,f87]) ).
fof(f161,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f147]) ).
fof(f162,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f161]) ).
fof(f165,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f150]) ).
fof(f166,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f165]) ).
fof(f168,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f157]) ).
fof(f169,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f168]) ).
fof(f174,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f26,f145]) ).
fof(f176,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f20,f145]) ).
fof(f179,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f145]) ).
fof(f182,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X1,X0),
inference(resolution,[status(thm)],[f179,f41]) ).
fof(f183,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f26,f179]) ).
fof(f185,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f20,f179]) ).
fof(f192,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f195,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f197,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f199,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f23,f27]) ).
fof(f201,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f204,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f27,f179]) ).
fof(f205,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f27,f145]) ).
fof(f207,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f27,f87]) ).
fof(f208,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f27,f42]) ).
fof(f209,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f27,f20]) ).
fof(f221,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f185,f41]) ).
fof(f223,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f20,f185]) ).
fof(f225,plain,
! [X0,X1,X2] : leq(X0,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f19,f185]) ).
fof(f228,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f27,f185]) ).
fof(f229,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f26,f185]) ).
fof(f237,plain,
! [X0,X1,X2] : leq(X0,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f20,f225]) ).
fof(f239,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f237,f41]) ).
fof(f241,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f20,f237]) ).
fof(f246,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f27,f237]) ).
fof(f247,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f26,f237]) ).
fof(f249,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f20,f237]) ).
fof(f257,plain,
! [X0,X1] : addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) = star(multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f29]) ).
fof(f258,plain,
addition(one,zero) = star(zero),
inference(paramodulation,[status(thm)],[f28,f29]) ).
fof(f260,plain,
! [X0,X1] : leq(one,addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f29,f237]) ).
fof(f261,plain,
! [X0,X1] : leq(multiplication(X0,star(X0)),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f29,f185]) ).
fof(f262,plain,
! [X0] : leq(multiplication(X0,star(X0)),star(X0)),
inference(paramodulation,[status(thm)],[f29,f179]) ).
fof(f263,plain,
! [X0] : leq(one,star(X0)),
inference(paramodulation,[status(thm)],[f29,f145]) ).
fof(f264,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(X0,star(X0))),
inference(paramodulation,[status(thm)],[f29,f65]) ).
fof(f265,plain,
! [X0] :
( star(X0) != one
| leq(multiplication(X0,star(X0)),one) ),
inference(paramodulation,[status(thm)],[f29,f87]) ).
fof(f266,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(one,multiplication(X0,star(X0))) ),
inference(paramodulation,[status(thm)],[f29,f42]) ).
fof(f267,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,star(X0)),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f29,f20]) ).
fof(f268,plain,
one = star(zero),
inference(forward_demodulation,[status(thm)],[f21,f258]) ).
fof(f269,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f29,f264]) ).
fof(f275,plain,
! [X0,X1] : addition(one,addition(X0,star(X1))) = addition(X0,star(X1)),
inference(resolution,[status(thm)],[f260,f41]) ).
fof(f277,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f20,f260]) ).
fof(f278,plain,
! [X0,X1] : leq(one,addition(star(X0),X1)),
inference(paramodulation,[status(thm)],[f19,f260]) ).
fof(f290,plain,
! [X0] :
( star(X0) != one
| leq(star(X0),one) ),
inference(paramodulation,[status(thm)],[f269,f87]) ).
fof(f292,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f269,f20]) ).
fof(f295,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(resolution,[status(thm)],[f278,f41]) ).
fof(f305,plain,
! [X0,X1] : leq(multiplication(star(X0),X0),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f30,f185]) ).
fof(f306,plain,
! [X0] : leq(multiplication(star(X0),X0),star(X0)),
inference(paramodulation,[status(thm)],[f30,f179]) ).
fof(f309,plain,
! [X0] :
( star(X0) != one
| leq(multiplication(star(X0),X0),one) ),
inference(paramodulation,[status(thm)],[f30,f87]) ).
fof(f310,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(one,multiplication(star(X0),X0)) ),
inference(paramodulation,[status(thm)],[f30,f42]) ).
fof(f311,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),X0),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f30,f20]) ).
fof(f317,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f20,f153]) ).
fof(f319,plain,
! [X0] : addition(star(X0),star(X0)) = addition(star(X0),one),
inference(paramodulation,[status(thm)],[f269,f153]) ).
fof(f320,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = addition(multiplication(star(X0),X0),one),
inference(paramodulation,[status(thm)],[f30,f153]) ).
fof(f321,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = addition(multiplication(X0,star(X0)),one),
inference(paramodulation,[status(thm)],[f29,f153]) ).
fof(f325,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f20,f153]) ).
fof(f334,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f153,f20]) ).
fof(f339,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f153,f185]) ).
fof(f340,plain,
! [X0,X1] : leq(addition(X0,X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f153,f179]) ).
fof(f343,plain,
! [X0,X1] :
( addition(X1,X0) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f153,f87]) ).
fof(f345,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f153,f20]) ).
fof(f348,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f317]) ).
fof(f349,plain,
! [X0] : star(X0) = addition(star(X0),one),
inference(forward_demodulation,[status(thm)],[f22,f319]) ).
fof(f364,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f334]) ).
fof(f366,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f345]) ).
fof(f367,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f366]) ).
fof(f381,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f349,f20]) ).
fof(f390,plain,
! [X0] : leq(star(X0),addition(multiplication(star(X0),X0),one)),
inference(paramodulation,[status(thm)],[f30,f340]) ).
fof(f391,plain,
! [X0] : leq(star(X0),addition(multiplication(X0,star(X0)),one)),
inference(paramodulation,[status(thm)],[f29,f340]) ).
fof(f392,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f27,f340]) ).
fof(f393,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f26,f340]) ).
fof(f395,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f20,f340]) ).
fof(f404,plain,
! [X0] : leq(addition(multiplication(star(X0),X0),one),star(X0)),
inference(paramodulation,[status(thm)],[f30,f340]) ).
fof(f405,plain,
! [X0] : leq(addition(multiplication(X0,star(X0)),one),star(X0)),
inference(paramodulation,[status(thm)],[f29,f340]) ).
fof(f406,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f27,f340]) ).
fof(f407,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f26,f340]) ).
fof(f409,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f20,f340]) ).
fof(f420,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f27,f392]) ).
fof(f421,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f26,f393]) ).
fof(f431,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f27,f406]) ).
fof(f432,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f26,f407]) ).
fof(f442,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f182]) ).
fof(f447,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = addition(one,multiplication(star(X0),X0)),
inference(paramodulation,[status(thm)],[f30,f182]) ).
fof(f448,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = addition(one,multiplication(X0,star(X0))),
inference(paramodulation,[status(thm)],[f29,f182]) ).
fof(f452,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f20,f182]) ).
fof(f457,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f19,f182]) ).
fof(f462,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f182,f20]) ).
fof(f475,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f182,f87]) ).
fof(f477,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f182,f20]) ).
fof(f480,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f30,f447]) ).
fof(f481,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f29,f448]) ).
fof(f487,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f20,f452]) ).
fof(f505,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f20,f477]) ).
fof(f506,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f505]) ).
fof(f507,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X1,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f27,f32]) ).
fof(f508,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X2)),X1)
| ~ leq(multiplication(X0,addition(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f26,f32]) ).
fof(f509,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(X0,multiplication(X1,X2))),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f182,f32]) ).
fof(f510,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(X2,multiplication(X0,X1))),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f153,f32]) ).
fof(f511,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),addition(multiplication(X0,X1),X2)),X1)
| ~ leq(addition(multiplication(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f65,f32]) ).
fof(f512,plain,
! [X0,X1] :
( leq(multiplication(star(X0),zero),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f21,f32]) ).
fof(f513,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f19,f32]) ).
fof(f514,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),X0),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f19,f32]) ).
fof(f515,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f22,f32]) ).
fof(f516,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(multiplication(X0,X1)),X3),X2)
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),X2) ),
inference(paramodulation,[status(thm)],[f23,f32]) ).
fof(f518,plain,
! [X0,X1] :
( leq(multiplication(star(one),X1),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f25,f32]) ).
fof(f519,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f24,f32]) ).
fof(f522,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f262,f41]) ).
fof(f523,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f23,f262]) ).
fof(f532,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f306,f41]) ).
fof(f542,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f457]) ).
fof(f548,plain,
! [X0] : addition(one,star(X0)) = addition(multiplication(star(X0),X0),one),
inference(paramodulation,[status(thm)],[f30,f457]) ).
fof(f549,plain,
! [X0] : addition(one,star(X0)) = addition(multiplication(X0,star(X0)),one),
inference(paramodulation,[status(thm)],[f29,f457]) ).
fof(f553,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f457]) ).
fof(f563,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),addition(multiplication(X1,X2),X0)),X2)
| ~ leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f457,f32]) ).
fof(f565,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X0,X1),X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f457,f20]) ).
fof(f580,plain,
! [X0,X1] :
( addition(X1,X0) != X0
| leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f457,f87]) ).
fof(f582,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f457,f20]) ).
fof(f585,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f542]) ).
fof(f588,plain,
! [X0] : star(X0) = addition(multiplication(star(X0),X0),one),
inference(forward_demodulation,[status(thm)],[f269,f548]) ).
fof(f589,plain,
! [X0] : star(X0) = addition(multiplication(X0,star(X0)),one),
inference(forward_demodulation,[status(thm)],[f269,f549]) ).
fof(f595,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f553]) ).
fof(f606,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f565]) ).
fof(f617,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f20,f582]) ).
fof(f618,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f457,f617]) ).
fof(f619,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f20,f618]) ).
fof(f620,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X1,X2),star(X2)),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f27,f34]) ).
fof(f621,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f26,f34]) ).
fof(f622,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(multiplication(X1,X2),X0),star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f457,f34]) ).
fof(f623,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X0,multiplication(X1,X2)),star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f182,f34]) ).
fof(f624,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(X2,multiplication(X0,X1)),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f153,f34]) ).
fof(f625,plain,
! [X0,X1,X2] :
( leq(multiplication(addition(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(addition(multiplication(X0,X1),X2),X0) ),
inference(paramodulation,[status(thm)],[f65,f34]) ).
fof(f627,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f19,f34]) ).
fof(f628,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,star(X2)),X1)
| ~ leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f19,f34]) ).
fof(f629,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f22,f34]) ).
fof(f630,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X3,star(X2)),multiplication(X0,X1))
| ~ leq(addition(multiplication(X0,multiplication(X1,X2)),X3),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f23,f34]) ).
fof(f631,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(addition(zero,X0),zero) ),
inference(paramodulation,[status(thm)],[f28,f34]) ).
fof(f632,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X0)),one)
| ~ leq(addition(X0,X1),one) ),
inference(paramodulation,[status(thm)],[f25,f34]) ).
fof(f633,plain,
! [X0,X1] :
( leq(multiplication(X1,star(one)),X0)
| ~ leq(addition(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f24,f34]) ).
fof(f634,plain,
! [X0,X1,X2] :
( leq(multiplication(X1,multiplication(X2,star(X2))),X0)
| ~ leq(multiplication(addition(X0,X1),X2),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f620]) ).
fof(f635,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f621]) ).
fof(f637,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f629]) ).
fof(f638,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),zero)
| ~ leq(X0,zero) ),
inference(forward_demodulation,[status(thm)],[f49,f631]) ).
fof(f647,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f27,f158]) ).
fof(f648,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f26,f158]) ).
fof(f650,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X0,X1)
| leq(addition(addition(X0,X1),X2),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f20,f158]) ).
fof(f668,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X1),X2) != multiplication(X0,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f27,f647]) ).
fof(f669,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X1)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f26,f648]) ).
fof(f672,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X0,X1)
| leq(addition(X0,addition(X1,X2)),addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f20,f650]) ).
fof(f682,plain,
( one != one
| leq(star(zero),one) ),
inference(paramodulation,[status(thm)],[f268,f290]) ).
fof(f684,definition,
( sQ0_spl
<=> leq(star(zero),one) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f687,definition,
( sQ1_spl
<=> one = one ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( sQ1_spl
| one != one ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f682,f684,f687]) ).
fof(f698,plain,
! [X0] :
( star(X0) != one
| leq(addition(multiplication(star(X0),X0),one),one) ),
inference(paramodulation,[status(thm)],[f30,f343]) ).
fof(f699,plain,
! [X0] :
( star(X0) != one
| leq(addition(multiplication(X0,star(X0)),one),one) ),
inference(paramodulation,[status(thm)],[f29,f343]) ).
fof(f700,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f27,f343]) ).
fof(f701,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f26,f343]) ).
fof(f703,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(addition(X0,addition(X1,X2)),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f20,f343]) ).
fof(f719,plain,
! [X0,X1,X2] :
( multiplication(addition(X1,X0),X2) != multiplication(X1,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f27,f700]) ).
fof(f720,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f26,f701]) ).
fof(f745,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(addition(one,multiplication(star(X0),X0)),multiplication(star(X0),X0)) ),
inference(paramodulation,[status(thm)],[f30,f475]) ).
fof(f746,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(addition(one,multiplication(X0,star(X0))),multiplication(X0,star(X0))) ),
inference(paramodulation,[status(thm)],[f29,f475]) ).
fof(f747,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f27,f475]) ).
fof(f748,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f26,f475]) ).
fof(f750,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f20,f475]) ).
fof(f774,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(star(X0),multiplication(star(X0),X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f745]) ).
fof(f775,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(star(X0),multiplication(X0,star(X0))) ),
inference(forward_demodulation,[status(thm)],[f29,f746]) ).
fof(f776,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X1),X2) != multiplication(X1,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f27,f747]) ).
fof(f777,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f26,f748]) ).
fof(f780,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,addition(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f20,f750]) ).
fof(f791,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f19,f35]) ).
fof(f793,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),one),
inference(paramodulation,[status(thm)],[f23,f35]) ).
fof(f794,plain,
strong_iteration(zero) = addition(zero,one),
inference(paramodulation,[status(thm)],[f28,f35]) ).
fof(f796,plain,
! [X0] :
( leq(multiplication(one,star(strong_iteration(X0))),X0)
| ~ leq(strong_iteration(X0),X0) ),
inference(paramodulation,[status(thm)],[f35,f34]) ).
fof(f797,plain,
! [X0] :
( leq(multiplication(star(X0),one),strong_iteration(X0))
| ~ leq(strong_iteration(X0),strong_iteration(X0)) ),
inference(paramodulation,[status(thm)],[f35,f32]) ).
fof(f798,plain,
! [X0] :
( strong_iteration(X0) != one
| leq(addition(multiplication(X0,strong_iteration(X0)),one),one) ),
inference(paramodulation,[status(thm)],[f35,f475]) ).
fof(f799,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(addition(one,multiplication(X0,strong_iteration(X0))),multiplication(X0,strong_iteration(X0))) ),
inference(paramodulation,[status(thm)],[f35,f343]) ).
fof(f800,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(addition(multiplication(X0,strong_iteration(X0)),one),multiplication(X0,strong_iteration(X0))) ),
inference(paramodulation,[status(thm)],[f35,f158]) ).
fof(f801,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f35,f457]) ).
fof(f802,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(paramodulation,[status(thm)],[f35,f182]) ).
fof(f803,plain,
! [X0] : leq(addition(one,multiplication(X0,strong_iteration(X0))),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f35,f340]) ).
fof(f804,plain,
! [X0] : leq(strong_iteration(X0),addition(one,multiplication(X0,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f35,f340]) ).
fof(f805,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f35,f153]) ).
fof(f806,plain,
! [X0,X1] : leq(multiplication(X0,strong_iteration(X0)),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f35,f237]) ).
fof(f807,plain,
! [X0,X1] : leq(one,addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f35,f185]) ).
fof(f808,plain,
! [X0] : leq(one,strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f35,f179]) ).
fof(f809,plain,
! [X0] : leq(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f35,f145]) ).
fof(f810,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(paramodulation,[status(thm)],[f35,f65]) ).
fof(f811,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(one,multiplication(X0,strong_iteration(X0))) ),
inference(paramodulation,[status(thm)],[f35,f87]) ).
fof(f812,plain,
! [X0] :
( strong_iteration(X0) != one
| leq(multiplication(X0,strong_iteration(X0)),one) ),
inference(paramodulation,[status(thm)],[f35,f42]) ).
fof(f813,plain,
! [X0,X1] : addition(multiplication(X0,strong_iteration(X0)),addition(one,X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f35,f20]) ).
fof(f816,plain,
strong_iteration(zero) = one,
inference(forward_demodulation,[status(thm)],[f49,f794]) ).
fof(f817,plain,
! [X0] :
( leq(star(strong_iteration(X0)),X0)
| ~ leq(strong_iteration(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f25,f796]) ).
fof(f818,plain,
! [X0] :
( leq(star(X0),strong_iteration(X0))
| ~ leq(strong_iteration(X0),strong_iteration(X0)) ),
inference(forward_demodulation,[status(thm)],[f24,f797]) ).
fof(f819,plain,
! [X0] : leq(star(X0),strong_iteration(X0)),
inference(forward_subsumption_resolution,[status(thm)],[f818,f82]) ).
fof(f820,plain,
! [X0] :
( strong_iteration(X0) != one
| leq(strong_iteration(X0),one) ),
inference(forward_demodulation,[status(thm)],[f35,f798]) ).
fof(f821,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(strong_iteration(X0),multiplication(X0,strong_iteration(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f800]) ).
fof(f822,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f35,f802]) ).
fof(f823,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f35,f810]) ).
fof(f829,plain,
! [X0] : addition(star(X0),strong_iteration(X0)) = strong_iteration(X0),
inference(resolution,[status(thm)],[f819,f41]) ).
fof(f838,plain,
! [X0] :
( strong_iteration(X0) != one
| leq(addition(strong_iteration(X0),one),one) ),
inference(paramodulation,[status(thm)],[f822,f343]) ).
fof(f840,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(strong_iteration(X0),one),
inference(paramodulation,[status(thm)],[f822,f457]) ).
fof(f852,plain,
! [X0,X1] : addition(one,addition(strong_iteration(X0),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f822,f20]) ).
fof(f858,plain,
! [X0] : strong_iteration(X0) = addition(strong_iteration(X0),one),
inference(forward_demodulation,[status(thm)],[f822,f840]) ).
fof(f862,plain,
! [X0,X1] : addition(one,addition(X0,strong_iteration(X1))) = addition(X0,strong_iteration(X1)),
inference(resolution,[status(thm)],[f807,f41]) ).
fof(f865,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(X1,strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f20,f807]) ).
fof(f866,plain,
! [X0,X1] : leq(one,addition(strong_iteration(X0),X1)),
inference(paramodulation,[status(thm)],[f19,f807]) ).
fof(f870,plain,
! [X0,X1] : leq(one,multiplication(strong_iteration(X0),strong_iteration(X1))),
inference(resolution,[status(thm)],[f37,f807]) ).
fof(f871,plain,
! [X0,X1] : leq(one,multiplication(strong_iteration(X0),star(X1))),
inference(resolution,[status(thm)],[f37,f260]) ).
fof(f873,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(X1),addition(X0,X2))),
inference(resolution,[status(thm)],[f37,f237]) ).
fof(f874,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(X1),addition(X2,X0))),
inference(resolution,[status(thm)],[f37,f185]) ).
fof(f875,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(X1),X0)),
inference(resolution,[status(thm)],[f37,f179]) ).
fof(f877,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(X2,X0)))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f27,f37]) ).
fof(f878,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(X1,X2)))
| ~ leq(X0,multiplication(X1,addition(X0,X2))) ),
inference(paramodulation,[status(thm)],[f26,f37]) ).
fof(f879,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X2),addition(multiplication(X2,X0),X1)))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f457,f37]) ).
fof(f880,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X2),addition(X1,multiplication(X2,X0))))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f182,f37]) ).
fof(f881,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),addition(X2,multiplication(X1,X0))))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f153,f37]) ).
fof(f882,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),addition(multiplication(X1,X0),X2)))
| ~ leq(X0,addition(multiplication(X1,X0),X2)) ),
inference(paramodulation,[status(thm)],[f65,f37]) ).
fof(f883,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(X1),zero))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f21,f37]) ).
fof(f884,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X2),X1))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f19,f37]) ).
fof(f885,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X2),X1))
| ~ leq(X0,addition(X1,multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f19,f37]) ).
fof(f886,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(X1,X0)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f22,f37]) ).
fof(f887,plain,
! [X0,X1,X2,X3] :
( leq(X0,multiplication(strong_iteration(multiplication(X1,X2)),X3))
| ~ leq(X0,addition(multiplication(X1,multiplication(X2,X0)),X3)) ),
inference(paramodulation,[status(thm)],[f23,f37]) ).
fof(f889,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(one),X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f25,f37]) ).
fof(f890,plain,
! [X0,X1] :
( leq(one,multiplication(strong_iteration(X0),X1))
| ~ leq(one,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f24,f37]) ).
fof(f893,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(forward_subsumption_resolution,[status(thm)],[f889,f145]) ).
fof(f894,plain,
! [X0,X1] : addition(X0,multiplication(strong_iteration(X1),X0)) = multiplication(strong_iteration(X1),X0),
inference(resolution,[status(thm)],[f875,f41]) ).
fof(f919,plain,
! [X0,X1] : addition(strong_iteration(X0),addition(one,X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f858,f20]) ).
fof(f936,plain,
! [X0,X1] : addition(one,addition(strong_iteration(X0),X1)) = addition(strong_iteration(X0),X1),
inference(resolution,[status(thm)],[f866,f41]) ).
fof(f950,plain,
! [X0] :
( strong_iteration(X0) != multiplication(strong_iteration(X0),zero)
| leq(addition(star(X0),multiplication(strong_iteration(X0),zero)),multiplication(strong_iteration(X0),zero)) ),
inference(paramodulation,[status(thm)],[f38,f475]) ).
fof(f951,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(addition(multiplication(strong_iteration(X0),zero),star(X0)),star(X0)) ),
inference(paramodulation,[status(thm)],[f38,f343]) ).
fof(f952,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(addition(star(X0),multiplication(strong_iteration(X0),zero)),star(X0)) ),
inference(paramodulation,[status(thm)],[f38,f158]) ).
fof(f953,plain,
! [X0] : addition(star(X0),strong_iteration(X0)) = addition(multiplication(strong_iteration(X0),zero),star(X0)),
inference(paramodulation,[status(thm)],[f38,f457]) ).
fof(f954,plain,
! [X0] : addition(multiplication(strong_iteration(X0),zero),strong_iteration(X0)) = addition(star(X0),multiplication(strong_iteration(X0),zero)),
inference(paramodulation,[status(thm)],[f38,f182]) ).
fof(f955,plain,
! [X0] : leq(addition(multiplication(strong_iteration(X0),zero),star(X0)),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f38,f340]) ).
fof(f956,plain,
! [X0] : leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),zero),star(X0))),
inference(paramodulation,[status(thm)],[f38,f340]) ).
fof(f957,plain,
! [X0] : addition(multiplication(strong_iteration(X0),zero),strong_iteration(X0)) = addition(multiplication(strong_iteration(X0),zero),star(X0)),
inference(paramodulation,[status(thm)],[f38,f153]) ).
fof(f958,plain,
! [X0,X1] : leq(star(X0),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f38,f237]) ).
fof(f959,plain,
! [X0,X1] : leq(multiplication(strong_iteration(X0),zero),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f38,f185]) ).
fof(f960,plain,
! [X0] : leq(multiplication(strong_iteration(X0),zero),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f38,f179]) ).
fof(f963,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(multiplication(strong_iteration(X0),zero),star(X0)) ),
inference(paramodulation,[status(thm)],[f38,f87]) ).
fof(f964,plain,
! [X0] :
( strong_iteration(X0) != multiplication(strong_iteration(X0),zero)
| leq(star(X0),multiplication(strong_iteration(X0),zero)) ),
inference(paramodulation,[status(thm)],[f38,f42]) ).
fof(f965,plain,
! [X0,X1] : addition(star(X0),addition(multiplication(strong_iteration(X0),zero),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f38,f20]) ).
fof(f972,plain,
! [X0] :
( strong_iteration(X0) != multiplication(strong_iteration(X0),zero)
| leq(strong_iteration(X0),multiplication(strong_iteration(X0),zero)) ),
inference(forward_demodulation,[status(thm)],[f38,f950]) ).
fof(f973,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(strong_iteration(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f38,f952]) ).
fof(f974,plain,
! [X0] : addition(multiplication(strong_iteration(X0),zero),strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f38,f954]) ).
fof(f978,plain,
! [X0,X1] : addition(X0,multiplication(strong_iteration(one),X1)) = multiplication(strong_iteration(one),X1),
inference(resolution,[status(thm)],[f893,f41]) ).
fof(f979,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(paramodulation,[status(thm)],[f24,f893]) ).
fof(f982,plain,
! [X0] : addition(X0,strong_iteration(one)) = strong_iteration(one),
inference(resolution,[status(thm)],[f979,f41]) ).
fof(f983,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)) = strong_iteration(X0),
inference(resolution,[status(thm)],[f809,f41]) ).
fof(f984,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1)))),strong_iteration(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f23,f809]) ).
fof(f1000,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(addition(strong_iteration(X0),star(X0)),star(X0)) ),
inference(paramodulation,[status(thm)],[f829,f343]) ).
fof(f1001,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(addition(star(X0),strong_iteration(X0)),star(X0)) ),
inference(paramodulation,[status(thm)],[f829,f158]) ).
fof(f1002,plain,
! [X0] : addition(star(X0),strong_iteration(X0)) = addition(strong_iteration(X0),star(X0)),
inference(paramodulation,[status(thm)],[f829,f457]) ).
fof(f1012,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(strong_iteration(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f829,f87]) ).
fof(f1014,plain,
! [X0,X1] : addition(star(X0),addition(strong_iteration(X0),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f829,f20]) ).
fof(f1020,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(strong_iteration(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f829,f1001]) ).
fof(f1021,plain,
! [X0] : strong_iteration(X0) = addition(strong_iteration(X0),star(X0)),
inference(forward_demodulation,[status(thm)],[f829,f1002]) ).
fof(f1025,plain,
! [X0,X1] : leq(star(X0),multiplication(strong_iteration(X1),strong_iteration(X0))),
inference(resolution,[status(thm)],[f958,f37]) ).
fof(f1026,plain,
! [X0,X1] : addition(star(X0),addition(X1,strong_iteration(X0))) = addition(X1,strong_iteration(X0)),
inference(resolution,[status(thm)],[f958,f41]) ).
fof(f1031,plain,
! [X0,X1,X2] : leq(star(X0),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f20,f958]) ).
fof(f1032,plain,
! [X0,X1] : leq(star(X0),addition(strong_iteration(X0),X1)),
inference(paramodulation,[status(thm)],[f19,f958]) ).
fof(f1039,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f20,f58]) ).
fof(f1046,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f19,f58]) ).
fof(f1047,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f19,f58]) ).
fof(f1049,plain,
! [X0,X1] : addition(X0,strong_iteration(X1)) = addition(one,addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f858,f58]) ).
fof(f1050,plain,
! [X0,X1] : addition(X0,strong_iteration(X1)) = addition(strong_iteration(X1),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f829,f58]) ).
fof(f1051,plain,
! [X0,X1] : addition(X0,strong_iteration(X1)) = addition(multiplication(strong_iteration(X1),zero),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f38,f58]) ).
fof(f1052,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f349,f58]) ).
fof(f1053,plain,
! [X0,X1] : addition(X0,strong_iteration(X1)) = addition(strong_iteration(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f822,f58]) ).
fof(f1054,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(star(X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f269,f58]) ).
fof(f1055,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(multiplication(star(X1),X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f30,f58]) ).
fof(f1056,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(multiplication(X1,star(X1)),addition(X0,one)),
inference(paramodulation,[status(thm)],[f29,f58]) ).
fof(f1057,plain,
! [X0,X1] : addition(X0,strong_iteration(X1)) = addition(one,addition(X0,multiplication(X1,strong_iteration(X1)))),
inference(paramodulation,[status(thm)],[f35,f58]) ).
fof(f1058,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(X2,X3),addition(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f27,f58]) ).
fof(f1059,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,X3),addition(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f26,f58]) ).
fof(f1061,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f20,f58]) ).
fof(f1062,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X2),addition(X0,X3)),
inference(paramodulation,[status(thm)],[f58,f58]) ).
fof(f1063,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X3,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f58,f58]) ).
fof(f1064,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f457,f58]) ).
fof(f1065,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f182,f58]) ).
fof(f1067,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f65,f58]) ).
fof(f1069,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f58]) ).
fof(f1070,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f58]) ).
fof(f1073,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f20,f58]) ).
fof(f1083,plain,
! [X0,X1] : addition(strong_iteration(X0),addition(one,X1)) = addition(X1,strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f858,f58]) ).
fof(f1084,plain,
! [X0,X1] : addition(star(X0),addition(strong_iteration(X0),X1)) = addition(X1,strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f829,f58]) ).
fof(f1085,plain,
! [X0,X1] : addition(star(X0),addition(multiplication(strong_iteration(X0),zero),X1)) = addition(X1,strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f38,f58]) ).
fof(f1086,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f349,f58]) ).
fof(f1087,plain,
! [X0,X1] : addition(one,addition(strong_iteration(X0),X1)) = addition(X1,strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f822,f58]) ).
fof(f1088,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f269,f58]) ).
fof(f1089,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),X0),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f30,f58]) ).
fof(f1090,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,star(X0)),X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f29,f58]) ).
fof(f1091,plain,
! [X0,X1] : addition(multiplication(X0,strong_iteration(X0)),addition(one,X1)) = addition(X1,strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f35,f58]) ).
fof(f1092,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(X3,multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f27,f58]) ).
fof(f1093,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(X3,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f26,f58]) ).
fof(f1095,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(X3,addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f20,f58]) ).
fof(f1096,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f58,f58]) ).
fof(f1097,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f58,f58]) ).
fof(f1098,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f457,f58]) ).
fof(f1099,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f182,f58]) ).
fof(f1100,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f153,f58]) ).
fof(f1101,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f65,f58]) ).
fof(f1103,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f58]) ).
fof(f1104,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f58]) ).
fof(f1106,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(strong_iteration(X1),X2))),
inference(paramodulation,[status(thm)],[f58,f866]) ).
fof(f1107,plain,
! [X0,X1,X2] : leq(one,addition(X0,addition(star(X1),X2))),
inference(paramodulation,[status(thm)],[f58,f278]) ).
fof(f1108,plain,
! [X0,X1,X2,X3] :
( leq(X0,multiplication(strong_iteration(X2),addition(X3,X1)))
| ~ leq(X0,addition(X1,addition(multiplication(X2,X0),X3))) ),
inference(paramodulation,[status(thm)],[f58,f37]) ).
fof(f1109,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X3,X0),star(X2)),X1)
| ~ leq(addition(X0,addition(multiplication(X1,X2),X3)),X1) ),
inference(paramodulation,[status(thm)],[f58,f34]) ).
fof(f1110,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X1),addition(X3,X0)),X2)
| ~ leq(addition(X0,addition(multiplication(X1,X2),X3)),X2) ),
inference(paramodulation,[status(thm)],[f58,f32]) ).
fof(f1112,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f58,f20]) ).
fof(f1119,plain,
! [X0,X1,X2] :
( addition(X2,addition(X0,X1)) != addition(X1,X2)
| leq(addition(X0,addition(X1,X2)),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f58,f475]) ).
fof(f1120,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f58,f343]) ).
fof(f1121,plain,
! [X0,X1,X2] :
( addition(X2,addition(X0,X1)) != X0
| leq(addition(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f58,f158]) ).
fof(f1122,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X2,X1),X0),
inference(paramodulation,[status(thm)],[f58,f457]) ).
fof(f1123,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X2,X0))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f58,f182]) ).
fof(f1124,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f58,f340]) ).
fof(f1125,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f58,f340]) ).
fof(f1126,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X2,X0))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f58,f153]) ).
fof(f1128,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X1,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f58,f185]) ).
fof(f1129,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f58,f179]) ).
fof(f1131,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f58,f65]) ).
fof(f1132,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f58,f87]) ).
fof(f1133,plain,
! [X0,X1,X2] :
( addition(X2,addition(X0,X1)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f58,f42]) ).
fof(f1134,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X2,addition(X0,X1)),X3),
inference(paramodulation,[status(thm)],[f58,f20]) ).
fof(f1135,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(paramodulation,[status(thm)],[f58,f19]) ).
fof(f1136,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(paramodulation,[status(thm)],[f58,f19]) ).
fof(f1140,plain,
! [X0,X1,X2,X3] :
( leq(X0,multiplication(strong_iteration(X3),addition(X1,X2)))
| ~ leq(X0,addition(X1,addition(X2,multiplication(X3,X0)))) ),
inference(paramodulation,[status(thm)],[f58,f37]) ).
fof(f1141,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(X0,X1),star(X3)),X2)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X3))),X2) ),
inference(paramodulation,[status(thm)],[f58,f34]) ).
fof(f1142,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X2),addition(X0,X1)),X3)
| ~ leq(addition(X0,addition(X1,multiplication(X2,X3))),X3) ),
inference(paramodulation,[status(thm)],[f58,f32]) ).
fof(f1144,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f58,f20]) ).
fof(f1151,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(addition(X0,addition(X1,X2)),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f58,f475]) ).
fof(f1152,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f58,f343]) ).
fof(f1153,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X0
| leq(addition(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f58,f158]) ).
fof(f1154,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X1,X2),X0),
inference(paramodulation,[status(thm)],[f58,f457]) ).
fof(f1155,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f58,f182]) ).
fof(f1158,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f58,f153]) ).
fof(f1160,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f58,f185]) ).
fof(f1163,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X1,X2)),
inference(paramodulation,[status(thm)],[f58,f65]) ).
fof(f1164,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f58,f87]) ).
fof(f1165,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f58,f42]) ).
fof(f1166,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X1,addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f58,f20]) ).
fof(f1171,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f20,f1039]) ).
fof(f1176,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f20,f1062]) ).
fof(f1177,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f20,f1063]) ).
fof(f1178,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f20,f1064]) ).
fof(f1179,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,X2))),
inference(forward_demodulation,[status(thm)],[f20,f1065]) ).
fof(f1180,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f182,f1179]) ).
fof(f1183,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f1067]) ).
fof(f1187,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f20,f1095]) ).
fof(f1188,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f20,f1096]) ).
fof(f1189,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f1097]) ).
fof(f1190,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f20,f1098]) ).
fof(f1191,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f457,f1190]) ).
fof(f1192,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f20,f1099]) ).
fof(f1193,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f1100]) ).
fof(f1194,plain,
! [X0,X1,X2] : addition(X0,addition(X0,addition(X1,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f1101]) ).
fof(f1195,plain,
! [X0,X1,X2] : addition(addition(X0,X1),X2) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f457,f1194]) ).
fof(f1198,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f20,f1112]) ).
fof(f1200,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,addition(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f20,f1120]) ).
fof(f1201,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f20,f1122]) ).
fof(f1202,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X2,X0)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f1123]) ).
fof(f1203,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f457,f1202]) ).
fof(f1204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f1203]) ).
fof(f1205,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,X0))),
inference(forward_demodulation,[status(thm)],[f20,f1124]) ).
fof(f1206,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f1125]) ).
fof(f1207,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X2,X0)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f1126]) ).
fof(f1208,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f457,f1207]) ).
fof(f1209,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f20,f1208]) ).
fof(f1210,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f20,f1209]) ).
fof(f1211,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,addition(X0,X1)),X3),
inference(forward_demodulation,[status(thm)],[f20,f1134]) ).
fof(f1212,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(addition(X0,X1),X3)),
inference(forward_demodulation,[status(thm)],[f20,f1211]) ).
fof(f1213,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f20,f1212]) ).
fof(f1217,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,addition(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f20,f1152]) ).
fof(f1218,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f20,f1154]) ).
fof(f1219,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f20,f1155]) ).
fof(f1222,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f20,f1158]) ).
fof(f1223,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f1222]) ).
fof(f1224,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f20,f1166]) ).
fof(f1225,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(addition(X2,X0),X3)),
inference(forward_demodulation,[status(thm)],[f20,f1224]) ).
fof(f1226,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f20,f1225]) ).
fof(f1237,plain,
! [X0] : addition(strong_iteration(one),X0) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f19,f982]) ).
fof(f1244,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(X1),strong_iteration(one)))
| ~ leq(X0,strong_iteration(one)) ),
inference(paramodulation,[status(thm)],[f982,f37]) ).
fof(f1245,plain,
! [X0,X1] :
( leq(multiplication(strong_iteration(one),star(X1)),X0)
| ~ leq(strong_iteration(one),X0) ),
inference(paramodulation,[status(thm)],[f982,f34]) ).
fof(f1246,plain,
! [X0,X1] :
( leq(multiplication(star(X1),strong_iteration(one)),X0)
| ~ leq(strong_iteration(one),X0) ),
inference(paramodulation,[status(thm)],[f982,f32]) ).
fof(f1251,plain,
! [X0,X1] : addition(X0,addition(strong_iteration(one),X1)) = addition(X1,strong_iteration(one)),
inference(paramodulation,[status(thm)],[f982,f58]) ).
fof(f1252,plain,
! [X0,X1] : addition(X0,strong_iteration(one)) = addition(strong_iteration(one),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f982,f58]) ).
fof(f1253,plain,
! [X0] :
( strong_iteration(one) != strong_iteration(one)
| leq(addition(X0,strong_iteration(one)),strong_iteration(one)) ),
inference(paramodulation,[status(thm)],[f982,f475]) ).
fof(f1267,plain,
! [X0] :
( strong_iteration(one) != strong_iteration(one)
| leq(X0,strong_iteration(one)) ),
inference(paramodulation,[status(thm)],[f982,f42]) ).
fof(f1268,plain,
! [X0,X1] : addition(X0,addition(strong_iteration(one),X1)) = addition(strong_iteration(one),X1),
inference(paramodulation,[status(thm)],[f982,f20]) ).
fof(f1276,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(X1),strong_iteration(one))),
inference(forward_subsumption_resolution,[status(thm)],[f1244,f979]) ).
fof(f1278,plain,
! [X0,X1] : addition(X0,addition(strong_iteration(one),X1)) = strong_iteration(one),
inference(forward_demodulation,[status(thm)],[f982,f1251]) ).
fof(f1279,plain,
! [X0,X1] : strong_iteration(one) = addition(strong_iteration(one),addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f982,f1252]) ).
fof(f1280,definition,
! [X0] :
( sQ2_spl
<=> leq(addition(X0,strong_iteration(one)),strong_iteration(one)) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f1283,definition,
( sQ3_spl
<=> strong_iteration(one) = strong_iteration(one) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f1285,plain,
( sQ3_spl
| strong_iteration(one) != strong_iteration(one) ),
inference(component_clause,[status(thm)],[f1283]) ).
fof(f1286,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f1253,f1280,f1283]) ).
fof(f1296,definition,
! [X0] :
( sQ4_spl
<=> leq(X0,strong_iteration(one)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f1299,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f1267,f1296,f1283]) ).
fof(f1300,plain,
( sQ3_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1285]) ).
fof(f1301,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f1300]) ).
fof(f1312,plain,
! [X0,X1] : addition(strong_iteration(X0),addition(star(X0),X1)) = addition(X1,strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f1021,f58]) ).
fof(f1313,plain,
! [X0,X1] : addition(X0,strong_iteration(X1)) = addition(star(X1),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f1021,f58]) ).
fof(f1314,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(addition(strong_iteration(X0),star(X0)),star(X0)) ),
inference(paramodulation,[status(thm)],[f1021,f475]) ).
fof(f1328,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(strong_iteration(X0),star(X0)) ),
inference(paramodulation,[status(thm)],[f1021,f42]) ).
fof(f1329,plain,
! [X0,X1] : addition(strong_iteration(X0),addition(star(X0),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f1021,f20]) ).
fof(f1338,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(strong_iteration(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f1021,f1314]) ).
fof(f1349,plain,
! [X0,X1] : addition(star(X0),addition(strong_iteration(X0),X1)) = addition(strong_iteration(X0),X1),
inference(resolution,[status(thm)],[f1032,f41]) ).
fof(f1354,plain,
! [X0,X1,X2] : leq(star(X0),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f58,f1032]) ).
fof(f1355,plain,
! [X0,X1,X2] : leq(star(X0),addition(X1,addition(strong_iteration(X0),X2))),
inference(paramodulation,[status(thm)],[f58,f1032]) ).
fof(f1406,plain,
! [X0] :
( strong_iteration(one) != strong_iteration(one)
| leq(addition(strong_iteration(one),X0),strong_iteration(one)) ),
inference(paramodulation,[status(thm)],[f1237,f158]) ).
fof(f1436,definition,
! [X0] :
( sQ5_spl
<=> leq(addition(strong_iteration(one),X0),strong_iteration(one)) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f1439,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f1406,f1436,f1283]) ).
fof(f1465,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(addition(star(X0),strong_iteration(X0)),star(X0)) ),
inference(paramodulation,[status(thm)],[f1021,f580]) ).
fof(f1468,plain,
! [X0] :
( strong_iteration(X0) != multiplication(strong_iteration(X0),zero)
| leq(addition(multiplication(strong_iteration(X0),zero),star(X0)),multiplication(strong_iteration(X0),zero)) ),
inference(paramodulation,[status(thm)],[f38,f580]) ).
fof(f1472,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(addition(multiplication(star(X0),X0),one),multiplication(star(X0),X0)) ),
inference(paramodulation,[status(thm)],[f30,f580]) ).
fof(f1473,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(addition(multiplication(X0,star(X0)),one),multiplication(X0,star(X0))) ),
inference(paramodulation,[status(thm)],[f29,f580]) ).
fof(f1474,plain,
! [X0] :
( strong_iteration(X0) != one
| leq(addition(one,multiplication(X0,strong_iteration(X0))),one) ),
inference(paramodulation,[status(thm)],[f35,f580]) ).
fof(f1475,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f27,f580]) ).
fof(f1476,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f26,f580]) ).
fof(f1478,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X0
| leq(addition(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f20,f580]) ).
fof(f1480,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X0,X1)
| leq(addition(addition(X0,X1),X2),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f58,f580]) ).
fof(f1481,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X0,X1)
| leq(addition(addition(X0,X1),X2),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f58,f580]) ).
fof(f1512,plain,
! [X0] :
( strong_iteration(X0) != star(X0)
| leq(strong_iteration(X0),star(X0)) ),
inference(forward_demodulation,[status(thm)],[f829,f1465]) ).
fof(f1521,plain,
! [X0,X1,X2] :
( multiplication(addition(X1,X0),X2) != multiplication(X0,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f27,f1475]) ).
fof(f1522,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X1)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f26,f1476]) ).
fof(f1526,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X0,X1)
| leq(addition(X0,addition(X1,X2)),addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f20,f1480]) ).
fof(f1527,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != addition(X0,X1)
| leq(addition(X0,addition(X1,X2)),addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f20,f1481]) ).
fof(f1542,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f20,f63]) ).
fof(f1544,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X3,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f58,f63]) ).
fof(f1545,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f58,f63]) ).
fof(f1546,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f457,f63]) ).
fof(f1547,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f182,f63]) ).
fof(f1548,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f153,f63]) ).
fof(f1549,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f65,f63]) ).
fof(f1551,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f63]) ).
fof(f1552,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f63]) ).
fof(f1555,plain,
! [X0,X1] : addition(star(X0),addition(strong_iteration(X0),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f1021,f63]) ).
fof(f1556,plain,
! [X0,X1] : addition(one,addition(strong_iteration(X0),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f858,f63]) ).
fof(f1557,plain,
! [X0,X1] : addition(strong_iteration(X0),addition(star(X0),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f829,f63]) ).
fof(f1558,plain,
! [X0,X1] : addition(multiplication(strong_iteration(X0),zero),addition(star(X0),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f38,f63]) ).
fof(f1559,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f349,f63]) ).
fof(f1560,plain,
! [X0,X1] : addition(strong_iteration(X0),addition(one,X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f822,f63]) ).
fof(f1561,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f269,f63]) ).
fof(f1562,plain,
! [X0,X1] : addition(multiplication(star(X0),X0),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f30,f63]) ).
fof(f1563,plain,
! [X0,X1] : addition(multiplication(X0,star(X0)),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f29,f63]) ).
fof(f1564,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,strong_iteration(X0)),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f35,f63]) ).
fof(f1565,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X2,X0),X1),X3),
inference(paramodulation,[status(thm)],[f27,f63]) ).
fof(f1566,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X2,X1)),X3),
inference(paramodulation,[status(thm)],[f26,f63]) ).
fof(f1568,plain,
! [X0,X1,X2,X3] : addition(X0,addition(addition(X1,X2),X3)) = addition(addition(X2,addition(X1,X0)),X3),
inference(paramodulation,[status(thm)],[f63,f63]) ).
fof(f1571,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f58,f63]) ).
fof(f1572,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X1,addition(X2,X0)),X3),
inference(paramodulation,[status(thm)],[f58,f63]) ).
fof(f1573,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f457,f63]) ).
fof(f1574,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f182,f63]) ).
fof(f1575,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f153,f63]) ).
fof(f1576,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,X2)) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f65,f63]) ).
fof(f1581,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(paramodulation,[status(thm)],[f63,f20]) ).
fof(f1583,plain,
! [X0,X1,X2] : leq(star(X0),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f63,f958]) ).
fof(f1586,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f63,f58]) ).
fof(f1587,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f63,f58]) ).
fof(f1588,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f63,f457]) ).
fof(f1589,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f63,f182]) ).
fof(f1590,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f63,f153]) ).
fof(f1593,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(addition(X1,X0),X2))) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f63,f65]) ).
fof(f1595,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X0
| leq(addition(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f63,f580]) ).
fof(f1596,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(X3,addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f63,f58]) ).
fof(f1597,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f63,f58]) ).
fof(f1598,plain,
! [X0,X1,X2] :
( addition(X1,addition(X0,X2)) != X2
| leq(addition(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f63,f475]) ).
fof(f1599,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != addition(X1,X2)
| leq(addition(X0,addition(X1,X2)),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f63,f343]) ).
fof(f1600,plain,
! [X0,X1,X2] :
( addition(X1,addition(X0,X2)) != addition(X0,X1)
| leq(addition(addition(X0,X1),X2),addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f63,f158]) ).
fof(f1601,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f63,f457]) ).
fof(f1602,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(addition(X2,X1),X0),
inference(paramodulation,[status(thm)],[f63,f182]) ).
fof(f1603,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f63,f340]) ).
fof(f1604,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f63,f340]) ).
fof(f1605,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f63,f153]) ).
fof(f1606,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X1,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f63,f237]) ).
fof(f1609,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f63,f145]) ).
fof(f1610,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(paramodulation,[status(thm)],[f63,f65]) ).
fof(f1611,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != addition(X1,X2)
| leq(X0,addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f63,f87]) ).
fof(f1612,plain,
! [X0,X1,X2] :
( addition(X1,addition(X0,X2)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f63,f42]) ).
fof(f1613,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X1,addition(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f63,f20]) ).
fof(f1614,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f63,f19]) ).
fof(f1615,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f63,f19]) ).
fof(f1618,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f63,f1545]) ).
fof(f1619,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f63,f1546]) ).
fof(f1620,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f1548]) ).
fof(f1621,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f63,f1549]) ).
fof(f1622,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f1621]) ).
fof(f1627,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f63,f1568]) ).
fof(f1628,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,X0),addition(X1,X3)),
inference(forward_demodulation,[status(thm)],[f63,f1627]) ).
fof(f1629,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X0,addition(X2,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f63,f1628]) ).
fof(f1633,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,addition(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f63,f1571]) ).
fof(f1634,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,X2),addition(X1,X3)),
inference(forward_demodulation,[status(thm)],[f63,f1633]) ).
fof(f1635,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X0,addition(X1,X3))),
inference(forward_demodulation,[status(thm)],[f63,f1634]) ).
fof(f1636,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f63,f1572]) ).
fof(f1637,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X2,X1),addition(X0,X3)),
inference(forward_demodulation,[status(thm)],[f63,f1636]) ).
fof(f1638,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X1,addition(X2,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f63,f1637]) ).
fof(f1639,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f63,f1573]) ).
fof(f1640,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X2),X1),
inference(forward_demodulation,[status(thm)],[f457,f1639]) ).
fof(f1641,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f63,f1574]) ).
fof(f1642,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f1641]) ).
fof(f1643,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f63,f1575]) ).
fof(f1644,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f63,f1643]) ).
fof(f1645,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,X2))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f63,f1576]) ).
fof(f1646,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X0),X1),
inference(forward_demodulation,[status(thm)],[f457,f1645]) ).
fof(f1648,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f63,f1587]) ).
fof(f1649,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f63,f1588]) ).
fof(f1650,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X1,X0)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f1590]) ).
fof(f1651,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f63,f1593]) ).
fof(f1652,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f1651]) ).
fof(f1654,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X3,addition(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f63,f1596]) ).
fof(f1655,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| leq(addition(X0,addition(X1,X2)),X2) ),
inference(forward_demodulation,[status(thm)],[f63,f1598]) ).
fof(f1656,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X1,X0)
| leq(addition(X0,addition(X1,X2)),addition(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f63,f1600]) ).
fof(f1657,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f63,f1601]) ).
fof(f1658,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(forward_demodulation,[status(thm)],[f63,f1602]) ).
fof(f1659,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f63,f1610]) ).
fof(f1660,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f1659]) ).
fof(f1661,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X0,addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f63,f1613]) ).
fof(f1662,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(addition(X1,X2),addition(X0,X3)),
inference(forward_demodulation,[status(thm)],[f63,f1661]) ).
fof(f1663,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,X3))) = addition(X2,addition(X1,addition(X0,X3))),
inference(forward_demodulation,[status(thm)],[f63,f1662]) ).
fof(f1666,plain,
( one != one
| leq(strong_iteration(zero),one) ),
inference(paramodulation,[status(thm)],[f816,f820]) ).
fof(f1668,definition,
( sQ6_spl
<=> leq(strong_iteration(zero),one) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f1671,plain,
( ~ sQ1_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f1666,f1668,f687]) ).
fof(f1672,plain,
( sQ1_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f689]) ).
fof(f1673,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f1672]) ).
fof(f1676,plain,
! [X0,X1] : addition(one,multiplication(strong_iteration(X0),strong_iteration(X1))) = multiplication(strong_iteration(X0),strong_iteration(X1)),
inference(resolution,[status(thm)],[f870,f41]) ).
fof(f1681,plain,
! [X0,X1] : addition(one,multiplication(strong_iteration(X0),star(X1))) = multiplication(strong_iteration(X0),star(X1)),
inference(resolution,[status(thm)],[f871,f41]) ).
fof(f1686,plain,
! [X0,X1,X2] : addition(X0,multiplication(strong_iteration(X1),addition(X0,X2))) = multiplication(strong_iteration(X1),addition(X0,X2)),
inference(resolution,[status(thm)],[f873,f41]) ).
fof(f1698,plain,
! [X0,X1] : leq(multiplication(X0,strong_iteration(X0)),multiplication(strong_iteration(X1),strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f35,f873]) ).
fof(f1699,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f27,f873]) ).
fof(f1700,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f26,f873]) ).
fof(f1702,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),multiplication(strong_iteration(X2),addition(X1,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f63,f873]) ).
fof(f1703,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),multiplication(strong_iteration(X2),addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f20,f873]) ).
fof(f1705,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(strong_iteration(X1),addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f58,f873]) ).
fof(f1706,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(strong_iteration(X1),addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f58,f873]) ).
fof(f1716,plain,
! [X0,X1,X2] : addition(X0,multiplication(strong_iteration(X1),addition(X2,X0))) = multiplication(strong_iteration(X1),addition(X2,X0)),
inference(resolution,[status(thm)],[f874,f41]) ).
fof(f1722,plain,
! [X0,X1] : leq(multiplication(strong_iteration(X0),zero),multiplication(strong_iteration(X1),strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f38,f874]) ).
fof(f1726,plain,
! [X0,X1] : leq(multiplication(star(X0),X0),multiplication(strong_iteration(X1),star(X0))),
inference(paramodulation,[status(thm)],[f30,f874]) ).
fof(f1727,plain,
! [X0,X1] : leq(multiplication(X0,star(X0)),multiplication(strong_iteration(X1),star(X0))),
inference(paramodulation,[status(thm)],[f29,f874]) ).
fof(f1729,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f27,f874]) ).
fof(f1730,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f26,f874]) ).
fof(f1732,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(strong_iteration(X1),addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f63,f874]) ).
fof(f1733,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(strong_iteration(X1),addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f20,f874]) ).
fof(f1735,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),multiplication(strong_iteration(X2),addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f58,f874]) ).
fof(f1736,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),multiplication(strong_iteration(X2),addition(X1,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f58,f874]) ).
fof(f1737,plain,
! [X0,X1,X2] : leq(addition(X0,X1),multiplication(strong_iteration(X2),addition(X1,X0))),
inference(paramodulation,[status(thm)],[f457,f874]) ).
fof(f1739,plain,
! [X0,X1,X2] : leq(addition(X0,X1),multiplication(strong_iteration(X2),addition(X1,X0))),
inference(paramodulation,[status(thm)],[f153,f874]) ).
fof(f1746,plain,
! [X0] : addition(multiplication(strong_iteration(X0),zero),strong_iteration(X0)) = strong_iteration(X0),
inference(resolution,[status(thm)],[f960,f41]) ).
fof(f1755,plain,
! [X0,X1] : addition(X0,multiplication(strong_iteration(X1),strong_iteration(one))) = multiplication(strong_iteration(X1),strong_iteration(one)),
inference(resolution,[status(thm)],[f1276,f41]) ).
fof(f1759,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,addition(X1,X2))) = multiplication(X0,addition(X1,X2)),
inference(resolution,[status(thm)],[f174,f41]) ).
fof(f1760,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X1),addition(X2,X3))),
inference(paramodulation,[status(thm)],[f23,f174]) ).
fof(f1763,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f24,f174]) ).
fof(f1764,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),X2),multiplication(X0,multiplication(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f23,f174]) ).
fof(f1770,plain,
! [X0,X1] : leq(multiplication(X0,star(X1)),multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f829,f174]) ).
fof(f1771,plain,
! [X0,X1] : leq(multiplication(X0,star(X1)),multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f38,f174]) ).
fof(f1773,plain,
! [X0,X1] : leq(multiplication(X0,one),multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f822,f174]) ).
fof(f1774,plain,
! [X0,X1] : leq(multiplication(X0,one),multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f269,f174]) ).
fof(f1777,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,strong_iteration(X1))),multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f35,f174]) ).
fof(f1778,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X1,X3),X2))),
inference(paramodulation,[status(thm)],[f27,f174]) ).
fof(f1779,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f26,f174]) ).
fof(f1780,plain,
! [X0,X1] : leq(multiplication(X0,zero),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f49,f174]) ).
fof(f1781,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f63,f174]) ).
fof(f1782,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f20,f174]) ).
fof(f1783,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,strong_iteration(one))),
inference(paramodulation,[status(thm)],[f982,f174]) ).
fof(f1784,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f58,f174]) ).
fof(f1785,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f58,f174]) ).
fof(f1794,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X1,X2))) = multiplication(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f26,f1759]) ).
fof(f1795,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f457,f1794]) ).
fof(f1796,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f23,f1760]) ).
fof(f1799,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f23,f1764]) ).
fof(f1802,plain,
! [X0,X1] : leq(X0,multiplication(X0,strong_iteration(X1))),
inference(forward_demodulation,[status(thm)],[f24,f1773]) ).
fof(f1803,plain,
! [X0,X1] : leq(X0,multiplication(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f24,f1774]) ).
fof(f1806,plain,
! [X0,X1] : addition(X0,multiplication(X0,strong_iteration(X1))) = multiplication(X0,strong_iteration(X1)),
inference(resolution,[status(thm)],[f1802,f41]) ).
fof(f1807,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f23,f1802]) ).
fof(f1815,plain,
! [X0,X1,X2,X3] :
( addition(X1,addition(X0,addition(X2,X3))) != X3
| leq(addition(addition(X0,X1),X2),X3) ),
inference(paramodulation,[status(thm)],[f63,f85]) ).
fof(f1816,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(addition(X0,X1),X2),X3) ),
inference(paramodulation,[status(thm)],[f20,f85]) ).
fof(f1817,plain,
! [X0,X1,X2] :
( addition(X1,addition(X2,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f58,f85]) ).
fof(f1823,plain,
! [X0,X1,X2] :
( addition(addition(X1,X2),X0) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f19,f85]) ).
fof(f1824,plain,
! [X0,X1,X2] :
( addition(addition(X1,X2),X0) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f19,f85]) ).
fof(f1827,plain,
! [X0,X1] :
( addition(X0,strong_iteration(X1)) != star(X1)
| leq(addition(X0,strong_iteration(X1)),star(X1)) ),
inference(paramodulation,[status(thm)],[f1021,f85]) ).
fof(f1828,plain,
! [X0,X1] :
( addition(X0,strong_iteration(X1)) != one
| leq(addition(X0,strong_iteration(X1)),one) ),
inference(paramodulation,[status(thm)],[f858,f85]) ).
fof(f1829,plain,
! [X0,X1] :
( addition(X0,strong_iteration(X1)) != strong_iteration(X1)
| leq(addition(X0,star(X1)),strong_iteration(X1)) ),
inference(paramodulation,[status(thm)],[f829,f85]) ).
fof(f1830,plain,
! [X0,X1] :
( addition(X0,strong_iteration(X1)) != multiplication(strong_iteration(X1),zero)
| leq(addition(X0,star(X1)),multiplication(strong_iteration(X1),zero)) ),
inference(paramodulation,[status(thm)],[f38,f85]) ).
fof(f1831,plain,
! [X0,X1] :
( addition(X0,star(X1)) != one
| leq(addition(X0,star(X1)),one) ),
inference(paramodulation,[status(thm)],[f349,f85]) ).
fof(f1832,plain,
! [X0,X1] :
( addition(X0,strong_iteration(X1)) != strong_iteration(X1)
| leq(addition(X0,one),strong_iteration(X1)) ),
inference(paramodulation,[status(thm)],[f822,f85]) ).
fof(f1833,plain,
! [X0,X1] :
( addition(X0,star(X1)) != star(X1)
| leq(addition(X0,one),star(X1)) ),
inference(paramodulation,[status(thm)],[f269,f85]) ).
fof(f1834,plain,
! [X0,X1] :
( addition(X0,star(X1)) != multiplication(star(X1),X1)
| leq(addition(X0,one),multiplication(star(X1),X1)) ),
inference(paramodulation,[status(thm)],[f30,f85]) ).
fof(f1835,plain,
! [X0,X1] :
( addition(X0,star(X1)) != multiplication(X1,star(X1))
| leq(addition(X0,one),multiplication(X1,star(X1))) ),
inference(paramodulation,[status(thm)],[f29,f85]) ).
fof(f1836,plain,
! [X0,X1] :
( addition(X0,strong_iteration(X1)) != one
| leq(addition(X0,multiplication(X1,strong_iteration(X1))),one) ),
inference(paramodulation,[status(thm)],[f35,f85]) ).
fof(f1837,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(addition(X1,X3),X2)) != multiplication(X3,X2)
| leq(addition(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f27,f85]) ).
fof(f1838,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(X1,addition(X2,X3))) != multiplication(X1,X3)
| leq(addition(X0,multiplication(X1,X2)),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f26,f85]) ).
fof(f1840,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X2,addition(X1,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(paramodulation,[status(thm)],[f63,f85]) ).
fof(f1841,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(paramodulation,[status(thm)],[f20,f85]) ).
fof(f1843,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X2,addition(X3,X1))) != addition(X2,X3)
| leq(addition(X0,X1),addition(X2,X3)) ),
inference(paramodulation,[status(thm)],[f58,f85]) ).
fof(f1844,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X3,addition(X1,X2))) != addition(X2,X3)
| leq(addition(X0,X1),addition(X2,X3)) ),
inference(paramodulation,[status(thm)],[f58,f85]) ).
fof(f1845,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != addition(X1,X2)
| leq(addition(X0,X1),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f457,f85]) ).
fof(f1846,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != addition(X2,X1)
| leq(addition(X0,X1),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f182,f85]) ).
fof(f1847,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X2,X1)
| leq(addition(X0,X1),addition(X2,X1)) ),
inference(paramodulation,[status(thm)],[f153,f85]) ).
fof(f1848,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != addition(X1,X2)
| leq(addition(X0,X1),addition(X1,X2)) ),
inference(paramodulation,[status(thm)],[f65,f85]) ).
fof(f1849,plain,
! [X0,X1] :
( addition(X0,X1) != zero
| leq(addition(X0,X1),zero) ),
inference(paramodulation,[status(thm)],[f21,f85]) ).
fof(f1850,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f19,f85]) ).
fof(f1851,plain,
! [X0,X1,X2] :
( addition(X0,addition(X2,X1)) != X2
| leq(addition(X0,X1),X2) ),
inference(paramodulation,[status(thm)],[f19,f85]) ).
fof(f1857,plain,
! [X0,X1,X2,X3] :
( addition(X0,addition(X1,addition(X2,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(forward_demodulation,[status(thm)],[f63,f1815]) ).
fof(f1858,plain,
! [X0,X1,X2,X3] :
( addition(X1,addition(X0,addition(X2,X3))) != X3
| leq(addition(X0,addition(X1,X2)),X3) ),
inference(forward_demodulation,[status(thm)],[f63,f1816]) ).
fof(f1861,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f63,f1823]) ).
fof(f1862,plain,
! [X0,X1,X2] :
( addition(X2,addition(X1,X0)) != X2
| leq(addition(X0,X1),X2) ),
inference(forward_demodulation,[status(thm)],[f63,f1824]) ).
fof(f1871,plain,
! [X0,X1] : addition(X0,multiplication(X0,star(X1))) = multiplication(X0,star(X1)),
inference(resolution,[status(thm)],[f1803,f41]) ).
fof(f1872,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f23,f1803]) ).
fof(f1877,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = multiplication(X0,addition(one,X1)),
inference(resolution,[status(thm)],[f1763,f41]) ).
fof(f1878,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f23,f1763]) ).
fof(f1886,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f58,f1763]) ).
fof(f1887,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f58,f1763]) ).
fof(f1888,plain,
! [X0,X1] : leq(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f457,f1763]) ).
fof(f1899,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f23,f1780]) ).
fof(f1902,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f23,f1780]) ).
fof(f1905,plain,
! [X0] : leq(multiplication(X0,zero),X0),
inference(paramodulation,[status(thm)],[f24,f1780]) ).
fof(f1907,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f1899]) ).
fof(f1910,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f1902]) ).
fof(f1913,plain,
! [X0] : addition(multiplication(X0,zero),X0) = X0,
inference(resolution,[status(thm)],[f1905,f41]) ).
fof(f1914,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f1905]) ).
fof(f1918,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f26,f104]) ).
fof(f1922,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f23,f104]) ).
fof(f1925,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f104]) ).
fof(f1926,plain,
! [X0,X1,X2,X3] : multiplication(multiplication(X0,X1),addition(X2,X3)) = addition(multiplication(multiplication(X0,X1),X3),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f23,f104]) ).
fof(f1929,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f104]) ).
fof(f1931,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(paramodulation,[status(thm)],[f104,f26]) ).
fof(f1932,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(X1,X2)))
| ~ leq(X0,multiplication(X1,addition(X2,X0))) ),
inference(paramodulation,[status(thm)],[f104,f37]) ).
fof(f1933,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),star(X2)),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(paramodulation,[status(thm)],[f104,f34]) ).
fof(f1934,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,X1)),X2)
| ~ leq(multiplication(X0,addition(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f104,f32]) ).
fof(f1935,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(X1,addition(X3,X2))) != multiplication(X1,X3)
| leq(addition(X0,multiplication(X1,X2)),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f104,f85]) ).
fof(f1936,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X3,X2)))),
inference(paramodulation,[status(thm)],[f104,f174]) ).
fof(f1937,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f104,f874]) ).
fof(f1938,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f104,f873]) ).
fof(f1939,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f104,f63]) ).
fof(f1940,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f104,f580]) ).
fof(f1941,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f104,f58]) ).
fof(f1942,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,X2),addition(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f104,f58]) ).
fof(f1943,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f104,f475]) ).
fof(f1944,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f104,f343]) ).
fof(f1945,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f104,f158]) ).
fof(f1948,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f104,f340]) ).
fof(f1949,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f104,f340]) ).
fof(f1951,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f104,f237]) ).
fof(f1952,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f104,f185]) ).
fof(f1956,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f104,f87]) ).
fof(f1957,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f104,f42]) ).
fof(f1958,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X2,X1)),X3),
inference(paramodulation,[status(thm)],[f104,f20]) ).
fof(f1963,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f23,f1922]) ).
fof(f1964,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f1963]) ).
fof(f1965,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f104,f1964]) ).
fof(f1966,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f104,f1965]) ).
fof(f1971,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(multiplication(X0,X1),X3),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f1926]) ).
fof(f1972,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f1971]) ).
fof(f1973,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f104,f1972]) ).
fof(f1974,plain,
! [X0,X1,X2,X3] : multiplication(X0,multiplication(X1,addition(X2,X3))) = multiplication(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f104,f1973]) ).
fof(f1980,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,star(X2))),X0)
| ~ leq(multiplication(X0,addition(X1,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f1933]) ).
fof(f1981,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f104,f1940]) ).
fof(f1982,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X1)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f104,f1943]) ).
fof(f1983,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X1)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f104,f1944]) ).
fof(f1984,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X1,X2)) != multiplication(X0,X2)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f104,f1945]) ).
fof(f1991,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f104,f1948]) ).
fof(f1992,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f104,f1949]) ).
fof(f2004,plain,
! [X0,X1] : addition(X0,addition(X1,multiplication(addition(X0,X1),zero))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f58,f1913]) ).
fof(f2005,plain,
! [X0,X1] : addition(X0,addition(multiplication(addition(X1,X0),zero),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f58,f1913]) ).
fof(f2007,plain,
! [X0] : addition(X0,multiplication(X0,zero)) = X0,
inference(paramodulation,[status(thm)],[f19,f1913]) ).
fof(f2009,plain,
! [X0,X1] : addition(multiplication(X0,multiplication(X1,zero)),multiplication(X0,X1)) = multiplication(X0,X1),
inference(paramodulation,[status(thm)],[f23,f1913]) ).
fof(f2015,plain,
! [X0] :
( leq(multiplication(star(X0),X0),zero)
| ~ leq(X0,zero) ),
inference(paramodulation,[status(thm)],[f1913,f32]) ).
fof(f2020,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(multiplication(addition(X0,X1),zero),X0),X1) ),
inference(paramodulation,[status(thm)],[f1913,f85]) ).
fof(f2021,plain,
! [X0,X1] : addition(X0,addition(X1,multiplication(addition(X0,X1),zero))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f1913,f58]) ).
fof(f2022,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(multiplication(addition(X0,X1),zero),X0)),
inference(paramodulation,[status(thm)],[f1913,f58]) ).
fof(f2026,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| leq(addition(X0,multiplication(X1,zero)),X1) ),
inference(paramodulation,[status(thm)],[f1913,f85]) ).
fof(f2027,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f1913,f174]) ).
fof(f2029,plain,
! [X0,X1] : leq(multiplication(X0,zero),multiplication(strong_iteration(X1),X0)),
inference(paramodulation,[status(thm)],[f1913,f873]) ).
fof(f2030,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,zero),X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f1913,f63]) ).
fof(f2032,plain,
! [X0,X1] : addition(multiplication(X0,zero),addition(X0,X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f1913,f58]) ).
fof(f2033,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,addition(X0,multiplication(X1,zero))),
inference(paramodulation,[status(thm)],[f1913,f58]) ).
fof(f2035,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(addition(X0,multiplication(X0,zero)),multiplication(X0,zero)) ),
inference(paramodulation,[status(thm)],[f1913,f343]) ).
fof(f2036,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(addition(multiplication(X0,zero),X0),multiplication(X0,zero)) ),
inference(paramodulation,[status(thm)],[f1913,f158]) ).
fof(f2042,plain,
! [X0,X1] : leq(multiplication(X0,zero),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1913,f237]) ).
fof(f2047,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(X0,multiplication(X0,zero)) ),
inference(paramodulation,[status(thm)],[f1913,f87]) ).
fof(f2049,plain,
! [X0,X1] : addition(multiplication(X0,zero),addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f1913,f20]) ).
fof(f2053,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X1,zero))) = multiplication(X0,X1),
inference(forward_demodulation,[status(thm)],[f104,f2009]) ).
fof(f2058,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(X0,multiplication(X0,zero)) ),
inference(forward_demodulation,[status(thm)],[f1913,f2036]) ).
fof(f2069,plain,
! [X0,X1] : addition(X0,addition(X1,multiplication(addition(X1,X0),zero))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f63,f2007]) ).
fof(f2070,plain,
! [X0,X1] : addition(X0,addition(X1,multiplication(addition(X0,X1),zero))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f20,f2007]) ).
fof(f2080,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(multiplication(X1,X0),zero)))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f2007,f37]) ).
fof(f2081,plain,
! [X0,X1] :
( leq(multiplication(multiplication(multiplication(X0,X1),zero),star(X1)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f2007,f34]) ).
fof(f2082,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),zero)),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f2007,f32]) ).
fof(f2084,plain,
! [X0,X1] : addition(X0,addition(X1,multiplication(addition(X1,X0),zero))) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2007,f63]) ).
fof(f2085,plain,
! [X0,X1] : addition(X0,addition(X1,multiplication(addition(X0,X1),zero))) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2007,f20]) ).
fof(f2086,plain,
! [X0,X1] :
( addition(X0,X1) != multiplication(X1,zero)
| leq(addition(X0,X1),multiplication(X1,zero)) ),
inference(paramodulation,[status(thm)],[f2007,f85]) ).
fof(f2090,plain,
! [X0,X1] : addition(multiplication(X0,zero),addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2007,f63]) ).
fof(f2091,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(addition(multiplication(X0,zero),X0),multiplication(X0,zero)) ),
inference(paramodulation,[status(thm)],[f2007,f580]) ).
fof(f2092,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,zero),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f2007,f58]) ).
fof(f2093,plain,
! [X0,X1] : addition(X0,X1) = addition(multiplication(X1,zero),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2007,f58]) ).
fof(f2094,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(addition(X0,multiplication(X0,zero)),multiplication(X0,zero)) ),
inference(paramodulation,[status(thm)],[f2007,f475]) ).
fof(f2108,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(X0,multiplication(X0,zero)) ),
inference(paramodulation,[status(thm)],[f2007,f42]) ).
fof(f2109,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,zero),X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f2007,f20]) ).
fof(f2114,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(X1,multiplication(X0,zero))))
| ~ leq(X0,multiplication(X1,X0)) ),
inference(forward_demodulation,[status(thm)],[f23,f2080]) ).
fof(f2115,plain,
! [X0,X1] :
( leq(multiplication(multiplication(X0,X1),multiplication(zero,star(X1))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f2081]) ).
fof(f2116,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,multiplication(zero,star(X1)))),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f2115]) ).
fof(f2117,plain,
! [X0,X1] :
( leq(multiplication(X0,multiplication(X1,zero)),X0)
| ~ leq(multiplication(X0,X1),X0) ),
inference(forward_demodulation,[status(thm)],[f28,f2116]) ).
fof(f2118,plain,
! [X0,X1] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,zero))),X1)
| ~ leq(multiplication(X0,X1),X1) ),
inference(forward_demodulation,[status(thm)],[f23,f2082]) ).
fof(f2119,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(X0,multiplication(X0,zero)) ),
inference(forward_demodulation,[status(thm)],[f1913,f2091]) ).
fof(f2120,plain,
! [X0] :
( X0 != multiplication(X0,zero)
| leq(X0,multiplication(X0,zero)) ),
inference(forward_demodulation,[status(thm)],[f2007,f2094]) ).
fof(f2131,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = multiplication(X0,addition(X1,one)),
inference(resolution,[status(thm)],[f1888,f41]) ).
fof(f2132,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f23,f1888]) ).
fof(f2141,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f63,f1888]) ).
fof(f2142,plain,
! [X0,X1,X2] : leq(X0,multiplication(X0,addition(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f20,f1888]) ).
fof(f2153,plain,
! [X0,X1] : multiplication(X0,strong_iteration(X1)) = addition(X0,multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f822,f110]) ).
fof(f2154,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f269,f110]) ).
fof(f2155,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,multiplication(star(X1),X1))),
inference(paramodulation,[status(thm)],[f30,f110]) ).
fof(f2156,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,multiplication(X1,star(X1)))),
inference(paramodulation,[status(thm)],[f29,f110]) ).
fof(f2158,plain,
! [X0] : multiplication(X0,strong_iteration(one)) = addition(X0,multiplication(X0,strong_iteration(one))),
inference(paramodulation,[status(thm)],[f982,f110]) ).
fof(f2159,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f58,f110]) ).
fof(f2160,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f58,f110]) ).
fof(f2161,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f457,f110]) ).
fof(f2162,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f182,f110]) ).
fof(f2163,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f153,f110]) ).
fof(f2164,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f65,f110]) ).
fof(f2166,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f110]) ).
fof(f2167,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f110]) ).
fof(f2169,plain,
! [X0] : multiplication(strong_iteration(one),addition(one,X0)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f1237,f110]) ).
fof(f2170,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(one,X1)) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f27,f110]) ).
fof(f2171,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X1,addition(X0,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f63,f110]) ).
fof(f2172,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f20,f110]) ).
fof(f2175,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(one,X2)) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f23,f110]) ).
fof(f2176,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(one,X1))) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f110,f110]) ).
fof(f2183,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(one,X1),X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f110,f104]) ).
fof(f2184,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(addition(X0,multiplication(X0,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f110,f104]) ).
fof(f2185,plain,
! [X0,X1] : leq(multiplication(X0,zero),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f110,f1780]) ).
fof(f2186,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(addition(one,X1),X2))),
inference(paramodulation,[status(thm)],[f110,f174]) ).
fof(f2187,plain,
! [X0,X1,X2] :
( leq(addition(one,X0),multiplication(strong_iteration(X1),X2))
| ~ leq(addition(one,X0),addition(addition(X1,multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f110,f37]) ).
fof(f2188,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(one,X1))),X0)
| ~ leq(addition(addition(X0,multiplication(X0,X1)),X2),X0) ),
inference(paramodulation,[status(thm)],[f110,f34]) ).
fof(f2189,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(one,X1))
| ~ leq(addition(addition(X0,multiplication(X0,X1)),X2),addition(one,X1)) ),
inference(paramodulation,[status(thm)],[f110,f32]) ).
fof(f2190,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(multiplication(X0,addition(one,X2)),addition(X1,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f110,f27]) ).
fof(f2191,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(addition(X0,multiplication(X0,X2)),multiplication(X1,addition(one,X2))),
inference(paramodulation,[status(thm)],[f110,f27]) ).
fof(f2192,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f110,f26]) ).
fof(f2193,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(one,X1),X2)) = addition(addition(X0,multiplication(X0,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f110,f26]) ).
fof(f2194,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(one,X1),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f110,f23]) ).
fof(f2195,plain,
! [X0] : multiplication(strong_iteration(one),addition(one,X0)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f110,f1237]) ).
fof(f2196,plain,
! [X0,X1] : leq(star(X0),multiplication(strong_iteration(X0),addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f1032]) ).
fof(f2198,plain,
! [X0,X1] : leq(one,multiplication(star(X0),addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f278]) ).
fof(f2199,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(paramodulation,[status(thm)],[f110,f27]) ).
fof(f2200,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(multiplication(X1,X0),X2)))
| ~ leq(X0,multiplication(multiplication(X1,X0),addition(one,X2))) ),
inference(paramodulation,[status(thm)],[f110,f37]) ).
fof(f2201,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(multiplication(multiplication(X0,X1),addition(one,X2)),X0) ),
inference(paramodulation,[status(thm)],[f110,f34]) ).
fof(f2202,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X1)
| ~ leq(multiplication(multiplication(X0,X1),addition(one,X2)),X1) ),
inference(paramodulation,[status(thm)],[f110,f32]) ).
fof(f2203,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X1,X0),X2))) = multiplication(addition(X1,X0),addition(one,X2)),
inference(paramodulation,[status(thm)],[f110,f63]) ).
fof(f2204,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),X2))) = multiplication(addition(X0,X1),addition(one,X2)),
inference(paramodulation,[status(thm)],[f110,f20]) ).
fof(f2206,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(X1,addition(one,X2))) != multiplication(X1,X2)
| leq(addition(X0,X1),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f110,f85]) ).
fof(f2207,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f174]) ).
fof(f2208,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(X0,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f110,f874]) ).
fof(f2209,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(X1),multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f873]) ).
fof(f2210,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f110,f63]) ).
fof(f2211,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),X0),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f110,f580]) ).
fof(f2212,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(X2,multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f58]) ).
fof(f2213,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(one,X2))) = addition(multiplication(X1,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f110,f58]) ).
fof(f2214,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != multiplication(X0,X1)
| leq(addition(X0,multiplication(X0,X1)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f110,f475]) ).
fof(f2215,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != X0
| leq(addition(multiplication(X0,X1),X0),X0) ),
inference(paramodulation,[status(thm)],[f110,f343]) ).
fof(f2216,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != X0
| leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f110,f158]) ).
fof(f2217,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f110,f457]) ).
fof(f2219,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f340]) ).
fof(f2220,plain,
! [X0,X1] : leq(multiplication(X0,addition(one,X1)),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f110,f340]) ).
fof(f2221,plain,
! [X0,X1] : addition(multiplication(X0,X1),multiplication(X0,addition(one,X1))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f110,f153]) ).
fof(f2222,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f237]) ).
fof(f2223,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f110,f185]) ).
fof(f2224,plain,
! [X0,X1] : leq(multiplication(X0,X1),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f179]) ).
fof(f2226,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(one,X1))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f110,f65]) ).
fof(f2227,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != X0
| leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f110,f87]) ).
fof(f2228,plain,
! [X0,X1] :
( multiplication(X0,addition(one,X1)) != multiplication(X0,X1)
| leq(X0,multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f110,f42]) ).
fof(f2229,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f110,f20]) ).
fof(f2236,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f23,f2170]) ).
fof(f2238,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f2175]) ).
fof(f2239,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,X2))) = multiplication(X0,addition(multiplication(X1,X2),X1)),
inference(forward_demodulation,[status(thm)],[f104,f2238]) ).
fof(f2240,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f457,f2176]) ).
fof(f2241,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f457,f2240]) ).
fof(f2248,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f63,f2183]) ).
fof(f2249,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X2),addition(X0,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f63,f2184]) ).
fof(f2250,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(X1,addition(one,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f2186]) ).
fof(f2251,plain,
! [X0,X1,X2] :
( leq(addition(one,X0),multiplication(strong_iteration(X1),X2))
| ~ leq(addition(one,X0),addition(multiplication(X1,X0),addition(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f63,f2187]) ).
fof(f2252,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(one,X1))),X0)
| ~ leq(addition(multiplication(X0,X1),addition(X0,X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f63,f2188]) ).
fof(f2253,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(one,X1))
| ~ leq(addition(multiplication(X0,X1),addition(X0,X2)),addition(one,X1)) ),
inference(forward_demodulation,[status(thm)],[f63,f2189]) ).
fof(f2254,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(multiplication(X0,X2),addition(X0,multiplication(X1,addition(one,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f2191]) ).
fof(f2255,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(addition(X0,multiplication(X0,X1)),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f63,f2193]) ).
fof(f2256,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(one,X2))) = addition(multiplication(X0,X1),addition(X0,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f63,f2255]) ).
fof(f2257,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f23,f2199]) ).
fof(f2258,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(multiplication(X1,X0),X2)))
| ~ leq(X0,multiplication(X1,multiplication(X0,addition(one,X2)))) ),
inference(forward_demodulation,[status(thm)],[f23,f2200]) ).
fof(f2259,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(X1,multiplication(X0,X2))))
| ~ leq(X0,multiplication(X1,multiplication(X0,addition(one,X2)))) ),
inference(forward_demodulation,[status(thm)],[f23,f2258]) ).
fof(f2260,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(multiplication(X0,X1),X2),star(X1)),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f2201]) ).
fof(f2261,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X1),multiplication(X2,star(X1))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f2260]) ).
fof(f2262,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X1)))),X0)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f2261]) ).
fof(f2263,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(multiplication(X0,X1),X2)),X1)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X1) ),
inference(forward_demodulation,[status(thm)],[f23,f2202]) ).
fof(f2264,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),multiplication(X0,multiplication(X1,X2))),X1)
| ~ leq(multiplication(X0,multiplication(X1,addition(one,X2))),X1) ),
inference(forward_demodulation,[status(thm)],[f23,f2263]) ).
fof(f2269,plain,
! [X0,X1] : multiplication(X0,addition(addition(one,X1),X1)) = addition(multiplication(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f104,f2221]) ).
fof(f2270,plain,
! [X0,X1] : multiplication(X0,addition(X1,addition(one,X1))) = addition(multiplication(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f63,f2269]) ).
fof(f2271,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(multiplication(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f182,f2270]) ).
fof(f2275,plain,
! [X0,X1] : addition(multiplication(X0,zero),addition(X1,X0)) = addition(X1,X0),
inference(resolution,[status(thm)],[f2042,f41]) ).
fof(f2276,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),addition(X2,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f23,f2042]) ).
fof(f2280,plain,
! [X0] : leq(multiplication(star(X0),zero),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f1021,f2042]) ).
fof(f2287,plain,
! [X0] : leq(multiplication(multiplication(star(X0),X0),zero),star(X0)),
inference(paramodulation,[status(thm)],[f30,f2042]) ).
fof(f2288,plain,
! [X0] : leq(multiplication(multiplication(X0,star(X0)),zero),star(X0)),
inference(paramodulation,[status(thm)],[f29,f2042]) ).
fof(f2291,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f104,f2042]) ).
fof(f2292,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f27,f2042]) ).
fof(f2293,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f26,f2042]) ).
fof(f2295,plain,
! [X0,X1,X2] : leq(multiplication(X0,zero),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f63,f2042]) ).
fof(f2296,plain,
! [X0,X1,X2] : leq(multiplication(X0,zero),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f20,f2042]) ).
fof(f2298,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,X1),zero),multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f2042]) ).
fof(f2300,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),zero),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f58,f2042]) ).
fof(f2301,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),zero),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f58,f2042]) ).
fof(f2302,plain,
! [X0,X1] : leq(multiplication(addition(X0,X1),zero),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f457,f2042]) ).
fof(f2304,plain,
! [X0,X1] : leq(multiplication(addition(X0,X1),zero),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f153,f2042]) ).
fof(f2307,plain,
! [X0,X1] : leq(multiplication(X0,zero),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f2042]) ).
fof(f2315,plain,
! [X0] : leq(multiplication(star(X0),multiplication(X0,zero)),star(X0)),
inference(forward_demodulation,[status(thm)],[f23,f2287]) ).
fof(f2316,plain,
! [X0] : leq(multiplication(X0,multiplication(star(X0),zero)),star(X0)),
inference(forward_demodulation,[status(thm)],[f23,f2288]) ).
fof(f2318,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f2291]) ).
fof(f2319,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(addition(X2,X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f2292]) ).
fof(f2320,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f23,f2293]) ).
fof(f2323,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f23,f2298]) ).
fof(f2325,plain,
! [X0,X1] : addition(multiplication(X0,zero),addition(X0,X1)) = addition(X0,X1),
inference(resolution,[status(thm)],[f2307,f41]) ).
fof(f2326,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),addition(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f23,f2307]) ).
fof(f2340,plain,
! [X0] : leq(multiplication(multiplication(X0,strong_iteration(X0)),zero),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f35,f2307]) ).
fof(f2341,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f104,f2307]) ).
fof(f2342,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f27,f2307]) ).
fof(f2343,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f26,f2307]) ).
fof(f2345,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),zero),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f63,f2307]) ).
fof(f2346,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),zero),addition(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f20,f2307]) ).
fof(f2350,plain,
! [X0,X1,X2] : leq(multiplication(X0,zero),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f58,f2307]) ).
fof(f2351,plain,
! [X0,X1,X2] : leq(multiplication(X0,zero),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f58,f2307]) ).
fof(f2367,plain,
! [X0] : leq(multiplication(X0,multiplication(strong_iteration(X0),zero)),strong_iteration(X0)),
inference(forward_demodulation,[status(thm)],[f23,f2340]) ).
fof(f2368,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f23,f2341]) ).
fof(f2369,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(addition(X0,X2),X1)),
inference(forward_demodulation,[status(thm)],[f23,f2342]) ).
fof(f2370,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f2343]) ).
fof(f2376,plain,
! [X0] : multiplication(X0,strong_iteration(one)) = addition(multiplication(X0,strong_iteration(one)),X0),
inference(paramodulation,[status(thm)],[f1237,f114]) ).
fof(f2377,plain,
! [X0,X1] : multiplication(X0,strong_iteration(X1)) = addition(multiplication(X0,strong_iteration(X1)),X0),
inference(paramodulation,[status(thm)],[f858,f114]) ).
fof(f2378,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(multiplication(X0,star(X1)),X0),
inference(paramodulation,[status(thm)],[f349,f114]) ).
fof(f2380,plain,
! [X0,X1] : multiplication(X0,strong_iteration(X1)) = addition(multiplication(X0,multiplication(X1,strong_iteration(X1))),X0),
inference(paramodulation,[status(thm)],[f35,f114]) ).
fof(f2382,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(multiplication(X0,addition(X2,X1)),X0),
inference(paramodulation,[status(thm)],[f63,f114]) ).
fof(f2383,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(multiplication(X0,addition(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f20,f114]) ).
fof(f2384,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f19,f114]) ).
fof(f2385,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f19,f114]) ).
fof(f2388,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(X1,one)) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f27,f114]) ).
fof(f2390,plain,
! [X0] : multiplication(strong_iteration(one),addition(X0,one)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f982,f114]) ).
fof(f2391,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X0,addition(X1,multiplication(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f58,f114]) ).
fof(f2392,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X1,addition(multiplication(addition(X0,X1),X2),X0)),
inference(paramodulation,[status(thm)],[f58,f114]) ).
fof(f2393,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f114]) ).
fof(f2394,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f114]) ).
fof(f2395,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(X2,one)) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f23,f114]) ).
fof(f2406,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,one),X2)) = addition(multiplication(X0,X2),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f114,f104]) ).
fof(f2407,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(addition(multiplication(X0,X2),X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f114,f104]) ).
fof(f2409,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(addition(X1,one),X2))),
inference(paramodulation,[status(thm)],[f114,f174]) ).
fof(f2410,plain,
! [X0,X1,X2] :
( leq(addition(X0,one),multiplication(strong_iteration(X1),X2))
| ~ leq(addition(X0,one),addition(addition(multiplication(X1,X0),X1),X2)) ),
inference(paramodulation,[status(thm)],[f114,f37]) ).
fof(f2411,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,one))),X0)
| ~ leq(addition(addition(multiplication(X0,X1),X0),X2),X0) ),
inference(paramodulation,[status(thm)],[f114,f34]) ).
fof(f2412,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(X1,one))
| ~ leq(addition(addition(multiplication(X0,X1),X0),X2),addition(X1,one)) ),
inference(paramodulation,[status(thm)],[f114,f32]) ).
fof(f2413,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(multiplication(X0,addition(X2,one)),addition(multiplication(X1,X2),X1)),
inference(paramodulation,[status(thm)],[f114,f27]) ).
fof(f2414,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(addition(multiplication(X0,X2),X0),multiplication(X1,addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f27]) ).
fof(f2415,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),X0)),
inference(paramodulation,[status(thm)],[f114,f26]) ).
fof(f2416,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,one),X2)) = addition(addition(multiplication(X0,X1),X0),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f114,f26]) ).
fof(f2417,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,one),X2)) = multiplication(addition(multiplication(X0,X1),X0),X2),
inference(paramodulation,[status(thm)],[f114,f23]) ).
fof(f2419,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(paramodulation,[status(thm)],[f114,f27]) ).
fof(f2420,plain,
! [X0,X1] :
( leq(X0,multiplication(strong_iteration(X1),X1))
| ~ leq(X0,multiplication(X1,addition(X0,one))) ),
inference(paramodulation,[status(thm)],[f114,f37]) ).
fof(f2421,plain,
! [X0,X1] :
( leq(multiplication(X0,star(X1)),X0)
| ~ leq(multiplication(X0,addition(X1,one)),X0) ),
inference(paramodulation,[status(thm)],[f114,f34]) ).
fof(f2422,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X0),X1)
| ~ leq(multiplication(X0,addition(X1,one)),X1) ),
inference(paramodulation,[status(thm)],[f114,f32]) ).
fof(f2423,plain,
! [X0] : multiplication(strong_iteration(one),addition(X0,one)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f114,f982]) ).
fof(f2424,plain,
! [X0,X1] : leq(star(X0),multiplication(strong_iteration(X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f958]) ).
fof(f2426,plain,
! [X0,X1] : leq(one,multiplication(star(X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f260]) ).
fof(f2427,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X1),addition(X2,one)) != X1
| leq(addition(multiplication(addition(X0,X1),X2),X0),X1) ),
inference(paramodulation,[status(thm)],[f114,f85]) ).
fof(f2428,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(addition(X0,X1),X2))) = multiplication(addition(X0,X1),addition(X2,one)),
inference(paramodulation,[status(thm)],[f114,f58]) ).
fof(f2429,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X1,addition(multiplication(addition(X0,X1),X2),X0)),
inference(paramodulation,[status(thm)],[f114,f58]) ).
fof(f2430,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X0,X1),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f237]) ).
fof(f2431,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,X0),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f185]) ).
fof(f2432,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,X1),zero),multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f2307]) ).
fof(f2434,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(X1,addition(X2,one))) != X1
| leq(addition(X0,multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f114,f85]) ).
fof(f2435,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f174]) ).
fof(f2436,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(X1),multiplication(X0,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f874]) ).
fof(f2437,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(X0,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f114,f873]) ).
fof(f2438,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f114,f63]) ).
fof(f2439,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != X0
| leq(addition(X0,multiplication(X0,X1)),X0) ),
inference(paramodulation,[status(thm)],[f114,f580]) ).
fof(f2440,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(X2,multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f58]) ).
fof(f2441,plain,
! [X0,X1,X2] : addition(X0,multiplication(X1,addition(X2,one))) = addition(X1,addition(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f114,f58]) ).
fof(f2442,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != X0
| leq(addition(multiplication(X0,X1),X0),X0) ),
inference(paramodulation,[status(thm)],[f114,f475]) ).
fof(f2443,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != multiplication(X0,X1)
| leq(addition(X0,multiplication(X0,X1)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f114,f343]) ).
fof(f2444,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),X0),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f114,f158]) ).
fof(f2446,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f114,f182]) ).
fof(f2447,plain,
! [X0,X1] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f340]) ).
fof(f2448,plain,
! [X0,X1] : leq(multiplication(X0,addition(X1,one)),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f114,f340]) ).
fof(f2449,plain,
! [X0,X1] : addition(X0,multiplication(X0,addition(X1,one))) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f114,f153]) ).
fof(f2450,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(X0,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f114,f237]) ).
fof(f2451,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(X0,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f185]) ).
fof(f2454,plain,
! [X0,X1] : addition(multiplication(X0,X1),multiplication(X0,addition(X1,one))) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f114,f65]) ).
fof(f2455,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != multiplication(X0,X1)
| leq(X0,multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f114,f87]) ).
fof(f2456,plain,
! [X0,X1] :
( multiplication(X0,addition(X1,one)) != X0
| leq(multiplication(X0,X1),X0) ),
inference(paramodulation,[status(thm)],[f114,f42]) ).
fof(f2457,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f114,f20]) ).
fof(f2458,plain,
! [X0,X1] : addition(X0,multiplication(X0,X1)) = multiplication(X0,addition(X1,one)),
inference(paramodulation,[status(thm)],[f114,f19]) ).
fof(f2459,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f114,f19]) ).
fof(f2470,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f23,f2388]) ).
fof(f2471,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f23,f2395]) ).
fof(f2472,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(X2,one))) = multiplication(X0,addition(X1,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f104,f2471]) ).
fof(f2491,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(multiplication(X0,X2),addition(multiplication(X0,X1),X0)),
inference(forward_demodulation,[status(thm)],[f63,f2406]) ).
fof(f2492,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,addition(multiplication(X0,X2),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f63,f2407]) ).
fof(f2493,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,addition(X2,one))) = addition(X0,multiplication(X0,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f104,f2492]) ).
fof(f2494,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(one,addition(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f2409]) ).
fof(f2495,plain,
! [X0,X1,X2] :
( leq(addition(X0,one),multiplication(strong_iteration(X1),X2))
| ~ leq(addition(X0,one),addition(X1,addition(multiplication(X1,X0),X2))) ),
inference(forward_demodulation,[status(thm)],[f63,f2410]) ).
fof(f2496,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(addition(X1,one))),X0)
| ~ leq(addition(X0,addition(multiplication(X0,X1),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f63,f2411]) ).
fof(f2497,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X0),X2),addition(X1,one))
| ~ leq(addition(X0,addition(multiplication(X0,X1),X2)),addition(X1,one)) ),
inference(forward_demodulation,[status(thm)],[f63,f2412]) ).
fof(f2498,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X0,addition(multiplication(X0,X2),multiplication(X1,addition(X2,one)))),
inference(forward_demodulation,[status(thm)],[f63,f2414]) ).
fof(f2499,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(addition(multiplication(X0,X1),X0),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f63,f2416]) ).
fof(f2500,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(X0,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f63,f2499]) ).
fof(f2501,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(X0,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f104,f2500]) ).
fof(f2503,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(X0,multiplication(X1,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f23,f2419]) ).
fof(f2504,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f23,f2432]) ).
fof(f2508,plain,
! [X0,X1] : multiplication(X0,addition(addition(X1,one),X1)) = addition(multiplication(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f104,f2454]) ).
fof(f2509,plain,
! [X0,X1] : multiplication(X0,addition(one,addition(X1,X1))) = addition(multiplication(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f63,f2508]) ).
fof(f2510,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(multiplication(X0,X1),X0),
inference(forward_demodulation,[status(thm)],[f22,f2509]) ).
fof(f2511,plain,
! [X0] : addition(multiplication(star(X0),zero),strong_iteration(X0)) = strong_iteration(X0),
inference(resolution,[status(thm)],[f2280,f41]) ).
fof(f2518,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X0,addition(X1,X2))) = addition(X0,addition(X1,X2)),
inference(resolution,[status(thm)],[f176,f41]) ).
fof(f2523,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(star(X0),addition(multiplication(strong_iteration(X0),zero),X1))),
inference(paramodulation,[status(thm)],[f38,f176]) ).
fof(f2527,plain,
! [X0,X1] : leq(star(X0),addition(one,addition(multiplication(star(X0),X0),X1))),
inference(paramodulation,[status(thm)],[f30,f176]) ).
fof(f2528,plain,
! [X0,X1] : leq(star(X0),addition(one,addition(multiplication(X0,star(X0)),X1))),
inference(paramodulation,[status(thm)],[f29,f176]) ).
fof(f2530,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(X0,strong_iteration(X0)),addition(one,X1))),
inference(paramodulation,[status(thm)],[f35,f176]) ).
fof(f2531,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),addition(multiplication(X0,X1),X3))),
inference(paramodulation,[status(thm)],[f104,f176]) ).
fof(f2532,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),addition(multiplication(X1,X2),X3))),
inference(paramodulation,[status(thm)],[f27,f176]) ).
fof(f2533,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3))),
inference(paramodulation,[status(thm)],[f26,f176]) ).
fof(f2534,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,one)),addition(multiplication(X0,X1),addition(X0,X2))),
inference(paramodulation,[status(thm)],[f114,f176]) ).
fof(f2536,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(addition(X1,X0),addition(X2,X3))),
inference(paramodulation,[status(thm)],[f63,f176]) ).
fof(f2537,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(addition(X0,X1),addition(X2,X3))),
inference(paramodulation,[status(thm)],[f20,f176]) ).
fof(f2539,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(one,X1)),addition(X0,addition(multiplication(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f110,f176]) ).
fof(f2541,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(addition(X0,X1),X3))),
inference(paramodulation,[status(thm)],[f58,f176]) ).
fof(f2542,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(addition(X2,X0),X3))),
inference(paramodulation,[status(thm)],[f58,f176]) ).
fof(f2543,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(addition(X1,X0),X2))),
inference(paramodulation,[status(thm)],[f457,f176]) ).
fof(f2552,plain,
! [X0,X1] : leq(addition(multiplication(addition(X0,X1),zero),X0),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1913,f176]) ).
fof(f2553,plain,
! [X0,X1,X2] : leq(addition(multiplication(addition(X0,X1),X2),X0),multiplication(addition(X0,X1),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f176]) ).
fof(f2555,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X1,addition(X0,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f63,f176]) ).
fof(f2556,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X0,addition(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f20,f176]) ).
fof(f2569,plain,
! [X0,X1] : leq(addition(X0,star(X1)),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f829,f176]) ).
fof(f2570,plain,
! [X0,X1] : leq(addition(X0,star(X1)),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f38,f176]) ).
fof(f2572,plain,
! [X0,X1] : leq(addition(X0,one),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f822,f176]) ).
fof(f2573,plain,
! [X0,X1] : leq(addition(X0,one),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f269,f176]) ).
fof(f2576,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,zero)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1913,f176]) ).
fof(f2577,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,strong_iteration(X1))),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f35,f176]) ).
fof(f2578,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(X1,addition(X3,X2)))),
inference(paramodulation,[status(thm)],[f104,f176]) ).
fof(f2579,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(addition(X1,X3),X2))),
inference(paramodulation,[status(thm)],[f27,f176]) ).
fof(f2580,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f26,f176]) ).
fof(f2581,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f176]) ).
fof(f2583,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f63,f176]) ).
fof(f2584,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f20,f176]) ).
fof(f2586,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,multiplication(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f176]) ).
fof(f2588,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X0,addition(X2,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f58,f176]) ).
fof(f2589,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X0,addition(X2,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f58,f176]) ).
fof(f2590,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f457,f176]) ).
fof(f2598,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X1,addition(X0,X2)))) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f63,f2518]) ).
fof(f2599,plain,
! [X0,X1,X2] : addition(X0,addition(addition(X0,X1),X2)) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f457,f2598]) ).
fof(f2600,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f63,f2599]) ).
fof(f2603,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X1,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f2536]) ).
fof(f2604,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f2537]) ).
fof(f2607,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,addition(X0,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f2541]) ).
fof(f2608,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f2542]) ).
fof(f2609,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,addition(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f2543]) ).
fof(f2621,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X1,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f2555]) ).
fof(f2622,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f2556]) ).
fof(f2634,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X1),addition(X3,X2))),
inference(paramodulation,[status(thm)],[f23,f183]) ).
fof(f2637,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,addition(X2,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f110,f183]) ).
fof(f2638,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,addition(X2,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f114,f183]) ).
fof(f2640,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),X2),multiplication(X0,multiplication(X1,addition(X3,X2)))),
inference(paramodulation,[status(thm)],[f23,f183]) ).
fof(f2646,plain,
! [X0,X1] : leq(multiplication(X0,star(X1)),multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f1021,f183]) ).
fof(f2649,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(strong_iteration(X1),zero)),multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f38,f183]) ).
fof(f2653,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(star(X1),X1)),multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f30,f183]) ).
fof(f2654,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,star(X1))),multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f29,f183]) ).
fof(f2657,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f104,f183]) ).
fof(f2658,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X3,X1),X2))),
inference(paramodulation,[status(thm)],[f27,f183]) ).
fof(f2659,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X3,X2)))),
inference(paramodulation,[status(thm)],[f26,f183]) ).
fof(f2660,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f183]) ).
fof(f2662,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f63,f183]) ).
fof(f2663,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(X0,addition(X2,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f20,f183]) ).
fof(f2664,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f2007,f183]) ).
fof(f2665,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f183]) ).
fof(f2667,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f58,f183]) ).
fof(f2668,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f58,f183]) ).
fof(f2669,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f457,f183]) ).
fof(f2671,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,X2)),multiplication(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f153,f183]) ).
fof(f2679,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f23,f2634]) ).
fof(f2682,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,addition(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f23,f2640]) ).
fof(f2690,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f23,f204]) ).
fof(f2692,plain,
! [X0,X1] : leq(X0,multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f25,f204]) ).
fof(f2693,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X0,X1)),multiplication(addition(X2,X0),addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f204]) ).
fof(f2694,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X0),multiplication(addition(X2,X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f204]) ).
fof(f2698,plain,
! [X0,X1] : leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),X1)),
inference(paramodulation,[status(thm)],[f1021,f204]) ).
fof(f2702,plain,
! [X0,X1] : leq(multiplication(one,X0),multiplication(star(X1),X0)),
inference(paramodulation,[status(thm)],[f349,f204]) ).
fof(f2705,plain,
! [X0,X1] : leq(multiplication(multiplication(star(X0),X0),X1),multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f30,f204]) ).
fof(f2706,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,star(X0)),X1),multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f29,f204]) ).
fof(f2709,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,addition(X1,X3)),X2)),
inference(paramodulation,[status(thm)],[f104,f204]) ).
fof(f2711,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,addition(X3,X1)),X2)),
inference(paramodulation,[status(thm)],[f26,f204]) ).
fof(f2712,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(multiplication(X0,addition(X2,one)),X1)),
inference(paramodulation,[status(thm)],[f114,f204]) ).
fof(f2714,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(X2,addition(X3,X0)),X1)),
inference(paramodulation,[status(thm)],[f63,f204]) ).
fof(f2715,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(X2,addition(X3,X0)),X1)),
inference(paramodulation,[status(thm)],[f20,f204]) ).
fof(f2717,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,addition(one,X1)),X2)),
inference(paramodulation,[status(thm)],[f110,f204]) ).
fof(f2719,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X0,addition(X1,X3)),X2)),
inference(paramodulation,[status(thm)],[f58,f204]) ).
fof(f2720,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,addition(X3,X0)),X2)),
inference(paramodulation,[status(thm)],[f58,f204]) ).
fof(f2721,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f457,f204]) ).
fof(f2723,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f153,f204]) ).
fof(f2736,plain,
! [X0,X1] : leq(X0,multiplication(star(X1),X0)),
inference(forward_demodulation,[status(thm)],[f25,f2702]) ).
fof(f2737,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(X0,X1)),multiplication(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f2705]) ).
fof(f2738,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(star(X0),X1)),multiplication(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f2706]) ).
fof(f2740,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,addition(X1,X3)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f2709]) ).
fof(f2741,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X1,X3),X2))),
inference(forward_demodulation,[status(thm)],[f23,f2740]) ).
fof(f2744,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,addition(X3,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f2711]) ).
fof(f2745,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X3,X1),X2))),
inference(forward_demodulation,[status(thm)],[f23,f2744]) ).
fof(f2746,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(addition(X2,one),X1))),
inference(forward_demodulation,[status(thm)],[f23,f2712]) ).
fof(f2749,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,addition(one,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f2717]) ).
fof(f2750,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(one,X1),X2))),
inference(forward_demodulation,[status(thm)],[f23,f2749]) ).
fof(f2752,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(multiplication(X0,X1),X3)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,X1),X3)) ),
inference(paramodulation,[status(thm)],[f23,f115]) ).
fof(f2757,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(one)) != multiplication(X0,X1)
| leq(multiplication(X0,strong_iteration(one)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1237,f115]) ).
fof(f2758,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,star(X1))
| leq(multiplication(X0,strong_iteration(X1)),multiplication(X0,star(X1))) ),
inference(paramodulation,[status(thm)],[f1021,f115]) ).
fof(f2759,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,one)
| leq(multiplication(X0,strong_iteration(X1)),multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f858,f115]) ).
fof(f2760,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,strong_iteration(X1))
| leq(multiplication(X0,star(X1)),multiplication(X0,strong_iteration(X1))) ),
inference(paramodulation,[status(thm)],[f829,f115]) ).
fof(f2761,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,multiplication(strong_iteration(X1),zero))
| leq(multiplication(X0,star(X1)),multiplication(X0,multiplication(strong_iteration(X1),zero))) ),
inference(paramodulation,[status(thm)],[f38,f115]) ).
fof(f2762,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,one)
| leq(multiplication(X0,star(X1)),multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f349,f115]) ).
fof(f2765,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,multiplication(star(X1),X1))
| leq(multiplication(X0,one),multiplication(X0,multiplication(star(X1),X1))) ),
inference(paramodulation,[status(thm)],[f30,f115]) ).
fof(f2766,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,multiplication(X1,star(X1)))
| leq(multiplication(X0,one),multiplication(X0,multiplication(X1,star(X1)))) ),
inference(paramodulation,[status(thm)],[f29,f115]) ).
fof(f2767,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(X0,X1)
| leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f1913,f115]) ).
fof(f2768,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,one)
| leq(multiplication(X0,multiplication(X1,strong_iteration(X1))),multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f35,f115]) ).
fof(f2769,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X3,X2))) != multiplication(X0,multiplication(X1,X3))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) ),
inference(paramodulation,[status(thm)],[f104,f115]) ).
fof(f2770,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X1,X3),X2)) != multiplication(X0,multiplication(X3,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(paramodulation,[status(thm)],[f27,f115]) ).
fof(f2771,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(X0,multiplication(X1,X3))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) ),
inference(paramodulation,[status(thm)],[f26,f115]) ).
fof(f2772,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(X1,addition(X2,one))) != multiplication(X0,X1)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f114,f115]) ).
fof(f2774,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(X2,addition(X1,X3))) != multiplication(X0,X3)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f63,f115]) ).
fof(f2775,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(X1,addition(X2,X3))) != multiplication(X0,X3)
| leq(multiplication(X0,addition(X1,X2)),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f20,f115]) ).
fof(f2776,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(X0,multiplication(X1,zero))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,zero))) ),
inference(paramodulation,[status(thm)],[f2007,f115]) ).
fof(f2777,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(X1,addition(one,X2))) != multiplication(X0,multiplication(X1,X2))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f110,f115]) ).
fof(f2779,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(X2,addition(X3,X1))) != multiplication(X0,addition(X2,X3))
| leq(multiplication(X0,X1),multiplication(X0,addition(X2,X3))) ),
inference(paramodulation,[status(thm)],[f58,f115]) ).
fof(f2780,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,addition(X3,addition(X1,X2))) != multiplication(X0,addition(X2,X3))
| leq(multiplication(X0,X1),multiplication(X0,addition(X2,X3))) ),
inference(paramodulation,[status(thm)],[f58,f115]) ).
fof(f2785,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(X0,zero)
| leq(multiplication(X0,X1),multiplication(X0,zero)) ),
inference(paramodulation,[status(thm)],[f21,f115]) ).
fof(f2786,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f19,f115]) ).
fof(f2787,plain,
! [X0,X1,X2] :
( multiplication(X0,addition(X2,X1)) != multiplication(X0,X2)
| leq(multiplication(X0,X1),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f19,f115]) ).
fof(f2789,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(multiplication(X0,X1),X3)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X1),X3)) ),
inference(forward_demodulation,[status(thm)],[f23,f2752]) ).
fof(f2790,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(multiplication(X0,X1),X3)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) ),
inference(forward_demodulation,[status(thm)],[f23,f2789]) ).
fof(f2791,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(X1,addition(X2,X3))) != multiplication(X0,multiplication(X1,X3))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,X3))) ),
inference(forward_demodulation,[status(thm)],[f23,f2790]) ).
fof(f2802,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,one)
| leq(multiplication(X0,strong_iteration(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f2759]) ).
fof(f2803,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != X0
| leq(multiplication(X0,strong_iteration(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f2802]) ).
fof(f2804,plain,
! [X0,X1] : leq(multiplication(X0,star(X1)),multiplication(X0,strong_iteration(X1))),
inference(trivial_equality_resolution,[status(thm)],[f2760]) ).
fof(f2805,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,one)
| leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f2762]) ).
fof(f2806,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != X0
| leq(multiplication(X0,star(X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f2805]) ).
fof(f2811,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,multiplication(star(X1),X1))
| leq(X0,multiplication(X0,multiplication(star(X1),X1))) ),
inference(forward_demodulation,[status(thm)],[f24,f2765]) ).
fof(f2812,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,multiplication(X1,star(X1)))
| leq(X0,multiplication(X0,multiplication(X1,star(X1)))) ),
inference(forward_demodulation,[status(thm)],[f24,f2766]) ).
fof(f2813,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(X0,X1)),
inference(trivial_equality_resolution,[status(thm)],[f2767]) ).
fof(f2814,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,one)
| leq(multiplication(X0,multiplication(X1,strong_iteration(X1))),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f2768]) ).
fof(f2815,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != X0
| leq(multiplication(X0,multiplication(X1,strong_iteration(X1))),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f2814]) ).
fof(f2821,plain,
! [X0,X1] : addition(X0,multiplication(star(X1),X0)) = multiplication(star(X1),X0),
inference(resolution,[status(thm)],[f2736,f41]) ).
fof(f2825,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = multiplication(addition(X1,one),X0),
inference(resolution,[status(thm)],[f2692,f41]) ).
fof(f2833,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,addition(X2,one)),X0)),
inference(paramodulation,[status(thm)],[f63,f2692]) ).
fof(f2834,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,addition(X2,one)),X0)),
inference(paramodulation,[status(thm)],[f20,f2692]) ).
fof(f2835,plain,
! [X0,X1] : leq(X0,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f19,f2692]) ).
fof(f2841,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = multiplication(addition(one,X1),X0),
inference(resolution,[status(thm)],[f2835,f41]) ).
fof(f2849,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,addition(X2,one)),X0)),
inference(paramodulation,[status(thm)],[f58,f2835]) ).
fof(f2850,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,addition(one,X2)),X0)),
inference(paramodulation,[status(thm)],[f58,f2835]) ).
fof(f2862,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(addition(X0,X2),X1)) = multiplication(addition(X0,X2),X1),
inference(resolution,[status(thm)],[f205,f41]) ).
fof(f2863,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f23,f205]) ).
fof(f2866,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X0,X1)),multiplication(addition(X0,X2),addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f205]) ).
fof(f2867,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X0),multiplication(addition(X0,X2),addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f205]) ).
fof(f2873,plain,
! [X0,X1] : leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),X1)),
inference(paramodulation,[status(thm)],[f829,f205]) ).
fof(f2874,plain,
! [X0,X1] : leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),X1)),
inference(paramodulation,[status(thm)],[f38,f205]) ).
fof(f2881,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,strong_iteration(X0)),X1),multiplication(strong_iteration(X0),X1)),
inference(paramodulation,[status(thm)],[f35,f205]) ).
fof(f2882,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,addition(X3,X1)),X2)),
inference(paramodulation,[status(thm)],[f104,f205]) ).
fof(f2884,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,addition(X1,X3)),X2)),
inference(paramodulation,[status(thm)],[f26,f205]) ).
fof(f2885,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,addition(X1,one)),X2)),
inference(paramodulation,[status(thm)],[f114,f205]) ).
fof(f2887,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,addition(X0,X3)),X2)),
inference(paramodulation,[status(thm)],[f63,f205]) ).
fof(f2888,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X0,addition(X1,X3)),X2)),
inference(paramodulation,[status(thm)],[f20,f205]) ).
fof(f2890,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(multiplication(X0,addition(one,X2)),X1)),
inference(paramodulation,[status(thm)],[f110,f205]) ).
fof(f2892,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(X2,addition(X3,X0)),X1)),
inference(paramodulation,[status(thm)],[f58,f205]) ).
fof(f2893,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(addition(X2,addition(X0,X3)),X1)),
inference(paramodulation,[status(thm)],[f58,f205]) ).
fof(f2902,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X0,X1)),X2) = multiplication(addition(X0,X1),X2),
inference(forward_demodulation,[status(thm)],[f27,f2862]) ).
fof(f2903,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f457,f2902]) ).
fof(f2913,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(strong_iteration(X0),X1)),multiplication(strong_iteration(X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f2881]) ).
fof(f2914,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,addition(X3,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f2882]) ).
fof(f2915,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X3,X1),X2))),
inference(forward_demodulation,[status(thm)],[f23,f2914]) ).
fof(f2918,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,addition(X1,X3)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f2884]) ).
fof(f2919,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X1,X3),X2))),
inference(forward_demodulation,[status(thm)],[f23,f2918]) ).
fof(f2920,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,addition(X1,one)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f2885]) ).
fof(f2921,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X1,one),X2))),
inference(forward_demodulation,[status(thm)],[f23,f2920]) ).
fof(f2923,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(addition(one,X2),X1))),
inference(forward_demodulation,[status(thm)],[f23,f2890]) ).
fof(f2924,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(strong_iteration(X1),addition(X2,addition(X3,X0)))),
inference(resolution,[status(thm)],[f223,f37]) ).
fof(f2925,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,addition(X3,X0)))) = addition(X1,addition(X2,addition(X3,X0))),
inference(resolution,[status(thm)],[f223,f41]) ).
fof(f2928,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(addition(X1,addition(X2,X0)),addition(X3,one))),
inference(paramodulation,[status(thm)],[f114,f223]) ).
fof(f2930,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X4,X0))))),
inference(paramodulation,[status(thm)],[f63,f223]) ).
fof(f2931,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X4,X0))))),
inference(paramodulation,[status(thm)],[f20,f223]) ).
fof(f2943,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,multiplication(addition(X2,X0),addition(X3,one)))),
inference(paramodulation,[status(thm)],[f114,f223]) ).
fof(f2945,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X4,X0))))),
inference(paramodulation,[status(thm)],[f63,f223]) ).
fof(f2946,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X4,X0))))),
inference(paramodulation,[status(thm)],[f20,f223]) ).
fof(f2957,plain,
! [X0,X1,X2] : leq(star(X0),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f1021,f223]) ).
fof(f2960,plain,
! [X0,X1,X2] : leq(multiplication(strong_iteration(X0),zero),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f38,f223]) ).
fof(f2964,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),X0),addition(X1,addition(X2,star(X0)))),
inference(paramodulation,[status(thm)],[f30,f223]) ).
fof(f2965,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(X0)),addition(X1,addition(X2,star(X0)))),
inference(paramodulation,[status(thm)],[f29,f223]) ).
fof(f2968,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,addition(X1,X4))))),
inference(paramodulation,[status(thm)],[f104,f223]) ).
fof(f2969,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(addition(X4,X0),X1)))),
inference(paramodulation,[status(thm)],[f27,f223]) ).
fof(f2970,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,addition(X4,X1))))),
inference(paramodulation,[status(thm)],[f26,f223]) ).
fof(f2971,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,multiplication(X0,addition(X3,one))))),
inference(paramodulation,[status(thm)],[f114,f223]) ).
fof(f2973,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X4,X0))))),
inference(paramodulation,[status(thm)],[f63,f223]) ).
fof(f2974,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X4,X0))))),
inference(paramodulation,[status(thm)],[f20,f223]) ).
fof(f2975,plain,
! [X0,X1,X2] : leq(multiplication(X0,zero),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f2007,f223]) ).
fof(f2976,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,addition(one,X1))))),
inference(paramodulation,[status(thm)],[f110,f223]) ).
fof(f2978,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,X1),addition(X2,addition(X3,addition(X0,addition(X1,X4))))),
inference(paramodulation,[status(thm)],[f58,f223]) ).
fof(f2979,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,X1),addition(X2,addition(X3,addition(X1,addition(X4,X0))))),
inference(paramodulation,[status(thm)],[f58,f223]) ).
fof(f2980,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X3,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f457,f223]) ).
fof(f2982,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X3,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f153,f223]) ).
fof(f3003,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X3,X1)),X2),
inference(paramodulation,[status(thm)],[f58,f116]) ).
fof(f3004,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,X2),multiplication(X1,X3))) = addition(multiplication(X1,addition(X2,X3)),X0),
inference(paramodulation,[status(thm)],[f58,f116]) ).
fof(f3006,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f182,f116]) ).
fof(f3011,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(multiplication(X0,X1),X3),X4)) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(paramodulation,[status(thm)],[f23,f116]) ).
fof(f3014,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X0,X1)),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(addition(one,X1),X2)),X3),
inference(paramodulation,[status(thm)],[f110,f116]) ).
fof(f3015,plain,
! [X0,X1,X2,X3] : addition(addition(multiplication(X0,X1),X0),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(addition(X1,one),X2)),X3),
inference(paramodulation,[status(thm)],[f114,f116]) ).
fof(f3016,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(one,X1)),X2),
inference(paramodulation,[status(thm)],[f24,f116]) ).
fof(f3018,plain,
! [X0,X1] : addition(multiplication(X0,X1),strong_iteration(X0)) = addition(multiplication(X0,addition(X1,strong_iteration(X0))),one),
inference(paramodulation,[status(thm)],[f35,f116]) ).
fof(f3019,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X0,addition(X2,X3)),X4)) = addition(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X3),X4)),
inference(paramodulation,[status(thm)],[f116,f116]) ).
fof(f3020,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,addition(X2,X3))) = addition(multiplication(X0,addition(X1,X3)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f104,f116]) ).
fof(f3021,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f27,f116]) ).
fof(f3022,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,addition(X2,X3))) = addition(multiplication(X0,addition(X1,X2)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f26,f116]) ).
fof(f3023,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,addition(X2,one))) = addition(multiplication(X0,addition(X1,X2)),X0),
inference(paramodulation,[status(thm)],[f114,f116]) ).
fof(f3024,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),zero)),
inference(paramodulation,[status(thm)],[f2007,f116]) ).
fof(f3025,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(multiplication(X0,X2),addition(one,X3))) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),X3)),
inference(paramodulation,[status(thm)],[f110,f116]) ).
fof(f3027,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,X4)))) = addition(multiplication(X0,addition(X1,X4)),addition(X2,X3)),
inference(paramodulation,[status(thm)],[f58,f116]) ).
fof(f3028,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),X4))) = addition(multiplication(X0,addition(X1,X3)),addition(X4,X2)),
inference(paramodulation,[status(thm)],[f58,f116]) ).
fof(f3029,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),addition(multiplication(X0,X3),X2)),
inference(paramodulation,[status(thm)],[f457,f116]) ).
fof(f3030,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),addition(X2,multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f182,f116]) ).
fof(f3031,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) = addition(multiplication(X0,addition(X1,X2)),addition(X3,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f153,f116]) ).
fof(f3033,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),zero),
inference(paramodulation,[status(thm)],[f21,f116]) ).
fof(f3034,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),X2),
inference(paramodulation,[status(thm)],[f19,f116]) ).
fof(f3035,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),X2),
inference(paramodulation,[status(thm)],[f19,f116]) ).
fof(f3036,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X0,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f22,f116]) ).
fof(f3037,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(multiplication(X0,X1),X2),addition(multiplication(X0,multiplication(X1,X3)),X4)) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(paramodulation,[status(thm)],[f23,f116]) ).
fof(f3040,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(X0,multiplication(X0,X2)),X3)) = addition(multiplication(X0,addition(X1,addition(one,X2))),X3),
inference(paramodulation,[status(thm)],[f110,f116]) ).
fof(f3041,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(multiplication(X0,X2),X0),X3)) = addition(multiplication(X0,addition(X1,addition(X2,one))),X3),
inference(paramodulation,[status(thm)],[f114,f116]) ).
fof(f3042,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X0,X2)) = addition(multiplication(X0,addition(X1,one)),X2),
inference(paramodulation,[status(thm)],[f24,f116]) ).
fof(f3043,plain,
! [X0,X1,X2,X3] :
( leq(X0,multiplication(strong_iteration(X1),addition(multiplication(X1,X2),X3)))
| ~ leq(X0,addition(multiplication(X1,addition(X0,X2)),X3)) ),
inference(paramodulation,[status(thm)],[f116,f37]) ).
fof(f3044,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(multiplication(X0,X2),X3),star(X1)),X0)
| ~ leq(addition(multiplication(X0,addition(X1,X2)),X3),X0) ),
inference(paramodulation,[status(thm)],[f116,f34]) ).
fof(f3045,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),addition(multiplication(X0,X2),X3)),X1)
| ~ leq(addition(multiplication(X0,addition(X1,X2)),X3),X1) ),
inference(paramodulation,[status(thm)],[f116,f32]) ).
fof(f3048,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),addition(multiplication(X0,addition(X1,X2)),X3)),
inference(paramodulation,[status(thm)],[f116,f176]) ).
fof(f3049,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X1,X2)),X3) != X3
| leq(addition(multiplication(X0,X1),multiplication(X0,X2)),X3) ),
inference(paramodulation,[status(thm)],[f116,f85]) ).
fof(f3050,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X3,X1)),X2),
inference(paramodulation,[status(thm)],[f116,f58]) ).
fof(f3051,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f116,f58]) ).
fof(f3055,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(X0,addition(X2,X1)),X3)),
inference(paramodulation,[status(thm)],[f116,f237]) ).
fof(f3058,plain,
! [X0,X1,X2,X3,X4,X5] : leq(addition(multiplication(X0,X1),X2),addition(X3,addition(X4,addition(multiplication(X0,addition(X5,X1)),X2)))),
inference(paramodulation,[status(thm)],[f116,f223]) ).
fof(f3059,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(multiplication(X0,X1),X2),multiplication(addition(multiplication(X0,addition(X1,X3)),X4),X2)),
inference(paramodulation,[status(thm)],[f116,f205]) ).
fof(f3060,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(X0,addition(multiplication(X1,addition(X2,X3)),X4)) != multiplication(X0,addition(multiplication(X1,X3),X4))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,addition(multiplication(X1,X3),X4))) ),
inference(paramodulation,[status(thm)],[f116,f115]) ).
fof(f3061,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(addition(multiplication(X0,addition(X4,X1)),X2),X3)),
inference(paramodulation,[status(thm)],[f116,f204]) ).
fof(f3062,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,addition(multiplication(X1,X2),X3)),multiplication(X0,addition(multiplication(X1,addition(X4,X2)),X3))),
inference(paramodulation,[status(thm)],[f116,f183]) ).
fof(f3063,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,multiplication(X1,X2)),addition(X0,addition(multiplication(X1,addition(X2,X3)),X4))),
inference(paramodulation,[status(thm)],[f116,f176]) ).
fof(f3064,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(multiplication(X0,X1),addition(addition(multiplication(X0,X2),X3),X4))),
inference(paramodulation,[status(thm)],[f116,f176]) ).
fof(f3065,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),zero),addition(multiplication(X0,addition(X1,X2)),X3)),
inference(paramodulation,[status(thm)],[f116,f2307]) ).
fof(f3066,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(multiplication(X0,X1),X2),zero),addition(multiplication(X0,addition(X3,X1)),X2)),
inference(paramodulation,[status(thm)],[f116,f2042]) ).
fof(f3067,plain,
! [X0,X1,X2,X3,X4] :
( addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) != addition(multiplication(X1,X3),X4)
| leq(addition(X0,multiplication(X1,X2)),addition(multiplication(X1,X3),X4)) ),
inference(paramodulation,[status(thm)],[f116,f85]) ).
fof(f3068,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,addition(multiplication(X1,addition(X2,X3)),X4))),
inference(paramodulation,[status(thm)],[f116,f174]) ).
fof(f3069,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),multiplication(strong_iteration(X3),addition(multiplication(X0,addition(X4,X1)),X2))),
inference(paramodulation,[status(thm)],[f116,f874]) ).
fof(f3070,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),addition(multiplication(X0,addition(X1,X3)),X4))),
inference(paramodulation,[status(thm)],[f116,f873]) ).
fof(f3071,plain,
! [X0,X1,X2,X3,X4] : addition(addition(multiplication(X0,X1),X2),addition(multiplication(X0,X3),X4)) = addition(addition(multiplication(X0,addition(X3,X1)),X2),X4),
inference(paramodulation,[status(thm)],[f116,f63]) ).
fof(f3072,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X3,X1)),X2) != addition(multiplication(X0,X1),X2)
| leq(addition(addition(multiplication(X0,X1),X2),multiplication(X0,X3)),addition(multiplication(X0,X1),X2)) ),
inference(paramodulation,[status(thm)],[f116,f580]) ).
fof(f3073,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(addition(multiplication(X0,X2),X3),X4)) = addition(X4,addition(multiplication(X0,addition(X1,X2)),X3)),
inference(paramodulation,[status(thm)],[f116,f58]) ).
fof(f3074,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) = addition(addition(multiplication(X1,X3),X4),addition(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f116,f58]) ).
fof(f3075,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X1,X2)),X3) != addition(multiplication(X0,X2),X3)
| leq(addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)),addition(multiplication(X0,X2),X3)) ),
inference(paramodulation,[status(thm)],[f116,f475]) ).
fof(f3076,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X3,X1)),X2) != multiplication(X0,X3)
| leq(addition(addition(multiplication(X0,X1),X2),multiplication(X0,X3)),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f116,f343]) ).
fof(f3077,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X1,X2)),X3) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f116,f158]) ).
fof(f3078,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,addition(X1,X2)),X3)) = addition(addition(multiplication(X0,X2),X3),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f116,f457]) ).
fof(f3083,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(X0,addition(X1,X3)),X4))),
inference(paramodulation,[status(thm)],[f116,f237]) ).
fof(f3084,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),addition(X3,addition(multiplication(X0,addition(X4,X1)),X2))),
inference(paramodulation,[status(thm)],[f116,f185]) ).
fof(f3085,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(X0,addition(X3,X1)),X2)),
inference(paramodulation,[status(thm)],[f116,f179]) ).
fof(f3086,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(X0,addition(X1,X2)),X3)),
inference(paramodulation,[status(thm)],[f116,f145]) ).
fof(f3087,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,addition(X1,X2)),X3)) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)),
inference(paramodulation,[status(thm)],[f116,f65]) ).
fof(f3088,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X3,X1)),X2) != multiplication(X0,X3)
| leq(addition(multiplication(X0,X1),X2),multiplication(X0,X3)) ),
inference(paramodulation,[status(thm)],[f116,f87]) ).
fof(f3089,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X1,X2)),X3) != addition(multiplication(X0,X2),X3)
| leq(multiplication(X0,X1),addition(multiplication(X0,X2),X3)) ),
inference(paramodulation,[status(thm)],[f116,f42]) ).
fof(f3090,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(addition(multiplication(X0,X2),X3),X4)) = addition(addition(multiplication(X0,addition(X1,X2)),X3),X4),
inference(paramodulation,[status(thm)],[f116,f20]) ).
fof(f3093,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,addition(X3,X2)),X0),
inference(forward_demodulation,[status(thm)],[f104,f3004]) ).
fof(f3095,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X1,X2)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f104,f3006]) ).
fof(f3096,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(X1,X2))),
inference(forward_demodulation,[status(thm)],[f104,f3095]) ).
fof(f3097,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f457,f3096]) ).
fof(f3104,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X0,multiplication(X1,X3)),X4)) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(forward_demodulation,[status(thm)],[f23,f3011]) ).
fof(f3105,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),X4) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(forward_demodulation,[status(thm)],[f116,f3104]) ).
fof(f3106,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,addition(X2,X3))),X4) = addition(multiplication(multiplication(X0,X1),addition(X3,X2)),X4),
inference(forward_demodulation,[status(thm)],[f104,f3105]) ).
fof(f3107,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,addition(X2,X3))),X4) = addition(multiplication(X0,multiplication(X1,addition(X3,X2))),X4),
inference(forward_demodulation,[status(thm)],[f23,f3106]) ).
fof(f3114,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X0,addition(multiplication(X0,X2),X3))) = addition(multiplication(X0,addition(addition(one,X1),X2)),X3),
inference(forward_demodulation,[status(thm)],[f63,f3014]) ).
fof(f3115,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X0,addition(multiplication(X0,X2),X3))) = addition(multiplication(X0,addition(X1,addition(one,X2))),X3),
inference(forward_demodulation,[status(thm)],[f63,f3114]) ).
fof(f3116,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3))) = addition(multiplication(X0,addition(addition(X1,one),X2)),X3),
inference(forward_demodulation,[status(thm)],[f63,f3015]) ).
fof(f3117,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,addition(X1,X2)),X3)) = addition(multiplication(X0,addition(addition(X1,one),X2)),X3),
inference(forward_demodulation,[status(thm)],[f116,f3116]) ).
fof(f3118,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,addition(X1,X2)),X3)) = addition(multiplication(X0,addition(one,addition(X1,X2))),X3),
inference(forward_demodulation,[status(thm)],[f63,f3117]) ).
fof(f3119,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(X1,addition(X2,X3))),X4) = addition(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X3),X4)),
inference(forward_demodulation,[status(thm)],[f116,f3019]) ).
fof(f3120,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(X1,addition(X2,X3))),X4) = addition(multiplication(X0,addition(addition(X1,X2),X3)),X4),
inference(forward_demodulation,[status(thm)],[f116,f3119]) ).
fof(f3121,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(X1,addition(X2,X3))),X4) = addition(multiplication(X0,addition(X2,addition(X1,X3))),X4),
inference(forward_demodulation,[status(thm)],[f63,f3120]) ).
fof(f3122,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(addition(X1,X2),X3)) = addition(multiplication(X0,addition(X3,X2)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f104,f3020]) ).
fof(f3123,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = addition(multiplication(X0,addition(X3,X1)),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f63,f3122]) ).
fof(f3124,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = multiplication(X0,addition(X2,addition(X3,X1))),
inference(forward_demodulation,[status(thm)],[f104,f3123]) ).
fof(f3125,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(addition(X1,X2),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f104,f3022]) ).
fof(f3126,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = addition(multiplication(X0,addition(X3,X2)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f63,f3125]) ).
fof(f3127,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(X1,addition(X2,X3))) = multiplication(X0,addition(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f104,f3126]) ).
fof(f3128,plain,
! [X0,X1,X2] : multiplication(X0,addition(addition(X1,one),X2)) = addition(multiplication(X0,addition(X2,X1)),X0),
inference(forward_demodulation,[status(thm)],[f104,f3023]) ).
fof(f3129,plain,
! [X0,X1,X2] : multiplication(X0,addition(one,addition(X1,X2))) = addition(multiplication(X0,addition(X2,X1)),X0),
inference(forward_demodulation,[status(thm)],[f63,f3128]) ).
fof(f3130,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(multiplication(X0,X1),zero)),
inference(forward_demodulation,[status(thm)],[f104,f3024]) ).
fof(f3131,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,multiplication(X1,zero))),
inference(forward_demodulation,[status(thm)],[f23,f3130]) ).
fof(f3132,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(multiplication(X1,zero),addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f104,f3131]) ).
fof(f3133,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X0,multiplication(X2,addition(one,X3)))) = addition(multiplication(X0,addition(X1,X2)),multiplication(multiplication(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f23,f3025]) ).
fof(f3134,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(one,X2)),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f104,f3133]) ).
fof(f3135,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(one,X2)),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f3134]) ).
fof(f3136,plain,
! [X0,X1,X2,X3] : multiplication(X0,addition(multiplication(X1,addition(one,X2)),X3)) = multiplication(X0,addition(multiplication(X1,X2),addition(X3,X1))),
inference(forward_demodulation,[status(thm)],[f104,f3135]) ).
fof(f3138,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(addition(X1,X3),X3)),X2),
inference(forward_demodulation,[status(thm)],[f116,f3029]) ).
fof(f3139,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X3,addition(X1,X3))),X2),
inference(forward_demodulation,[status(thm)],[f63,f3138]) ).
fof(f3140,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),X2),
inference(forward_demodulation,[status(thm)],[f182,f3139]) ).
fof(f3141,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,addition(X1,X2)),addition(X3,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f116,f3031]) ).
fof(f3145,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),zero),
inference(forward_demodulation,[status(thm)],[f104,f3033]) ).
fof(f3146,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f21,f3145]) ).
fof(f3147,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,addition(X2,X1)),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f104,f3036]) ).
fof(f3148,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X1,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f104,f3147]) ).
fof(f3149,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f182,f3148]) ).
fof(f3150,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X0,multiplication(X1,X3)),X4)) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(forward_demodulation,[status(thm)],[f23,f3037]) ).
fof(f3151,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),X4) = addition(multiplication(multiplication(X0,X1),addition(X2,X3)),X4),
inference(forward_demodulation,[status(thm)],[f116,f3150]) ).
fof(f3152,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,addition(X2,X3))),X4) = addition(multiplication(multiplication(X0,X1),addition(X3,X2)),X4),
inference(forward_demodulation,[status(thm)],[f104,f3151]) ).
fof(f3153,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,addition(X2,X3))),X4) = addition(multiplication(X0,multiplication(X1,addition(X3,X2))),X4),
inference(forward_demodulation,[status(thm)],[f23,f3152]) ).
fof(f3160,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X0,X2),addition(X0,X3))) = addition(multiplication(X0,addition(X1,addition(one,X2))),X3),
inference(forward_demodulation,[status(thm)],[f63,f3040]) ).
fof(f3161,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),addition(X0,X3)) = addition(multiplication(X0,addition(X1,addition(one,X2))),X3),
inference(forward_demodulation,[status(thm)],[f116,f3160]) ).
fof(f3162,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X0,addition(multiplication(X0,X2),X3))) = addition(multiplication(X0,addition(X1,addition(X2,one))),X3),
inference(forward_demodulation,[status(thm)],[f63,f3041]) ).
fof(f3163,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,addition(X2,X1)),X3)),
inference(forward_demodulation,[status(thm)],[f104,f3048]) ).
fof(f3164,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X2,X1)),X3) != X3
| leq(multiplication(X0,addition(X1,X2)),X3) ),
inference(forward_demodulation,[status(thm)],[f104,f3049]) ).
fof(f3165,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f104,f3051]) ).
fof(f3171,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,addition(X1,X3)),X4),X2)),
inference(forward_demodulation,[status(thm)],[f23,f3059]) ).
fof(f3172,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(multiplication(X0,X1),addition(X3,addition(multiplication(X0,X2),X4)))),
inference(forward_demodulation,[status(thm)],[f63,f3064]) ).
fof(f3173,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,zero)),addition(multiplication(X0,addition(X1,X2)),X3)),
inference(forward_demodulation,[status(thm)],[f23,f3065]) ).
fof(f3174,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,X2),addition(multiplication(X1,X3),X4))) = addition(addition(multiplication(X1,addition(X3,X2)),X0),X4),
inference(forward_demodulation,[status(thm)],[f63,f3071]) ).
fof(f3175,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) = addition(addition(multiplication(X1,addition(X3,X2)),X0),X4),
inference(forward_demodulation,[status(thm)],[f116,f3174]) ).
fof(f3176,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) = addition(X0,addition(multiplication(X1,addition(X3,X2)),X4)),
inference(forward_demodulation,[status(thm)],[f63,f3175]) ).
fof(f3177,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X1,addition(X3,X2)),X0) != addition(multiplication(X1,X2),X0)
| leq(addition(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),addition(multiplication(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f63,f3072]) ).
fof(f3178,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X1,addition(X2,X3)),X0) != addition(multiplication(X1,X3),X0)
| leq(addition(X0,multiplication(X1,addition(X2,X3))),addition(multiplication(X1,X3),X0)) ),
inference(forward_demodulation,[status(thm)],[f104,f3177]) ).
fof(f3179,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),X4))) = addition(X4,addition(multiplication(X0,addition(X1,X3)),X2)),
inference(forward_demodulation,[status(thm)],[f63,f3073]) ).
fof(f3180,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,addition(X2,X3)),X4)) = addition(X4,addition(multiplication(X1,X3),addition(X0,multiplication(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f3074]) ).
fof(f3181,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X1,X2)),X3) != addition(multiplication(X0,X2),X3)
| leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(multiplication(X0,X2),X3)) ),
inference(forward_demodulation,[status(thm)],[f116,f3075]) ).
fof(f3182,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X1,addition(X3,X2)),X0) != multiplication(X1,X3)
| leq(addition(X0,addition(multiplication(X1,X2),multiplication(X1,X3))),multiplication(X1,X3)) ),
inference(forward_demodulation,[status(thm)],[f63,f3076]) ).
fof(f3183,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X1,addition(X2,X3)),X0) != multiplication(X1,X2)
| leq(addition(X0,multiplication(X1,addition(X2,X3))),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f104,f3182]) ).
fof(f3184,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(X0,addition(X1,X2)),X3) != multiplication(X0,X1)
| leq(addition(multiplication(X0,addition(X1,X2)),X3),multiplication(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f116,f3077]) ).
fof(f3185,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,addition(X1,X2))),X3) = addition(addition(multiplication(X0,X2),X3),multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f116,f3078]) ).
fof(f3186,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(addition(multiplication(X0,X1),X3),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f457,f3185]) ).
fof(f3187,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,addition(multiplication(X0,X1),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f63,f3186]) ).
fof(f3188,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(X3,multiplication(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f104,f3187]) ).
fof(f3203,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,addition(X1,X2))),X3) = addition(multiplication(X0,X1),addition(multiplication(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f116,f3087]) ).
fof(f3204,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,X2)),X3) = addition(multiplication(X0,X2),addition(multiplication(X0,X1),X3)),
inference(forward_demodulation,[status(thm)],[f457,f3203]) ).
fof(f3205,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),X4))) = addition(addition(multiplication(X0,addition(X1,X3)),X2),X4),
inference(forward_demodulation,[status(thm)],[f63,f3090]) ).
fof(f3206,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X0,X3),X4))) = addition(X2,addition(multiplication(X0,addition(X1,X3)),X4)),
inference(forward_demodulation,[status(thm)],[f63,f3205]) ).
fof(f3211,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(strong_iteration(X1),addition(X2,addition(X0,X3)))),
inference(resolution,[status(thm)],[f241,f37]) ).
fof(f3212,plain,
! [X0,X1,X2,X3] : addition(X0,addition(X1,addition(X2,addition(X0,X3)))) = addition(X1,addition(X2,addition(X0,X3))),
inference(resolution,[status(thm)],[f241,f41]) ).
fof(f3216,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(addition(X1,addition(X0,X2)),addition(X3,one))),
inference(paramodulation,[status(thm)],[f114,f241]) ).
fof(f3218,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X0,X4))))),
inference(paramodulation,[status(thm)],[f63,f241]) ).
fof(f3219,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X0,X4))))),
inference(paramodulation,[status(thm)],[f20,f241]) ).
fof(f3231,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(X0,addition(X3,X1)),X4))),
inference(paramodulation,[status(thm)],[f116,f241]) ).
fof(f3232,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,multiplication(addition(X0,X2),addition(X3,one)))),
inference(paramodulation,[status(thm)],[f114,f241]) ).
fof(f3234,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X0,X4))))),
inference(paramodulation,[status(thm)],[f63,f241]) ).
fof(f3235,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X0,X4))))),
inference(paramodulation,[status(thm)],[f20,f241]) ).
fof(f3248,plain,
! [X0,X1,X2] : leq(star(X0),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f829,f241]) ).
fof(f3249,plain,
! [X0,X1,X2] : leq(star(X0),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f38,f241]) ).
fof(f3255,plain,
! [X0,X1,X2] : leq(multiplication(X0,zero),addition(X1,addition(X2,X0))),
inference(paramodulation,[status(thm)],[f1913,f241]) ).
fof(f3256,plain,
! [X0,X1,X2] : leq(multiplication(X0,strong_iteration(X0)),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f35,f241]) ).
fof(f3257,plain,
! [X0,X1,X2,X3,X4,X5] : leq(multiplication(X0,X1),addition(X2,addition(X3,addition(multiplication(X0,addition(X1,X4)),X5)))),
inference(paramodulation,[status(thm)],[f116,f241]) ).
fof(f3258,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,addition(X4,X1))))),
inference(paramodulation,[status(thm)],[f104,f241]) ).
fof(f3259,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(addition(X0,X4),X1)))),
inference(paramodulation,[status(thm)],[f27,f241]) ).
fof(f3260,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,addition(X1,X4))))),
inference(paramodulation,[status(thm)],[f26,f241]) ).
fof(f3261,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X0,addition(X1,one))))),
inference(paramodulation,[status(thm)],[f114,f241]) ).
fof(f3263,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,X1),addition(X2,addition(X3,addition(X1,addition(X0,X4))))),
inference(paramodulation,[status(thm)],[f63,f241]) ).
fof(f3264,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,X1),addition(X2,addition(X3,addition(X0,addition(X1,X4))))),
inference(paramodulation,[status(thm)],[f20,f241]) ).
fof(f3266,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,multiplication(X0,addition(one,X3))))),
inference(paramodulation,[status(thm)],[f110,f241]) ).
fof(f3268,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X4,X0))))),
inference(paramodulation,[status(thm)],[f58,f241]) ).
fof(f3269,plain,
! [X0,X1,X2,X3,X4] : leq(X0,addition(X1,addition(X2,addition(X3,addition(X0,X4))))),
inference(paramodulation,[status(thm)],[f58,f241]) ).
fof(f3293,plain,
! [X0,X1,X2] : leq(one,multiplication(strong_iteration(X0),addition(X1,star(X2)))),
inference(resolution,[status(thm)],[f277,f37]) ).
fof(f3294,plain,
! [X0,X1,X2] : addition(one,addition(X0,addition(X1,star(X2)))) = addition(X0,addition(X1,star(X2))),
inference(resolution,[status(thm)],[f277,f41]) ).
fof(f3298,plain,
! [X0,X1,X2] : leq(one,multiplication(addition(X0,star(X1)),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f277]) ).
fof(f3300,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,star(X3))))),
inference(paramodulation,[status(thm)],[f63,f277]) ).
fof(f3301,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,star(X3))))),
inference(paramodulation,[status(thm)],[f20,f277]) ).
fof(f3315,plain,
! [X0,X1,X2] : leq(one,addition(X0,multiplication(star(X1),addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f277]) ).
fof(f3317,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,star(X3))))),
inference(paramodulation,[status(thm)],[f63,f277]) ).
fof(f3318,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,star(X3))))),
inference(paramodulation,[status(thm)],[f20,f277]) ).
fof(f3326,plain,
! [X0,X1,X2] : leq(addition(X0,X1),multiplication(strong_iteration(X2),addition(X1,X0))),
inference(resolution,[status(thm)],[f339,f37]) ).
fof(f3327,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X2,addition(X1,X0))) = addition(X2,addition(X1,X0)),
inference(resolution,[status(thm)],[f339,f41]) ).
fof(f3332,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(X1,addition(multiplication(strong_iteration(X0),zero),star(X0)))),
inference(paramodulation,[status(thm)],[f38,f339]) ).
fof(f3336,plain,
! [X0,X1] : leq(star(X0),addition(X1,addition(multiplication(star(X0),X0),one))),
inference(paramodulation,[status(thm)],[f30,f339]) ).
fof(f3337,plain,
! [X0,X1] : leq(star(X0),addition(X1,addition(multiplication(X0,star(X0)),one))),
inference(paramodulation,[status(thm)],[f29,f339]) ).
fof(f3339,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(X1,addition(one,multiplication(X0,strong_iteration(X0))))),
inference(paramodulation,[status(thm)],[f35,f339]) ).
fof(f3341,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(X3,addition(multiplication(X0,X1),multiplication(X0,X2)))),
inference(paramodulation,[status(thm)],[f104,f339]) ).
fof(f3342,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(X3,addition(multiplication(X1,X2),multiplication(X0,X2)))),
inference(paramodulation,[status(thm)],[f27,f339]) ).
fof(f3344,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,one)),addition(X2,addition(X0,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f114,f339]) ).
fof(f3346,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(X2,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f63,f339]) ).
fof(f3347,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(X2,addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f20,f339]) ).
fof(f3349,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(one,X1)),addition(X2,addition(multiplication(X0,X1),X0))),
inference(paramodulation,[status(thm)],[f110,f339]) ).
fof(f3351,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(addition(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f58,f339]) ).
fof(f3352,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(addition(X2,X0),X1))),
inference(paramodulation,[status(thm)],[f58,f339]) ).
fof(f3363,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(multiplication(X1,addition(X3,X2)),X0)),
inference(paramodulation,[status(thm)],[f116,f339]) ).
fof(f3364,plain,
! [X0,X1,X2] : leq(addition(X0,X1),multiplication(addition(X1,X0),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f339]) ).
fof(f3366,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X3,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f63,f339]) ).
fof(f3367,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X2,addition(X3,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f20,f339]) ).
fof(f3381,plain,
! [X0,X1] : leq(addition(multiplication(strong_iteration(X0),zero),star(X0)),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f38,f339]) ).
fof(f3385,plain,
! [X0,X1] : leq(addition(multiplication(star(X0),X0),one),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f30,f339]) ).
fof(f3386,plain,
! [X0,X1] : leq(addition(multiplication(X0,star(X0)),one),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f29,f339]) ).
fof(f3388,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,strong_iteration(X0))),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f35,f339]) ).
fof(f3390,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),multiplication(X0,X2)),addition(X3,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f104,f339]) ).
fof(f3391,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),addition(X3,multiplication(addition(X2,X0),X1))),
inference(paramodulation,[status(thm)],[f27,f339]) ).
fof(f3393,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X0,X1)),addition(X2,multiplication(X0,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f114,f339]) ).
fof(f3395,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(X2,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f63,f339]) ).
fof(f3396,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(X1,addition(X2,X0)))),
inference(paramodulation,[status(thm)],[f20,f339]) ).
fof(f3398,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X0),addition(X2,multiplication(X0,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f110,f339]) ).
fof(f3400,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X3,addition(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f58,f339]) ).
fof(f3401,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X3,addition(X1,addition(X2,X0)))),
inference(paramodulation,[status(thm)],[f58,f339]) ).
fof(f3410,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X2,addition(X0,X1)))) = addition(X2,addition(X0,X1)),
inference(forward_demodulation,[status(thm)],[f63,f3327]) ).
fof(f3422,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(X3,multiplication(X0,addition(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f104,f3341]) ).
fof(f3423,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(X3,multiplication(addition(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f27,f3342]) ).
fof(f3429,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(X1,addition(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f3351]) ).
fof(f3430,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(X0,addition(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f63,f3352]) ).
fof(f3454,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(X3,multiplication(X0,addition(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f104,f3390]) ).
fof(f3455,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(X3,multiplication(addition(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f27,f3391]) ).
fof(f3461,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(X1,addition(X0,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f3400]) ).
fof(f3462,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X3,addition(X0,addition(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f63,f3401]) ).
fof(f3477,plain,
! [X0,X1] : addition(multiplication(star(X0),X1),star(X0)) = addition(multiplication(star(X0),addition(X1,X0)),one),
inference(paramodulation,[status(thm)],[f588,f116]) ).
fof(f3478,plain,
! [X0] :
( leq(X0,multiplication(strong_iteration(star(X0)),one))
| ~ leq(X0,star(X0)) ),
inference(paramodulation,[status(thm)],[f588,f37]) ).
fof(f3480,plain,
! [X0] :
( leq(multiplication(star(star(X0)),one),X0)
| ~ leq(star(X0),X0) ),
inference(paramodulation,[status(thm)],[f588,f32]) ).
fof(f3482,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(multiplication(X0,multiplication(star(X1),X1)),X0),
inference(paramodulation,[status(thm)],[f588,f114]) ).
fof(f3486,plain,
! [X0,X1,X2] : leq(multiplication(star(X0),X0),addition(X1,addition(X2,star(X0)))),
inference(paramodulation,[status(thm)],[f588,f241]) ).
fof(f3488,plain,
! [X0,X1] : leq(multiplication(multiplication(star(X0),X0),X1),multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f588,f205]) ).
fof(f3489,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,one)
| leq(multiplication(X0,multiplication(star(X1),X1)),multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f588,f115]) ).
fof(f3492,plain,
! [X0,X1] : leq(addition(X0,multiplication(star(X1),X1)),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f588,f176]) ).
fof(f3493,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(star(X0),X0),addition(one,X1))),
inference(paramodulation,[status(thm)],[f588,f176]) ).
fof(f3494,plain,
! [X0] : leq(multiplication(multiplication(star(X0),X0),zero),star(X0)),
inference(paramodulation,[status(thm)],[f588,f2307]) ).
fof(f3496,plain,
! [X0,X1] :
( addition(X0,star(X1)) != one
| leq(addition(X0,multiplication(star(X1),X1)),one) ),
inference(paramodulation,[status(thm)],[f588,f85]) ).
fof(f3497,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(star(X1),X1)),multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f588,f174]) ).
fof(f3499,plain,
! [X0,X1] : leq(multiplication(star(X0),X0),multiplication(strong_iteration(X1),star(X0))),
inference(paramodulation,[status(thm)],[f588,f873]) ).
fof(f3500,plain,
! [X0,X1] : addition(one,addition(multiplication(star(X0),X0),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f588,f63]) ).
fof(f3502,plain,
! [X0,X1] : addition(multiplication(star(X0),X0),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f588,f58]) ).
fof(f3503,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(X0,multiplication(star(X1),X1))),
inference(paramodulation,[status(thm)],[f588,f58]) ).
fof(f3505,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(addition(one,multiplication(star(X0),X0)),multiplication(star(X0),X0)) ),
inference(paramodulation,[status(thm)],[f588,f343]) ).
fof(f3506,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(addition(multiplication(star(X0),X0),one),multiplication(star(X0),X0)) ),
inference(paramodulation,[status(thm)],[f588,f158]) ).
fof(f3507,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = addition(one,multiplication(star(X0),X0)),
inference(paramodulation,[status(thm)],[f588,f457]) ).
fof(f3512,plain,
! [X0,X1] : leq(multiplication(star(X0),X0),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f588,f237]) ).
fof(f3516,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = addition(multiplication(star(X0),X0),one),
inference(paramodulation,[status(thm)],[f588,f65]) ).
fof(f3517,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(one,multiplication(star(X0),X0)) ),
inference(paramodulation,[status(thm)],[f588,f87]) ).
fof(f3518,plain,
! [X0] :
( star(X0) != one
| leq(multiplication(star(X0),X0),one) ),
inference(paramodulation,[status(thm)],[f588,f42]) ).
fof(f3519,plain,
! [X0,X1] : addition(multiplication(star(X0),X0),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f588,f20]) ).
fof(f3523,plain,
! [X0] :
( leq(X0,strong_iteration(star(X0)))
| ~ leq(X0,star(X0)) ),
inference(forward_demodulation,[status(thm)],[f24,f3478]) ).
fof(f3524,plain,
! [X0] :
( leq(star(star(X0)),X0)
| ~ leq(star(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f3480]) ).
fof(f3527,plain,
! [X0,X1] : leq(multiplication(star(X0),multiplication(X0,X1)),multiplication(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f3488]) ).
fof(f3528,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,one)
| leq(multiplication(X0,multiplication(star(X1),X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f3489]) ).
fof(f3529,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != X0
| leq(multiplication(X0,multiplication(star(X1),X1)),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f3528]) ).
fof(f3532,plain,
! [X0] : leq(multiplication(star(X0),multiplication(X0,zero)),star(X0)),
inference(forward_demodulation,[status(thm)],[f23,f3494]) ).
fof(f3536,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(star(X0),multiplication(star(X0),X0)) ),
inference(forward_demodulation,[status(thm)],[f30,f3505]) ).
fof(f3537,plain,
! [X0] :
( star(X0) != multiplication(star(X0),X0)
| leq(star(X0),multiplication(star(X0),X0)) ),
inference(forward_demodulation,[status(thm)],[f588,f3506]) ).
fof(f3538,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f30,f3507]) ).
fof(f3543,plain,
! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f588,f3516]) ).
fof(f3546,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one),
inference(paramodulation,[status(thm)],[f23,f589]) ).
fof(f3550,plain,
! [X0,X1] : addition(multiplication(X0,X1),star(X0)) = addition(multiplication(X0,addition(X1,star(X0))),one),
inference(paramodulation,[status(thm)],[f589,f116]) ).
fof(f3552,plain,
! [X0] :
( leq(multiplication(one,star(star(X0))),X0)
| ~ leq(star(X0),X0) ),
inference(paramodulation,[status(thm)],[f589,f34]) ).
fof(f3555,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(multiplication(X0,multiplication(X1,star(X1))),X0),
inference(paramodulation,[status(thm)],[f589,f114]) ).
fof(f3559,plain,
! [X0,X1,X2] : leq(multiplication(X0,star(X0)),addition(X1,addition(X2,star(X0)))),
inference(paramodulation,[status(thm)],[f589,f241]) ).
fof(f3561,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,star(X0)),X1),multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f589,f205]) ).
fof(f3562,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,one)
| leq(multiplication(X0,multiplication(X1,star(X1))),multiplication(X0,one)) ),
inference(paramodulation,[status(thm)],[f589,f115]) ).
fof(f3565,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,star(X1))),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f589,f176]) ).
fof(f3566,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(X0,star(X0)),addition(one,X1))),
inference(paramodulation,[status(thm)],[f589,f176]) ).
fof(f3567,plain,
! [X0] : leq(multiplication(multiplication(X0,star(X0)),zero),star(X0)),
inference(paramodulation,[status(thm)],[f589,f2307]) ).
fof(f3569,plain,
! [X0,X1] :
( addition(X0,star(X1)) != one
| leq(addition(X0,multiplication(X1,star(X1))),one) ),
inference(paramodulation,[status(thm)],[f589,f85]) ).
fof(f3570,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,star(X1))),multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f589,f174]) ).
fof(f3572,plain,
! [X0,X1] : leq(multiplication(X0,star(X0)),multiplication(strong_iteration(X1),star(X0))),
inference(paramodulation,[status(thm)],[f589,f873]) ).
fof(f3573,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,star(X0)),X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f589,f63]) ).
fof(f3575,plain,
! [X0,X1] : addition(multiplication(X0,star(X0)),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f589,f58]) ).
fof(f3576,plain,
! [X0,X1] : addition(X0,star(X1)) = addition(one,addition(X0,multiplication(X1,star(X1)))),
inference(paramodulation,[status(thm)],[f589,f58]) ).
fof(f3578,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(addition(one,multiplication(X0,star(X0))),multiplication(X0,star(X0))) ),
inference(paramodulation,[status(thm)],[f589,f343]) ).
fof(f3579,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(addition(multiplication(X0,star(X0)),one),multiplication(X0,star(X0))) ),
inference(paramodulation,[status(thm)],[f589,f158]) ).
fof(f3580,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = addition(one,multiplication(X0,star(X0))),
inference(paramodulation,[status(thm)],[f589,f457]) ).
fof(f3585,plain,
! [X0,X1] : leq(multiplication(X0,star(X0)),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f589,f237]) ).
fof(f3589,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = addition(multiplication(X0,star(X0)),one),
inference(paramodulation,[status(thm)],[f589,f65]) ).
fof(f3590,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(one,multiplication(X0,star(X0))) ),
inference(paramodulation,[status(thm)],[f589,f87]) ).
fof(f3591,plain,
! [X0] :
( star(X0) != one
| leq(multiplication(X0,star(X0)),one) ),
inference(paramodulation,[status(thm)],[f589,f42]) ).
fof(f3592,plain,
! [X0,X1] : addition(multiplication(X0,star(X0)),addition(one,X1)) = addition(star(X0),X1),
inference(paramodulation,[status(thm)],[f589,f20]) ).
fof(f3599,plain,
! [X0] :
( leq(star(star(X0)),X0)
| ~ leq(star(X0),X0) ),
inference(forward_demodulation,[status(thm)],[f25,f3552]) ).
fof(f3602,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(star(X0),X1)),multiplication(star(X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f3561]) ).
fof(f3603,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != multiplication(X0,one)
| leq(multiplication(X0,multiplication(X1,star(X1))),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f3562]) ).
fof(f3604,plain,
! [X0,X1] :
( multiplication(X0,star(X1)) != X0
| leq(multiplication(X0,multiplication(X1,star(X1))),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f3603]) ).
fof(f3607,plain,
! [X0] : leq(multiplication(X0,multiplication(star(X0),zero)),star(X0)),
inference(forward_demodulation,[status(thm)],[f23,f3567]) ).
fof(f3611,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(star(X0),multiplication(X0,star(X0))) ),
inference(forward_demodulation,[status(thm)],[f29,f3578]) ).
fof(f3612,plain,
! [X0] :
( star(X0) != multiplication(X0,star(X0))
| leq(star(X0),multiplication(X0,star(X0))) ),
inference(forward_demodulation,[status(thm)],[f589,f3579]) ).
fof(f3613,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f29,f3580]) ).
fof(f3618,plain,
! [X0] : addition(multiplication(X0,star(X0)),star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f589,f3589]) ).
fof(f3619,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f23,f791]) ).
fof(f3624,plain,
! [X0,X1] : multiplication(X0,strong_iteration(X1)) = addition(X0,multiplication(X0,multiplication(X1,strong_iteration(X1)))),
inference(paramodulation,[status(thm)],[f791,f110]) ).
fof(f3629,plain,
! [X0,X1,X2] : leq(multiplication(X0,strong_iteration(X0)),addition(X1,addition(X2,strong_iteration(X0)))),
inference(paramodulation,[status(thm)],[f791,f223]) ).
fof(f3631,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,multiplication(X1,strong_iteration(X1)))
| leq(multiplication(X0,one),multiplication(X0,multiplication(X1,strong_iteration(X1)))) ),
inference(paramodulation,[status(thm)],[f791,f115]) ).
fof(f3632,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,strong_iteration(X0)),X1),multiplication(strong_iteration(X0),X1)),
inference(paramodulation,[status(thm)],[f791,f204]) ).
fof(f3633,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,strong_iteration(X1))),multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f791,f183]) ).
fof(f3635,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(one,addition(multiplication(X0,strong_iteration(X0)),X1))),
inference(paramodulation,[status(thm)],[f791,f176]) ).
fof(f3637,plain,
! [X0] : leq(multiplication(multiplication(X0,strong_iteration(X0)),zero),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f791,f2042]) ).
fof(f3638,plain,
! [X0,X1] :
( addition(X0,strong_iteration(X1)) != multiplication(X1,strong_iteration(X1))
| leq(addition(X0,one),multiplication(X1,strong_iteration(X1))) ),
inference(paramodulation,[status(thm)],[f791,f85]) ).
fof(f3640,plain,
! [X0,X1] : leq(multiplication(X0,strong_iteration(X0)),multiplication(strong_iteration(X1),strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f791,f874]) ).
fof(f3642,plain,
! [X0,X1] : addition(multiplication(X0,strong_iteration(X0)),addition(one,X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f791,f63]) ).
fof(f3643,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(addition(multiplication(X0,strong_iteration(X0)),one),multiplication(X0,strong_iteration(X0))) ),
inference(paramodulation,[status(thm)],[f791,f580]) ).
fof(f3644,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,strong_iteration(X0)),X1)) = addition(X1,strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f791,f58]) ).
fof(f3645,plain,
! [X0,X1] : addition(X0,strong_iteration(X1)) = addition(multiplication(X1,strong_iteration(X1)),addition(X0,one)),
inference(paramodulation,[status(thm)],[f791,f58]) ).
fof(f3646,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(addition(one,multiplication(X0,strong_iteration(X0))),multiplication(X0,strong_iteration(X0))) ),
inference(paramodulation,[status(thm)],[f791,f475]) ).
fof(f3650,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f791,f182]) ).
fof(f3653,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(paramodulation,[status(thm)],[f791,f153]) ).
fof(f3655,plain,
! [X0,X1] : leq(multiplication(X0,strong_iteration(X0)),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f791,f185]) ).
fof(f3659,plain,
! [X0] :
( strong_iteration(X0) != one
| leq(multiplication(X0,strong_iteration(X0)),one) ),
inference(paramodulation,[status(thm)],[f791,f87]) ).
fof(f3660,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(one,multiplication(X0,strong_iteration(X0))) ),
inference(paramodulation,[status(thm)],[f791,f42]) ).
fof(f3661,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,strong_iteration(X0)),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f791,f20]) ).
fof(f3668,plain,
! [X0,X1] :
( multiplication(X0,strong_iteration(X1)) != multiplication(X0,multiplication(X1,strong_iteration(X1)))
| leq(X0,multiplication(X0,multiplication(X1,strong_iteration(X1)))) ),
inference(forward_demodulation,[status(thm)],[f24,f3631]) ).
fof(f3669,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(strong_iteration(X0),X1)),multiplication(strong_iteration(X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f3632]) ).
fof(f3671,plain,
! [X0] : leq(multiplication(X0,multiplication(strong_iteration(X0),zero)),strong_iteration(X0)),
inference(forward_demodulation,[status(thm)],[f23,f3637]) ).
fof(f3673,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(strong_iteration(X0),multiplication(X0,strong_iteration(X0))) ),
inference(forward_demodulation,[status(thm)],[f35,f3643]) ).
fof(f3674,plain,
! [X0] :
( strong_iteration(X0) != multiplication(X0,strong_iteration(X0))
| leq(strong_iteration(X0),multiplication(X0,strong_iteration(X0))) ),
inference(forward_demodulation,[status(thm)],[f791,f3646]) ).
fof(f3678,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f791,f3650]) ).
fof(f3681,plain,
! [X0] : addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f35,f3653]) ).
fof(f3683,plain,
! [X0,X1,X2] : leq(one,multiplication(strong_iteration(X0),addition(X1,strong_iteration(X2)))),
inference(resolution,[status(thm)],[f865,f37]) ).
fof(f3684,plain,
! [X0,X1,X2] : addition(one,addition(X0,addition(X1,strong_iteration(X2)))) = addition(X0,addition(X1,strong_iteration(X2))),
inference(resolution,[status(thm)],[f865,f41]) ).
fof(f3688,plain,
! [X0,X1,X2] : leq(one,multiplication(addition(X0,strong_iteration(X1)),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f865]) ).
fof(f3690,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,strong_iteration(X3))))),
inference(paramodulation,[status(thm)],[f63,f865]) ).
fof(f3691,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,strong_iteration(X3))))),
inference(paramodulation,[status(thm)],[f20,f865]) ).
fof(f3705,plain,
! [X0,X1,X2] : leq(one,addition(X0,multiplication(strong_iteration(X1),addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f865]) ).
fof(f3707,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,strong_iteration(X3))))),
inference(paramodulation,[status(thm)],[f63,f865]) ).
fof(f3708,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,strong_iteration(X3))))),
inference(paramodulation,[status(thm)],[f20,f865]) ).
fof(f3719,plain,
! [X0,X1] : addition(star(X0),multiplication(strong_iteration(X1),strong_iteration(X0))) = multiplication(strong_iteration(X1),strong_iteration(X0)),
inference(resolution,[status(thm)],[f1025,f41]) ).
fof(f3728,plain,
! [X0,X1,X2] : leq(one,multiplication(strong_iteration(X0),addition(strong_iteration(X1),X2))),
inference(resolution,[status(thm)],[f1106,f37]) ).
fof(f3729,plain,
! [X0,X1,X2] : addition(one,addition(X0,addition(strong_iteration(X1),X2))) = addition(X0,addition(strong_iteration(X1),X2)),
inference(resolution,[status(thm)],[f1106,f41]) ).
fof(f3732,plain,
! [X0,X1,X2] : leq(one,multiplication(addition(strong_iteration(X0),X1),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f1106]) ).
fof(f3734,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(strong_iteration(X2),X3)))),
inference(paramodulation,[status(thm)],[f63,f1106]) ).
fof(f3735,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(strong_iteration(X2),X3)))),
inference(paramodulation,[status(thm)],[f20,f1106]) ).
fof(f3749,plain,
! [X0,X1,X2] : leq(one,addition(X0,multiplication(strong_iteration(X1),addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f1106]) ).
fof(f3751,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,strong_iteration(X3))))),
inference(paramodulation,[status(thm)],[f58,f1106]) ).
fof(f3752,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(strong_iteration(X2),X3)))),
inference(paramodulation,[status(thm)],[f58,f1106]) ).
fof(f3766,plain,
! [X0,X1,X2] : leq(one,multiplication(strong_iteration(X0),addition(star(X1),X2))),
inference(resolution,[status(thm)],[f1107,f37]) ).
fof(f3767,plain,
! [X0,X1,X2] : addition(one,addition(X0,addition(star(X1),X2))) = addition(X0,addition(star(X1),X2)),
inference(resolution,[status(thm)],[f1107,f41]) ).
fof(f3770,plain,
! [X0,X1,X2] : leq(one,multiplication(addition(star(X0),X1),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f1107]) ).
fof(f3772,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(star(X2),X3)))),
inference(paramodulation,[status(thm)],[f63,f1107]) ).
fof(f3773,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(star(X2),X3)))),
inference(paramodulation,[status(thm)],[f20,f1107]) ).
fof(f3787,plain,
! [X0,X1,X2] : leq(one,addition(X0,multiplication(star(X1),addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f1107]) ).
fof(f3789,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(X2,star(X3))))),
inference(paramodulation,[status(thm)],[f58,f1107]) ).
fof(f3790,plain,
! [X0,X1,X2,X3] : leq(one,addition(X0,addition(X1,addition(star(X2),X3)))),
inference(paramodulation,[status(thm)],[f58,f1107]) ).
fof(f3803,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X2,X0))) = addition(X1,addition(X2,X0)),
inference(resolution,[status(thm)],[f1129,f41]) ).
fof(f3808,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),zero),addition(X1,star(X0)))),
inference(paramodulation,[status(thm)],[f38,f1129]) ).
fof(f3812,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(star(X0),X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f30,f1129]) ).
fof(f3813,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(X0,strong_iteration(X0)),addition(X1,one))),
inference(paramodulation,[status(thm)],[f791,f1129]) ).
fof(f3814,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(X0,star(X0)),addition(X1,one))),
inference(paramodulation,[status(thm)],[f29,f1129]) ).
fof(f3815,plain,
! [X0,X1] : leq(star(X0),addition(one,addition(X1,multiplication(star(X0),X0)))),
inference(paramodulation,[status(thm)],[f588,f1129]) ).
fof(f3816,plain,
! [X0,X1] : leq(star(X0),addition(one,addition(X1,multiplication(X0,star(X0))))),
inference(paramodulation,[status(thm)],[f589,f1129]) ).
fof(f3818,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(one,addition(X1,multiplication(X0,strong_iteration(X0))))),
inference(paramodulation,[status(thm)],[f35,f1129]) ).
fof(f3819,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(addition(multiplication(X0,X2),X3),addition(X4,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f116,f1129]) ).
fof(f3820,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X1),addition(X3,multiplication(X0,X2)))),
inference(paramodulation,[status(thm)],[f104,f1129]) ).
fof(f3821,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),addition(X3,multiplication(X0,X2)))),
inference(paramodulation,[status(thm)],[f27,f1129]) ).
fof(f3822,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),addition(X3,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f26,f1129]) ).
fof(f3823,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,one)),addition(X0,addition(X2,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f114,f1129]) ).
fof(f3825,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X3,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f63,f1129]) ).
fof(f3826,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X3,addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f20,f1129]) ).
fof(f3828,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(one,X1)),addition(multiplication(X0,X1),addition(X2,X0))),
inference(paramodulation,[status(thm)],[f110,f1129]) ).
fof(f3830,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(addition(X0,X1),addition(X3,X2))),
inference(paramodulation,[status(thm)],[f58,f1129]) ).
fof(f3831,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(addition(X2,X0),addition(X3,X1))),
inference(paramodulation,[status(thm)],[f58,f1129]) ).
fof(f3833,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(addition(X0,X1),addition(X2,X1))),
inference(paramodulation,[status(thm)],[f182,f1129]) ).
fof(f3841,plain,
! [X0,X1] : leq(addition(X0,multiplication(addition(X1,X0),zero)),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1913,f1129]) ).
fof(f3842,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(multiplication(X1,addition(X2,X3)),X0)),
inference(paramodulation,[status(thm)],[f116,f1129]) ).
fof(f3843,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(addition(X1,X0),X2)),multiplication(addition(X1,X0),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f1129]) ).
fof(f3845,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f63,f1129]) ).
fof(f3846,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f20,f1129]) ).
fof(f3857,plain,
! [X0,X1] : leq(addition(star(X0),X1),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f1021,f1129]) ).
fof(f3858,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f858,f1129]) ).
fof(f3860,plain,
! [X0,X1] : leq(addition(multiplication(strong_iteration(X0),zero),X1),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f38,f1129]) ).
fof(f3861,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f349,f1129]) ).
fof(f3864,plain,
! [X0,X1] : leq(addition(multiplication(star(X0),X0),X1),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f30,f1129]) ).
fof(f3865,plain,
! [X0,X1] : leq(addition(multiplication(X0,strong_iteration(X0)),X1),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f791,f1129]) ).
fof(f3866,plain,
! [X0,X1] : leq(addition(multiplication(X0,star(X0)),X1),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f29,f1129]) ).
fof(f3867,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f588,f1129]) ).
fof(f3868,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f589,f1129]) ).
fof(f3870,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f35,f1129]) ).
fof(f3871,plain,
! [X0,X1,X2,X3,X4] : leq(addition(addition(multiplication(X0,X1),X2),X3),addition(X3,addition(multiplication(X0,addition(X4,X1)),X2))),
inference(paramodulation,[status(thm)],[f116,f1129]) ).
fof(f3872,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f104,f1129]) ).
fof(f3873,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f27,f1129]) ).
fof(f3874,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f26,f1129]) ).
fof(f3875,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,multiplication(X0,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f1129]) ).
fof(f3877,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f63,f1129]) ).
fof(f3878,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f20,f1129]) ).
fof(f3879,plain,
! [X0,X1] : leq(addition(multiplication(X0,zero),X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f2007,f1129]) ).
fof(f3880,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(X0,addition(one,X1)))),
inference(paramodulation,[status(thm)],[f110,f1129]) ).
fof(f3882,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f58,f1129]) ).
fof(f3883,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X2,addition(X1,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f58,f1129]) ).
fof(f3884,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f457,f1129]) ).
fof(f3885,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f182,f1129]) ).
fof(f3886,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X2,addition(X1,X0))),
inference(paramodulation,[status(thm)],[f153,f1129]) ).
fof(f3887,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),X2),addition(X2,addition(X0,X1))),
inference(paramodulation,[status(thm)],[f65,f1129]) ).
fof(f3889,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f19,f1129]) ).
fof(f3890,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,X2))),
inference(paramodulation,[status(thm)],[f19,f1129]) ).
fof(f3892,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X2,X1)))) = addition(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f63,f3803]) ).
fof(f3895,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(X3,addition(multiplication(X0,X2),addition(X4,multiplication(X0,X1))))),
inference(forward_demodulation,[status(thm)],[f63,f3819]) ).
fof(f3898,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,addition(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f3830]) ).
fof(f3899,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,addition(X3,X1)))),
inference(forward_demodulation,[status(thm)],[f63,f3831]) ).
fof(f3902,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X0,addition(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f63,f3833]) ).
fof(f3916,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,addition(multiplication(X1,X2),X3)),addition(X3,addition(multiplication(X1,addition(X4,X2)),X0))),
inference(forward_demodulation,[status(thm)],[f63,f3871]) ).
fof(f3919,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,addition(X0,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f3882]) ).
fof(f3920,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,addition(X3,X1)))),
inference(forward_demodulation,[status(thm)],[f63,f3883]) ).
fof(f3921,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f63,f3884]) ).
fof(f3922,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(forward_demodulation,[status(thm)],[f63,f3885]) ).
fof(f3923,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f63,f3886]) ).
fof(f3924,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,X0))),
inference(forward_demodulation,[status(thm)],[f63,f3887]) ).
fof(f3928,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f27,f192]) ).
fof(f3930,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(multiplication(X0,X1),addition(X1,one)),
inference(paramodulation,[status(thm)],[f114,f192]) ).
fof(f3932,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(multiplication(X0,X1),addition(one,X1)),
inference(paramodulation,[status(thm)],[f110,f192]) ).
fof(f3936,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f23,f192]) ).
fof(f3938,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f192]) ).
fof(f3939,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(addition(X1,multiplication(X1,X2)),multiplication(X0,addition(one,X2))),
inference(paramodulation,[status(thm)],[f110,f192]) ).
fof(f3940,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(addition(multiplication(X1,X2),X1),multiplication(X0,addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f192]) ).
fof(f3942,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f23,f192]) ).
fof(f3944,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f192]) ).
fof(f3945,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(multiplication(X1,addition(one,X2)),addition(X0,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f110,f192]) ).
fof(f3946,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(multiplication(X1,addition(X2,one)),addition(multiplication(X0,X2),X0)),
inference(paramodulation,[status(thm)],[f114,f192]) ).
fof(f3950,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f192,f27]) ).
fof(f3952,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,X0),X3)) = addition(multiplication(X0,addition(X1,X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f192,f116]) ).
fof(f3953,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(X1,one)) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(paramodulation,[status(thm)],[f192,f114]) ).
fof(f3954,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X2),multiplication(X1,X0)))
| ~ leq(X0,multiplication(addition(X1,X2),X0)) ),
inference(paramodulation,[status(thm)],[f192,f37]) ).
fof(f3955,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,X2),star(X2)),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f192,f34]) ).
fof(f3956,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,X2)),X2)
| ~ leq(multiplication(addition(X0,X1),X2),X2) ),
inference(paramodulation,[status(thm)],[f192,f32]) ).
fof(f3958,plain,
! [X0,X1] : multiplication(multiplication(X0,X1),addition(one,X1)) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(paramodulation,[status(thm)],[f192,f110]) ).
fof(f3959,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f192,f1129]) ).
fof(f3960,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),addition(X3,multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f192,f1129]) ).
fof(f3961,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),addition(X3,multiplication(addition(X0,X2),X1))),
inference(paramodulation,[status(thm)],[f192,f339]) ).
fof(f3962,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(X3,addition(multiplication(X0,X2),multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f192,f339]) ).
fof(f3963,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(addition(X4,X0),X1)))),
inference(paramodulation,[status(thm)],[f192,f241]) ).
fof(f3964,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(addition(X0,X4),X1)))),
inference(paramodulation,[status(thm)],[f192,f223]) ).
fof(f3966,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X3,X1),X2)) != multiplication(X0,multiplication(X3,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(paramodulation,[status(thm)],[f192,f115]) ).
fof(f3968,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X1,X3),X2))),
inference(paramodulation,[status(thm)],[f192,f183]) ).
fof(f3969,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(addition(X3,X1),X2))),
inference(paramodulation,[status(thm)],[f192,f176]) ).
fof(f3970,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),addition(multiplication(X0,X2),X3))),
inference(paramodulation,[status(thm)],[f192,f176]) ).
fof(f3971,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f192,f2307]) ).
fof(f3972,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),zero),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f192,f2042]) ).
fof(f3973,plain,
! [X0,X1,X2,X3] :
( addition(X0,multiplication(addition(X3,X1),X2)) != multiplication(X3,X2)
| leq(addition(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f192,f85]) ).
fof(f3974,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X3,X1),X2))),
inference(paramodulation,[status(thm)],[f192,f174]) ).
fof(f3975,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f192,f874]) ).
fof(f3976,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f192,f873]) ).
fof(f3977,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),X3),
inference(paramodulation,[status(thm)],[f192,f63]) ).
fof(f3978,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f192,f580]) ).
fof(f3979,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(X3,multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f192,f58]) ).
fof(f3980,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(X1,X3),addition(X0,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f192,f58]) ).
fof(f3981,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f192,f475]) ).
fof(f3982,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f192,f343]) ).
fof(f3983,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f192,f158]) ).
fof(f3986,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),multiplication(addition(X0,X2),X1)),
inference(paramodulation,[status(thm)],[f192,f340]) ).
fof(f3987,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f192,f340]) ).
fof(f3989,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f192,f237]) ).
fof(f3990,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f192,f185]) ).
fof(f3994,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X2),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f192,f87]) ).
fof(f3995,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f192,f42]) ).
fof(f3996,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X2,X0),X1),X3),
inference(paramodulation,[status(thm)],[f192,f20]) ).
fof(f4002,plain,
! [X0,X1] : multiplication(addition(X0,multiplication(X0,X1)),X1) = multiplication(X0,multiplication(X1,addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f23,f3930]) ).
fof(f4003,plain,
! [X0,X1] : multiplication(addition(multiplication(X0,X1),X0),X1) = multiplication(X0,multiplication(X1,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f23,f3932]) ).
fof(f4005,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(one,X2)) = addition(multiplication(X1,X2),addition(X1,multiplication(X0,addition(one,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f3939]) ).
fof(f4006,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),addition(X2,one)) = addition(X1,addition(multiplication(X1,X2),multiplication(X0,addition(X2,one)))),
inference(forward_demodulation,[status(thm)],[f63,f3940]) ).
fof(f4014,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(X1,one))) = multiplication(addition(X0,multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f23,f3953]) ).
fof(f4015,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X2,star(X2))),X1)
| ~ leq(multiplication(addition(X0,X1),X2),X1) ),
inference(forward_demodulation,[status(thm)],[f23,f3955]) ).
fof(f4016,plain,
! [X0,X1] : multiplication(X0,multiplication(X1,addition(one,X1))) = multiplication(addition(multiplication(X0,X1),X0),X1),
inference(forward_demodulation,[status(thm)],[f23,f3958]) ).
fof(f4017,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(X3,multiplication(addition(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f192,f3961]) ).
fof(f4018,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(X3,multiplication(addition(X1,X0),X2))),
inference(forward_demodulation,[status(thm)],[f192,f3962]) ).
fof(f4023,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(addition(X2,X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f3971]) ).
fof(f4024,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(addition(X0,X2),X1)),
inference(forward_demodulation,[status(thm)],[f23,f3972]) ).
fof(f4025,plain,
! [X0,X1,X2] :
( multiplication(addition(X1,X0),X2) != multiplication(X1,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f192,f3978]) ).
fof(f4026,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X1),X2) != multiplication(X0,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f192,f3981]) ).
fof(f4027,plain,
! [X0,X1,X2] :
( multiplication(addition(X1,X0),X2) != multiplication(X0,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f192,f3982]) ).
fof(f4028,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,X1),X2) != multiplication(X1,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f192,f3983]) ).
fof(f4035,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f192,f3986]) ).
fof(f4036,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,X1),X2),multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f192,f3987]) ).
fof(f4043,plain,
! [X0,X1,X2] : addition(addition(X0,X1),addition(X1,addition(X0,X2))) = addition(X1,addition(X0,X2)),
inference(resolution,[status(thm)],[f1609,f41]) ).
fof(f4048,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(strong_iteration(X0),zero),addition(star(X0),X1))),
inference(paramodulation,[status(thm)],[f38,f1609]) ).
fof(f4052,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(star(X0),X0),addition(one,X1))),
inference(paramodulation,[status(thm)],[f30,f1609]) ).
fof(f4053,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(X0,strong_iteration(X0)),addition(one,X1))),
inference(paramodulation,[status(thm)],[f791,f1609]) ).
fof(f4054,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(X0,star(X0)),addition(one,X1))),
inference(paramodulation,[status(thm)],[f29,f1609]) ).
fof(f4055,plain,
! [X0,X1] : leq(star(X0),addition(one,addition(multiplication(star(X0),X0),X1))),
inference(paramodulation,[status(thm)],[f588,f1609]) ).
fof(f4056,plain,
! [X0,X1] : leq(star(X0),addition(one,addition(multiplication(X0,star(X0)),X1))),
inference(paramodulation,[status(thm)],[f589,f1609]) ).
fof(f4058,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(one,addition(multiplication(X0,strong_iteration(X0)),X1))),
inference(paramodulation,[status(thm)],[f35,f1609]) ).
fof(f4059,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(addition(multiplication(X0,X2),X3),addition(multiplication(X0,X1),X4))),
inference(paramodulation,[status(thm)],[f116,f1609]) ).
fof(f4060,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),addition(multiplication(X1,X2),X3))),
inference(paramodulation,[status(thm)],[f192,f1609]) ).
fof(f4062,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),addition(multiplication(X0,X2),X3))),
inference(paramodulation,[status(thm)],[f27,f1609]) ).
fof(f4063,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),addition(multiplication(X0,X1),X3))),
inference(paramodulation,[status(thm)],[f26,f1609]) ).
fof(f4064,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,one)),addition(X0,addition(multiplication(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f114,f1609]) ).
fof(f4066,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(addition(X1,X0),X3))),
inference(paramodulation,[status(thm)],[f63,f1609]) ).
fof(f4067,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(addition(X0,X1),X3))),
inference(paramodulation,[status(thm)],[f20,f1609]) ).
fof(f4069,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(one,X1)),addition(multiplication(X0,X1),addition(X0,X2))),
inference(paramodulation,[status(thm)],[f110,f1609]) ).
fof(f4071,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(addition(X0,X1),addition(X2,X3))),
inference(paramodulation,[status(thm)],[f58,f1609]) ).
fof(f4072,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(addition(X2,X0),addition(X1,X3))),
inference(paramodulation,[status(thm)],[f58,f1609]) ).
fof(f4073,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(addition(X1,X0),addition(X1,X2))),
inference(paramodulation,[status(thm)],[f457,f1609]) ).
fof(f4082,plain,
! [X0,X1] : leq(addition(X0,multiplication(addition(X0,X1),zero)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1913,f1609]) ).
fof(f4084,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(addition(X0,X1),X2)),multiplication(addition(X0,X1),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f1609]) ).
fof(f4086,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f63,f1609]) ).
fof(f4087,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f20,f1609]) ).
fof(f4088,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f58,f1609]) ).
fof(f4100,plain,
! [X0,X1] : leq(addition(star(X0),X1),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f829,f1609]) ).
fof(f4101,plain,
! [X0,X1] : leq(addition(star(X0),X1),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f38,f1609]) ).
fof(f4103,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f822,f1609]) ).
fof(f4104,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f269,f1609]) ).
fof(f4105,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f30,f1609]) ).
fof(f4106,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f791,f1609]) ).
fof(f4107,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f29,f1609]) ).
fof(f4108,plain,
! [X0,X1] : leq(addition(multiplication(star(X0),X0),X1),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f588,f1609]) ).
fof(f4109,plain,
! [X0,X1] : leq(addition(multiplication(X0,star(X0)),X1),addition(X1,star(X0))),
inference(paramodulation,[status(thm)],[f589,f1609]) ).
fof(f4110,plain,
! [X0,X1] : leq(addition(multiplication(X0,zero),X1),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f1913,f1609]) ).
fof(f4111,plain,
! [X0,X1] : leq(addition(multiplication(X0,strong_iteration(X0)),X1),addition(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f35,f1609]) ).
fof(f4112,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),addition(X2,addition(multiplication(X0,addition(X1,X3)),X4))),
inference(paramodulation,[status(thm)],[f116,f1609]) ).
fof(f4113,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(addition(X3,X0),X1))),
inference(paramodulation,[status(thm)],[f192,f1609]) ).
fof(f4114,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(X0,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f104,f1609]) ).
fof(f4115,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(addition(X0,X3),X1))),
inference(paramodulation,[status(thm)],[f27,f1609]) ).
fof(f4116,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f26,f1609]) ).
fof(f4117,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(X0,addition(X1,one)))),
inference(paramodulation,[status(thm)],[f114,f1609]) ).
fof(f4119,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X2,addition(X1,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f63,f1609]) ).
fof(f4120,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X2,addition(X0,addition(X1,X3)))),
inference(paramodulation,[status(thm)],[f20,f1609]) ).
fof(f4122,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,multiplication(X0,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f1609]) ).
fof(f4124,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X1,addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f58,f1609]) ).
fof(f4125,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X1,addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f58,f1609]) ).
fof(f4134,plain,
! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,addition(X1,X2)))) = addition(X0,addition(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f4043]) ).
fof(f4137,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(X3,addition(multiplication(X0,X2),addition(multiplication(X0,X1),X4)))),
inference(forward_demodulation,[status(thm)],[f63,f4059]) ).
fof(f4138,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(X3,addition(multiplication(X0,addition(X2,X1)),X4))),
inference(forward_demodulation,[status(thm)],[f116,f4137]) ).
fof(f4140,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,addition(X2,X1)),X3)),
inference(forward_demodulation,[status(thm)],[f116,f4063]) ).
fof(f4142,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,addition(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f4066]) ).
fof(f4143,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,addition(X0,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f4067]) ).
fof(f4145,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,addition(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f4071]) ).
fof(f4146,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,addition(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f4072]) ).
fof(f4147,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X1,addition(X1,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4073]) ).
fof(f4148,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X2,X1))),
inference(forward_demodulation,[status(thm)],[f457,f4147]) ).
fof(f4166,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X0,addition(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f4119]) ).
fof(f4167,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X1,addition(X0,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f4120]) ).
fof(f4169,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f104,f195]) ).
fof(f4170,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X0),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f26,f195]) ).
fof(f4171,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(multiplication(X0,X1),X2),X0),X1) = multiplication(multiplication(X0,X1),addition(multiplication(X2,X1),one)),
inference(paramodulation,[status(thm)],[f114,f195]) ).
fof(f4173,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)),
inference(paramodulation,[status(thm)],[f110,f195]) ).
fof(f4174,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f19,f195]) ).
fof(f4175,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f19,f195]) ).
fof(f4176,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(multiplication(X0,X1),X2),X3),X4) = addition(multiplication(X0,multiplication(X1,multiplication(X2,X4))),multiplication(X3,X4)),
inference(paramodulation,[status(thm)],[f23,f195]) ).
fof(f4179,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,multiplication(X1,X2)),X3),X4) = addition(multiplication(X0,multiplication(X1,multiplication(X2,X4))),multiplication(X3,X4)),
inference(paramodulation,[status(thm)],[f23,f195]) ).
fof(f4180,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,zero),X1),X2) = addition(multiplication(X0,zero),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f28,f195]) ).
fof(f4182,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(one,X3)) = addition(multiplication(X0,addition(X1,multiplication(X1,X3))),multiplication(X2,addition(one,X3))),
inference(paramodulation,[status(thm)],[f110,f195]) ).
fof(f4183,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,one)) = addition(multiplication(X0,addition(multiplication(X1,X3),X1)),multiplication(X2,addition(X3,one))),
inference(paramodulation,[status(thm)],[f114,f195]) ).
fof(f4185,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),multiplication(X2,X3)),X4) = addition(multiplication(X0,multiplication(X1,X4)),multiplication(X2,multiplication(X3,X4))),
inference(paramodulation,[status(thm)],[f23,f195]) ).
fof(f4187,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f25,f195]) ).
fof(f4188,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(one,X3)) = addition(multiplication(X0,multiplication(X1,addition(one,X3))),addition(X2,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f110,f195]) ).
fof(f4189,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),addition(X3,one)) = addition(multiplication(X0,multiplication(X1,addition(X3,one))),addition(multiplication(X2,X3),X2)),
inference(paramodulation,[status(thm)],[f114,f195]) ).
fof(f4191,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(multiplication(X0,X2),X0),X1),
inference(paramodulation,[status(thm)],[f195,f104]) ).
fof(f4192,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,X2),X2)) = multiplication(addition(multiplication(X0,X1),X0),X2),
inference(paramodulation,[status(thm)],[f195,f26]) ).
fof(f4193,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(addition(multiplication(X0,X2),X3),X4)) = addition(multiplication(X0,addition(X1,multiplication(X2,X4))),multiplication(X3,X4)),
inference(paramodulation,[status(thm)],[f195,f116]) ).
fof(f4194,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(multiplication(X2,X1),one)) = multiplication(addition(multiplication(multiplication(X0,X1),X2),X0),X1),
inference(paramodulation,[status(thm)],[f195,f114]) ).
fof(f4195,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(X3,X1)))
| ~ leq(multiplication(X0,X1),multiplication(addition(multiplication(X2,X0),X3),X1)) ),
inference(paramodulation,[status(thm)],[f195,f37]) ).
fof(f4196,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X2,X3),star(multiplication(X1,X3))),X0)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),X0) ),
inference(paramodulation,[status(thm)],[f195,f34]) ).
fof(f4197,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X2,X3)),multiplication(X1,X3))
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(X1,X3)) ),
inference(paramodulation,[status(thm)],[f195,f32]) ).
fof(f4199,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(paramodulation,[status(thm)],[f195,f110]) ).
fof(f4200,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,multiplication(X1,X2)),X3),addition(X3,multiplication(addition(multiplication(X0,X1),X4),X2))),
inference(paramodulation,[status(thm)],[f195,f1609]) ).
fof(f4201,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),addition(multiplication(X2,X3),addition(multiplication(X0,multiplication(X1,X3)),X4))),
inference(paramodulation,[status(thm)],[f195,f1609]) ).
fof(f4202,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(addition(multiplication(X3,X4),X0),X1))),
inference(paramodulation,[status(thm)],[f195,f1129]) ).
fof(f4203,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),addition(multiplication(X2,X3),addition(X4,multiplication(X0,multiplication(X1,X3))))),
inference(paramodulation,[status(thm)],[f195,f1129]) ).
fof(f4204,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),addition(X4,multiplication(addition(multiplication(X2,X3),X0),X1))),
inference(paramodulation,[status(thm)],[f195,f339]) ).
fof(f4205,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),addition(X4,addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))))),
inference(paramodulation,[status(thm)],[f195,f339]) ).
fof(f4206,plain,
! [X0,X1,X2,X3,X4,X5] : leq(multiplication(X0,multiplication(X1,X2)),addition(X3,addition(X4,multiplication(addition(multiplication(X0,X1),X5),X2)))),
inference(paramodulation,[status(thm)],[f195,f241]) ).
fof(f4207,plain,
! [X0,X1,X2,X3,X4,X5] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(addition(multiplication(X4,X5),X0),X1)))),
inference(paramodulation,[status(thm)],[f195,f223]) ).
fof(f4208,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(multiplication(X0,multiplication(X1,X2)),X3),multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3)),
inference(paramodulation,[status(thm)],[f195,f205]) ).
fof(f4209,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(X0,multiplication(addition(multiplication(X1,X2),X4),X3)) != multiplication(X0,multiplication(X4,X3))
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X0,multiplication(X4,X3))) ),
inference(paramodulation,[status(thm)],[f195,f115]) ).
fof(f4211,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(multiplication(X3,X4),X1),X2))),
inference(paramodulation,[status(thm)],[f195,f183]) ).
fof(f4212,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,multiplication(X1,multiplication(X2,X3))),addition(X0,multiplication(addition(multiplication(X1,X2),X4),X3))),
inference(paramodulation,[status(thm)],[f195,f176]) ).
fof(f4213,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),addition(multiplication(X0,multiplication(X1,X3)),addition(multiplication(X2,X3),X4))),
inference(paramodulation,[status(thm)],[f195,f176]) ).
fof(f4214,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,multiplication(X1,X2)),zero),multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f195,f2307]) ).
fof(f4215,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),zero),multiplication(addition(multiplication(X2,X3),X0),X1)),
inference(paramodulation,[status(thm)],[f195,f2042]) ).
fof(f4216,plain,
! [X0,X1,X2,X3,X4] :
( addition(X0,multiplication(addition(multiplication(X1,X2),X4),X3)) != multiplication(X4,X3)
| leq(addition(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X4,X3)) ),
inference(paramodulation,[status(thm)],[f195,f85]) ).
fof(f4217,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X0,multiplication(addition(multiplication(X1,X2),X4),X3))),
inference(paramodulation,[status(thm)],[f195,f174]) ).
fof(f4218,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(addition(multiplication(X3,X4),X0),X1))),
inference(paramodulation,[status(thm)],[f195,f874]) ).
fof(f4219,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(strong_iteration(X3),multiplication(addition(multiplication(X0,X1),X4),X2))),
inference(paramodulation,[status(thm)],[f195,f873]) ).
fof(f4220,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),X4)) = addition(multiplication(addition(multiplication(X2,X3),X0),X1),X4),
inference(paramodulation,[status(thm)],[f195,f63]) ).
fof(f4221,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X2,X3),X0),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f195,f580]) ).
fof(f4222,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) = addition(X4,multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f195,f58]) ).
fof(f4223,plain,
! [X0,X1,X2,X3,X4] : addition(X0,multiplication(addition(multiplication(X1,X2),X3),X4)) = addition(multiplication(X3,X4),addition(X0,multiplication(X1,multiplication(X2,X4)))),
inference(paramodulation,[status(thm)],[f195,f58]) ).
fof(f4224,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X0,X1),X3),X2) != multiplication(X3,X2)
| leq(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f195,f475]) ).
fof(f4225,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X2,X3),X0),X1) != multiplication(X2,multiplication(X3,X1))
| leq(addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),multiplication(X2,multiplication(X3,X1))) ),
inference(paramodulation,[status(thm)],[f195,f343]) ).
fof(f4226,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X0,X1),X3),X2) != multiplication(X0,multiplication(X1,X2))
| leq(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),multiplication(X0,multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f195,f158]) ).
fof(f4227,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X1),X3),X2)) = addition(multiplication(X3,X2),multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f195,f457]) ).
fof(f4229,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),multiplication(addition(multiplication(X2,X3),X0),X1)),
inference(paramodulation,[status(thm)],[f195,f340]) ).
fof(f4230,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3)))),
inference(paramodulation,[status(thm)],[f195,f340]) ).
fof(f4231,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(multiplication(X2,X3),X0),X1)) = addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f195,f153]) ).
fof(f4232,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),addition(X3,multiplication(addition(multiplication(X0,X1),X4),X2))),
inference(paramodulation,[status(thm)],[f195,f237]) ).
fof(f4233,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(multiplication(X3,X4),X0),X1))),
inference(paramodulation,[status(thm)],[f195,f185]) ).
fof(f4235,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(paramodulation,[status(thm)],[f195,f145]) ).
fof(f4237,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X2,X3),X0),X1) != multiplication(X2,multiplication(X3,X1))
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))) ),
inference(paramodulation,[status(thm)],[f195,f87]) ).
fof(f4238,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X0,X1),X3),X2) != multiplication(X3,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f195,f42]) ).
fof(f4239,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(multiplication(X0,X1),X3),X2),X4),
inference(paramodulation,[status(thm)],[f195,f20]) ).
fof(f4240,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))) = multiplication(addition(multiplication(X2,X3),X0),X1),
inference(paramodulation,[status(thm)],[f195,f19]) ).
fof(f4241,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f195,f19]) ).
fof(f4242,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,multiplication(X1,X2)),X0),X1) = multiplication(multiplication(X0,X1),addition(multiplication(X2,X1),one)),
inference(forward_demodulation,[status(thm)],[f23,f4171]) ).
fof(f4243,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,multiplication(X1,X2)),X0),X1) = multiplication(X0,multiplication(X1,addition(multiplication(X2,X1),one))),
inference(forward_demodulation,[status(thm)],[f23,f4242]) ).
fof(f4246,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(multiplication(X1,X2),X1)),X2) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)),
inference(forward_demodulation,[status(thm)],[f104,f4173]) ).
fof(f4247,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(multiplication(X1,X2),X1),X2)) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(one,X2)),
inference(forward_demodulation,[status(thm)],[f23,f4246]) ).
fof(f4248,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(multiplication(X1,X2),X1),X2)) = multiplication(X0,multiplication(multiplication(X1,X2),addition(one,X2))),
inference(forward_demodulation,[status(thm)],[f23,f4247]) ).
fof(f4249,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(multiplication(X1,X2),X1),X2)) = multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))),
inference(forward_demodulation,[status(thm)],[f23,f4248]) ).
fof(f4250,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,multiplication(X1,X2)),X3),X4) = addition(multiplication(X0,multiplication(X1,multiplication(X2,X4))),multiplication(X3,X4)),
inference(forward_demodulation,[status(thm)],[f23,f4176]) ).
fof(f4259,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(multiplication(X2,X1),one))) = multiplication(addition(multiplication(multiplication(X0,X1),X2),X0),X1),
inference(forward_demodulation,[status(thm)],[f23,f4194]) ).
fof(f4260,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(multiplication(X2,X1),one))) = multiplication(addition(multiplication(X0,multiplication(X1,X2)),X0),X1),
inference(forward_demodulation,[status(thm)],[f23,f4259]) ).
fof(f4261,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X2,multiplication(X3,star(multiplication(X1,X3)))),X0)
| ~ leq(multiplication(addition(multiplication(X0,X1),X2),X3),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f4196]) ).
fof(f4264,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(multiplication(X1,X2),addition(one,X2))) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(forward_demodulation,[status(thm)],[f23,f4199]) ).
fof(f4265,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))) = multiplication(addition(multiplication(X0,X1),multiplication(X0,multiplication(X1,X2))),X2),
inference(forward_demodulation,[status(thm)],[f23,f4264]) ).
fof(f4266,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))) = multiplication(multiplication(X0,addition(multiplication(X1,X2),X1)),X2),
inference(forward_demodulation,[status(thm)],[f104,f4265]) ).
fof(f4267,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(one,X2)))) = multiplication(X0,multiplication(addition(multiplication(X1,X2),X1),X2)),
inference(forward_demodulation,[status(thm)],[f23,f4266]) ).
fof(f4268,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(multiplication(X1,X2),X3)),multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3)),
inference(forward_demodulation,[status(thm)],[f23,f4208]) ).
fof(f4269,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3)),
inference(forward_demodulation,[status(thm)],[f23,f4268]) ).
fof(f4270,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(addition(multiplication(X0,X1),X4),multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f23,f4269]) ).
fof(f4273,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(multiplication(X1,X2),zero)),multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(forward_demodulation,[status(thm)],[f23,f4214]) ).
fof(f4274,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,multiplication(X2,zero))),multiplication(addition(multiplication(X0,X1),X3),X2)),
inference(forward_demodulation,[status(thm)],[f23,f4273]) ).
fof(f4275,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(addition(multiplication(X2,X3),X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f4215]) ).
fof(f4276,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X0,X1),X2),X3) != multiplication(X2,X3)
| leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f195,f4224]) ).
fof(f4277,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(multiplication(X0,X1),X2),X3) != multiplication(X0,multiplication(X1,X3))
| leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(X0,multiplication(X1,X3))) ),
inference(forward_demodulation,[status(thm)],[f195,f4226]) ).
fof(f4278,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(multiplication(X0,X1),X2)),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f195,f4227]) ).
fof(f4279,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,X1)),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f116,f4278]) ).
fof(f4280,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f22,f4279]) ).
fof(f4284,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(multiplication(X0,X1),X2),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f192,f4231]) ).
fof(f4285,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(multiplication(X1,X2),X0)),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f63,f4284]) ).
fof(f4286,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f182,f4285]) ).
fof(f4291,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X1),strong_iteration(one))),
inference(paramodulation,[status(thm)],[f23,f1783]) ).
fof(f4294,plain,
! [X0,X1] : leq(addition(X0,multiplication(X0,X1)),multiplication(X0,strong_iteration(one))),
inference(paramodulation,[status(thm)],[f110,f1783]) ).
fof(f4295,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X0),multiplication(X0,strong_iteration(one))),
inference(paramodulation,[status(thm)],[f114,f1783]) ).
fof(f4297,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,X1),X2),multiplication(X0,multiplication(X1,strong_iteration(one)))),
inference(paramodulation,[status(thm)],[f23,f1783]) ).
fof(f4301,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,strong_iteration(one)))),
inference(forward_demodulation,[status(thm)],[f23,f4291]) ).
fof(f4304,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X1,strong_iteration(one)))),
inference(forward_demodulation,[status(thm)],[f23,f4297]) ).
fof(f4309,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(X1,multiplication(strong_iteration(X0),X1)),
inference(paramodulation,[status(thm)],[f822,f197]) ).
fof(f4310,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),X1)),
inference(paramodulation,[status(thm)],[f269,f197]) ).
fof(f4311,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(star(X0),X0),X1)),
inference(paramodulation,[status(thm)],[f30,f197]) ).
fof(f4312,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(X1,multiplication(multiplication(X0,strong_iteration(X0)),X1)),
inference(paramodulation,[status(thm)],[f791,f197]) ).
fof(f4313,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(multiplication(X0,star(X0)),X1)),
inference(paramodulation,[status(thm)],[f29,f197]) ).
fof(f4315,plain,
! [X0] : multiplication(strong_iteration(one),X0) = addition(X0,multiplication(strong_iteration(one),X0)),
inference(paramodulation,[status(thm)],[f982,f197]) ).
fof(f4316,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f58,f197]) ).
fof(f4317,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(paramodulation,[status(thm)],[f58,f197]) ).
fof(f4318,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f457,f197]) ).
fof(f4319,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f182,f197]) ).
fof(f4320,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f153,f197]) ).
fof(f4321,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f65,f197]) ).
fof(f4323,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f197]) ).
fof(f4324,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f197]) ).
fof(f4326,plain,
! [X0] : multiplication(addition(one,X0),strong_iteration(one)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f1237,f197]) ).
fof(f4327,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f104,f197]) ).
fof(f4328,plain,
! [X0,X1] : multiplication(addition(one,X0),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f26,f197]) ).
fof(f4329,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X2,addition(X1,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f63,f197]) ).
fof(f4330,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(X1,addition(X2,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f20,f197]) ).
fof(f4332,plain,
! [X0] : multiplication(addition(one,X0),X0) = multiplication(X0,addition(one,X0)),
inference(paramodulation,[status(thm)],[f110,f197]) ).
fof(f4333,plain,
! [X0,X1] : multiplication(addition(one,addition(one,X0)),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f197,f197]) ).
fof(f4334,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f23,f197]) ).
fof(f4337,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(addition(one,X1),addition(X0,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f110,f197]) ).
fof(f4338,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(addition(X1,one),addition(multiplication(X0,X1),X0)),
inference(paramodulation,[status(thm)],[f114,f197]) ).
fof(f4344,plain,
! [X0,X1] : leq(addition(zero,multiplication(X0,zero)),addition(X1,addition(one,X0))),
inference(paramodulation,[status(thm)],[f197,f2042]) ).
fof(f4345,plain,
! [X0] : addition(addition(one,X0),addition(zero,multiplication(X0,zero))) = addition(one,X0),
inference(paramodulation,[status(thm)],[f197,f2007]) ).
fof(f4346,plain,
! [X0] : addition(addition(zero,multiplication(X0,zero)),addition(one,X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f197,f1913]) ).
fof(f4348,plain,
! [X0,X1] : leq(addition(zero,multiplication(X0,zero)),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f197,f1780]) ).
fof(f4350,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(one,X1),strong_iteration(one))),
inference(paramodulation,[status(thm)],[f197,f1783]) ).
fof(f4351,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(one,X2)),X3) = addition(multiplication(X0,multiplication(X1,X3)),addition(X3,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f197,f195]) ).
fof(f4352,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(one,X1)),X2),X3) = addition(multiplication(X0,addition(X3,multiplication(X1,X3))),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f197,f195]) ).
fof(f4353,plain,
! [X0,X1,X2] : multiplication(addition(addition(one,X0),X1),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f197,f192]) ).
fof(f4354,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(addition(X2,multiplication(X1,X2)),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f197,f192]) ).
fof(f4355,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,X0),X1),addition(addition(X2,multiplication(X0,X2)),X3)) = addition(multiplication(addition(one,X0),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f197,f116]) ).
fof(f4356,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X1,X0)),addition(multiplication(addition(one,X1),X2),X3)) = addition(multiplication(addition(one,X1),addition(X0,X2)),X3),
inference(paramodulation,[status(thm)],[f197,f116]) ).
fof(f4357,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(addition(one,X1),X2),X0)),
inference(paramodulation,[status(thm)],[f197,f205]) ).
fof(f4358,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(X2,addition(one,X1)),X0)),
inference(paramodulation,[status(thm)],[f197,f204]) ).
fof(f4359,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(one,X1),addition(X2,X0))),
inference(paramodulation,[status(thm)],[f197,f183]) ).
fof(f4360,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(addition(X1,multiplication(X0,X1)),addition(one,X0)),
inference(paramodulation,[status(thm)],[f197,f114]) ).
fof(f4361,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(addition(one,X0),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f197,f110]) ).
fof(f4362,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(multiplication(addition(one,X0),X2),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f197,f104]) ).
fof(f4363,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(addition(X2,multiplication(X0,X2)),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f197,f104]) ).
fof(f4364,plain,
! [X0,X1] : leq(multiplication(addition(one,X0),zero),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f197,f1780]) ).
fof(f4365,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(one,X1),addition(X0,X2))),
inference(paramodulation,[status(thm)],[f197,f174]) ).
fof(f4366,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(addition(one,X1)),X2))
| ~ leq(X0,addition(addition(X0,multiplication(X1,X0)),X2)) ),
inference(paramodulation,[status(thm)],[f197,f37]) ).
fof(f4367,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X0)),addition(one,X1))
| ~ leq(addition(addition(X0,multiplication(X1,X0)),X2),addition(one,X1)) ),
inference(paramodulation,[status(thm)],[f197,f34]) ).
fof(f4368,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(one,X1)),X2),X0)
| ~ leq(addition(addition(X0,multiplication(X1,X0)),X2),X0) ),
inference(paramodulation,[status(thm)],[f197,f32]) ).
fof(f4369,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f197,f27]) ).
fof(f4370,plain,
! [X0,X1,X2] : multiplication(addition(addition(one,X0),X1),X2) = addition(addition(X2,multiplication(X0,X2)),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f197,f27]) ).
fof(f4371,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(multiplication(addition(one,X0),X1),addition(X2,multiplication(X0,X2))),
inference(paramodulation,[status(thm)],[f197,f26]) ).
fof(f4372,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(addition(X1,multiplication(X0,X1)),multiplication(addition(one,X0),X2)),
inference(paramodulation,[status(thm)],[f197,f26]) ).
fof(f4373,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f197,f23]) ).
fof(f4374,plain,
! [X0] : multiplication(addition(one,X0),strong_iteration(one)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f197,f1237]) ).
fof(f4375,plain,
! [X0,X1,X2] : leq(one,addition(X0,multiplication(addition(one,X1),strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f197,f1106]) ).
fof(f4376,plain,
! [X0,X1] : leq(star(X0),multiplication(addition(one,X1),strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f197,f1032]) ).
fof(f4377,plain,
! [X0,X1] : leq(one,multiplication(addition(one,X0),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f197,f866]) ).
fof(f4378,plain,
! [X0,X1,X2] : leq(one,addition(X0,multiplication(addition(one,X1),star(X2)))),
inference(paramodulation,[status(thm)],[f197,f1107]) ).
fof(f4379,plain,
! [X0,X1] : leq(one,multiplication(addition(one,X0),star(X1))),
inference(paramodulation,[status(thm)],[f197,f278]) ).
fof(f4380,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X0,X1),X1)) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f197,f104]) ).
fof(f4381,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(one,X0),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f197,f26]) ).
fof(f4382,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(one,X2),multiplication(X0,X3))) = addition(multiplication(X0,addition(X1,X3)),multiplication(X2,multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f197,f116]) ).
fof(f4383,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(X2),multiplication(X1,multiplication(X2,X0))))
| ~ leq(X0,multiplication(addition(one,X1),multiplication(X2,X0))) ),
inference(paramodulation,[status(thm)],[f197,f37]) ).
fof(f4384,plain,
! [X0,X1,X2] :
( leq(multiplication(multiplication(X0,multiplication(X1,X2)),star(X2)),X1)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X1) ),
inference(paramodulation,[status(thm)],[f197,f34]) ).
fof(f4385,plain,
! [X0,X1,X2] :
( leq(multiplication(star(X1),multiplication(X0,multiplication(X1,X2))),X2)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f197,f32]) ).
fof(f4386,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X1,X0)))) = multiplication(addition(one,X2),addition(X1,X0)),
inference(paramodulation,[status(thm)],[f197,f63]) ).
fof(f4387,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X0,X1)))) = multiplication(addition(one,X2),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f197,f20]) ).
fof(f4388,plain,
! [X0] : multiplication(X0,addition(one,X0)) = multiplication(addition(one,X0),X0),
inference(paramodulation,[status(thm)],[f197,f110]) ).
fof(f4389,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,multiplication(addition(one,X2),X0))),
inference(paramodulation,[status(thm)],[f197,f1609]) ).
fof(f4390,plain,
! [X0,X1,X2] : leq(multiplication(addition(one,X0),X1),addition(multiplication(X0,X1),addition(X1,X2))),
inference(paramodulation,[status(thm)],[f197,f1609]) ).
fof(f4391,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(addition(one,X0),X1))),
inference(paramodulation,[status(thm)],[f197,f1129]) ).
fof(f4392,plain,
! [X0,X1,X2] : leq(multiplication(addition(one,X0),X1),addition(multiplication(X0,X1),addition(X2,X1))),
inference(paramodulation,[status(thm)],[f197,f1129]) ).
fof(f4393,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X1),addition(X2,multiplication(addition(one,X0),X1))),
inference(paramodulation,[status(thm)],[f197,f339]) ).
fof(f4394,plain,
! [X0,X1,X2] : leq(multiplication(addition(one,X0),X1),addition(X2,addition(multiplication(X0,X1),X1))),
inference(paramodulation,[status(thm)],[f197,f339]) ).
fof(f4395,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,multiplication(addition(one,X3),X0)))),
inference(paramodulation,[status(thm)],[f197,f241]) ).
fof(f4396,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(addition(one,X0),X1)))),
inference(paramodulation,[status(thm)],[f197,f223]) ).
fof(f4398,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(one,X2),X1)) != multiplication(X0,multiplication(X2,X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(paramodulation,[status(thm)],[f197,f115]) ).
fof(f4400,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(one,X1),X2))),
inference(paramodulation,[status(thm)],[f197,f183]) ).
fof(f4401,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,multiplication(addition(one,X2),X1))),
inference(paramodulation,[status(thm)],[f197,f176]) ).
fof(f4402,plain,
! [X0,X1,X2] : leq(multiplication(addition(one,X0),X1),addition(X1,addition(multiplication(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f197,f176]) ).
fof(f4403,plain,
! [X0,X1] : leq(multiplication(X0,zero),multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f197,f2307]) ).
fof(f4404,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,X1),zero),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f197,f2042]) ).
fof(f4405,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(addition(one,X2),X1)) != multiplication(X2,X1)
| leq(addition(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f197,f85]) ).
fof(f4406,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(addition(one,X2),X1))),
inference(paramodulation,[status(thm)],[f197,f174]) ).
fof(f4407,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(addition(one,X0),X1))),
inference(paramodulation,[status(thm)],[f197,f874]) ).
fof(f4408,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(X1),multiplication(addition(one,X2),X0))),
inference(paramodulation,[status(thm)],[f197,f873]) ).
fof(f4409,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(one,X0),X1),X2),
inference(paramodulation,[status(thm)],[f197,f63]) ).
fof(f4410,plain,
! [X0,X1] :
( multiplication(addition(one,X0),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),X1),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f197,f580]) ).
fof(f4411,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(X2,multiplication(addition(one,X1),X0)),
inference(paramodulation,[status(thm)],[f197,f58]) ).
fof(f4412,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(one,X1),X2)) = addition(multiplication(X1,X2),addition(X0,X2)),
inference(paramodulation,[status(thm)],[f197,f58]) ).
fof(f4413,plain,
! [X0,X1] :
( multiplication(addition(one,X1),X0) != multiplication(X1,X0)
| leq(addition(X0,multiplication(X1,X0)),multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f197,f475]) ).
fof(f4414,plain,
! [X0,X1] :
( multiplication(addition(one,X0),X1) != X1
| leq(addition(multiplication(X0,X1),X1),X1) ),
inference(paramodulation,[status(thm)],[f197,f343]) ).
fof(f4415,plain,
! [X0,X1] :
( multiplication(addition(one,X1),X0) != X0
| leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(paramodulation,[status(thm)],[f197,f158]) ).
fof(f4416,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f197,f457]) ).
fof(f4418,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f197,f340]) ).
fof(f4419,plain,
! [X0,X1] : leq(multiplication(addition(one,X0),X1),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f197,f340]) ).
fof(f4420,plain,
! [X0,X1] : addition(multiplication(X0,X1),multiplication(addition(one,X0),X1)) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f197,f153]) ).
fof(f4421,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(one,X2),X0))),
inference(paramodulation,[status(thm)],[f197,f237]) ).
fof(f4422,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(one,X0),X1))),
inference(paramodulation,[status(thm)],[f197,f185]) ).
fof(f4425,plain,
! [X0,X1] : addition(X0,multiplication(addition(one,X1),X0)) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f197,f65]) ).
fof(f4426,plain,
! [X0,X1] :
( multiplication(addition(one,X0),X1) != X1
| leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f197,f87]) ).
fof(f4427,plain,
! [X0,X1] :
( multiplication(addition(one,X1),X0) != multiplication(X1,X0)
| leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f197,f42]) ).
fof(f4428,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(one,X1),X0),X2),
inference(paramodulation,[status(thm)],[f197,f20]) ).
fof(f4429,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f23,f4311]) ).
fof(f4430,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(X1,multiplication(X0,multiplication(strong_iteration(X0),X1))),
inference(forward_demodulation,[status(thm)],[f23,f4312]) ).
fof(f4431,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(X0,multiplication(star(X0),X1))),
inference(forward_demodulation,[status(thm)],[f23,f4313]) ).
fof(f4440,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,addition(X1,multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f457,f4333]) ).
fof(f4441,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f457,f4440]) ).
fof(f4446,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(X1,addition(one,addition(X0,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f63,f4337]) ).
fof(f4447,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(one,addition(X1,addition(multiplication(X0,X1),X0))),
inference(forward_demodulation,[status(thm)],[f63,f4338]) ).
fof(f4453,plain,
! [X0,X1] : leq(multiplication(X0,zero),addition(X1,addition(one,X0))),
inference(forward_demodulation,[status(thm)],[f49,f4344]) ).
fof(f4454,plain,
! [X0] : addition(X0,addition(one,addition(zero,multiplication(X0,zero)))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f63,f4345]) ).
fof(f4455,plain,
! [X0] : addition(X0,addition(one,multiplication(X0,zero))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f49,f4454]) ).
fof(f4456,plain,
! [X0] : addition(multiplication(X0,zero),addition(zero,addition(one,X0))) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f63,f4346]) ).
fof(f4457,plain,
! [X0] : addition(multiplication(X0,zero),addition(one,X0)) = addition(one,X0),
inference(forward_demodulation,[status(thm)],[f49,f4456]) ).
fof(f4459,plain,
! [X0,X1] : leq(multiplication(X0,zero),multiplication(addition(one,X0),X1)),
inference(forward_demodulation,[status(thm)],[f49,f4348]) ).
fof(f4460,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f63,f4353]) ).
fof(f4461,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X1,X2),addition(X2,multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f63,f4354]) ).
fof(f4462,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(one,X0),X1),addition(multiplication(X0,X2),addition(X2,X3))) = addition(multiplication(addition(one,X0),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f63,f4355]) ).
fof(f4463,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X1,addition(multiplication(addition(one,X0),X2),X3))) = addition(multiplication(addition(one,X0),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f63,f4356]) ).
fof(f4464,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(X1,addition(one,X2)),X0)),
inference(forward_demodulation,[status(thm)],[f63,f4357]) ).
fof(f4465,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(X1,one)) = addition(multiplication(X0,X1),addition(X1,addition(one,X0))),
inference(forward_demodulation,[status(thm)],[f63,f4360]) ).
fof(f4466,plain,
! [X0,X1] : multiplication(addition(one,X0),addition(one,X1)) = addition(X0,addition(one,addition(X1,multiplication(X0,X1)))),
inference(forward_demodulation,[status(thm)],[f63,f4361]) ).
fof(f4467,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(multiplication(X0,X2),addition(X2,multiplication(addition(one,X0),X1))),
inference(forward_demodulation,[status(thm)],[f63,f4363]) ).
fof(f4468,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(addition(one,X1)),X2))
| ~ leq(X0,addition(multiplication(X1,X0),addition(X0,X2))) ),
inference(forward_demodulation,[status(thm)],[f63,f4366]) ).
fof(f4469,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(addition(one,X1)),X2)),
inference(forward_subsumption_resolution,[status(thm)],[f4468,f237]) ).
fof(f4470,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),addition(one,X0))
| ~ leq(addition(multiplication(X0,X1),addition(X1,X2)),addition(one,X0)) ),
inference(forward_demodulation,[status(thm)],[f63,f4367]) ).
fof(f4471,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(one,X0)),X2),X1)
| ~ leq(addition(multiplication(X0,X1),addition(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f63,f4368]) ).
fof(f4472,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(addition(X2,multiplication(X0,X2)),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f4370]) ).
fof(f4473,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(one,X1)),X2) = addition(multiplication(X0,X2),addition(X2,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f63,f4472]) ).
fof(f4474,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),addition(X1,X2)) = addition(multiplication(X0,X1),addition(X1,multiplication(addition(one,X0),X2))),
inference(forward_demodulation,[status(thm)],[f63,f4372]) ).
fof(f4475,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(multiplication(X1,X2),star(X2))),X1)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f23,f4384]) ).
fof(f4476,plain,
! [X0,X1,X2] :
( leq(multiplication(X0,multiplication(X1,multiplication(X2,star(X2)))),X1)
| ~ leq(multiplication(addition(one,X0),multiplication(X1,X2)),X1) ),
inference(forward_demodulation,[status(thm)],[f23,f4475]) ).
fof(f4480,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(addition(one,X0),X1)),
inference(forward_demodulation,[status(thm)],[f23,f4404]) ).
fof(f4484,plain,
! [X0,X1] : multiplication(addition(addition(one,X0),X0),X1) = addition(multiplication(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f192,f4420]) ).
fof(f4485,plain,
! [X0,X1] : multiplication(addition(X0,addition(one,X0)),X1) = addition(multiplication(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f63,f4484]) ).
fof(f4486,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(multiplication(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f182,f4485]) ).
fof(f4487,plain,
! [X0,X1] : addition(multiplication(X0,zero),multiplication(strong_iteration(X1),X0)) = multiplication(strong_iteration(X1),X0),
inference(resolution,[status(thm)],[f2029,f41]) ).
fof(f4488,plain,
! [X0,X1] : leq(addition(zero,multiplication(X0,zero)),multiplication(strong_iteration(X1),addition(one,X0))),
inference(paramodulation,[status(thm)],[f197,f2029]) ).
fof(f4489,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(strong_iteration(X2),multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f23,f2029]) ).
fof(f4494,plain,
! [X0,X1] : leq(multiplication(X0,zero),multiplication(strong_iteration(X1),addition(one,X0))),
inference(forward_demodulation,[status(thm)],[f49,f4488]) ).
fof(f4499,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f104,f199]) ).
fof(f4500,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,X1)),X2) = multiplication(X0,addition(X2,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f26,f199]) ).
fof(f4501,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)),X2) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)),
inference(paramodulation,[status(thm)],[f114,f199]) ).
fof(f4502,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,X0)),X2) = multiplication(addition(one,X1),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f197,f199]) ).
fof(f4503,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1) = multiplication(multiplication(X0,X1),addition(one,multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f110,f199]) ).
fof(f4504,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f19,f199]) ).
fof(f4505,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f19,f199]) ).
fof(f4506,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(one,X0),multiplication(X1,X2)),X3) = addition(addition(X3,multiplication(X0,X3)),multiplication(X1,multiplication(X2,X3))),
inference(paramodulation,[status(thm)],[f197,f199]) ).
fof(f4507,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),multiplication(X2,X3)),X4) = addition(multiplication(X0,multiplication(X1,X4)),multiplication(X2,multiplication(X3,X4))),
inference(paramodulation,[status(thm)],[f23,f199]) ).
fof(f4509,plain,
! [X0,X1,X2] : multiplication(addition(one,multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f25,f199]) ).
fof(f4510,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(one,X3)) = addition(addition(X0,multiplication(X0,X3)),multiplication(X1,multiplication(X2,addition(one,X3)))),
inference(paramodulation,[status(thm)],[f110,f199]) ).
fof(f4511,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,one)) = addition(addition(multiplication(X0,X3),X0),multiplication(X1,multiplication(X2,addition(X3,one)))),
inference(paramodulation,[status(thm)],[f114,f199]) ).
fof(f4513,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,multiplication(multiplication(X1,X2),X3)),X4) = addition(multiplication(X0,X4),multiplication(X1,multiplication(X2,multiplication(X3,X4)))),
inference(paramodulation,[status(thm)],[f23,f199]) ).
fof(f4516,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(one,X2))),X3) = addition(multiplication(X0,X3),multiplication(X1,addition(X3,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f197,f199]) ).
fof(f4517,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,multiplication(X1,multiplication(X2,X3))),X4) = addition(multiplication(X0,X4),multiplication(X1,multiplication(X2,multiplication(X3,X4)))),
inference(paramodulation,[status(thm)],[f23,f199]) ).
fof(f4518,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X1,zero)),X2) = addition(multiplication(X0,X2),multiplication(X1,zero)),
inference(paramodulation,[status(thm)],[f28,f199]) ).
fof(f4520,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(one,X3)) = addition(multiplication(X0,addition(one,X3)),multiplication(X1,addition(X2,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f110,f199]) ).
fof(f4521,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,one)) = addition(multiplication(X0,addition(X3,one)),multiplication(X1,addition(multiplication(X2,X3),X2))),
inference(paramodulation,[status(thm)],[f114,f199]) ).
fof(f4524,plain,
! [X0,X1,X2] : multiplication(X0,addition(multiplication(X1,X2),X2)) = multiplication(addition(X0,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f199,f104]) ).
fof(f4525,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(X0,X2)),X1),
inference(paramodulation,[status(thm)],[f199,f26]) ).
fof(f4526,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(addition(X0,multiplication(X2,X3)),X4)) = addition(multiplication(X0,addition(X1,X4)),multiplication(X2,multiplication(X3,X4))),
inference(paramodulation,[status(thm)],[f199,f116]) ).
fof(f4527,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)) = multiplication(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f199,f114]) ).
fof(f4528,plain,
! [X0,X1,X2,X3] :
( leq(X0,multiplication(strong_iteration(X1),multiplication(X2,multiplication(X3,X0))))
| ~ leq(X0,multiplication(addition(X1,multiplication(X2,X3)),X0)) ),
inference(paramodulation,[status(thm)],[f199,f37]) ).
fof(f4529,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(multiplication(X1,multiplication(X2,X3)),star(X3)),X0)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X0) ),
inference(paramodulation,[status(thm)],[f199,f34]) ).
fof(f4530,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),multiplication(X1,multiplication(X2,X3))),X3)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X3) ),
inference(paramodulation,[status(thm)],[f199,f32]) ).
fof(f4531,plain,
! [X0,X1,X2] : multiplication(addition(one,X0),multiplication(X1,X2)) = multiplication(addition(X1,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f199,f197]) ).
fof(f4532,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,X1),addition(one,multiplication(X2,X1))) = multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1),
inference(paramodulation,[status(thm)],[f199,f110]) ).
fof(f4533,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(addition(X0,multiplication(X3,X4)),X1))),
inference(paramodulation,[status(thm)],[f199,f1609]) ).
fof(f4534,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),addition(multiplication(X1,multiplication(X2,X3)),addition(multiplication(X0,X3),X4))),
inference(paramodulation,[status(thm)],[f199,f1609]) ).
fof(f4535,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,multiplication(X1,X2)),X3),addition(X3,multiplication(addition(X4,multiplication(X0,X1)),X2))),
inference(paramodulation,[status(thm)],[f199,f1129]) ).
fof(f4536,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),addition(multiplication(X1,multiplication(X2,X3)),addition(X4,multiplication(X0,X3)))),
inference(paramodulation,[status(thm)],[f199,f1129]) ).
fof(f4537,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),addition(X4,multiplication(addition(X3,multiplication(X0,X1)),X2))),
inference(paramodulation,[status(thm)],[f199,f339]) ).
fof(f4538,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),addition(X4,addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)))),
inference(paramodulation,[status(thm)],[f199,f339]) ).
fof(f4539,plain,
! [X0,X1,X2,X3,X4,X5] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(addition(X0,multiplication(X4,X5)),X1)))),
inference(paramodulation,[status(thm)],[f199,f241]) ).
fof(f4540,plain,
! [X0,X1,X2,X3,X4,X5] : leq(multiplication(X0,multiplication(X1,X2)),addition(X3,addition(X4,multiplication(addition(X5,multiplication(X0,X1)),X2)))),
inference(paramodulation,[status(thm)],[f199,f223]) ).
fof(f4542,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(X0,multiplication(addition(X1,multiplication(X3,X4)),X2)) != multiplication(X0,multiplication(X3,multiplication(X4,X2)))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,multiplication(X4,X2)))) ),
inference(paramodulation,[status(thm)],[f199,f115]) ).
fof(f4543,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(multiplication(X0,multiplication(X1,X2)),X3),multiplication(multiplication(addition(X4,multiplication(X0,X1)),X2),X3)),
inference(paramodulation,[status(thm)],[f199,f204]) ).
fof(f4544,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X0,multiplication(addition(X4,multiplication(X1,X2)),X3))),
inference(paramodulation,[status(thm)],[f199,f183]) ).
fof(f4545,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(addition(X1,multiplication(X3,X4)),X2))),
inference(paramodulation,[status(thm)],[f199,f176]) ).
fof(f4546,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),addition(multiplication(X0,X3),addition(multiplication(X1,multiplication(X2,X3)),X4))),
inference(paramodulation,[status(thm)],[f199,f176]) ).
fof(f4547,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),zero),multiplication(addition(X0,multiplication(X2,X3)),X1)),
inference(paramodulation,[status(thm)],[f199,f2307]) ).
fof(f4548,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,multiplication(X1,X2)),zero),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f199,f2042]) ).
fof(f4549,plain,
! [X0,X1,X2,X3,X4] :
( addition(X0,multiplication(addition(X1,multiplication(X3,X4)),X2)) != multiplication(X3,multiplication(X4,X2))
| leq(addition(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,X2))) ),
inference(paramodulation,[status(thm)],[f199,f85]) ).
fof(f4550,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X1,multiplication(X3,X4)),X2))),
inference(paramodulation,[status(thm)],[f199,f174]) ).
fof(f4551,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(strong_iteration(X3),multiplication(addition(X4,multiplication(X0,X1)),X2))),
inference(paramodulation,[status(thm)],[f199,f874]) ).
fof(f4552,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(addition(X0,multiplication(X3,X4)),X1))),
inference(paramodulation,[status(thm)],[f199,f873]) ).
fof(f4553,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(X3,multiplication(X0,X1)),X2),X4),
inference(paramodulation,[status(thm)],[f199,f63]) ).
fof(f4554,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,multiplication(X0,X1)),X2) != multiplication(X0,multiplication(X1,X2))
| leq(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),multiplication(X0,multiplication(X1,X2))) ),
inference(paramodulation,[status(thm)],[f199,f580]) ).
fof(f4555,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),X4)) = addition(X4,multiplication(addition(X0,multiplication(X2,X3)),X1)),
inference(paramodulation,[status(thm)],[f199,f58]) ).
fof(f4556,plain,
! [X0,X1,X2,X3,X4] : addition(X0,multiplication(addition(X1,multiplication(X2,X3)),X4)) = addition(multiplication(X2,multiplication(X3,X4)),addition(X0,multiplication(X1,X4))),
inference(paramodulation,[status(thm)],[f199,f58]) ).
fof(f4557,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X0,multiplication(X2,X3)),X1) != multiplication(X2,multiplication(X3,X1))
| leq(addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),multiplication(X2,multiplication(X3,X1))) ),
inference(paramodulation,[status(thm)],[f199,f475]) ).
fof(f4558,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,multiplication(X0,X1)),X2) != multiplication(X3,X2)
| leq(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f199,f343]) ).
fof(f4559,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X0,multiplication(X2,X3)),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f199,f158]) ).
fof(f4562,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f199,f340]) ).
fof(f4563,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3))),
inference(paramodulation,[status(thm)],[f199,f340]) ).
fof(f4564,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(addition(X3,multiplication(X0,X1)),X2)) = addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)),
inference(paramodulation,[status(thm)],[f199,f153]) ).
fof(f4565,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,multiplication(X3,X4)),X1))),
inference(paramodulation,[status(thm)],[f199,f237]) ).
fof(f4566,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),addition(X3,multiplication(addition(X4,multiplication(X0,X1)),X2))),
inference(paramodulation,[status(thm)],[f199,f185]) ).
fof(f4567,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f199,f179]) ).
fof(f4569,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X0,multiplication(X2,X3)),X1)) = addition(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f199,f65]) ).
fof(f4570,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,multiplication(X0,X1)),X2) != multiplication(X3,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f199,f87]) ).
fof(f4571,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X0,multiplication(X2,X3)),X1) != multiplication(X2,multiplication(X3,X1))
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X3,X1))) ),
inference(paramodulation,[status(thm)],[f199,f42]) ).
fof(f4572,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),X4)) = addition(multiplication(addition(X0,multiplication(X2,X3)),X1),X4),
inference(paramodulation,[status(thm)],[f199,f20]) ).
fof(f4573,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,multiplication(X1,X2)),multiplication(X3,X2)) = multiplication(addition(X3,multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f199,f19]) ).
fof(f4574,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(paramodulation,[status(thm)],[f199,f19]) ).
fof(f4577,plain,
! [X0,X1,X2] : multiplication(multiplication(X0,addition(X1,multiplication(X1,X2))),X2) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)),
inference(forward_demodulation,[status(thm)],[f104,f4501]) ).
fof(f4578,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(multiplication(X0,multiplication(X1,X2)),addition(X2,one)),
inference(forward_demodulation,[status(thm)],[f23,f4577]) ).
fof(f4579,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(X0,multiplication(multiplication(X1,X2),addition(X2,one))),
inference(forward_demodulation,[status(thm)],[f23,f4578]) ).
fof(f4580,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)) = multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))),
inference(forward_demodulation,[status(thm)],[f23,f4579]) ).
fof(f4581,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1) = multiplication(multiplication(X0,X1),addition(one,multiplication(X2,X1))),
inference(forward_demodulation,[status(thm)],[f23,f4503]) ).
fof(f4582,plain,
! [X0,X1,X2] : multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1) = multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))),
inference(forward_demodulation,[status(thm)],[f23,f4581]) ).
fof(f4583,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(one,multiplication(X1,X2))),X3) = addition(addition(X3,multiplication(X0,X3)),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f63,f4506]) ).
fof(f4584,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(one,multiplication(X1,X2))),X3) = addition(multiplication(X0,X3),addition(X3,multiplication(X1,multiplication(X2,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f4583]) ).
fof(f4587,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(one,X3)) = addition(multiplication(X0,X3),addition(X0,multiplication(X1,multiplication(X2,addition(one,X3))))),
inference(forward_demodulation,[status(thm)],[f63,f4510]) ).
fof(f4588,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),addition(X3,one)) = addition(X0,addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,addition(X3,one))))),
inference(forward_demodulation,[status(thm)],[f63,f4511]) ).
fof(f4590,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(X0,multiplication(X1,multiplication(X2,X3))),X4) = addition(multiplication(X0,X4),multiplication(X1,multiplication(X2,multiplication(X3,X4)))),
inference(forward_demodulation,[status(thm)],[f23,f4513]) ).
fof(f4598,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(multiplication(X1,X2),addition(X2,one))) = multiplication(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f23,f4527]) ).
fof(f4599,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))) = multiplication(addition(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f23,f4598]) ).
fof(f4600,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))) = multiplication(multiplication(X0,addition(X1,multiplication(X1,X2))),X2),
inference(forward_demodulation,[status(thm)],[f104,f4599]) ).
fof(f4601,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,multiplication(X2,addition(X2,one)))) = multiplication(X0,multiplication(addition(X1,multiplication(X1,X2)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f4600]) ).
fof(f4602,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(multiplication(X2,X3),star(X3))),X0)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f4529]) ).
fof(f4603,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(X1,multiplication(X2,multiplication(X3,star(X3)))),X0)
| ~ leq(multiplication(addition(X0,multiplication(X1,X2)),X3),X0) ),
inference(forward_demodulation,[status(thm)],[f23,f4602]) ).
fof(f4604,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))) = multiplication(addition(X0,multiplication(multiplication(X0,X1),X2)),X1),
inference(forward_demodulation,[status(thm)],[f23,f4532]) ).
fof(f4605,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,addition(one,multiplication(X2,X1)))) = multiplication(addition(X0,multiplication(X0,multiplication(X1,X2))),X1),
inference(forward_demodulation,[status(thm)],[f23,f4604]) ).
fof(f4606,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),addition(X4,multiplication(addition(X2,multiplication(X0,X1)),X3))),
inference(forward_demodulation,[status(thm)],[f195,f4537]) ).
fof(f4607,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),addition(X4,multiplication(addition(multiplication(X1,X2),X0),X3))),
inference(forward_demodulation,[status(thm)],[f195,f4538]) ).
fof(f4610,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(multiplication(X1,X2),X3)),multiplication(multiplication(addition(X4,multiplication(X0,X1)),X2),X3)),
inference(forward_demodulation,[status(thm)],[f23,f4543]) ).
fof(f4611,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(multiplication(addition(X4,multiplication(X0,X1)),X2),X3)),
inference(forward_demodulation,[status(thm)],[f23,f4610]) ).
fof(f4612,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(addition(X4,multiplication(X0,X1)),multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f23,f4611]) ).
fof(f4613,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(addition(X0,multiplication(X2,X3)),X1)),
inference(forward_demodulation,[status(thm)],[f23,f4547]) ).
fof(f4614,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(multiplication(X1,X2),zero)),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f4548]) ).
fof(f4615,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,multiplication(X2,zero))),multiplication(addition(X3,multiplication(X0,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f4614]) ).
fof(f4616,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X2,multiplication(X0,X1)),X3) != multiplication(X0,multiplication(X1,X3))
| leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(X0,multiplication(X1,X3))) ),
inference(forward_demodulation,[status(thm)],[f195,f4554]) ).
fof(f4617,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X0,multiplication(X1,X2)),X3) != multiplication(X1,multiplication(X2,X3))
| leq(multiplication(addition(X0,multiplication(X1,X2)),X3),multiplication(X1,multiplication(X2,X3))) ),
inference(forward_demodulation,[status(thm)],[f199,f4557]) ).
fof(f4618,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X2,multiplication(X0,X1)),X3) != multiplication(X2,X3)
| leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(X2,X3)) ),
inference(forward_demodulation,[status(thm)],[f195,f4558]) ).
fof(f4619,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X0,multiplication(X1,X2)),X3) != multiplication(X0,X3)
| leq(multiplication(addition(X0,multiplication(X1,X2)),X3),multiplication(X0,X3)) ),
inference(forward_demodulation,[status(thm)],[f199,f4559]) ).
fof(f4625,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(addition(X2,multiplication(X0,X1)),X3)),
inference(forward_demodulation,[status(thm)],[f195,f4562]) ).
fof(f4626,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),multiplication(addition(multiplication(X1,X2),X0),X3)),
inference(forward_demodulation,[status(thm)],[f195,f4563]) ).
fof(f4627,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,multiplication(X0,X1))),X3) = addition(multiplication(X0,multiplication(X1,X3)),multiplication(X2,X3)),
inference(forward_demodulation,[status(thm)],[f195,f4564]) ).
fof(f4628,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,X2)),X3) = addition(multiplication(X1,multiplication(X2,X3)),multiplication(X0,X3)),
inference(forward_demodulation,[status(thm)],[f182,f4627]) ).
fof(f4629,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,multiplication(X1,X2)),X0),X3) = addition(multiplication(X0,X3),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f192,f4569]) ).
fof(f4630,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,X2)),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f63,f4629]) ).
fof(f4631,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),X2),X3) = addition(multiplication(X2,X3),multiplication(X0,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f22,f4630]) ).
fof(f4632,plain,
! [X0,X1] : addition(addition(X0,one),addition(X0,strong_iteration(X1))) = addition(X0,strong_iteration(X1)),
inference(resolution,[status(thm)],[f2572,f41]) ).
fof(f4636,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(star(X0),X0),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f588,f2572]) ).
fof(f4637,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(X0,star(X0)),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f589,f2572]) ).
fof(f4639,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f35,f2572]) ).
fof(f4641,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(addition(X1,X0),strong_iteration(X2))),
inference(paramodulation,[status(thm)],[f63,f2572]) ).
fof(f4642,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(addition(X0,X1),strong_iteration(X2))),
inference(paramodulation,[status(thm)],[f20,f2572]) ).
fof(f4643,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f19,f2572]) ).
fof(f4644,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f19,f2572]) ).
fof(f4649,plain,
! [X0] : leq(addition(multiplication(strong_iteration(X0),zero),one),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f1913,f2572]) ).
fof(f4650,plain,
! [X0,X1] : leq(addition(multiplication(strong_iteration(X0),X1),one),multiplication(strong_iteration(X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f2572]) ).
fof(f4652,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),one),addition(X1,addition(X0,strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f63,f2572]) ).
fof(f4653,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),one),addition(X0,addition(X1,strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f20,f2572]) ).
fof(f4655,plain,
! [X0,X1] : leq(addition(X0,one),addition(strong_iteration(X1),X0)),
inference(paramodulation,[status(thm)],[f19,f2572]) ).
fof(f4656,plain,
! [X0,X1] : leq(addition(X0,one),addition(strong_iteration(X1),X0)),
inference(paramodulation,[status(thm)],[f19,f2572]) ).
fof(f4659,plain,
! [X0,X1] : addition(one,addition(X0,addition(X0,strong_iteration(X1)))) = addition(X0,strong_iteration(X1)),
inference(forward_demodulation,[status(thm)],[f63,f4632]) ).
fof(f4660,plain,
! [X0,X1] : addition(one,addition(strong_iteration(X0),X1)) = addition(X1,strong_iteration(X0)),
inference(forward_demodulation,[status(thm)],[f457,f4659]) ).
fof(f4665,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X0,addition(X1,strong_iteration(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4641]) ).
fof(f4666,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X1,addition(X0,strong_iteration(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4642]) ).
fof(f4672,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X0,addition(X1,strong_iteration(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4652]) ).
fof(f4673,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X1,addition(X0,strong_iteration(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4653]) ).
fof(f4675,plain,
! [X0,X1] : addition(addition(X0,one),addition(X0,star(X1))) = addition(X0,star(X1)),
inference(resolution,[status(thm)],[f2573,f41]) ).
fof(f4679,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(star(X0),X0),star(X1))),
inference(paramodulation,[status(thm)],[f588,f2573]) ).
fof(f4680,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(X0,star(X0)),star(X1))),
inference(paramodulation,[status(thm)],[f589,f2573]) ).
fof(f4682,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(X0,strong_iteration(X0)),star(X1))),
inference(paramodulation,[status(thm)],[f35,f2573]) ).
fof(f4684,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(addition(X1,X0),star(X2))),
inference(paramodulation,[status(thm)],[f63,f2573]) ).
fof(f4685,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(addition(X0,X1),star(X2))),
inference(paramodulation,[status(thm)],[f20,f2573]) ).
fof(f4686,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f19,f2573]) ).
fof(f4687,plain,
! [X0,X1] : leq(addition(one,X0),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f19,f2573]) ).
fof(f4692,plain,
! [X0] : leq(addition(multiplication(star(X0),zero),one),star(X0)),
inference(paramodulation,[status(thm)],[f1913,f2573]) ).
fof(f4693,plain,
! [X0,X1] : leq(addition(multiplication(star(X0),X1),one),multiplication(star(X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f2573]) ).
fof(f4695,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),one),addition(X1,addition(X0,star(X2)))),
inference(paramodulation,[status(thm)],[f63,f2573]) ).
fof(f4696,plain,
! [X0,X1,X2] : leq(addition(addition(X0,X1),one),addition(X0,addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f20,f2573]) ).
fof(f4697,plain,
! [X0,X1] : leq(addition(X0,one),addition(star(X1),X0)),
inference(paramodulation,[status(thm)],[f19,f2573]) ).
fof(f4698,plain,
! [X0,X1] : leq(addition(X0,one),addition(star(X1),X0)),
inference(paramodulation,[status(thm)],[f19,f2573]) ).
fof(f4701,plain,
! [X0,X1] : addition(one,addition(X0,addition(X0,star(X1)))) = addition(X0,star(X1)),
inference(forward_demodulation,[status(thm)],[f63,f4675]) ).
fof(f4702,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(forward_demodulation,[status(thm)],[f457,f4701]) ).
fof(f4707,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X0,addition(X1,star(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4684]) ).
fof(f4708,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X1,addition(X0,star(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4685]) ).
fof(f4714,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X0,addition(X1,star(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4695]) ).
fof(f4715,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X1,addition(X0,star(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4696]) ).
fof(f4720,plain,
! [X0] : multiplication(strong_iteration(one),X0) = addition(multiplication(strong_iteration(one),X0),X0),
inference(paramodulation,[status(thm)],[f1237,f201]) ).
fof(f4721,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(strong_iteration(X0),X1),X1),
inference(paramodulation,[status(thm)],[f858,f201]) ).
fof(f4722,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(multiplication(star(X0),X1),X1),
inference(paramodulation,[status(thm)],[f349,f201]) ).
fof(f4723,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(multiplication(multiplication(star(X0),X0),X1),X1),
inference(paramodulation,[status(thm)],[f588,f201]) ).
fof(f4724,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(multiplication(multiplication(X0,star(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f589,f201]) ).
fof(f4726,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(multiplication(X0,strong_iteration(X0)),X1),X1),
inference(paramodulation,[status(thm)],[f35,f201]) ).
fof(f4728,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(multiplication(addition(X1,X0),X2),X2),
inference(paramodulation,[status(thm)],[f63,f201]) ).
fof(f4729,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(multiplication(addition(X0,X1),X2),X2),
inference(paramodulation,[status(thm)],[f20,f201]) ).
fof(f4730,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f19,f201]) ).
fof(f4731,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f19,f201]) ).
fof(f4733,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(X1,X2)) = multiplication(addition(multiplication(X0,X1),X1),X2),
inference(paramodulation,[status(thm)],[f195,f201]) ).
fof(f4734,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(addition(multiplication(X0,X1),X2),X1)),X2),
inference(paramodulation,[status(thm)],[f116,f201]) ).
fof(f4735,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f104,f201]) ).
fof(f4736,plain,
! [X0,X1] : multiplication(addition(X0,one),multiplication(X0,X1)) = multiplication(X0,addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f26,f201]) ).
fof(f4738,plain,
! [X0] : multiplication(addition(X0,one),X0) = multiplication(X0,addition(X0,one)),
inference(paramodulation,[status(thm)],[f114,f201]) ).
fof(f4739,plain,
! [X0] : multiplication(addition(X0,one),strong_iteration(one)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f982,f201]) ).
fof(f4740,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X1,addition(X2,multiplication(X0,addition(X1,X2)))),
inference(paramodulation,[status(thm)],[f58,f201]) ).
fof(f4741,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X2,addition(multiplication(X0,addition(X1,X2)),X1)),
inference(paramodulation,[status(thm)],[f58,f201]) ).
fof(f4742,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f201]) ).
fof(f4743,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f201]) ).
fof(f4746,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),one),X2) = addition(multiplication(X0,multiplication(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f23,f201]) ).
fof(f4749,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(addition(X0,multiplication(X0,X1)),addition(one,X1)),
inference(paramodulation,[status(thm)],[f110,f201]) ).
fof(f4750,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(addition(multiplication(X0,X1),X0),addition(X1,one)),
inference(paramodulation,[status(thm)],[f114,f201]) ).
fof(f4756,plain,
! [X0,X1] : leq(addition(multiplication(X0,zero),zero),multiplication(strong_iteration(X1),addition(X0,one))),
inference(paramodulation,[status(thm)],[f201,f2029]) ).
fof(f4757,plain,
! [X0,X1] : leq(addition(multiplication(X0,zero),zero),addition(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f201,f2307]) ).
fof(f4758,plain,
! [X0,X1] : leq(addition(multiplication(X0,zero),zero),addition(X1,addition(X0,one))),
inference(paramodulation,[status(thm)],[f201,f2042]) ).
fof(f4760,plain,
! [X0] : addition(addition(multiplication(X0,zero),zero),addition(X0,one)) = addition(X0,one),
inference(paramodulation,[status(thm)],[f201,f1913]) ).
fof(f4762,plain,
! [X0,X1] : leq(addition(multiplication(X0,zero),zero),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f201,f1780]) ).
fof(f4764,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(X1,addition(X2,one))),X3) = addition(multiplication(X0,X3),multiplication(X1,addition(multiplication(X2,X3),X3))),
inference(paramodulation,[status(thm)],[f201,f199]) ).
fof(f4767,plain,
! [X0,X1] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(X0,one),strong_iteration(one))),
inference(paramodulation,[status(thm)],[f201,f1783]) ).
fof(f4768,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,X1),addition(X2,one)),X3) = addition(multiplication(X0,multiplication(X1,X3)),addition(multiplication(X2,X3),X3)),
inference(paramodulation,[status(thm)],[f201,f195]) ).
fof(f4769,plain,
! [X0,X1,X2,X3] : multiplication(addition(multiplication(X0,addition(X1,one)),X2),X3) = addition(multiplication(X0,addition(multiplication(X1,X3),X3)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f201,f195]) ).
fof(f4770,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),X2) = addition(multiplication(X1,X2),addition(multiplication(X0,X2),X2)),
inference(paramodulation,[status(thm)],[f201,f192]) ).
fof(f4771,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(addition(multiplication(X1,X2),X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f201,f192]) ).
fof(f4772,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),X1),addition(addition(multiplication(X0,X2),X2),X3)) = addition(multiplication(addition(X0,one),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f201,f116]) ).
fof(f4773,plain,
! [X0,X1,X2,X3] : addition(addition(multiplication(X0,X1),X1),addition(multiplication(addition(X0,one),X2),X3)) = addition(multiplication(addition(X0,one),addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f201,f116]) ).
fof(f4774,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(addition(X0,one),X2),X1)),
inference(paramodulation,[status(thm)],[f201,f205]) ).
fof(f4775,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(X2,addition(X0,one)),X1)),
inference(paramodulation,[status(thm)],[f201,f204]) ).
fof(f4776,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(X0,one),addition(X2,X1))),
inference(paramodulation,[status(thm)],[f201,f183]) ).
fof(f4777,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(addition(multiplication(X0,X1),X1),addition(X0,one)),
inference(paramodulation,[status(thm)],[f201,f114]) ).
fof(f4778,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(addition(X0,one),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f201,f110]) ).
fof(f4779,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(multiplication(addition(X0,one),X2),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f201,f104]) ).
fof(f4780,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(addition(multiplication(X0,X2),X2),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f201,f104]) ).
fof(f4781,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),zero),addition(multiplication(X0,X1),X1)),
inference(paramodulation,[status(thm)],[f201,f1780]) ).
fof(f4782,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(X0,one),addition(X1,X2))),
inference(paramodulation,[status(thm)],[f201,f174]) ).
fof(f4783,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(addition(X1,one)),X2))
| ~ leq(X0,addition(addition(multiplication(X1,X0),X0),X2)) ),
inference(paramodulation,[status(thm)],[f201,f37]) ).
fof(f4784,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X1)),addition(X0,one))
| ~ leq(addition(addition(multiplication(X0,X1),X1),X2),addition(X0,one)) ),
inference(paramodulation,[status(thm)],[f201,f34]) ).
fof(f4785,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X0,one)),X2),X1)
| ~ leq(addition(addition(multiplication(X0,X1),X1),X2),X1) ),
inference(paramodulation,[status(thm)],[f201,f32]) ).
fof(f4786,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(multiplication(X0,X2),addition(multiplication(X1,X2),X2)),
inference(paramodulation,[status(thm)],[f201,f27]) ).
fof(f4787,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),X2) = addition(addition(multiplication(X0,X2),X2),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f201,f27]) ).
fof(f4788,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),addition(multiplication(X0,X2),X2)),
inference(paramodulation,[status(thm)],[f201,f26]) ).
fof(f4789,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(addition(multiplication(X0,X1),X1),multiplication(addition(X0,one),X2)),
inference(paramodulation,[status(thm)],[f201,f26]) ).
fof(f4790,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),multiplication(X1,X2)) = multiplication(addition(multiplication(X0,X1),X1),X2),
inference(paramodulation,[status(thm)],[f201,f23]) ).
fof(f4791,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X1),X2) = multiplication(addition(X0,one),multiplication(X1,X2)),
inference(paramodulation,[status(thm)],[f201,f195]) ).
fof(f4792,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(addition(multiplication(X0,X1),X2),X1)),X2),
inference(paramodulation,[status(thm)],[f201,f116]) ).
fof(f4793,plain,
! [X0,X1] : multiplication(X0,addition(X1,multiplication(X0,X1))) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f201,f104]) ).
fof(f4794,plain,
! [X0,X1] : multiplication(X0,addition(multiplication(X0,X1),X1)) = multiplication(addition(X0,one),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f201,f26]) ).
fof(f4795,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(addition(X0,one),X2)) = addition(multiplication(X0,addition(X1,X2)),X2),
inference(paramodulation,[status(thm)],[f201,f116]) ).
fof(f4796,plain,
! [X0] : multiplication(X0,addition(X0,one)) = multiplication(addition(X0,one),X0),
inference(paramodulation,[status(thm)],[f201,f114]) ).
fof(f4798,plain,
! [X0,X1] :
( leq(multiplication(X1,star(X1)),X0)
| ~ leq(multiplication(addition(X0,one),X1),X0) ),
inference(paramodulation,[status(thm)],[f201,f34]) ).
fof(f4799,plain,
! [X0,X1] :
( leq(multiplication(star(X0),X1),X1)
| ~ leq(multiplication(addition(X0,one),X1),X1) ),
inference(paramodulation,[status(thm)],[f201,f32]) ).
fof(f4800,plain,
! [X0] : multiplication(addition(X0,one),strong_iteration(one)) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f201,f982]) ).
fof(f4801,plain,
! [X0,X1] : leq(addition(multiplication(X0,strong_iteration(X1)),one),multiplication(addition(X0,one),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f201,f2572]) ).
fof(f4802,plain,
! [X0,X1,X2] : leq(one,addition(X0,multiplication(addition(X1,one),strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f201,f865]) ).
fof(f4803,plain,
! [X0,X1] : leq(star(X0),multiplication(addition(X1,one),strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f201,f958]) ).
fof(f4804,plain,
! [X0,X1] : leq(one,multiplication(addition(X0,one),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f201,f807]) ).
fof(f4805,plain,
! [X0,X1] : leq(addition(multiplication(X0,star(X1)),one),multiplication(addition(X0,one),star(X1))),
inference(paramodulation,[status(thm)],[f201,f2573]) ).
fof(f4806,plain,
! [X0,X1,X2] : leq(one,addition(X0,multiplication(addition(X1,one),star(X2)))),
inference(paramodulation,[status(thm)],[f201,f277]) ).
fof(f4807,plain,
! [X0,X1] : leq(one,multiplication(addition(X0,one),star(X1))),
inference(paramodulation,[status(thm)],[f201,f260]) ).
fof(f4808,plain,
! [X0,X1,X2] : leq(one,multiplication(addition(X0,one),addition(star(X1),X2))),
inference(paramodulation,[status(thm)],[f201,f1107]) ).
fof(f4809,plain,
! [X0,X1,X2] : leq(one,multiplication(addition(X0,one),addition(strong_iteration(X1),X2))),
inference(paramodulation,[status(thm)],[f201,f1106]) ).
fof(f4810,plain,
! [X0,X1,X2] : leq(one,multiplication(addition(X0,one),addition(X1,strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f201,f865]) ).
fof(f4811,plain,
! [X0,X1,X2] : leq(one,multiplication(addition(X0,one),addition(X1,star(X2)))),
inference(paramodulation,[status(thm)],[f201,f277]) ).
fof(f4812,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(addition(X1,one),addition(X2,addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f201,f241]) ).
fof(f4813,plain,
! [X0,X1,X2,X3] : leq(X0,multiplication(addition(X1,one),addition(X2,addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f201,f223]) ).
fof(f4814,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,addition(X0,X2))),multiplication(addition(X1,one),addition(X0,X2))),
inference(paramodulation,[status(thm)],[f201,f1609]) ).
fof(f4815,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,addition(X2,X0))),multiplication(addition(X1,one),addition(X2,X0))),
inference(paramodulation,[status(thm)],[f201,f1129]) ).
fof(f4816,plain,
! [X0,X1,X2] : leq(addition(X0,X1),multiplication(addition(X2,one),addition(X1,X0))),
inference(paramodulation,[status(thm)],[f201,f339]) ).
fof(f4817,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,multiplication(addition(X2,one),addition(X0,X3)))),
inference(paramodulation,[status(thm)],[f201,f241]) ).
fof(f4818,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,multiplication(addition(X2,one),addition(X3,X0)))),
inference(paramodulation,[status(thm)],[f201,f223]) ).
fof(f4819,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,addition(X1,X2)),X1),multiplication(addition(X0,one),addition(X1,X2))),
inference(paramodulation,[status(thm)],[f201,f176]) ).
fof(f4820,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,one),addition(X1,X2)) != X2
| leq(addition(multiplication(X0,addition(X1,X2)),X1),X2) ),
inference(paramodulation,[status(thm)],[f201,f85]) ).
fof(f4821,plain,
! [X0,X1,X2] : addition(X0,addition(X1,multiplication(X2,addition(X0,X1)))) = multiplication(addition(X2,one),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f201,f58]) ).
fof(f4822,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X2,addition(multiplication(X0,addition(X1,X2)),X1)),
inference(paramodulation,[status(thm)],[f201,f58]) ).
fof(f4823,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,one),addition(X0,X2))),
inference(paramodulation,[status(thm)],[f201,f237]) ).
fof(f4824,plain,
! [X0,X1,X2] : leq(X0,multiplication(addition(X1,one),addition(X2,X0))),
inference(paramodulation,[status(thm)],[f201,f185]) ).
fof(f4825,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X2),addition(X2,multiplication(addition(X0,one),X1))),
inference(paramodulation,[status(thm)],[f201,f1609]) ).
fof(f4826,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,one),X1),addition(X1,addition(multiplication(X0,X1),X2))),
inference(paramodulation,[status(thm)],[f201,f1609]) ).
fof(f4827,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,multiplication(addition(X2,one),X0))),
inference(paramodulation,[status(thm)],[f201,f1129]) ).
fof(f4828,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,one),X1),addition(X1,addition(X2,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f201,f1129]) ).
fof(f4829,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X0)),addition(X2,multiplication(addition(X1,one),X0))),
inference(paramodulation,[status(thm)],[f201,f339]) ).
fof(f4830,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,one),X1),addition(X2,addition(X1,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f201,f339]) ).
fof(f4831,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(X2,addition(X3,multiplication(addition(X0,one),X1)))),
inference(paramodulation,[status(thm)],[f201,f241]) ).
fof(f4832,plain,
! [X0,X1,X2,X3] : leq(X0,addition(X1,addition(X2,multiplication(addition(X3,one),X0)))),
inference(paramodulation,[status(thm)],[f201,f223]) ).
fof(f4834,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(X1,one),X2)) != multiplication(X0,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f201,f115]) ).
fof(f4836,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,multiplication(addition(X2,one),X1))),
inference(paramodulation,[status(thm)],[f201,f183]) ).
fof(f4837,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(addition(X1,one),X2))),
inference(paramodulation,[status(thm)],[f201,f176]) ).
fof(f4838,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,one),X1),addition(multiplication(X0,X1),addition(X1,X2))),
inference(paramodulation,[status(thm)],[f201,f176]) ).
fof(f4839,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,X1),zero),multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f201,f2307]) ).
fof(f4840,plain,
! [X0,X1] : leq(multiplication(X0,zero),multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f201,f2042]) ).
fof(f4841,plain,
! [X0,X1,X2] :
( addition(X0,multiplication(addition(X1,one),X2)) != X2
| leq(addition(X0,multiplication(X1,X2)),X2) ),
inference(paramodulation,[status(thm)],[f201,f85]) ).
fof(f4842,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(addition(X1,one),X2))),
inference(paramodulation,[status(thm)],[f201,f174]) ).
fof(f4843,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(X1),multiplication(addition(X2,one),X0))),
inference(paramodulation,[status(thm)],[f201,f874]) ).
fof(f4844,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),multiplication(addition(X0,one),X1))),
inference(paramodulation,[status(thm)],[f201,f873]) ).
fof(f4845,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(X1,one),X0),X2),
inference(paramodulation,[status(thm)],[f201,f63]) ).
fof(f4846,plain,
! [X0,X1] :
( multiplication(addition(X1,one),X0) != X0
| leq(addition(X0,multiplication(X1,X0)),X0) ),
inference(paramodulation,[status(thm)],[f201,f580]) ).
fof(f4847,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(X2,multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f201,f58]) ).
fof(f4848,plain,
! [X0,X1,X2] : addition(X0,multiplication(addition(X1,one),X2)) = addition(X2,addition(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f201,f58]) ).
fof(f4849,plain,
! [X0,X1] :
( multiplication(addition(X0,one),X1) != X1
| leq(addition(multiplication(X0,X1),X1),X1) ),
inference(paramodulation,[status(thm)],[f201,f475]) ).
fof(f4850,plain,
! [X0,X1] :
( multiplication(addition(X1,one),X0) != multiplication(X1,X0)
| leq(addition(X0,multiplication(X1,X0)),multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f201,f343]) ).
fof(f4851,plain,
! [X0,X1] :
( multiplication(addition(X0,one),X1) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),X1),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f201,f158]) ).
fof(f4853,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(multiplication(X1,X0),X0),
inference(paramodulation,[status(thm)],[f201,f182]) ).
fof(f4854,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,X0)),multiplication(addition(X1,one),X0)),
inference(paramodulation,[status(thm)],[f201,f340]) ).
fof(f4855,plain,
! [X0,X1] : leq(multiplication(addition(X0,one),X1),addition(X1,multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f201,f340]) ).
fof(f4856,plain,
! [X0,X1] : addition(X0,multiplication(addition(X1,one),X0)) = addition(X0,multiplication(X1,X0)),
inference(paramodulation,[status(thm)],[f201,f153]) ).
fof(f4857,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),addition(X2,multiplication(addition(X0,one),X1))),
inference(paramodulation,[status(thm)],[f201,f237]) ).
fof(f4858,plain,
! [X0,X1,X2] : leq(X0,addition(X1,multiplication(addition(X2,one),X0))),
inference(paramodulation,[status(thm)],[f201,f185]) ).
fof(f4861,plain,
! [X0,X1] : addition(multiplication(X0,X1),multiplication(addition(X0,one),X1)) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f201,f65]) ).
fof(f4862,plain,
! [X0,X1] :
( multiplication(addition(X1,one),X0) != multiplication(X1,X0)
| leq(X0,multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f201,f87]) ).
fof(f4863,plain,
! [X0,X1] :
( multiplication(addition(X0,one),X1) != X1
| leq(multiplication(X0,X1),X1) ),
inference(paramodulation,[status(thm)],[f201,f42]) ).
fof(f4864,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),X2),
inference(paramodulation,[status(thm)],[f201,f20]) ).
fof(f4865,plain,
! [X0,X1] : addition(X0,multiplication(X1,X0)) = multiplication(addition(X1,one),X0),
inference(paramodulation,[status(thm)],[f201,f19]) ).
fof(f4866,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f201,f19]) ).
fof(f4870,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(multiplication(star(X0),multiplication(X0,X1)),X1),
inference(forward_demodulation,[status(thm)],[f23,f4723]) ).
fof(f4871,plain,
! [X0,X1] : multiplication(star(X0),X1) = addition(multiplication(X0,multiplication(star(X0),X1)),X1),
inference(forward_demodulation,[status(thm)],[f23,f4724]) ).
fof(f4876,plain,
! [X0,X1] : multiplication(strong_iteration(X0),X1) = addition(multiplication(X0,multiplication(strong_iteration(X0),X1)),X1),
inference(forward_demodulation,[status(thm)],[f23,f4726]) ).
fof(f4881,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(X2,addition(multiplication(X0,X1),X1))),X2),
inference(forward_demodulation,[status(thm)],[f63,f4734]) ).
fof(f4894,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(multiplication(X0,X1),addition(X0,addition(one,X1))),
inference(forward_demodulation,[status(thm)],[f63,f4749]) ).
fof(f4895,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(X0,addition(multiplication(X0,X1),addition(X1,one))),
inference(forward_demodulation,[status(thm)],[f63,f4750]) ).
fof(f4902,plain,
! [X0,X1] : leq(multiplication(X0,zero),multiplication(strong_iteration(X1),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f21,f4756]) ).
fof(f4903,plain,
! [X0,X1] : leq(multiplication(X0,zero),addition(addition(X0,one),X1)),
inference(forward_demodulation,[status(thm)],[f21,f4757]) ).
fof(f4904,plain,
! [X0,X1] : leq(multiplication(X0,zero),addition(one,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f63,f4903]) ).
fof(f4905,plain,
! [X0,X1] : leq(multiplication(X0,zero),addition(X1,addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f21,f4758]) ).
fof(f4909,plain,
! [X0] : addition(zero,addition(multiplication(X0,zero),addition(X0,one))) = addition(X0,one),
inference(forward_demodulation,[status(thm)],[f63,f4760]) ).
fof(f4910,plain,
! [X0] : addition(multiplication(X0,zero),addition(X0,one)) = addition(X0,one),
inference(forward_demodulation,[status(thm)],[f49,f4909]) ).
fof(f4912,plain,
! [X0,X1] : leq(multiplication(X0,zero),multiplication(addition(X0,one),X1)),
inference(forward_demodulation,[status(thm)],[f21,f4762]) ).
fof(f4918,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(multiplication(X1,X2),addition(multiplication(X0,X2),X2)),
inference(forward_demodulation,[status(thm)],[f63,f4770]) ).
fof(f4919,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,addition(multiplication(X1,X2),multiplication(X0,X2))),
inference(forward_demodulation,[status(thm)],[f63,f4771]) ).
fof(f4920,plain,
! [X0,X1,X2] : multiplication(addition(X0,addition(X1,one)),X2) = addition(X2,multiplication(addition(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f192,f4919]) ).
fof(f4921,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,one),X1),addition(X2,addition(multiplication(X0,X2),X3))) = addition(multiplication(addition(X0,one),addition(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f63,f4772]) ).
fof(f4922,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,X0),addition(multiplication(addition(X1,one),X2),X3))) = addition(multiplication(addition(X1,one),addition(X0,X2)),X3),
inference(forward_demodulation,[status(thm)],[f63,f4773]) ).
fof(f4923,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,X1),X1),multiplication(addition(one,addition(X0,X2)),X1)),
inference(forward_demodulation,[status(thm)],[f63,f4774]) ).
fof(f4924,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(X1,one)) = addition(X1,addition(multiplication(X0,X1),addition(X0,one))),
inference(forward_demodulation,[status(thm)],[f63,f4777]) ).
fof(f4925,plain,
! [X0,X1] : multiplication(addition(X0,one),addition(one,X1)) = addition(one,addition(X0,addition(multiplication(X0,X1),X1))),
inference(forward_demodulation,[status(thm)],[f63,f4778]) ).
fof(f4926,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X2,addition(multiplication(X0,X2),multiplication(addition(X0,one),X1))),
inference(forward_demodulation,[status(thm)],[f63,f4780]) ).
fof(f4927,plain,
! [X0,X1,X2] :
( leq(X0,multiplication(strong_iteration(addition(X1,one)),X2))
| ~ leq(X0,addition(X0,addition(multiplication(X1,X0),X2))) ),
inference(forward_demodulation,[status(thm)],[f63,f4783]) ).
fof(f4928,plain,
! [X0,X1,X2] : leq(X0,multiplication(strong_iteration(addition(X1,one)),X2)),
inference(forward_subsumption_resolution,[status(thm)],[f4927,f145]) ).
fof(f4929,plain,
! [X0,X1,X2] :
( leq(multiplication(X2,star(X0)),addition(X1,one))
| ~ leq(addition(X0,addition(multiplication(X1,X0),X2)),addition(X1,one)) ),
inference(forward_demodulation,[status(thm)],[f63,f4784]) ).
fof(f4930,plain,
! [X0,X1,X2] :
( leq(multiplication(star(addition(X1,one)),X2),X0)
| ~ leq(addition(X0,addition(multiplication(X1,X0),X2)),X0) ),
inference(forward_demodulation,[status(thm)],[f63,f4785]) ).
fof(f4931,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(addition(multiplication(X0,X2),X2),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f63,f4787]) ).
fof(f4932,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(X2,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f63,f4931]) ).
fof(f4933,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(X2,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f192,f4932]) ).
fof(f4934,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(X1,X2)) = addition(X1,addition(multiplication(X0,X1),multiplication(addition(X0,one),X2))),
inference(forward_demodulation,[status(thm)],[f63,f4789]) ).
fof(f4935,plain,
! [X0,X1,X2] : multiplication(addition(X0,one),addition(multiplication(X0,X1),X2)) = addition(multiplication(X0,addition(X2,addition(multiplication(X0,X1),X1))),X2),
inference(forward_demodulation,[status(thm)],[f63,f4792]) ).
fof(f4939,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,zero)),multiplication(addition(X0,one),X1)),
inference(forward_demodulation,[status(thm)],[f23,f4839]) ).
fof(f4943,plain,
! [X0,X1] : multiplication(addition(addition(X0,one),X0),X1) = addition(multiplication(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f192,f4861]) ).
fof(f4944,plain,
! [X0,X1] : multiplication(addition(one,addition(X0,X0)),X1) = addition(multiplication(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f63,f4943]) ).
fof(f4945,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(multiplication(X0,X1),X1),
inference(forward_demodulation,[status(thm)],[f22,f4944]) ).
fof(f4951,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(star(X0),addition(X1,multiplication(strong_iteration(X0),zero)))),
inference(paramodulation,[status(thm)],[f38,f2590]) ).
fof(f4955,plain,
! [X0,X1] : leq(star(X0),addition(one,addition(X1,multiplication(star(X0),X0)))),
inference(paramodulation,[status(thm)],[f30,f2590]) ).
fof(f4956,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(one,addition(X1,multiplication(X0,strong_iteration(X0))))),
inference(paramodulation,[status(thm)],[f791,f2590]) ).
fof(f4957,plain,
! [X0,X1] : leq(star(X0),addition(one,addition(X1,multiplication(X0,star(X0))))),
inference(paramodulation,[status(thm)],[f29,f2590]) ).
fof(f4958,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(star(X0),X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f588,f2590]) ).
fof(f4959,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),addition(multiplication(X0,multiplication(X1,X3)),addition(X4,multiplication(X2,X3)))),
inference(paramodulation,[status(thm)],[f195,f2590]) ).
fof(f4960,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(X0,star(X0)),addition(X1,one))),
inference(paramodulation,[status(thm)],[f589,f2590]) ).
fof(f4962,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(X0,strong_iteration(X0)),addition(X1,one))),
inference(paramodulation,[status(thm)],[f35,f2590]) ).
fof(f4963,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,addition(X1,X2)),X3),addition(multiplication(X0,X1),addition(X4,addition(multiplication(X0,X2),X3)))),
inference(paramodulation,[status(thm)],[f116,f2590]) ).
fof(f4964,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(X0,multiplication(X1,X2)),X3),addition(multiplication(X0,X3),addition(X4,multiplication(X1,multiplication(X2,X3))))),
inference(paramodulation,[status(thm)],[f199,f2590]) ).
fof(f4965,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X1,X2),addition(X3,multiplication(X0,X2)))),
inference(paramodulation,[status(thm)],[f192,f2590]) ).
fof(f4966,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X2),addition(X3,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f104,f2590]) ).
fof(f4967,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(X0,X2),addition(X3,multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f27,f2590]) ).
fof(f4968,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,addition(X1,X2)),addition(multiplication(X0,X1),addition(X3,multiplication(X0,X2)))),
inference(paramodulation,[status(thm)],[f26,f2590]) ).
fof(f4969,plain,
! [X0,X1,X2] : leq(multiplication(addition(X0,one),X1),addition(multiplication(X0,X1),addition(X2,X1))),
inference(paramodulation,[status(thm)],[f201,f2590]) ).
fof(f4970,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(X1,one)),addition(multiplication(X0,X1),addition(X2,X0))),
inference(paramodulation,[status(thm)],[f114,f2590]) ).
fof(f4972,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(addition(X1,X0),addition(X3,X2))),
inference(paramodulation,[status(thm)],[f63,f2590]) ).
fof(f4973,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(addition(X0,X1),addition(X3,X2))),
inference(paramodulation,[status(thm)],[f20,f2590]) ).
fof(f4975,plain,
! [X0,X1,X2] : leq(multiplication(addition(one,X0),X1),addition(X1,addition(X2,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f197,f2590]) ).
fof(f4976,plain,
! [X0,X1,X2] : leq(multiplication(X0,addition(one,X1)),addition(X0,addition(X2,multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f110,f2590]) ).
fof(f4978,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X2,addition(X3,addition(X0,X1)))),
inference(paramodulation,[status(thm)],[f58,f2590]) ).
fof(f4979,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X3,addition(X2,X0)))),
inference(paramodulation,[status(thm)],[f58,f2590]) ).
fof(f4980,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X1,addition(X2,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f457,f2590]) ).
fof(f4982,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,addition(X2,addition(X1,X0)))),
inference(paramodulation,[status(thm)],[f153,f2590]) ).
fof(f4989,plain,
! [X0,X1] : leq(addition(multiplication(addition(X0,X1),zero),X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f1913,f2590]) ).
fof(f4990,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(X0,addition(X1,X3)),X2)),
inference(paramodulation,[status(thm)],[f116,f2590]) ).
fof(f4991,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,addition(X1,X2)),X2),multiplication(addition(X0,one),addition(X1,X2))),
inference(paramodulation,[status(thm)],[f201,f2590]) ).
fof(f4992,plain,
! [X0,X1,X2] : leq(addition(multiplication(addition(X0,X1),X2),X1),multiplication(addition(X0,X1),addition(X2,one))),
inference(paramodulation,[status(thm)],[f114,f2590]) ).
fof(f4994,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X1,addition(X0,addition(X3,X2)))),
inference(paramodulation,[status(thm)],[f63,f2590]) ).
fof(f4995,plain,
! [X0,X1,X2,X3] : leq(addition(addition(X0,X1),X2),addition(X0,addition(X1,addition(X3,X2)))),
inference(paramodulation,[status(thm)],[f20,f2590]) ).
fof(f5006,plain,
! [X0,X1] : leq(addition(X0,star(X1)),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f1021,f2590]) ).
fof(f5009,plain,
! [X0,X1] : leq(addition(X0,multiplication(strong_iteration(X1),zero)),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f38,f2590]) ).
fof(f5013,plain,
! [X0,X1] : leq(addition(X0,multiplication(star(X1),X1)),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f30,f2590]) ).
fof(f5014,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,strong_iteration(X1))),addition(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f791,f2590]) ).
fof(f5015,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,star(X1))),addition(X0,star(X1))),
inference(paramodulation,[status(thm)],[f29,f2590]) ).
fof(f5017,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(addition(multiplication(X3,X4),X1),X2))),
inference(paramodulation,[status(thm)],[f195,f2590]) ).
fof(f5021,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,addition(multiplication(X1,X2),X3)),addition(X0,addition(multiplication(X1,addition(X4,X2)),X3))),
inference(paramodulation,[status(thm)],[f116,f2590]) ).
fof(f5022,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,multiplication(X1,multiplication(X2,X3))),addition(X0,multiplication(addition(X4,multiplication(X1,X2)),X3))),
inference(paramodulation,[status(thm)],[f199,f2590]) ).
fof(f5023,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(addition(X1,X3),X2))),
inference(paramodulation,[status(thm)],[f192,f2590]) ).
fof(f5024,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f104,f2590]) ).
fof(f5025,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(addition(X3,X1),X2))),
inference(paramodulation,[status(thm)],[f27,f2590]) ).
fof(f5026,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(X1,addition(X3,X2)))),
inference(paramodulation,[status(thm)],[f26,f2590]) ).
fof(f5027,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,multiplication(addition(X2,one),X1))),
inference(paramodulation,[status(thm)],[f201,f2590]) ).
fof(f5028,plain,
! [X0,X1,X2] : leq(addition(X0,X1),addition(X0,multiplication(X1,addition(X2,one)))),
inference(paramodulation,[status(thm)],[f114,f2590]) ).
fof(f5030,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X0,addition(X2,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f63,f2590]) ).
fof(f5031,plain,
! [X0,X1,X2,X3] : leq(addition(X0,X1),addition(X0,addition(X2,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f20,f2590]) ).
fof(f5032,plain,
! [X0,X1] : leq(addition(X0,multiplication(X1,zero)),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f2007,f2590]) ).
fof(f5033,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(addition(one,X1),X2))),
inference(paramodulation,[status(thm)],[f197,f2590]) ).
fof(f5034,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,X2)),addition(X0,multiplication(X1,addition(one,X2)))),
inference(paramodulation,[status(thm)],[f110,f2590]) ).
fof(f5036,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X1,addition(X2,X3)))),
inference(paramodulation,[status(thm)],[f58,f2590]) ).
fof(f5037,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,addition(X3,X1)))),
inference(paramodulation,[status(thm)],[f58,f2590]) ).
fof(f5038,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f457,f2590]) ).
fof(f5040,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X2,X1))),
inference(paramodulation,[status(thm)],[f153,f2590]) ).
fof(f5052,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X1,addition(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4972]) ).
fof(f5053,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,addition(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4973]) ).
fof(f5060,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X0,addition(X1,addition(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4994]) ).
fof(f5061,plain,
! [X0,X1,X2,X3] : leq(addition(X0,addition(X1,X2)),addition(X1,addition(X0,addition(X3,X2)))),
inference(forward_demodulation,[status(thm)],[f63,f4995]) ).
fof(f5075,plain,
! [X0,X1] :
( multiplication(strong_iteration(one),X0) != multiplication(X1,X0)
| leq(multiplication(strong_iteration(one),X0),multiplication(X1,X0)) ),
inference(paramodulation,[status(thm)],[f1237,f208]) ).
fof(f5076,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(star(X0),X1)
| leq(multiplication(strong_iteration(X0),X1),multiplication(star(X0),X1)) ),
inference(paramodulation,[status(thm)],[f1021,f208]) ).
fof(f5077,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(one,X1)
| leq(multiplication(strong_iteration(X0),X1),multiplication(one,X1)) ),
inference(paramodulation,[status(thm)],[f858,f208]) ).
fof(f5078,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(strong_iteration(X0),X1)
| leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),X1)) ),
inference(paramodulation,[status(thm)],[f829,f208]) ).
fof(f5079,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(multiplication(strong_iteration(X0),zero),X1)
| leq(multiplication(star(X0),X1),multiplication(multiplication(strong_iteration(X0),zero),X1)) ),
inference(paramodulation,[status(thm)],[f38,f208]) ).
fof(f5080,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != multiplication(one,X1)
| leq(multiplication(star(X0),X1),multiplication(one,X1)) ),
inference(paramodulation,[status(thm)],[f349,f208]) ).
fof(f5083,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(star(X1),X1),X0)
| leq(multiplication(one,X0),multiplication(multiplication(star(X1),X1),X0)) ),
inference(paramodulation,[status(thm)],[f30,f208]) ).
fof(f5084,plain,
! [X0,X1] :
( multiplication(strong_iteration(X1),X0) != multiplication(multiplication(X1,strong_iteration(X1)),X0)
| leq(multiplication(one,X0),multiplication(multiplication(X1,strong_iteration(X1)),X0)) ),
inference(paramodulation,[status(thm)],[f791,f208]) ).
fof(f5085,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(X1,star(X1)),X0)
| leq(multiplication(one,X0),multiplication(multiplication(X1,star(X1)),X0)) ),
inference(paramodulation,[status(thm)],[f29,f208]) ).
fof(f5086,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != multiplication(one,X1)
| leq(multiplication(multiplication(star(X0),X0),X1),multiplication(one,X1)) ),
inference(paramodulation,[status(thm)],[f588,f208]) ).
fof(f5087,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(multiplication(X0,multiplication(X1,X2)),X3),multiplication(multiplication(X4,X2),X3)) ),
inference(paramodulation,[status(thm)],[f195,f208]) ).
fof(f5088,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != multiplication(one,X1)
| leq(multiplication(multiplication(X0,star(X0)),X1),multiplication(one,X1)) ),
inference(paramodulation,[status(thm)],[f589,f208]) ).
fof(f5090,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(one,X1)
| leq(multiplication(multiplication(X0,strong_iteration(X0)),X1),multiplication(one,X1)) ),
inference(paramodulation,[status(thm)],[f35,f208]) ).
fof(f5091,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(X0,addition(X1,X3)),X4),X2) != multiplication(addition(multiplication(X0,X3),X4),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(addition(multiplication(X0,X3),X4),X2)) ),
inference(paramodulation,[status(thm)],[f116,f208]) ).
fof(f5092,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(X0,multiplication(X3,X4)),X1),X2) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X3,multiplication(X4,X1)),X2)) ),
inference(paramodulation,[status(thm)],[f199,f208]) ).
fof(f5093,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(addition(X3,X0),X1),X2) != multiplication(multiplication(X3,X1),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X3,X1),X2)) ),
inference(paramodulation,[status(thm)],[f192,f208]) ).
fof(f5094,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X3,X1)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,X3),X2)) ),
inference(paramodulation,[status(thm)],[f104,f208]) ).
fof(f5096,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X1,X3)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(multiplication(X0,X3),X2)) ),
inference(paramodulation,[status(thm)],[f26,f208]) ).
fof(f5097,plain,
! [X0,X1,X2] :
( multiplication(multiplication(addition(X0,one),X1),X2) != multiplication(X1,X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(X1,X2)) ),
inference(paramodulation,[status(thm)],[f201,f208]) ).
fof(f5098,plain,
! [X0,X1,X2] :
( multiplication(multiplication(X0,addition(X1,one)),X2) != multiplication(X0,X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(X0,X2)) ),
inference(paramodulation,[status(thm)],[f114,f208]) ).
fof(f5100,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X1,addition(X0,X3)),X2) != multiplication(X3,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f63,f208]) ).
fof(f5101,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X0,addition(X1,X3)),X2) != multiplication(X3,X2)
| leq(multiplication(addition(X0,X1),X2),multiplication(X3,X2)) ),
inference(paramodulation,[status(thm)],[f20,f208]) ).
fof(f5102,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(multiplication(X0,zero),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,zero),X1)) ),
inference(paramodulation,[status(thm)],[f2007,f208]) ).
fof(f5103,plain,
! [X0,X1,X2] :
( multiplication(multiplication(addition(one,X2),X0),X1) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X2,X0),X1)) ),
inference(paramodulation,[status(thm)],[f197,f208]) ).
fof(f5104,plain,
! [X0,X1,X2] :
( multiplication(multiplication(X0,addition(one,X2)),X1) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(multiplication(X0,X2),X1)) ),
inference(paramodulation,[status(thm)],[f110,f208]) ).
fof(f5106,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X2,addition(X3,X0)),X1) != multiplication(addition(X2,X3),X1)
| leq(multiplication(X0,X1),multiplication(addition(X2,X3),X1)) ),
inference(paramodulation,[status(thm)],[f58,f208]) ).
fof(f5107,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,addition(X0,X2)),X1) != multiplication(addition(X2,X3),X1)
| leq(multiplication(X0,X1),multiplication(addition(X2,X3),X1)) ),
inference(paramodulation,[status(thm)],[f58,f208]) ).
fof(f5112,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(zero,X1)
| leq(multiplication(X0,X1),multiplication(zero,X1)) ),
inference(paramodulation,[status(thm)],[f21,f208]) ).
fof(f5113,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f19,f208]) ).
fof(f5114,plain,
! [X0,X1,X2] :
( multiplication(addition(X2,X0),X1) != multiplication(X2,X1)
| leq(multiplication(X0,X1),multiplication(X2,X1)) ),
inference(paramodulation,[status(thm)],[f19,f208]) ).
fof(f5122,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(one,X1)
| leq(multiplication(strong_iteration(X0),X1),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5077]) ).
fof(f5123,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != X1
| leq(multiplication(strong_iteration(X0),X1),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5122]) ).
fof(f5124,plain,
! [X0,X1] : leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),X1)),
inference(trivial_equality_resolution,[status(thm)],[f5078]) ).
fof(f5125,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(multiplication(strong_iteration(X0),zero),X1)
| leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),multiplication(zero,X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f5079]) ).
fof(f5126,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(multiplication(strong_iteration(X0),zero),X1)
| leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),zero)) ),
inference(forward_demodulation,[status(thm)],[f28,f5125]) ).
fof(f5127,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(strong_iteration(X0),multiplication(zero,X1))
| leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),zero)) ),
inference(forward_demodulation,[status(thm)],[f23,f5126]) ).
fof(f5128,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(strong_iteration(X0),zero)
| leq(multiplication(star(X0),X1),multiplication(strong_iteration(X0),zero)) ),
inference(forward_demodulation,[status(thm)],[f28,f5127]) ).
fof(f5129,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != multiplication(one,X1)
| leq(multiplication(star(X0),X1),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5080]) ).
fof(f5130,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != X1
| leq(multiplication(star(X0),X1),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5129]) ).
fof(f5135,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(star(X1),X1),X0)
| leq(X0,multiplication(multiplication(star(X1),X1),X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f5083]) ).
fof(f5136,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(star(X1),X1),X0)
| leq(X0,multiplication(star(X1),multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f23,f5135]) ).
fof(f5137,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(star(X1),multiplication(X1,X0))
| leq(X0,multiplication(star(X1),multiplication(X1,X0))) ),
inference(forward_demodulation,[status(thm)],[f23,f5136]) ).
fof(f5138,plain,
! [X0,X1] :
( multiplication(strong_iteration(X1),X0) != multiplication(multiplication(X1,strong_iteration(X1)),X0)
| leq(X0,multiplication(multiplication(X1,strong_iteration(X1)),X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f5084]) ).
fof(f5139,plain,
! [X0,X1] :
( multiplication(strong_iteration(X1),X0) != multiplication(multiplication(X1,strong_iteration(X1)),X0)
| leq(X0,multiplication(X1,multiplication(strong_iteration(X1),X0))) ),
inference(forward_demodulation,[status(thm)],[f23,f5138]) ).
fof(f5140,plain,
! [X0,X1] :
( multiplication(strong_iteration(X1),X0) != multiplication(X1,multiplication(strong_iteration(X1),X0))
| leq(X0,multiplication(X1,multiplication(strong_iteration(X1),X0))) ),
inference(forward_demodulation,[status(thm)],[f23,f5139]) ).
fof(f5141,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(X1,star(X1)),X0)
| leq(X0,multiplication(multiplication(X1,star(X1)),X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f5085]) ).
fof(f5142,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(multiplication(X1,star(X1)),X0)
| leq(X0,multiplication(X1,multiplication(star(X1),X0))) ),
inference(forward_demodulation,[status(thm)],[f23,f5141]) ).
fof(f5143,plain,
! [X0,X1] :
( multiplication(star(X1),X0) != multiplication(X1,multiplication(star(X1),X0))
| leq(X0,multiplication(X1,multiplication(star(X1),X0))) ),
inference(forward_demodulation,[status(thm)],[f23,f5142]) ).
fof(f5144,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != multiplication(one,X1)
| leq(multiplication(star(X0),multiplication(X0,X1)),multiplication(one,X1)) ),
inference(forward_demodulation,[status(thm)],[f23,f5086]) ).
fof(f5145,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != multiplication(one,X1)
| leq(multiplication(star(X0),multiplication(X0,X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5144]) ).
fof(f5146,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != X1
| leq(multiplication(star(X0),multiplication(X0,X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5145]) ).
fof(f5147,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(X0,multiplication(multiplication(X1,X2),X3)),multiplication(multiplication(X4,X2),X3)) ),
inference(forward_demodulation,[status(thm)],[f23,f5087]) ).
fof(f5148,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(multiplication(X4,X2),X3)) ),
inference(forward_demodulation,[status(thm)],[f23,f5147]) ).
fof(f5149,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(multiplication(X0,X1),X4),X2),X3) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X4,multiplication(X2,X3))) ),
inference(forward_demodulation,[status(thm)],[f23,f5148]) ).
fof(f5150,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(X0,X1),X4),multiplication(X2,X3)) != multiplication(multiplication(X4,X2),X3)
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X4,multiplication(X2,X3))) ),
inference(forward_demodulation,[status(thm)],[f23,f5149]) ).
fof(f5151,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(X0,X1),X4),multiplication(X2,X3)) != multiplication(X4,multiplication(X2,X3))
| leq(multiplication(X0,multiplication(X1,multiplication(X2,X3))),multiplication(X4,multiplication(X2,X3))) ),
inference(forward_demodulation,[status(thm)],[f23,f5150]) ).
fof(f5152,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != multiplication(one,X1)
| leq(multiplication(X0,multiplication(star(X0),X1)),multiplication(one,X1)) ),
inference(forward_demodulation,[status(thm)],[f23,f5088]) ).
fof(f5153,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != multiplication(one,X1)
| leq(multiplication(X0,multiplication(star(X0),X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5152]) ).
fof(f5154,plain,
! [X0,X1] :
( multiplication(star(X0),X1) != X1
| leq(multiplication(X0,multiplication(star(X0),X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5153]) ).
fof(f5158,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(one,X1)
| leq(multiplication(X0,multiplication(strong_iteration(X0),X1)),multiplication(one,X1)) ),
inference(forward_demodulation,[status(thm)],[f23,f5090]) ).
fof(f5159,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != multiplication(one,X1)
| leq(multiplication(X0,multiplication(strong_iteration(X0),X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5158]) ).
fof(f5160,plain,
! [X0,X1] :
( multiplication(strong_iteration(X0),X1) != X1
| leq(multiplication(X0,multiplication(strong_iteration(X0),X1)),X1) ),
inference(forward_demodulation,[status(thm)],[f25,f5159]) ).
fof(f5161,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(X0,addition(X1,X3)),X4),X2) != multiplication(addition(multiplication(X0,X3),X4),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X0,X3),X4),X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5091]) ).
fof(f5162,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(X0,multiplication(X3,X4)),X1),X2) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X3,multiplication(X4,X1)),X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5092]) ).
fof(f5163,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(X0,multiplication(X3,X4)),X1),X2) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(multiplication(X4,X1),X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5162]) ).
fof(f5164,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(multiplication(addition(X0,multiplication(X3,X4)),X1),X2) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,multiplication(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f23,f5163]) ).
fof(f5165,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(X0,multiplication(X3,X4)),multiplication(X1,X2)) != multiplication(multiplication(X3,multiplication(X4,X1)),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,multiplication(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f23,f5164]) ).
fof(f5166,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(X0,multiplication(X3,X4)),multiplication(X1,X2)) != multiplication(X3,multiplication(multiplication(X4,X1),X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,multiplication(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f23,f5165]) ).
fof(f5167,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(X0,multiplication(X3,X4)),multiplication(X1,X2)) != multiplication(X3,multiplication(X4,multiplication(X1,X2)))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X4,multiplication(X1,X2)))) ),
inference(forward_demodulation,[status(thm)],[f23,f5166]) ).
fof(f5168,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(addition(X3,X0),X1),X2) != multiplication(multiplication(X3,X1),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X3,X1),X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5093]) ).
fof(f5169,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(addition(X3,X0),X1),X2) != multiplication(multiplication(X3,X1),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5168]) ).
fof(f5170,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,X0),multiplication(X1,X2)) != multiplication(multiplication(X3,X1),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5169]) ).
fof(f5171,plain,
! [X0,X1,X2,X3] :
( multiplication(addition(X3,X0),multiplication(X1,X2)) != multiplication(X3,multiplication(X1,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X3,multiplication(X1,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5170]) ).
fof(f5172,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X3,X1)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X3),X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5094]) ).
fof(f5173,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X3,X1)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5172]) ).
fof(f5174,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X3,X1),X2)) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5173]) ).
fof(f5175,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X3,X1),X2)) != multiplication(X0,multiplication(X3,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5174]) ).
fof(f5180,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X1,X3)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(multiplication(X0,X3),X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5096]) ).
fof(f5181,plain,
! [X0,X1,X2,X3] :
( multiplication(multiplication(X0,addition(X1,X3)),X2) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5180]) ).
fof(f5182,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X1,X3),X2)) != multiplication(multiplication(X0,X3),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5181]) ).
fof(f5183,plain,
! [X0,X1,X2,X3] :
( multiplication(X0,multiplication(addition(X1,X3),X2)) != multiplication(X0,multiplication(X3,X2))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,multiplication(X3,X2))) ),
inference(forward_demodulation,[status(thm)],[f23,f5182]) ).
fof(f5184,plain,
! [X0,X1,X2] :
( multiplication(multiplication(addition(X0,one),X1),X2) != multiplication(X1,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5097]) ).
fof(f5185,plain,
! [X0,X1,X2] :
( multiplication(addition(X0,one),multiplication(X1,X2)) != multiplication(X1,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X1,X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5184]) ).
fof(f5186,plain,
! [X0,X1,X2] :
( multiplication(multiplication(X0,addition(X1,one)),X2) != multiplication(X0,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5098]) ).
fof(f5187,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(X1,one),X2)) != multiplication(X0,X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5186]) ).
fof(f5190,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(multiplication(X0,zero),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(zero,X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f5102]) ).
fof(f5191,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(multiplication(X0,zero),X1)
| leq(multiplication(X0,X1),multiplication(X0,zero)) ),
inference(forward_demodulation,[status(thm)],[f28,f5190]) ).
fof(f5192,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(X0,multiplication(zero,X1))
| leq(multiplication(X0,X1),multiplication(X0,zero)) ),
inference(forward_demodulation,[status(thm)],[f23,f5191]) ).
fof(f5193,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(X0,zero)
| leq(multiplication(X0,X1),multiplication(X0,zero)) ),
inference(forward_demodulation,[status(thm)],[f28,f5192]) ).
fof(f5194,plain,
! [X0,X1,X2] :
( multiplication(multiplication(addition(one,X2),X0),X1) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f5103]) ).
fof(f5195,plain,
! [X0,X1,X2] :
( multiplication(addition(one,X2),multiplication(X0,X1)) != multiplication(multiplication(X2,X0),X1)
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f5194]) ).
fof(f5196,plain,
! [X0,X1,X2] :
( multiplication(addition(one,X2),multiplication(X0,X1)) != multiplication(X2,multiplication(X0,X1))
| leq(multiplication(X0,X1),multiplication(X2,multiplication(X0,X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f5195]) ).
fof(f5197,plain,
! [X0,X1,X2] :
( multiplication(multiplication(X0,addition(one,X2)),X1) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f5104]) ).
fof(f5198,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(one,X2),X1)) != multiplication(multiplication(X0,X2),X1)
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f5197]) ).
fof(f5199,plain,
! [X0,X1,X2] :
( multiplication(X0,multiplication(addition(one,X2),X1)) != multiplication(X0,multiplication(X2,X1))
| leq(multiplication(X0,X1),multiplication(X0,multiplication(X2,X1))) ),
inference(forward_demodulation,[status(thm)],[f23,f5198]) ).
fof(f5203,plain,
! [X0,X1] :
( multiplication(X0,X1) != multiplication(zero,X1)
| leq(multiplication(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f28,f5112]) ).
fof(f5204,plain,
! [X0,X1] :
( multiplication(X0,X1) != zero
| leq(multiplication(X0,X1),zero) ),
inference(forward_demodulation,[status(thm)],[f28,f5203]) ).
fof(f5206,plain,
! [X0,X1] : addition(multiplication(X0,zero),X1) = addition(multiplication(addition(addition(multiplication(X0,zero),X1),X0),zero),X1),
inference(paramodulation,[status(thm)],[f1913,f209]) ).
fof(f5208,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),addition(X1,one)) = addition(multiplication(addition(addition(multiplication(X0,X1),X2),X0),X1),X2),
inference(paramodulation,[status(thm)],[f114,f209]) ).
fof(f5209,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X3,X0),X1),X2),
inference(paramodulation,[status(thm)],[f58,f209]) ).
fof(f5210,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,X2),multiplication(X3,X2))) = addition(multiplication(addition(X1,X3),X2),X0),
inference(paramodulation,[status(thm)],[f58,f209]) ).
fof(f5212,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X2,X0),X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f182,f209]) ).
fof(f5217,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X1,X0)),addition(multiplication(X2,X0),X3)) = addition(multiplication(addition(addition(one,X1),X2),X0),X3),
inference(paramodulation,[status(thm)],[f197,f209]) ).
fof(f5218,plain,
! [X0,X1,X2,X3] : addition(addition(multiplication(X0,X1),X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(addition(X0,one),X2),X1),X3),
inference(paramodulation,[status(thm)],[f201,f209]) ).
fof(f5219,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) = addition(multiplication(addition(multiplication(X0,X1),X3),X2),X4),
inference(paramodulation,[status(thm)],[f23,f209]) ).
fof(f5221,plain,
! [X0,X1,X2] : addition(X0,addition(multiplication(X1,X0),X2)) = addition(multiplication(addition(one,X1),X0),X2),
inference(paramodulation,[status(thm)],[f25,f209]) ).
fof(f5222,plain,
! [X0,X1,X2,X3] : addition(addition(X0,multiplication(X0,X1)),addition(multiplication(X2,addition(one,X1)),X3)) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(paramodulation,[status(thm)],[f110,f209]) ).
fof(f5223,plain,
! [X0,X1,X2,X3] : addition(addition(multiplication(X0,X1),X0),addition(multiplication(X2,addition(X1,one)),X3)) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(paramodulation,[status(thm)],[f114,f209]) ).
fof(f5225,plain,
! [X0,X1] : addition(multiplication(X0,X1),star(X1)) = addition(multiplication(addition(X0,star(X1)),X1),one),
inference(paramodulation,[status(thm)],[f588,f209]) ).
fof(f5227,plain,
! [X0,X1] : addition(multiplication(X0,star(X1)),star(X1)) = addition(multiplication(addition(X0,X1),star(X1)),one),
inference(paramodulation,[status(thm)],[f589,f209]) ).
fof(f5228,plain,
! [X0,X1] : addition(multiplication(X0,zero),X1) = addition(multiplication(addition(X0,X1),zero),X1),
inference(paramodulation,[status(thm)],[f1913,f209]) ).
fof(f5229,plain,
! [X0,X1] : addition(multiplication(X0,strong_iteration(X1)),strong_iteration(X1)) = addition(multiplication(addition(X0,X1),strong_iteration(X1)),one),
inference(paramodulation,[status(thm)],[f35,f209]) ).
fof(f5230,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(addition(X2,X3),X1),X4)) = addition(multiplication(addition(X0,X2),X1),addition(multiplication(X3,X1),X4)),
inference(paramodulation,[status(thm)],[f209,f209]) ).
fof(f5231,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,addition(X1,X3)),X4)) = addition(multiplication(addition(X0,X2),X1),addition(multiplication(X2,X3),X4)),
inference(paramodulation,[status(thm)],[f116,f209]) ).
fof(f5232,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),multiplication(addition(X2,multiplication(X3,X4)),X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(X3,multiplication(X4,X1))),
inference(paramodulation,[status(thm)],[f199,f209]) ).
fof(f5233,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,X3),X1)) = addition(multiplication(addition(X0,X3),X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f192,f209]) ).
fof(f5234,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,addition(X3,X1))) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f104,f209]) ).
fof(f5235,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,X3),X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(X3,X1)),
inference(paramodulation,[status(thm)],[f27,f209]) ).
fof(f5236,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,addition(X1,X3))) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f26,f209]) ).
fof(f5237,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(addition(X2,one),X1)) = addition(multiplication(addition(X0,X2),X1),X1),
inference(paramodulation,[status(thm)],[f201,f209]) ).
fof(f5238,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,addition(X1,one))) = addition(multiplication(addition(X0,X2),X1),X2),
inference(paramodulation,[status(thm)],[f114,f209]) ).
fof(f5239,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),zero)),
inference(paramodulation,[status(thm)],[f2007,f209]) ).
fof(f5240,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(one,X2),multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),multiplication(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f197,f209]) ).
fof(f5241,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(multiplication(X2,X1),addition(one,X3))) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),X3)),
inference(paramodulation,[status(thm)],[f110,f209]) ).
fof(f5243,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(X3,multiplication(X4,X1)))) = addition(multiplication(addition(X0,X4),X1),addition(X2,X3)),
inference(paramodulation,[status(thm)],[f58,f209]) ).
fof(f5244,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),X4))) = addition(multiplication(addition(X0,X3),X1),addition(X4,X2)),
inference(paramodulation,[status(thm)],[f58,f209]) ).
fof(f5245,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),addition(multiplication(X3,X1),X2)),
inference(paramodulation,[status(thm)],[f457,f209]) ).
fof(f5246,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),addition(X2,multiplication(X3,X1))),
inference(paramodulation,[status(thm)],[f182,f209]) ).
fof(f5247,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) = addition(multiplication(addition(X0,X2),X1),addition(X3,multiplication(X2,X1))),
inference(paramodulation,[status(thm)],[f153,f209]) ).
fof(f5249,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),zero),
inference(paramodulation,[status(thm)],[f21,f209]) ).
fof(f5250,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),X2),
inference(paramodulation,[status(thm)],[f19,f209]) ).
fof(f5251,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),X2),
inference(paramodulation,[status(thm)],[f19,f209]) ).
fof(f5252,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),multiplication(X2,X1)) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,X1)),
inference(paramodulation,[status(thm)],[f22,f209]) ).
fof(f5253,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(X1,multiplication(X2,X1)),X3)) = addition(multiplication(addition(X0,addition(one,X2)),X1),X3),
inference(paramodulation,[status(thm)],[f197,f209]) ).
fof(f5254,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(addition(multiplication(X2,X1),X1),X3)) = addition(multiplication(addition(X0,addition(X2,one)),X1),X3),
inference(paramodulation,[status(thm)],[f201,f209]) ).
fof(f5255,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(X2,multiplication(X3,X1)),X4)) = addition(multiplication(addition(X0,multiplication(X2,X3)),X1),X4),
inference(paramodulation,[status(thm)],[f23,f209]) ).
fof(f5257,plain,
! [X0,X1,X2] : addition(multiplication(X0,X1),addition(X1,X2)) = addition(multiplication(addition(X0,one),X1),X2),
inference(paramodulation,[status(thm)],[f25,f209]) ).
fof(f5258,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(one,X1)),addition(addition(X2,multiplication(X2,X1)),X3)) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(paramodulation,[status(thm)],[f110,f209]) ).
fof(f5259,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,one)),addition(addition(multiplication(X2,X1),X2),X3)) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(paramodulation,[status(thm)],[f114,f209]) ).
fof(f5261,plain,
! [X0,X1] : addition(multiplication(addition(addition(multiplication(X0,zero),X1),X0),zero),X1) = addition(multiplication(X0,zero),X1),
inference(paramodulation,[status(thm)],[f209,f1913]) ).
fof(f5263,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X3),X4)) = addition(multiplication(X0,addition(X1,X3)),addition(multiplication(X2,X3),X4)),
inference(paramodulation,[status(thm)],[f209,f116]) ).
fof(f5264,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),addition(X1,one)) = addition(multiplication(addition(addition(multiplication(X0,X1),X2),X0),X1),X2),
inference(paramodulation,[status(thm)],[f209,f114]) ).
fof(f5265,plain,
! [X0,X1,X2,X3] :
( leq(X0,multiplication(strong_iteration(X1),addition(multiplication(X2,X0),X3)))
| ~ leq(X0,addition(multiplication(addition(X1,X2),X0),X3)) ),
inference(paramodulation,[status(thm)],[f209,f37]) ).
fof(f5266,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(addition(multiplication(X1,X2),X3),star(X2)),X0)
| ~ leq(addition(multiplication(addition(X0,X1),X2),X3),X0) ),
inference(paramodulation,[status(thm)],[f209,f34]) ).
fof(f5267,plain,
! [X0,X1,X2,X3] :
( leq(multiplication(star(X0),addition(multiplication(X1,X2),X3)),X2)
| ~ leq(addition(multiplication(addition(X0,X1),X2),X3),X2) ),
inference(paramodulation,[status(thm)],[f209,f32]) ).
fof(f5272,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(addition(X0,X3),X1),X2)),
inference(paramodulation,[status(thm)],[f209,f2590]) ).
fof(f5274,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(multiplication(addition(X1,X3),X2),X0)),
inference(paramodulation,[status(thm)],[f209,f1129]) ).
fof(f5275,plain,
! [X0,X1,X2,X3] : leq(addition(X0,multiplication(X1,X2)),addition(multiplication(addition(X3,X1),X2),X0)),
inference(paramodulation,[status(thm)],[f209,f339]) ).
fof(f5276,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(addition(X3,X0),X1),X4))),
inference(paramodulation,[status(thm)],[f209,f241]) ).
fof(f5278,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),multiplication(X2,X1)),addition(multiplication(addition(X0,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f209,f176]) ).
fof(f5279,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X0,X2),X1),X3) != X3
| leq(addition(multiplication(X0,X1),multiplication(X2,X1)),X3) ),
inference(paramodulation,[status(thm)],[f209,f85]) ).
fof(f5280,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X3,X0),X1),X2),
inference(paramodulation,[status(thm)],[f209,f58]) ).
fof(f5281,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f209,f58]) ).
fof(f5285,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(addition(X2,X0),X1),X3)),
inference(paramodulation,[status(thm)],[f209,f237]) ).
fof(f5288,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(addition(X0,X3),X1),X4),X2) != multiplication(addition(multiplication(X3,X1),X4),X2)
| leq(multiplication(multiplication(X0,X1),X2),multiplication(addition(multiplication(X3,X1),X4),X2)) ),
inference(paramodulation,[status(thm)],[f209,f208]) ).
fof(f5289,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,addition(multiplication(X1,X2),X3)),addition(X0,addition(multiplication(addition(X4,X1),X2),X3))),
inference(paramodulation,[status(thm)],[f209,f2590]) ).
fof(f5290,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(addition(X0,X1),X2),X3),addition(multiplication(X0,X2),addition(X4,addition(multiplication(X1,X2),X3)))),
inference(paramodulation,[status(thm)],[f209,f2590]) ).
fof(f5291,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),addition(X2,addition(multiplication(addition(X0,X3),X1),X4))),
inference(paramodulation,[status(thm)],[f209,f1609]) ).
fof(f5292,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(addition(X0,X1),X2),X3),addition(addition(multiplication(X1,X2),X3),addition(multiplication(X0,X2),X4))),
inference(paramodulation,[status(thm)],[f209,f1609]) ).
fof(f5293,plain,
! [X0,X1,X2,X3,X4] : leq(addition(addition(multiplication(X0,X1),X2),X3),addition(X3,addition(multiplication(addition(X4,X0),X1),X2))),
inference(paramodulation,[status(thm)],[f209,f1129]) ).
fof(f5294,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(addition(X0,X1),X2),X3),addition(addition(multiplication(X1,X2),X3),addition(X4,multiplication(X0,X2)))),
inference(paramodulation,[status(thm)],[f209,f1129]) ).
fof(f5297,plain,
! [X0,X1,X2,X3,X4,X5] : leq(multiplication(X0,X1),addition(X2,addition(X3,addition(multiplication(addition(X0,X4),X1),X5)))),
inference(paramodulation,[status(thm)],[f209,f241]) ).
fof(f5298,plain,
! [X0,X1,X2,X3,X4,X5] : leq(addition(multiplication(X0,X1),X2),addition(X3,addition(X4,addition(multiplication(addition(X5,X0),X1),X2)))),
inference(paramodulation,[status(thm)],[f209,f223]) ).
fof(f5299,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(multiplication(X0,X1),X2),multiplication(addition(multiplication(addition(X0,X3),X1),X4),X2)),
inference(paramodulation,[status(thm)],[f209,f205]) ).
fof(f5300,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(X0,addition(multiplication(addition(X1,X3),X2),X4)) != multiplication(X0,addition(multiplication(X3,X2),X4))
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,addition(multiplication(X3,X2),X4))) ),
inference(paramodulation,[status(thm)],[f209,f115]) ).
fof(f5301,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(addition(multiplication(X0,X1),X2),X3),multiplication(addition(multiplication(addition(X4,X0),X1),X2),X3)),
inference(paramodulation,[status(thm)],[f209,f204]) ).
fof(f5302,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,addition(multiplication(X1,X2),X3)),multiplication(X0,addition(multiplication(addition(X4,X1),X2),X3))),
inference(paramodulation,[status(thm)],[f209,f183]) ).
fof(f5303,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,multiplication(X1,X2)),addition(X0,addition(multiplication(addition(X1,X3),X2),X4))),
inference(paramodulation,[status(thm)],[f209,f176]) ).
fof(f5304,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(addition(X0,X1),X2),X3),addition(multiplication(X0,X2),addition(addition(multiplication(X1,X2),X3),X4))),
inference(paramodulation,[status(thm)],[f209,f176]) ).
fof(f5305,plain,
! [X0,X1,X2,X3] : leq(multiplication(multiplication(X0,X1),zero),addition(multiplication(addition(X0,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f209,f2307]) ).
fof(f5306,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(multiplication(X0,X1),X2),zero),addition(multiplication(addition(X3,X0),X1),X2)),
inference(paramodulation,[status(thm)],[f209,f2042]) ).
fof(f5307,plain,
! [X0,X1,X2,X3,X4] :
( addition(X0,addition(multiplication(addition(X1,X3),X2),X4)) != addition(multiplication(X3,X2),X4)
| leq(addition(X0,multiplication(X1,X2)),addition(multiplication(X3,X2),X4)) ),
inference(paramodulation,[status(thm)],[f209,f85]) ).
fof(f5308,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(X0,addition(multiplication(addition(X1,X3),X2),X4))),
inference(paramodulation,[status(thm)],[f209,f174]) ).
fof(f5309,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),multiplication(strong_iteration(X3),addition(multiplication(addition(X4,X0),X1),X2))),
inference(paramodulation,[status(thm)],[f209,f874]) ).
fof(f5310,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),multiplication(strong_iteration(X2),addition(multiplication(addition(X0,X3),X1),X4))),
inference(paramodulation,[status(thm)],[f209,f873]) ).
fof(f5311,plain,
! [X0,X1,X2,X3,X4] : addition(addition(multiplication(X0,X1),X2),addition(multiplication(X3,X1),X4)) = addition(addition(multiplication(addition(X3,X0),X1),X2),X4),
inference(paramodulation,[status(thm)],[f209,f63]) ).
fof(f5312,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X3,X0),X1),X2) != addition(multiplication(X0,X1),X2)
| leq(addition(addition(multiplication(X0,X1),X2),multiplication(X3,X1)),addition(multiplication(X0,X1),X2)) ),
inference(paramodulation,[status(thm)],[f209,f580]) ).
fof(f5313,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(addition(multiplication(X2,X1),X3),X4)) = addition(X4,addition(multiplication(addition(X0,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f209,f58]) ).
fof(f5314,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(addition(X1,X2),X3),X4)) = addition(addition(multiplication(X2,X3),X4),addition(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f209,f58]) ).
fof(f5315,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X0,X2),X1),X3) != addition(multiplication(X2,X1),X3)
| leq(addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)),addition(multiplication(X2,X1),X3)) ),
inference(paramodulation,[status(thm)],[f209,f475]) ).
fof(f5316,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X3,X0),X1),X2) != multiplication(X3,X1)
| leq(addition(addition(multiplication(X0,X1),X2),multiplication(X3,X1)),multiplication(X3,X1)) ),
inference(paramodulation,[status(thm)],[f209,f343]) ).
fof(f5317,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X0,X2),X1),X3) != multiplication(X0,X1)
| leq(addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)),multiplication(X0,X1)) ),
inference(paramodulation,[status(thm)],[f209,f158]) ).
fof(f5318,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X1),X3)) = addition(addition(multiplication(X2,X1),X3),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f209,f457]) ).
fof(f5323,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,X1),addition(X2,addition(multiplication(addition(X0,X3),X1),X4))),
inference(paramodulation,[status(thm)],[f209,f237]) ).
fof(f5324,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(X0,X1),X2),addition(X3,addition(multiplication(addition(X4,X0),X1),X2))),
inference(paramodulation,[status(thm)],[f209,f185]) ).
fof(f5325,plain,
! [X0,X1,X2,X3] : leq(addition(multiplication(X0,X1),X2),addition(multiplication(addition(X3,X0),X1),X2)),
inference(paramodulation,[status(thm)],[f209,f179]) ).
fof(f5326,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X1),X3)),
inference(paramodulation,[status(thm)],[f209,f145]) ).
fof(f5327,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(addition(X0,X2),X1),X3)) = addition(multiplication(X0,X1),addition(multiplication(X2,X1),X3)),
inference(paramodulation,[status(thm)],[f209,f65]) ).
fof(f5328,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X3,X0),X1),X2) != multiplication(X3,X1)
| leq(addition(multiplication(X0,X1),X2),multiplication(X3,X1)) ),
inference(paramodulation,[status(thm)],[f209,f87]) ).
fof(f5329,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X0,X2),X1),X3) != addition(multiplication(X2,X1),X3)
| leq(multiplication(X0,X1),addition(multiplication(X2,X1),X3)) ),
inference(paramodulation,[status(thm)],[f209,f42]) ).
fof(f5330,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(addition(multiplication(X2,X1),X3),X4)) = addition(addition(multiplication(addition(X0,X2),X1),X3),X4),
inference(paramodulation,[status(thm)],[f209,f20]) ).
fof(f5333,plain,
! [X0,X1] : addition(multiplication(X0,zero),X1) = addition(multiplication(addition(X1,addition(multiplication(X0,zero),X0)),zero),X1),
inference(forward_demodulation,[status(thm)],[f63,f5206]) ).
fof(f5334,plain,
! [X0,X1] : addition(multiplication(X0,zero),X1) = addition(multiplication(addition(X1,X0),zero),X1),
inference(forward_demodulation,[status(thm)],[f1913,f5333]) ).
fof(f5336,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),addition(X1,one)) = addition(multiplication(addition(X2,addition(multiplication(X0,X1),X0)),X1),X2),
inference(forward_demodulation,[status(thm)],[f63,f5208]) ).
fof(f5337,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(addition(X1,X2),X3)) = addition(multiplication(addition(X2,X1),X3),X0),
inference(forward_demodulation,[status(thm)],[f192,f5210]) ).
fof(f5339,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X0,X1),X2),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f192,f5212]) ).
fof(f5340,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X0,X1)),X2),
inference(forward_demodulation,[status(thm)],[f192,f5339]) ).
fof(f5341,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f457,f5340]) ).
fof(f5348,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X1,addition(multiplication(X2,X1),X3))) = addition(multiplication(addition(addition(one,X0),X2),X1),X3),
inference(forward_demodulation,[status(thm)],[f63,f5217]) ).
fof(f5349,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X1,addition(multiplication(X2,X1),X3))) = addition(multiplication(addition(X0,addition(one,X2)),X1),X3),
inference(forward_demodulation,[status(thm)],[f63,f5348]) ).
fof(f5350,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X1,X0),addition(multiplication(X2,X0),X3))) = addition(multiplication(addition(addition(X1,one),X2),X0),X3),
inference(forward_demodulation,[status(thm)],[f63,f5218]) ).
fof(f5351,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(addition(X1,X2),X0),X3)) = addition(multiplication(addition(addition(X1,one),X2),X0),X3),
inference(forward_demodulation,[status(thm)],[f209,f5350]) ).
fof(f5352,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(addition(X1,X2),X0),X3)) = addition(multiplication(addition(one,addition(X1,X2)),X0),X3),
inference(forward_demodulation,[status(thm)],[f63,f5351]) ).
fof(f5354,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X0,addition(multiplication(X2,addition(one,X1)),X3))) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(forward_demodulation,[status(thm)],[f63,f5222]) ).
fof(f5355,plain,
! [X0,X1,X2,X3] : addition(X0,addition(multiplication(X0,X1),addition(multiplication(X2,addition(X1,one)),X3))) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(forward_demodulation,[status(thm)],[f63,f5223]) ).
fof(f5360,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(addition(X0,addition(X1,X2)),X3),X4) = addition(multiplication(addition(X0,X1),X3),addition(multiplication(X2,X3),X4)),
inference(forward_demodulation,[status(thm)],[f209,f5230]) ).
fof(f5361,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(addition(X0,addition(X1,X2)),X3),X4) = addition(multiplication(addition(addition(X0,X1),X2),X3),X4),
inference(forward_demodulation,[status(thm)],[f209,f5360]) ).
fof(f5362,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(addition(X0,addition(X1,X2)),X3),X4) = addition(multiplication(addition(X1,addition(X0,X2)),X3),X4),
inference(forward_demodulation,[status(thm)],[f63,f5361]) ).
fof(f5363,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(addition(X0,multiplication(X1,X2)),X3),X4) = addition(multiplication(addition(X3,X0),X4),multiplication(X1,multiplication(X2,X4))),
inference(forward_demodulation,[status(thm)],[f192,f5232]) ).
fof(f5364,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),X4) = addition(multiplication(addition(X3,X2),X4),multiplication(X0,multiplication(X1,X4))),
inference(forward_demodulation,[status(thm)],[f63,f5363]) ).
fof(f5365,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),X4) = multiplication(addition(addition(X3,X2),multiplication(X0,X1)),X4),
inference(forward_demodulation,[status(thm)],[f199,f5364]) ).
fof(f5366,plain,
! [X0,X1,X2,X3,X4] : multiplication(addition(multiplication(X0,X1),addition(X2,X3)),X4) = multiplication(addition(X2,addition(X3,multiplication(X0,X1))),X4),
inference(forward_demodulation,[status(thm)],[f63,f5365]) ).
fof(f5367,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,X1),X2),X3) = addition(multiplication(addition(X2,X1),X3),multiplication(X0,X3)),
inference(forward_demodulation,[status(thm)],[f192,f5233]) ).
fof(f5368,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = addition(multiplication(addition(X2,X0),X3),multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f63,f5367]) ).
fof(f5369,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X1,addition(X2,X0)),X3),
inference(forward_demodulation,[status(thm)],[f192,f5368]) ).
fof(f5370,plain,
! [X0,X1,X2,X3] : multiplication(addition(addition(X0,X1),X2),X3) = addition(multiplication(addition(X2,X0),X3),multiplication(X1,X3)),
inference(forward_demodulation,[status(thm)],[f192,f5235]) ).
fof(f5371,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = addition(multiplication(addition(X2,X1),X3),multiplication(X0,X3)),
inference(forward_demodulation,[status(thm)],[f63,f5370]) ).
fof(f5372,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X0,addition(X2,X1)),X3),
inference(forward_demodulation,[status(thm)],[f192,f5371]) ).
fof(f5373,plain,
! [X0,X1,X2] : multiplication(addition(addition(X0,one),X1),X2) = addition(multiplication(addition(X1,X0),X2),X2),
inference(forward_demodulation,[status(thm)],[f192,f5237]) ).
fof(f5374,plain,
! [X0,X1,X2] : multiplication(addition(one,addition(X0,X1)),X2) = addition(multiplication(addition(X1,X0),X2),X2),
inference(forward_demodulation,[status(thm)],[f63,f5373]) ).
fof(f5375,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(multiplication(X0,X2),zero)),
inference(forward_demodulation,[status(thm)],[f192,f5239]) ).
fof(f5376,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,multiplication(X2,zero))),
inference(forward_demodulation,[status(thm)],[f23,f5375]) ).
fof(f5377,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(one,X1),X2)),X3) = addition(multiplication(addition(X0,X2),X3),multiplication(X1,multiplication(X2,X3))),
inference(forward_demodulation,[status(thm)],[f199,f5240]) ).
fof(f5378,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(one,X1),X2)),X3) = multiplication(addition(addition(X0,X2),multiplication(X1,X2)),X3),
inference(forward_demodulation,[status(thm)],[f199,f5377]) ).
fof(f5379,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,multiplication(addition(one,X1),X2)),X3) = multiplication(addition(X2,addition(X0,multiplication(X1,X2))),X3),
inference(forward_demodulation,[status(thm)],[f63,f5378]) ).
fof(f5380,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,multiplication(X1,addition(one,X3)))) = addition(multiplication(addition(X0,X2),X1),multiplication(multiplication(X2,X1),X3)),
inference(forward_demodulation,[status(thm)],[f23,f5241]) ).
fof(f5381,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(X2,multiplication(X1,addition(one,X3)))) = addition(multiplication(addition(X0,X2),X1),multiplication(X2,multiplication(X1,X3))),
inference(forward_demodulation,[status(thm)],[f23,f5380]) ).
fof(f5383,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(addition(X0,X3),X3),X1),X2),
inference(forward_demodulation,[status(thm)],[f209,f5245]) ).
fof(f5384,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X3,addition(X0,X3)),X1),X2),
inference(forward_demodulation,[status(thm)],[f63,f5383]) ).
fof(f5385,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X2,multiplication(X3,X1))) = addition(multiplication(addition(X0,X3),X1),X2),
inference(forward_demodulation,[status(thm)],[f182,f5384]) ).
fof(f5386,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(addition(X0,X1),X2),addition(X3,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f209,f5247]) ).
fof(f5390,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),zero),
inference(forward_demodulation,[status(thm)],[f192,f5249]) ).
fof(f5391,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f21,f5390]) ).
fof(f5392,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(addition(X1,X0),X2),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f192,f5252]) ).
fof(f5393,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X0,addition(X1,X0)),X2),
inference(forward_demodulation,[status(thm)],[f192,f5392]) ).
fof(f5394,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f182,f5393]) ).
fof(f5395,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(multiplication(X2,X1),addition(X1,X3))) = addition(multiplication(addition(X0,addition(one,X2)),X1),X3),
inference(forward_demodulation,[status(thm)],[f63,f5253]) ).
fof(f5396,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),addition(X2,X3)) = addition(multiplication(addition(X0,addition(one,X1)),X2),X3),
inference(forward_demodulation,[status(thm)],[f209,f5395]) ).
fof(f5397,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),addition(X1,addition(multiplication(X2,X1),X3))) = addition(multiplication(addition(X0,addition(X2,one)),X1),X3),
inference(forward_demodulation,[status(thm)],[f63,f5254]) ).
fof(f5399,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(one,X1)),addition(multiplication(X2,X1),addition(X2,X3))) = addition(multiplication(addition(X0,X2),addition(one,X1)),X3),
inference(forward_demodulation,[status(thm)],[f63,f5258]) ).
fof(f5400,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,addition(X1,one)),addition(X2,addition(multiplication(X2,X1),X3))) = addition(multiplication(addition(X0,X2),addition(X1,one)),X3),
inference(forward_demodulation,[status(thm)],[f63,f5259]) ).
fof(f5403,plain,
! [X0,X1] : addition(multiplication(addition(X0,addition(multiplication(X1,zero),X1)),zero),X0) = addition(multiplication(X1,zero),X0),
inference(forward_demodulation,[status(thm)],[f63,f5261]) ).
fof(f5404,plain,
! [X0,X1] : addition(multiplication(addition(X0,X1),zero),X0) = addition(multiplication(X1,zero),X0),
inference(forward_demodulation,[status(thm)],[f1913,f5403]) ).
fof(f5406,plain,
! [X0,X1,X2] : multiplication(addition(multiplication(X0,X1),X2),addition(X1,one)) = addition(multiplication(addition(X2,addition(multiplication(X0,X1),X0)),X1),X2),
inference(forward_demodulation,[status(thm)],[f63,f5264]) ).
fof(f5408,plain,
! [X0,X1,X2,X3] : leq(multiplication(addition(X0,X1),X2),addition(multiplication(addition(X1,X0),X2),X3)),
inference(forward_demodulation,[status(thm)],[f192,f5278]) ).
fof(f5409,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X1,X0),X2),X3) != X3
| leq(multiplication(addition(X0,X1),X2),X3) ),
inference(forward_demodulation,[status(thm)],[f192,f5279]) ).
fof(f5410,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f192,f5281]) ).
fof(f5416,plain,
! [X0,X1,X2,X3,X4] :
( multiplication(addition(multiplication(addition(X0,X3),X1),X4),X2) != multiplication(addition(multiplication(X3,X1),X4),X2)
| leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(X3,X1),X4),X2)) ),
inference(forward_demodulation,[status(thm)],[f23,f5288]) ).
fof(f5417,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(addition(X0,X1),X2),X3),addition(X3,addition(multiplication(X1,X2),addition(multiplication(X0,X2),X4)))),
inference(forward_demodulation,[status(thm)],[f63,f5292]) ).
fof(f5418,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(addition(X0,X1),X2),X3),addition(X3,addition(multiplication(addition(X1,X0),X2),X4))),
inference(forward_demodulation,[status(thm)],[f209,f5417]) ).
fof(f5419,plain,
! [X0,X1,X2,X3,X4] : leq(addition(X0,addition(multiplication(X1,X2),X3)),addition(X3,addition(multiplication(addition(X4,X1),X2),X0))),
inference(forward_demodulation,[status(thm)],[f63,f5293]) ).
fof(f5420,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(addition(X0,X1),X2),X3),addition(X3,addition(multiplication(X1,X2),addition(X4,multiplication(X0,X2))))),
inference(forward_demodulation,[status(thm)],[f63,f5294]) ).
fof(f5425,plain,
! [X0,X1,X2,X3,X4] : leq(multiplication(X0,multiplication(X1,X2)),multiplication(addition(multiplication(addition(X0,X3),X1),X4),X2)),
inference(forward_demodulation,[status(thm)],[f23,f5299]) ).
fof(f5426,plain,
! [X0,X1,X2,X3,X4] : leq(addition(multiplication(addition(X0,X1),X2),X3),addition(multiplication(X0,X2),addition(X3,addition(multiplication(X1,X2),X4)))),
inference(forward_demodulation,[status(thm)],[f63,f5304]) ).
fof(f5427,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,zero)),addition(multiplication(addition(X0,X2),X1),X3)),
inference(forward_demodulation,[status(thm)],[f23,f5305]) ).
fof(f5428,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(X1,X2),addition(multiplication(X3,X2),X4))) = addition(addition(multiplication(addition(X3,X1),X2),X0),X4),
inference(forward_demodulation,[status(thm)],[f63,f5311]) ).
fof(f5429,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(addition(X1,X2),X3),X4)) = addition(addition(multiplication(addition(X2,X1),X3),X0),X4),
inference(forward_demodulation,[status(thm)],[f209,f5428]) ).
fof(f5430,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(addition(X1,X2),X3),X4)) = addition(X0,addition(multiplication(addition(X2,X1),X3),X4)),
inference(forward_demodulation,[status(thm)],[f63,f5429]) ).
fof(f5431,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X3,X1),X2),X0) != addition(multiplication(X1,X2),X0)
| leq(addition(X0,addition(multiplication(X1,X2),multiplication(X3,X2))),addition(multiplication(X1,X2),X0)) ),
inference(forward_demodulation,[status(thm)],[f63,f5312]) ).
fof(f5432,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X1,X2),X3),X0) != addition(multiplication(X2,X3),X0)
| leq(addition(X0,multiplication(addition(X1,X2),X3)),addition(multiplication(X2,X3),X0)) ),
inference(forward_demodulation,[status(thm)],[f192,f5431]) ).
fof(f5433,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),X4))) = addition(X4,addition(multiplication(addition(X0,X3),X1),X2)),
inference(forward_demodulation,[status(thm)],[f63,f5313]) ).
fof(f5434,plain,
! [X0,X1,X2,X3,X4] : addition(X0,addition(multiplication(addition(X1,X2),X3),X4)) = addition(X4,addition(multiplication(X2,X3),addition(X0,multiplication(X1,X3)))),
inference(forward_demodulation,[status(thm)],[f63,f5314]) ).
fof(f5435,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X0,X1),X2),X3) != addition(multiplication(X1,X2),X3)
| leq(addition(multiplication(addition(X0,X1),X2),X3),addition(multiplication(X1,X2),X3)) ),
inference(forward_demodulation,[status(thm)],[f209,f5315]) ).
fof(f5436,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X3,X1),X2),X0) != multiplication(X3,X2)
| leq(addition(X0,addition(multiplication(X1,X2),multiplication(X3,X2))),multiplication(X3,X2)) ),
inference(forward_demodulation,[status(thm)],[f63,f5316]) ).
fof(f5437,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X1,X2),X3),X0) != multiplication(X1,X3)
| leq(addition(X0,multiplication(addition(X1,X2),X3)),multiplication(X1,X3)) ),
inference(forward_demodulation,[status(thm)],[f192,f5436]) ).
fof(f5438,plain,
! [X0,X1,X2,X3] :
( addition(multiplication(addition(X0,X1),X2),X3) != multiplication(X0,X2)
| leq(addition(multiplication(addition(X0,X1),X2),X3),multiplication(X0,X2)) ),
inference(forward_demodulation,[status(thm)],[f209,f5317]) ).
fof(f5439,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X0,X1)),X2),X3) = addition(addition(multiplication(X1,X2),X3),multiplication(X0,X2)),
inference(forward_demodulation,[status(thm)],[f209,f5318]) ).
fof(f5440,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(addition(multiplication(X0,X2),X3),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f457,f5439]) ).
fof(f5441,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,addition(multiplication(X0,X2),multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f63,f5440]) ).
fof(f5442,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(X3,multiplication(addition(X1,X0),X2)),
inference(forward_demodulation,[status(thm)],[f192,f5441]) ).
fof(f5457,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,addition(X0,X1)),X2),X3) = addition(multiplication(X0,X2),addition(multiplication(X1,X2),X3)),
inference(forward_demodulation,[status(thm)],[f209,f5327]) ).
fof(f5458,plain,
! [X0,X1,X2,X3] : addition(multiplication(addition(X0,X1),X2),X3) = addition(multiplication(X1,X2),addition(multiplication(X0,X2),X3)),
inference(forward_demodulation,[status(thm)],[f457,f5457]) ).
fof(f5459,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),X4))) = addition(addition(multiplication(addition(X0,X3),X1),X2),X4),
inference(forward_demodulation,[status(thm)],[f63,f5330]) ).
fof(f5460,plain,
! [X0,X1,X2,X3,X4] : addition(multiplication(X0,X1),addition(X2,addition(multiplication(X3,X1),X4))) = addition(X2,addition(multiplication(addition(X0,X3),X1),X4)),
inference(forward_demodulation,[status(thm)],[f63,f5459]) ).
fof(f5465,plain,
! [X0,X1,X2] : addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(multiplication(X0,X1),X2)))))) = star(multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f23,f257]) ).
fof(f5468,plain,
! [X0,X1,X2] : addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))) = star(multiplication(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f23,f257]) ).
fof(f5469,plain,
! [X0] : addition(one,multiplication(X0,zero)) = star(multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f28,f257]) ).
fof(f5471,plain,
! [X0,X1] : addition(one,multiplication(addition(one,X0),multiplication(X1,star(addition(X1,multiplication(X0,X1)))))) = star(multiplication(addition(one,X0),X1)),
inference(paramodulation,[status(thm)],[f197,f257]) ).
fof(f5472,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,one),multiplication(X1,star(addition(multiplication(X0,X1),X1))))) = star(multiplication(addition(X0,one),X1)),
inference(paramodulation,[status(thm)],[f201,f257]) ).
fof(f5473,plain,
! [X0,X1,X2] : addition(one,multiplication(multiplication(X0,X1),multiplication(X2,star(multiplication(X0,multiplication(X1,X2)))))) = star(multiplication(multiplication(X0,X1),X2)),
inference(paramodulation,[status(thm)],[f23,f257]) ).
fof(f5476,plain,
! [X0,X1] : addition(one,multiplication(X0,multiplication(addition(one,X1),star(addition(X0,multiplication(X0,X1)))))) = star(multiplication(X0,addition(one,X1))),
inference(paramodulation,[status(thm)],[f110,f257]) ).
fof(f5477,plain,
! [X0,X1] : addition(one,multiplication(X0,multiplication(addition(X1,one),star(addition(multiplication(X0,X1),X0))))) = star(multiplication(X0,addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f257]) ).
fof(f5479,plain,
! [X0,X1,X2] : multiplication(star(multiplication(X0,X1)),X2) = addition(X2,multiplication(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),X2)),
inference(paramodulation,[status(thm)],[f257,f197]) ).
fof(f5481,plain,
! [X0,X1,X2] : multiplication(X0,star(multiplication(X1,X2))) = addition(X0,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))))),
inference(paramodulation,[status(thm)],[f257,f110]) ).
fof(f5483,plain,
! [X0,X1,X2] :
( multiplication(star(multiplication(X1,X2)),X0) != multiplication(multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))),X0)
| leq(multiplication(one,X0),multiplication(multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))),X0)) ),
inference(paramodulation,[status(thm)],[f257,f208]) ).
fof(f5484,plain,
! [X0,X1,X2] : leq(addition(X0,multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))),addition(X0,star(multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f257,f2590]) ).
fof(f5485,plain,
! [X0,X1,X2] : leq(star(multiplication(X0,X1)),addition(one,addition(X2,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))))),
inference(paramodulation,[status(thm)],[f257,f2590]) ).
fof(f5486,plain,
! [X0,X1,X2] : leq(addition(one,X0),addition(X0,star(multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f257,f1609]) ).
fof(f5487,plain,
! [X0,X1,X2] : leq(star(multiplication(X0,X1)),addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),addition(one,X2))),
inference(paramodulation,[status(thm)],[f257,f1609]) ).
fof(f5488,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),X2),addition(X2,star(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f257,f1129]) ).
fof(f5489,plain,
! [X0,X1,X2] : leq(star(multiplication(X0,X1)),addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),addition(X2,one))),
inference(paramodulation,[status(thm)],[f257,f1129]) ).
fof(f5490,plain,
! [X0,X1,X2] : leq(addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one),addition(X2,star(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f257,f339]) ).
fof(f5491,plain,
! [X0,X1,X2] : leq(star(multiplication(X0,X1)),addition(X2,addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one))),
inference(paramodulation,[status(thm)],[f257,f339]) ).
fof(f5493,plain,
! [X0,X1,X2,X3] : leq(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),addition(X2,addition(X3,star(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f257,f223]) ).
fof(f5495,plain,
! [X0,X1,X2] :
( multiplication(X0,star(multiplication(X1,X2))) != multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))))
| leq(multiplication(X0,one),multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))))) ),
inference(paramodulation,[status(thm)],[f257,f115]) ).
fof(f5496,plain,
! [X0,X1,X2] : leq(multiplication(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),X2),multiplication(star(multiplication(X0,X1)),X2)),
inference(paramodulation,[status(thm)],[f257,f204]) ).
fof(f5497,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))),multiplication(X0,star(multiplication(X1,X2)))),
inference(paramodulation,[status(thm)],[f257,f183]) ).
fof(f5499,plain,
! [X0,X1,X2] : leq(star(multiplication(X0,X1)),addition(one,addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),X2))),
inference(paramodulation,[status(thm)],[f257,f176]) ).
fof(f5501,plain,
! [X0,X1] : leq(multiplication(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),zero),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f257,f2042]) ).
fof(f5502,plain,
! [X0,X1,X2] :
( addition(X0,star(multiplication(X1,X2))) != multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))
| leq(addition(X0,one),multiplication(X1,multiplication(X2,star(multiplication(X1,X2))))) ),
inference(paramodulation,[status(thm)],[f257,f85]) ).
fof(f5504,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),multiplication(strong_iteration(X2),star(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f257,f874]) ).
fof(f5506,plain,
! [X0,X1,X2] : addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),addition(one,X2)) = addition(star(multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f257,f63]) ).
fof(f5507,plain,
! [X0,X1] :
( star(multiplication(X0,X1)) != multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))
| leq(addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one),multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) ),
inference(paramodulation,[status(thm)],[f257,f580]) ).
fof(f5508,plain,
! [X0,X1,X2] : addition(one,addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),X2)) = addition(X2,star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f257,f58]) ).
fof(f5509,plain,
! [X0,X1,X2] : addition(X0,star(multiplication(X1,X2))) = addition(multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))),addition(X0,one)),
inference(paramodulation,[status(thm)],[f257,f58]) ).
fof(f5510,plain,
! [X0,X1] :
( star(multiplication(X0,X1)) != multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))
| leq(addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) ),
inference(paramodulation,[status(thm)],[f257,f475]) ).
fof(f5511,plain,
! [X0,X1] :
( star(multiplication(X0,X1)) != one
| leq(addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one),one) ),
inference(paramodulation,[status(thm)],[f257,f343]) ).
fof(f5513,plain,
! [X0,X1] : addition(one,star(multiplication(X0,X1))) = addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one),
inference(paramodulation,[status(thm)],[f257,f457]) ).
fof(f5514,plain,
! [X0,X1] : addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),star(multiplication(X0,X1))) = addition(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f257,f182]) ).
fof(f5515,plain,
! [X0,X1] : leq(addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f257,f340]) ).
fof(f5516,plain,
! [X0,X1] : leq(star(multiplication(X0,X1)),addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one)),
inference(paramodulation,[status(thm)],[f257,f340]) ).
fof(f5517,plain,
! [X0,X1] : addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),star(multiplication(X0,X1))) = addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one),
inference(paramodulation,[status(thm)],[f257,f153]) ).
fof(f5519,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),addition(X2,star(multiplication(X0,X1)))),
inference(paramodulation,[status(thm)],[f257,f185]) ).
fof(f5520,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),star(multiplication(X0,X1))),
inference(paramodulation,[status(thm)],[f257,f179]) ).
fof(f5523,plain,
! [X0,X1] :
( star(multiplication(X0,X1)) != one
| leq(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one) ),
inference(paramodulation,[status(thm)],[f257,f87]) ).
fof(f5524,plain,
! [X0,X1] :
( star(multiplication(X0,X1)) != multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))
| leq(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) ),
inference(paramodulation,[status(thm)],[f257,f42]) ).
fof(f5525,plain,
! [X0,X1,X2] : addition(one,addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),X2)) = addition(star(multiplication(X0,X1)),X2),
inference(paramodulation,[status(thm)],[f257,f20]) ).
fof(f5526,plain,
! [X0,X1,X2] : addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))) = star(multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f23,f5465]) ).
fof(f5527,plain,
! [X0,X1,X2] : addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))) = star(multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f5526]) ).
fof(f5534,plain,
! [X0,X1,X2] : addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))) = star(multiplication(multiplication(X0,X1),X2)),
inference(forward_demodulation,[status(thm)],[f23,f5473]) ).
fof(f5535,plain,
! [X0,X1,X2] : addition(one,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X0,multiplication(X1,X2))))))) = star(multiplication(X0,multiplication(X1,X2))),
inference(forward_demodulation,[status(thm)],[f23,f5534]) ).
fof(f5543,plain,
! [X0,X1,X2] : multiplication(star(multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(multiplication(X1,star(multiplication(X0,X1))),X2))),
inference(forward_demodulation,[status(thm)],[f23,f5479]) ).
fof(f5544,plain,
! [X0,X1,X2] : multiplication(star(multiplication(X0,X1)),X2) = addition(X2,multiplication(X0,multiplication(X1,multiplication(star(multiplication(X0,X1)),X2)))),
inference(forward_demodulation,[status(thm)],[f23,f5543]) ).
fof(f5545,plain,
! [X0,X1,X2] :
( multiplication(star(multiplication(X1,X2)),X0) != multiplication(multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))),X0)
| leq(X0,multiplication(multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))),X0)) ),
inference(forward_demodulation,[status(thm)],[f25,f5483]) ).
fof(f5546,plain,
! [X0,X1,X2] :
( multiplication(star(multiplication(X1,X2)),X0) != multiplication(multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))),X0)
| leq(X0,multiplication(X1,multiplication(multiplication(X2,star(multiplication(X1,X2))),X0))) ),
inference(forward_demodulation,[status(thm)],[f23,f5545]) ).
fof(f5547,plain,
! [X0,X1,X2] :
( multiplication(star(multiplication(X1,X2)),X0) != multiplication(multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))),X0)
| leq(X0,multiplication(X1,multiplication(X2,multiplication(star(multiplication(X1,X2)),X0)))) ),
inference(forward_demodulation,[status(thm)],[f23,f5546]) ).
fof(f5548,plain,
! [X0,X1,X2] :
( multiplication(star(multiplication(X1,X2)),X0) != multiplication(X1,multiplication(multiplication(X2,star(multiplication(X1,X2))),X0))
| leq(X0,multiplication(X1,multiplication(X2,multiplication(star(multiplication(X1,X2)),X0)))) ),
inference(forward_demodulation,[status(thm)],[f23,f5547]) ).
fof(f5549,plain,
! [X0,X1,X2] :
( multiplication(star(multiplication(X1,X2)),X0) != multiplication(X1,multiplication(X2,multiplication(star(multiplication(X1,X2)),X0)))
| leq(X0,multiplication(X1,multiplication(X2,multiplication(star(multiplication(X1,X2)),X0)))) ),
inference(forward_demodulation,[status(thm)],[f23,f5548]) ).
fof(f5551,plain,
! [X0,X1,X2] :
( multiplication(X0,star(multiplication(X1,X2))) != multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))))
| leq(X0,multiplication(X0,multiplication(X1,multiplication(X2,star(multiplication(X1,X2)))))) ),
inference(forward_demodulation,[status(thm)],[f24,f5495]) ).
fof(f5552,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(multiplication(X1,star(multiplication(X0,X1))),X2)),multiplication(star(multiplication(X0,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f5496]) ).
fof(f5553,plain,
! [X0,X1,X2] : leq(multiplication(X0,multiplication(X1,multiplication(star(multiplication(X0,X1)),X2))),multiplication(star(multiplication(X0,X1)),X2)),
inference(forward_demodulation,[status(thm)],[f23,f5552]) ).
fof(f5555,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(multiplication(X1,star(multiplication(X0,X1))),zero)),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f23,f5501]) ).
fof(f5556,plain,
! [X0,X1] : leq(multiplication(X0,multiplication(X1,multiplication(star(multiplication(X0,X1)),zero))),star(multiplication(X0,X1))),
inference(forward_demodulation,[status(thm)],[f23,f5555]) ).
fof(f5558,plain,
! [X0,X1] :
( star(multiplication(X0,X1)) != multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))
| leq(star(multiplication(X0,X1)),multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) ),
inference(forward_demodulation,[status(thm)],[f257,f5510]) ).
fof(f5560,plain,
! [X0,X1] : star(multiplication(X0,X1)) = addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),one),
inference(forward_demodulation,[status(thm)],[f269,f5513]) ).
fof(f5561,plain,
! [X0,X1] : addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),star(multiplication(X0,X1))) = star(multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f257,f5514]) ).
fof(f5563,plain,
! [X0,X1] : addition(addition(one,X0),addition(X0,strong_iteration(X1))) = addition(X0,strong_iteration(X1)),
inference(resolution,[status(thm)],[f3858,f41]) ).
fof(f5566,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(star(X0),X0),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f30,f3858]) ).
fof(f5567,plain,
! [X0,X1,X2] : leq(star(multiplication(X0,X1)),addition(multiplication(X0,multiplication(X1,star(multiplication(X0,X1)))),strong_iteration(X2))),
inference(paramodulation,[status(thm)],[f257,f3858]) ).
fof(f5568,plain,
! [X0,X1] : leq(strong_iteration(X0),addition(multiplication(X0,strong_iteration(X0)),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f791,f3858]) ).
fof(f5569,plain,
! [X0,X1] : leq(star(X0),addition(multiplication(X0,star(X0)),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f29,f3858]) ).
fof(f5572,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(addition(X0,X1),strong_iteration(X2))),
inference(paramodulation,[status(thm)],[f58,f3858]) ).
fof(f5573,plain,
! [X0,X1,X2] : leq(addition(X0,addition(one,X1)),addition(addition(X1,X0),strong_iteration(X2))),
inference(paramodulation,[status(thm)],[f58,f3858]) ).
fof(f5585,plain,
! [X0] : leq(addition(one,multiplication(strong_iteration(X0),zero)),strong_iteration(X0)),
inference(paramodulation,[status(thm)],[f1913,f3858]) ).
fof(f5586,plain,
! [X0,X1] : leq(addition(one,multiplication(X0,strong_iteration(X1))),multiplication(addition(X0,one),strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f201,f3858]) ).
fof(f5587,plain,
! [X0,X1] : leq(addition(one,multiplication(strong_iteration(X0),X1)),multiplication(strong_iteration(X0),addition(X1,one))),
inference(paramodulation,[status(thm)],[f114,f3858]) ).
fof(f5589,plain,
! [X0,X1,X2] : leq(addition(one,addition(X0,X1)),addition(X1,addition(X0,strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f63,f3858]) ).
fof(f5590,plain,
! [X0,X1,X2] : leq(addition(one,addition(X0,X1)),addition(X0,addition(X1,strong_iteration(X2)))),
inference(paramodulation,[status(thm)],[f20,f3858]) ).
fof(f5592,plain,
! [X0,X1] : leq(addition(one,X0),addition(strong_iteration(X1),X0)),
inference(paramodulation,[status(thm)],[f19,f3858]) ).
fof(f5593,plain,
! [X0,X1] : leq(addition(one,X0),addition(strong_iteration(X1),X0)),
inference(paramodulation,[status(thm)],[f19,f3858]) ).
fof(f5596,plain,
! [X0,X1] : addition(X0,addition(one,addition(X0,strong_iteration(X1)))) = addition(X0,strong_iteration(X1)),
inference(forward_demodulation,[status(thm)],[f63,f5563]) ).
fof(f5600,plain,
! [X0,X1,X2] : leq(addition(X0,addition(X1,one)),addition(X1,addition(X0,strong_iteration(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f5572]) ).
fof(f5601,plain,
! [X0,X1,X2] : leq(addition(X0,addition(one,X1)),addition(X0,addition(X1,strong_iteration(X2)))),
inference(forward_demodulation,[status(thm)],[f63,f5573]) ).
fof(f5616,plain,
! [X0,X1] :
( star(multiplication(X0,X1)) != multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))
| leq(one,multiplication(multiplication(X0,X1),star(multiplication(X0,X1)))) ),
inference(paramodulation,[status(thm)],[f23,f266]) ).
fof(f5617,plain,
( star(zero) != zero
| leq(one,multiplication(zero,star(zero))) ),
inference(paramodulation,[status(thm)],[f28,f266]) ).
fof(f5618,plain,
( star(one) != star(one)
| leq(one,multiplication(one,star(one))) ),
inference(paramodulation,[status(thm)],[f25,f266]) ).
fof(f5619,plain,
( star(zero) != multiplication(zero,one)
| leq(one,multiplication(zero,star(zero))) ),
inference(paramodulation,[status(thm)],[f268,f266]) ).
fof(f5621,plain,
! [X0,X1] :
( star(multiplication(X0,X1)) != multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))
| leq(one,multiplication(X0,multiplication(X1,star(multiplication(X0,X1))))) ),
inference(forward_demodulation,[status(thm)],[f23,f5616]) ).
fof(f5622,definition,
( sQ7_spl
<=> leq(one,multiplication(zero,star(zero))) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f5623,plain,
( ~ sQ7_spl
| leq(one,multiplication(zero,star(zero))) ),
inference(component_clause,[status(thm)],[f5622]) ).
fof(f5625,definition,
( sQ8_spl
<=> star(zero) = zero ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f5628,plain,
( ~ sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f5617,f5622,f5625]) ).
fof(f5629,definition,
( sQ9_spl
<=> leq(one,multiplication(one,star(one))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f5632,definition,
( sQ10_spl
<=> star(one) = star(one) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f5635,plain,
( ~ sQ10_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f5618,f5629,f5632]) ).
fof(f5636,definition,
( sQ11_spl
<=> star(zero) = multiplication(zero,one) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f5639,plain,
( ~ sQ11_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f5619,f5622,f5636]) ).
fof(f5640,plain,
( ~ sQ7_spl
| leq(one,zero) ),
inference(forward_demodulation,[status(thm)],[f28,f5623]) ).
fof(f5642,plain,
( ~ sQ7_spl
| addition(one,zero) = zero ),
inference(resolution,[status(thm)],[f5640,f41]) ).
fof(f5643,plain,
( ~ sQ7_spl
| one = zero ),
inference(forward_demodulation,[status(thm)],[f21,f5642]) ).
fof(f5679,plain,
( ~ sQ7_spl
| strong_iteration(zero) = zero ),
inference(backward_demodulation,[status(thm)],[f5643,f816]) ).
fof(f5690,plain,
! [X0] :
( ~ sQ7_spl
| multiplication(zero,X0) = X0 ),
inference(backward_demodulation,[status(thm)],[f5643,f25]) ).
fof(f5828,plain,
! [X0] :
( ~ sQ7_spl
| zero = X0 ),
inference(paramodulation,[status(thm)],[f28,f5690]) ).
fof(f5864,plain,
! [X0,X1] :
( ~ sQ7_spl
| leq(X0,multiplication(strong_iteration(zero),X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(paramodulation,[status(thm)],[f5690,f37]) ).
fof(f5907,plain,
! [X0,X1] :
( ~ sQ7_spl
| leq(X0,multiplication(zero,X1))
| ~ leq(X0,addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f5679,f5864]) ).
fof(f5908,plain,
! [X0,X1] :
( ~ sQ7_spl
| leq(X0,X1)
| ~ leq(X0,addition(X0,X1)) ),
inference(forward_demodulation,[status(thm)],[f5690,f5907]) ).
fof(f5909,plain,
! [X0,X1] :
( ~ sQ7_spl
| leq(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f5908,f145]) ).
fof(f5923,plain,
! [X0,X1] :
( ~ sQ7_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f5828,f5828]) ).
fof(model,axiom,
( sQ0_spl
| sQ1_spl
| sQ2_spl
| sQ3_spl
| sQ4_spl
| sQ5_spl
| sQ6_spl
| sQ7_spl
| sQ9_spl ) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : KLE182+1 : TPTP v9.3.1. Released v6.4.0.
% 0.00/0.05 % Command : drodi -satmode(on) -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n018.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sun Sep 20 22:51:42 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.42 % Drodi V4.1.1
% 4.12/1.03 % SZS status Satisfiable for theBenchmark: Theory is satisfiable
% 4.12/1.03 % SZS output start Saturation for theBenchmark
% See solution above
% 4.12/1.07 % Elapsed time: 0.644187 seconds
% 4.12/1.07 % CPU time: 4.629094 seconds
% 4.12/1.07 % Total memory used: 48.142 MB
% 4.12/1.07 % Net memory used: 45.268 MB
%------------------------------------------------------------------------------