TSTP Solution File: KLE011+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE011+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed May 31 12:15:28 EDT 2023
% Result : Theorem 69.92s 9.31s
% Output : CNFRefutation 70.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 85
% Syntax : Number of formulae : 611 ( 154 unt; 0 def)
% Number of atoms : 1285 ( 502 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1221 ( 547 ~; 573 |; 21 &)
% ( 76 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 76 ( 74 usr; 72 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 218 (; 213 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f21,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f35,plain,
( ! [X0] :
( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(miniscoping,[status(esa)],[f34]) ).
fof(f36,plain,
( ! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0,X1] :
( test(X0)
| ~ complement(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f40,plain,
( ! [X0,X1] :
( ~ complement(X1,X0)
| ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) )
& ! [X0,X1] :
( complement(X1,X0)
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| addition(X0,X1) != one ) ),
inference(miniscoping,[status(esa)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X1,X0) = zero ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f44,plain,
! [X0,X1] :
( complement(X0,X1)
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| addition(X1,X0) != one ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f45,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f46,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) = X1
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
! [X0] :
( test(X0)
| c(X0) = zero ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f51,plain,
! [X0] :
( test(X0)
| c(X0) = zero ),
inference(cnf_transformation,[status(esa)],[f50]) ).
fof(f52,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& one != addition(addition(multiplication(addition(X1,c(X1)),X0),multiplication(addition(X0,c(X0)),X1)),multiplication(c(X0),c(X1))) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
( test(sk0_2)
& test(sk0_1)
& one != addition(addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),multiplication(addition(sk0_1,c(sk0_1)),sk0_2)),multiplication(c(sk0_1),c(sk0_2))) ),
inference(skolemization,[status(esa)],[f52]) ).
fof(f54,plain,
test(sk0_2),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f55,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f56,plain,
one != addition(addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),multiplication(addition(sk0_1,c(sk0_1)),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f48]) ).
fof(f58,plain,
one != addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(c(sk0_1),c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f20,f56]) ).
fof(f59,plain,
one != addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(addition(sk0_1,c(sk0_1)),sk0_2))),
inference(forward_demodulation,[status(thm)],[f19,f58]) ).
fof(f60,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f43,f57]) ).
fof(f61,plain,
! [X0] :
( addition(X0,c(X0)) = one
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f19,f60]) ).
fof(f62,plain,
addition(sk0_1,c(sk0_1)) = one,
inference(resolution,[status(thm)],[f61,f55]) ).
fof(f63,plain,
addition(sk0_2,c(sk0_2)) = one,
inference(resolution,[status(thm)],[f61,f54]) ).
fof(f64,plain,
one != addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(one,sk0_2))),
inference(backward_demodulation,[status(thm)],[f62,f59]) ).
fof(f65,plain,
one != addition(multiplication(one,sk0_1),addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(one,sk0_2))),
inference(forward_demodulation,[status(thm)],[f63,f64]) ).
fof(f66,plain,
one != addition(sk0_1,addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(one,sk0_2))),
inference(forward_demodulation,[status(thm)],[f25,f65]) ).
fof(f67,plain,
one != addition(sk0_1,addition(multiplication(one,sk0_2),multiplication(c(sk0_1),c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f19,f66]) ).
fof(f68,plain,
one != addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f25,f67]) ).
fof(f69,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f75,plain,
! [X0] : addition(sk0_2,addition(c(sk0_2),X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f63,f20]) ).
fof(f76,plain,
! [X0] : addition(sk0_1,addition(c(sk0_1),X0)) = addition(one,X0),
inference(paramodulation,[status(thm)],[f62,f20]) ).
fof(f77,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f78,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f77]) ).
fof(f81,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f91,plain,
addition(sk0_2,one) = addition(sk0_2,c(sk0_2)),
inference(paramodulation,[status(thm)],[f63,f81]) ).
fof(f92,plain,
addition(one,sk0_2) = addition(sk0_2,c(sk0_2)),
inference(forward_demodulation,[status(thm)],[f19,f91]) ).
fof(f93,plain,
addition(one,sk0_2) = one,
inference(forward_demodulation,[status(thm)],[f63,f92]) ).
fof(f94,plain,
addition(sk0_1,one) = addition(sk0_1,c(sk0_1)),
inference(paramodulation,[status(thm)],[f62,f81]) ).
fof(f95,plain,
addition(one,sk0_1) = addition(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f94]) ).
fof(f96,plain,
addition(one,sk0_1) = one,
inference(forward_demodulation,[status(thm)],[f62,f95]) ).
fof(f97,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f81]) ).
fof(f119,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f120,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f119]) ).
fof(f130,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f142,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(f167,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),X2)
| addition(X0,addition(X1,X2)) != X2 ),
inference(paramodulation,[status(thm)],[f20,f33]) ).
fof(f171,plain,
( spl0_5
<=> one = c(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f173,plain,
( one != c(sk0_2)
| spl0_5 ),
inference(component_clause,[status(thm)],[f171]) ).
fof(f179,plain,
( spl0_7
<=> one = c(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f181,plain,
( one != c(sk0_1)
| spl0_7 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f186,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f19,f33]) ).
fof(f257,plain,
addition(c(sk0_2),one) = addition(c(sk0_2),sk0_2),
inference(paramodulation,[status(thm)],[f63,f97]) ).
fof(f258,plain,
addition(one,c(sk0_2)) = addition(c(sk0_2),sk0_2),
inference(forward_demodulation,[status(thm)],[f19,f257]) ).
fof(f259,plain,
addition(one,c(sk0_2)) = addition(sk0_2,c(sk0_2)),
inference(forward_demodulation,[status(thm)],[f19,f258]) ).
fof(f260,plain,
addition(one,c(sk0_2)) = one,
inference(forward_demodulation,[status(thm)],[f63,f259]) ).
fof(f261,plain,
addition(c(sk0_1),one) = addition(c(sk0_1),sk0_1),
inference(paramodulation,[status(thm)],[f62,f97]) ).
fof(f262,plain,
addition(one,c(sk0_1)) = addition(c(sk0_1),sk0_1),
inference(forward_demodulation,[status(thm)],[f19,f261]) ).
fof(f263,plain,
addition(one,c(sk0_1)) = addition(sk0_1,c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f262]) ).
fof(f264,plain,
addition(one,c(sk0_1)) = one,
inference(forward_demodulation,[status(thm)],[f62,f263]) ).
fof(f279,plain,
! [X0,X1] :
( leq(addition(X0,X1),X1)
| addition(X1,X0) != X1 ),
inference(paramodulation,[status(thm)],[f97,f186]) ).
fof(f329,plain,
( spl0_18
<=> addition(one,c(sk0_1)) = one ),
introduced(split_symbol_definition) ).
fof(f330,plain,
( addition(one,c(sk0_1)) = one
| ~ spl0_18 ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f331,plain,
( addition(one,c(sk0_1)) != one
| spl0_18 ),
inference(component_clause,[status(thm)],[f329]) ).
fof(f334,plain,
( spl0_19
<=> addition(one,c(sk0_2)) = one ),
introduced(split_symbol_definition) ).
fof(f336,plain,
( addition(one,c(sk0_2)) != one
| spl0_19 ),
inference(component_clause,[status(thm)],[f334]) ).
fof(f373,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| addition(addition(X1,X0),X0) = X0 ),
inference(resolution,[status(thm)],[f279,f32]) ).
fof(f374,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| addition(X1,addition(X0,X0)) = X0 ),
inference(forward_demodulation,[status(thm)],[f20,f373]) ).
fof(f375,plain,
! [X0,X1] :
( addition(X0,X1) != X0
| addition(X1,X0) = X0 ),
inference(forward_demodulation,[status(thm)],[f22,f374]) ).
fof(f503,plain,
! [X0,X1,X2] :
( leq(addition(X0,X1),X2)
| addition(X1,addition(X0,X2)) != X2 ),
inference(paramodulation,[status(thm)],[f19,f167]) ).
fof(f507,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| addition(addition(X1,X0),X2) = X2 ),
inference(resolution,[status(thm)],[f503,f32]) ).
fof(f508,plain,
! [X0,X1,X2] :
( addition(X0,addition(X1,X2)) != X2
| addition(X1,addition(X0,X2)) = X2 ),
inference(forward_demodulation,[status(thm)],[f20,f507]) ).
fof(f547,plain,
! [X0] : addition(sk0_2,addition(X0,c(sk0_2))) = addition(one,X0),
inference(paramodulation,[status(thm)],[f19,f75]) ).
fof(f584,plain,
! [X0] : addition(zero,X0) = X0,
inference(resolution,[status(thm)],[f21,f375]) ).
fof(f617,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X1,X2),multiplication(X0,X2)),
inference(paramodulation,[status(thm)],[f19,f27]) ).
fof(f618,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = multiplication(addition(X1,X0),X2),
inference(forward_demodulation,[status(thm)],[f27,f617]) ).
fof(f623,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f684,plain,
! [X0] : addition(sk0_1,addition(X0,c(sk0_1))) = addition(one,X0),
inference(paramodulation,[status(thm)],[f19,f76]) ).
fof(f2369,plain,
! [X0,X1,X2,X3] : multiplication(addition(X0,addition(X1,X2)),X3) = multiplication(addition(X2,addition(X0,X1)),X3),
inference(paramodulation,[status(thm)],[f20,f618]) ).
fof(f2448,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| addition(X1,addition(X0,X1)) = X1 ),
inference(paramodulation,[status(thm)],[f22,f508]) ).
fof(f2449,plain,
! [X0,X1] :
( addition(X0,X1) != X1
| addition(X1,X0) = X1 ),
inference(forward_demodulation,[status(thm)],[f97,f2448]) ).
fof(f2633,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,c(X1)) = one ),
inference(resolution,[status(thm)],[f38,f61]) ).
fof(f2637,plain,
( spl0_54
<=> multiplication(sk0_1,c(sk0_1)) = zero ),
introduced(split_symbol_definition) ).
fof(f2639,plain,
( multiplication(sk0_1,c(sk0_1)) != zero
| spl0_54 ),
inference(component_clause,[status(thm)],[f2637]) ).
fof(f2640,plain,
( spl0_55
<=> multiplication(c(sk0_1),sk0_1) = zero ),
introduced(split_symbol_definition) ).
fof(f2642,plain,
( multiplication(c(sk0_1),sk0_1) != zero
| spl0_55 ),
inference(component_clause,[status(thm)],[f2640]) ).
fof(f2645,plain,
( spl0_56
<=> complement(c(sk0_2),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f2646,plain,
( complement(c(sk0_2),sk0_2)
| ~ spl0_56 ),
inference(component_clause,[status(thm)],[f2645]) ).
fof(f2703,plain,
( spl0_72
<=> multiplication(one,zero) = zero ),
introduced(split_symbol_definition) ).
fof(f2705,plain,
( multiplication(one,zero) != zero
| spl0_72 ),
inference(component_clause,[status(thm)],[f2703]) ).
fof(f2706,plain,
( spl0_73
<=> multiplication(zero,one) = zero ),
introduced(split_symbol_definition) ).
fof(f2708,plain,
( multiplication(zero,one) != zero
| spl0_73 ),
inference(component_clause,[status(thm)],[f2706]) ).
fof(f2752,plain,
! [X0,X1] :
( complement(X0,X1)
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| addition(X0,X1) != one ),
inference(paramodulation,[status(thm)],[f19,f44]) ).
fof(f2757,plain,
( zero != zero
| spl0_73 ),
inference(forward_demodulation,[status(thm)],[f24,f2708]) ).
fof(f2758,plain,
( $false
| spl0_73 ),
inference(trivial_equality_resolution,[status(esa)],[f2757]) ).
fof(f2759,plain,
spl0_73,
inference(contradiction_clause,[status(thm)],[f2758]) ).
fof(f2760,plain,
( zero != zero
| spl0_72 ),
inference(forward_demodulation,[status(thm)],[f25,f2705]) ).
fof(f2761,plain,
( $false
| spl0_72 ),
inference(trivial_equality_resolution,[status(esa)],[f2760]) ).
fof(f2762,plain,
spl0_72,
inference(contradiction_clause,[status(thm)],[f2761]) ).
fof(f2767,plain,
! [X0] :
( addition(c(X0),c(c(X0))) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f2633,f57]) ).
fof(f2768,plain,
addition(c(sk0_1),c(c(sk0_1))) = one,
inference(resolution,[status(thm)],[f2767,f55]) ).
fof(f2769,plain,
addition(c(sk0_2),c(c(sk0_2))) = one,
inference(resolution,[status(thm)],[f2767,f54]) ).
fof(f2770,plain,
! [X0,X1] :
( addition(c(X0),c(c(X0))) = one
| ~ complement(X1,X0) ),
inference(resolution,[status(thm)],[f2767,f38]) ).
fof(f2771,plain,
( spl0_76
<=> complement(c(c(sk0_1)),c(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f2772,plain,
( complement(c(c(sk0_1)),c(sk0_1))
| ~ spl0_76 ),
inference(component_clause,[status(thm)],[f2771]) ).
fof(f2773,plain,
( ~ complement(c(c(sk0_1)),c(sk0_1))
| spl0_76 ),
inference(component_clause,[status(thm)],[f2771]) ).
fof(f2796,plain,
( spl0_81
<=> addition(c(c(sk0_1)),c(sk0_1)) = c(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f2797,plain,
( addition(c(c(sk0_1)),c(sk0_1)) = c(sk0_1)
| ~ spl0_81 ),
inference(component_clause,[status(thm)],[f2796]) ).
fof(f2799,plain,
( one != c(sk0_1)
| addition(c(c(sk0_1)),c(sk0_1)) = c(sk0_1) ),
inference(paramodulation,[status(thm)],[f2768,f375]) ).
fof(f2800,plain,
( ~ spl0_7
| spl0_81 ),
inference(split_clause,[status(thm)],[f2799,f179,f2796]) ).
fof(f2838,plain,
( spl0_88
<=> multiplication(c(c(sk0_1)),one) = zero ),
introduced(split_symbol_definition) ).
fof(f2839,plain,
( multiplication(c(c(sk0_1)),one) = zero
| ~ spl0_88 ),
inference(component_clause,[status(thm)],[f2838]) ).
fof(f2840,plain,
( multiplication(c(c(sk0_1)),one) != zero
| spl0_88 ),
inference(component_clause,[status(thm)],[f2838]) ).
fof(f2885,plain,
( c(c(sk0_1)) != zero
| spl0_88 ),
inference(forward_demodulation,[status(thm)],[f24,f2840]) ).
fof(f2898,plain,
addition(sk0_2,one) = addition(one,c(c(sk0_2))),
inference(paramodulation,[status(thm)],[f2769,f75]) ).
fof(f2899,plain,
addition(one,sk0_2) = addition(one,c(c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f19,f2898]) ).
fof(f2900,plain,
one = addition(one,c(c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f93,f2899]) ).
fof(f2917,plain,
( spl0_98
<=> addition(c(c(sk0_2)),c(sk0_2)) = c(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f2918,plain,
( addition(c(c(sk0_2)),c(sk0_2)) = c(sk0_2)
| ~ spl0_98 ),
inference(component_clause,[status(thm)],[f2917]) ).
fof(f2920,plain,
( one != c(sk0_2)
| addition(c(c(sk0_2)),c(sk0_2)) = c(sk0_2) ),
inference(paramodulation,[status(thm)],[f2769,f375]) ).
fof(f2921,plain,
( ~ spl0_5
| spl0_98 ),
inference(split_clause,[status(thm)],[f2920,f171,f2917]) ).
fof(f2956,plain,
( spl0_104
<=> multiplication(one,c(c(sk0_2))) = zero ),
introduced(split_symbol_definition) ).
fof(f2957,plain,
( multiplication(one,c(c(sk0_2))) = zero
| ~ spl0_104 ),
inference(component_clause,[status(thm)],[f2956]) ).
fof(f3602,plain,
! [X0] :
( ~ test(X0)
| addition(X0,sk0_0(X0)) = one ),
inference(resolution,[status(thm)],[f37,f43]) ).
fof(f3603,plain,
! [X0] :
( multiplication(X0,sk0_0(X0)) = zero
| ~ test(X0) ),
inference(resolution,[status(thm)],[f41,f37]) ).
fof(f3604,plain,
! [X0] :
( multiplication(c(X0),X0) = zero
| ~ test(X0) ),
inference(resolution,[status(thm)],[f41,f57]) ).
fof(f3609,plain,
( addition(c(sk0_2),c(c(sk0_2))) = c(sk0_2)
| ~ spl0_98 ),
inference(forward_demodulation,[status(thm)],[f19,f2918]) ).
fof(f3610,plain,
( one = c(sk0_2)
| ~ spl0_98 ),
inference(forward_demodulation,[status(thm)],[f2769,f3609]) ).
fof(f3637,plain,
( one != addition(sk0_1,addition(sk0_2,multiplication(c(sk0_1),one)))
| ~ spl0_98 ),
inference(backward_demodulation,[status(thm)],[f3610,f68]) ).
fof(f3638,plain,
( one != addition(sk0_1,addition(sk0_2,c(sk0_1)))
| ~ spl0_98 ),
inference(forward_demodulation,[status(thm)],[f24,f3637]) ).
fof(f3639,plain,
( one != addition(one,sk0_2)
| ~ spl0_98 ),
inference(forward_demodulation,[status(thm)],[f684,f3638]) ).
fof(f3640,plain,
( one != one
| ~ spl0_98 ),
inference(forward_demodulation,[status(thm)],[f93,f3639]) ).
fof(f3641,plain,
( $false
| ~ spl0_98 ),
inference(trivial_equality_resolution,[status(esa)],[f3640]) ).
fof(f3642,plain,
~ spl0_98,
inference(contradiction_clause,[status(thm)],[f3641]) ).
fof(f3653,plain,
( addition(c(sk0_1),c(c(sk0_1))) = c(sk0_1)
| ~ spl0_81 ),
inference(forward_demodulation,[status(thm)],[f19,f2797]) ).
fof(f3654,plain,
( one = c(sk0_1)
| ~ spl0_81 ),
inference(forward_demodulation,[status(thm)],[f2768,f3653]) ).
fof(f3682,plain,
( one != addition(sk0_1,addition(sk0_2,multiplication(one,c(sk0_2))))
| ~ spl0_81 ),
inference(backward_demodulation,[status(thm)],[f3654,f68]) ).
fof(f3683,plain,
( one != addition(sk0_1,addition(sk0_2,c(sk0_2)))
| ~ spl0_81 ),
inference(forward_demodulation,[status(thm)],[f25,f3682]) ).
fof(f3684,plain,
( one != addition(sk0_1,one)
| ~ spl0_81 ),
inference(forward_demodulation,[status(thm)],[f63,f3683]) ).
fof(f3685,plain,
( one != addition(one,sk0_1)
| ~ spl0_81 ),
inference(forward_demodulation,[status(thm)],[f19,f3684]) ).
fof(f3686,plain,
( one != one
| ~ spl0_81 ),
inference(forward_demodulation,[status(thm)],[f96,f3685]) ).
fof(f3687,plain,
( $false
| ~ spl0_81 ),
inference(trivial_equality_resolution,[status(esa)],[f3686]) ).
fof(f3688,plain,
~ spl0_81,
inference(contradiction_clause,[status(thm)],[f3687]) ).
fof(f4108,plain,
addition(sk0_1,sk0_0(sk0_1)) = one,
inference(resolution,[status(thm)],[f3602,f55]) ).
fof(f4110,plain,
! [X0,X1] :
( addition(X0,sk0_0(X0)) = one
| ~ complement(X1,X0) ),
inference(resolution,[status(thm)],[f3602,f38]) ).
fof(f4111,plain,
( spl0_128
<=> complement(sk0_0(sk0_1),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f4112,plain,
( complement(sk0_0(sk0_1),sk0_1)
| ~ spl0_128 ),
inference(component_clause,[status(thm)],[f4111]) ).
fof(f4114,plain,
( spl0_129
<=> multiplication(sk0_1,sk0_0(sk0_1)) = zero ),
introduced(split_symbol_definition) ).
fof(f4116,plain,
( multiplication(sk0_1,sk0_0(sk0_1)) != zero
| spl0_129 ),
inference(component_clause,[status(thm)],[f4114]) ).
fof(f4117,plain,
( spl0_130
<=> multiplication(sk0_0(sk0_1),sk0_1) = zero ),
introduced(split_symbol_definition) ).
fof(f4119,plain,
( multiplication(sk0_0(sk0_1),sk0_1) != zero
| spl0_130 ),
inference(component_clause,[status(thm)],[f4117]) ).
fof(f4120,plain,
( complement(sk0_0(sk0_1),sk0_1)
| multiplication(sk0_1,sk0_0(sk0_1)) != zero
| multiplication(sk0_0(sk0_1),sk0_1) != zero ),
inference(resolution,[status(thm)],[f4108,f44]) ).
fof(f4121,plain,
( spl0_128
| ~ spl0_129
| ~ spl0_130 ),
inference(split_clause,[status(thm)],[f4120,f4111,f4114,f4117]) ).
fof(f4187,plain,
( spl0_139
<=> multiplication(sk0_2,sk0_0(sk0_2)) = zero ),
introduced(split_symbol_definition) ).
fof(f4189,plain,
( multiplication(sk0_2,sk0_0(sk0_2)) != zero
| spl0_139 ),
inference(component_clause,[status(thm)],[f4187]) ).
fof(f4190,plain,
( spl0_140
<=> multiplication(sk0_0(sk0_2),sk0_2) = zero ),
introduced(split_symbol_definition) ).
fof(f4192,plain,
( multiplication(sk0_0(sk0_2),sk0_2) != zero
| spl0_140 ),
inference(component_clause,[status(thm)],[f4190]) ).
fof(f4435,plain,
! [X0] :
( addition(c(X0),sk0_0(c(X0))) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f4110,f57]) ).
fof(f4527,plain,
addition(c(sk0_1),sk0_0(c(sk0_1))) = one,
inference(resolution,[status(thm)],[f4435,f55]) ).
fof(f4531,plain,
! [X0] :
( c(sk0_1) = X0
| ~ complement(sk0_1,X0) ),
inference(resolution,[status(thm)],[f49,f55]) ).
fof(f4534,plain,
! [X0,X1] :
( c(X0) = zero
| c(X0) = X1
| ~ complement(X0,X1) ),
inference(resolution,[status(thm)],[f51,f49]) ).
fof(f4556,plain,
( spl0_165
<=> addition(c(sk0_2),zero) = one ),
introduced(split_symbol_definition) ).
fof(f4557,plain,
( addition(c(sk0_2),zero) = one
| ~ spl0_165 ),
inference(component_clause,[status(thm)],[f4556]) ).
fof(f4573,plain,
( spl0_168
<=> addition(one,c(zero)) = one ),
introduced(split_symbol_definition) ).
fof(f4574,plain,
( addition(one,c(zero)) = one
| ~ spl0_168 ),
inference(component_clause,[status(thm)],[f4573]) ).
fof(f4575,plain,
( addition(one,c(zero)) != one
| spl0_168 ),
inference(component_clause,[status(thm)],[f4573]) ).
fof(f4588,plain,
( spl0_171
<=> addition(c(sk0_1),zero) = one ),
introduced(split_symbol_definition) ).
fof(f4589,plain,
( addition(c(sk0_1),zero) = one
| ~ spl0_171 ),
inference(component_clause,[status(thm)],[f4588]) ).
fof(f4634,plain,
( spl0_179
<=> one = c(zero) ),
introduced(split_symbol_definition) ).
fof(f4636,plain,
( one != c(zero)
| spl0_179 ),
inference(component_clause,[status(thm)],[f4634]) ).
fof(f4653,plain,
( spl0_182
<=> addition(c(sk0_2),c(zero)) = one ),
introduced(split_symbol_definition) ).
fof(f4654,plain,
( addition(c(sk0_2),c(zero)) = one
| ~ spl0_182 ),
inference(component_clause,[status(thm)],[f4653]) ).
fof(f4655,plain,
( addition(c(sk0_2),c(zero)) != one
| spl0_182 ),
inference(component_clause,[status(thm)],[f4653]) ).
fof(f4740,plain,
( one != one
| spl0_19 ),
inference(forward_demodulation,[status(thm)],[f260,f336]) ).
fof(f4741,plain,
( $false
| spl0_19 ),
inference(trivial_equality_resolution,[status(esa)],[f4740]) ).
fof(f4742,plain,
spl0_19,
inference(contradiction_clause,[status(thm)],[f4741]) ).
fof(f4743,plain,
( one != one
| spl0_18 ),
inference(forward_demodulation,[status(thm)],[f264,f331]) ).
fof(f4744,plain,
( $false
| spl0_18 ),
inference(trivial_equality_resolution,[status(esa)],[f4743]) ).
fof(f4745,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f4744]) ).
fof(f4755,plain,
( addition(c(zero),c(sk0_2)) = one
| ~ spl0_182 ),
inference(forward_demodulation,[status(thm)],[f19,f4654]) ).
fof(f4763,plain,
( c(sk0_1) = one
| ~ spl0_171 ),
inference(forward_demodulation,[status(thm)],[f21,f4589]) ).
fof(f4764,plain,
( $false
| spl0_7
| ~ spl0_171 ),
inference(forward_subsumption_resolution,[status(thm)],[f4763,f181]) ).
fof(f4765,plain,
( spl0_7
| ~ spl0_171 ),
inference(contradiction_clause,[status(thm)],[f4764]) ).
fof(f4770,plain,
( c(sk0_2) = one
| ~ spl0_165 ),
inference(forward_demodulation,[status(thm)],[f21,f4557]) ).
fof(f4771,plain,
( $false
| spl0_5
| ~ spl0_165 ),
inference(forward_subsumption_resolution,[status(thm)],[f4770,f173]) ).
fof(f4772,plain,
( spl0_5
| ~ spl0_165 ),
inference(contradiction_clause,[status(thm)],[f4771]) ).
fof(f5074,plain,
( spl0_197
<=> addition(c(sk0_1),sk0_0(zero)) = one ),
introduced(split_symbol_definition) ).
fof(f5075,plain,
( addition(c(sk0_1),sk0_0(zero)) = one
| ~ spl0_197 ),
inference(component_clause,[status(thm)],[f5074]) ).
fof(f5076,plain,
( addition(c(sk0_1),sk0_0(zero)) != one
| spl0_197 ),
inference(component_clause,[status(thm)],[f5074]) ).
fof(f5117,plain,
addition(sk0_0(c(sk0_1)),one) = addition(sk0_0(c(sk0_1)),c(sk0_1)),
inference(paramodulation,[status(thm)],[f4527,f97]) ).
fof(f5118,plain,
addition(one,sk0_0(c(sk0_1))) = addition(sk0_0(c(sk0_1)),c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f5117]) ).
fof(f5119,plain,
addition(one,sk0_0(c(sk0_1))) = addition(c(sk0_1),sk0_0(c(sk0_1))),
inference(forward_demodulation,[status(thm)],[f19,f5118]) ).
fof(f5120,plain,
addition(one,sk0_0(c(sk0_1))) = one,
inference(forward_demodulation,[status(thm)],[f4527,f5119]) ).
fof(f5185,plain,
( spl0_208
<=> addition(one,sk0_0(zero)) = one ),
introduced(split_symbol_definition) ).
fof(f5187,plain,
( addition(one,sk0_0(zero)) != one
| spl0_208 ),
inference(component_clause,[status(thm)],[f5185]) ).
fof(f5743,plain,
! [X0] :
( multiplication(sk0_0(X0),X0) = zero
| ~ test(X0) ),
inference(resolution,[status(thm)],[f42,f37]) ).
fof(f5744,plain,
! [X0] :
( multiplication(X0,c(X0)) = zero
| ~ test(X0) ),
inference(resolution,[status(thm)],[f42,f57]) ).
fof(f5808,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,f69]) ).
fof(f6034,plain,
! [X0] : addition(X0,one) = addition(sk0_1,addition(X0,sk0_0(sk0_1))),
inference(paramodulation,[status(thm)],[f4108,f78]) ).
fof(f6415,plain,
( spl0_217
<=> one = sk0_0(zero) ),
introduced(split_symbol_definition) ).
fof(f6416,plain,
( one = sk0_0(zero)
| ~ spl0_217 ),
inference(component_clause,[status(thm)],[f6415]) ).
fof(f6417,plain,
( one != sk0_0(zero)
| spl0_217 ),
inference(component_clause,[status(thm)],[f6415]) ).
fof(f6434,plain,
( spl0_221
<=> addition(zero,c(zero)) = one ),
introduced(split_symbol_definition) ).
fof(f6435,plain,
( addition(zero,c(zero)) = one
| ~ spl0_221 ),
inference(component_clause,[status(thm)],[f6434]) ).
fof(f6459,plain,
( spl0_222
<=> addition(c(zero),one) = c(zero) ),
introduced(split_symbol_definition) ).
fof(f6460,plain,
( addition(c(zero),one) = c(zero)
| ~ spl0_222 ),
inference(component_clause,[status(thm)],[f6459]) ).
fof(f6462,plain,
( one != c(zero)
| addition(c(zero),one) = c(zero)
| ~ spl0_168 ),
inference(paramodulation,[status(thm)],[f4574,f2449]) ).
fof(f6463,plain,
( ~ spl0_179
| spl0_222
| ~ spl0_168 ),
inference(split_clause,[status(thm)],[f6462,f4634,f6459,f4573]) ).
fof(f6470,plain,
( spl0_223
<=> addition(c(zero),one) = one ),
introduced(split_symbol_definition) ).
fof(f6471,plain,
( addition(c(zero),one) = one
| ~ spl0_223 ),
inference(component_clause,[status(thm)],[f6470]) ).
fof(f6472,plain,
( addition(c(zero),one) != one
| spl0_223 ),
inference(component_clause,[status(thm)],[f6470]) ).
fof(f6495,plain,
( addition(one,c(zero)) = one
| ~ spl0_223 ),
inference(forward_demodulation,[status(thm)],[f19,f6471]) ).
fof(f6496,plain,
( c(zero) = one
| ~ spl0_221 ),
inference(forward_demodulation,[status(thm)],[f584,f6435]) ).
fof(f6497,plain,
( $false
| spl0_179
| ~ spl0_221 ),
inference(forward_subsumption_resolution,[status(thm)],[f6496,f4636]) ).
fof(f6498,plain,
( spl0_179
| ~ spl0_221 ),
inference(contradiction_clause,[status(thm)],[f6497]) ).
fof(f6499,plain,
( one != one
| ~ spl0_223
| spl0_168 ),
inference(forward_demodulation,[status(thm)],[f6495,f4575]) ).
fof(f6500,plain,
( $false
| ~ spl0_223
| spl0_168 ),
inference(trivial_equality_resolution,[status(esa)],[f6499]) ).
fof(f6501,plain,
( ~ spl0_223
| spl0_168 ),
inference(contradiction_clause,[status(thm)],[f6500]) ).
fof(f6506,plain,
( addition(one,c(zero)) != one
| spl0_223 ),
inference(forward_demodulation,[status(thm)],[f19,f6472]) ).
fof(f6611,plain,
( spl0_230
<=> addition(sk0_0(zero),c(sk0_1)) = sk0_0(zero) ),
introduced(split_symbol_definition) ).
fof(f6612,plain,
( addition(sk0_0(zero),c(sk0_1)) = sk0_0(zero)
| ~ spl0_230 ),
inference(component_clause,[status(thm)],[f6611]) ).
fof(f6614,plain,
( one != sk0_0(zero)
| addition(sk0_0(zero),c(sk0_1)) = sk0_0(zero)
| ~ spl0_197 ),
inference(paramodulation,[status(thm)],[f5075,f2449]) ).
fof(f6615,plain,
( ~ spl0_217
| spl0_230
| ~ spl0_197 ),
inference(split_clause,[status(thm)],[f6614,f6415,f6611,f5074]) ).
fof(f6817,plain,
( spl0_251
<=> addition(c(sk0_2),c(zero)) = c(zero) ),
introduced(split_symbol_definition) ).
fof(f6818,plain,
( addition(c(sk0_2),c(zero)) = c(zero)
| ~ spl0_251 ),
inference(component_clause,[status(thm)],[f6817]) ).
fof(f6820,plain,
( one != c(zero)
| addition(c(sk0_2),c(zero)) = c(zero)
| ~ spl0_182 ),
inference(paramodulation,[status(thm)],[f4755,f375]) ).
fof(f6821,plain,
( ~ spl0_179
| spl0_251
| ~ spl0_182 ),
inference(split_clause,[status(thm)],[f6820,f4634,f6817,f4653]) ).
fof(f6824,plain,
( spl0_252
<=> addition(c(zero),c(sk0_2)) = c(zero) ),
introduced(split_symbol_definition) ).
fof(f6825,plain,
( addition(c(zero),c(sk0_2)) = c(zero)
| ~ spl0_252 ),
inference(component_clause,[status(thm)],[f6824]) ).
fof(f6826,plain,
( addition(c(zero),c(sk0_2)) != c(zero)
| spl0_252 ),
inference(component_clause,[status(thm)],[f6824]) ).
fof(f6849,plain,
( addition(c(zero),c(sk0_2)) = c(zero)
| ~ spl0_251 ),
inference(forward_demodulation,[status(thm)],[f19,f6818]) ).
fof(f6850,plain,
( $false
| spl0_252
| ~ spl0_251 ),
inference(forward_subsumption_resolution,[status(thm)],[f6849,f6826]) ).
fof(f6851,plain,
( spl0_252
| ~ spl0_251 ),
inference(contradiction_clause,[status(thm)],[f6850]) ).
fof(f6855,plain,
( addition(c(zero),c(sk0_2)) != one
| spl0_182 ),
inference(forward_demodulation,[status(thm)],[f19,f4655]) ).
fof(f6872,plain,
( spl0_259
<=> addition(c(sk0_2),sk0_0(zero)) = one ),
introduced(split_symbol_definition) ).
fof(f6873,plain,
( addition(c(sk0_2),sk0_0(zero)) = one
| ~ spl0_259 ),
inference(component_clause,[status(thm)],[f6872]) ).
fof(f6874,plain,
( addition(c(sk0_2),sk0_0(zero)) != one
| spl0_259 ),
inference(component_clause,[status(thm)],[f6872]) ).
fof(f7200,plain,
( spl0_267
<=> addition(sk0_0(zero),c(sk0_2)) = sk0_0(zero) ),
introduced(split_symbol_definition) ).
fof(f7201,plain,
( addition(sk0_0(zero),c(sk0_2)) = sk0_0(zero)
| ~ spl0_267 ),
inference(component_clause,[status(thm)],[f7200]) ).
fof(f7202,plain,
( addition(sk0_0(zero),c(sk0_2)) != sk0_0(zero)
| spl0_267 ),
inference(component_clause,[status(thm)],[f7200]) ).
fof(f9556,plain,
( spl0_290
<=> addition(c(zero),c(zero)) = one ),
introduced(split_symbol_definition) ).
fof(f9557,plain,
( addition(c(zero),c(zero)) = one
| ~ spl0_290 ),
inference(component_clause,[status(thm)],[f9556]) ).
fof(f9558,plain,
( addition(c(zero),c(zero)) != one
| spl0_290 ),
inference(component_clause,[status(thm)],[f9556]) ).
fof(f9636,plain,
( c(zero) = one
| ~ spl0_290 ),
inference(forward_demodulation,[status(thm)],[f22,f9557]) ).
fof(f9749,plain,
( spl0_306
<=> addition(c(zero),c(c(zero))) = one ),
introduced(split_symbol_definition) ).
fof(f9750,plain,
( addition(c(zero),c(c(zero))) = one
| ~ spl0_306 ),
inference(component_clause,[status(thm)],[f9749]) ).
fof(f9921,plain,
( addition(c(zero),one) = addition(c(zero),c(c(zero)))
| ~ spl0_306 ),
inference(paramodulation,[status(thm)],[f9750,f81]) ).
fof(f9922,plain,
( addition(one,c(zero)) = addition(c(zero),c(c(zero)))
| ~ spl0_306 ),
inference(forward_demodulation,[status(thm)],[f19,f9921]) ).
fof(f9923,plain,
( addition(one,c(zero)) = one
| ~ spl0_306 ),
inference(forward_demodulation,[status(thm)],[f9750,f9922]) ).
fof(f9924,plain,
( $false
| spl0_223
| ~ spl0_306 ),
inference(forward_subsumption_resolution,[status(thm)],[f9923,f6506]) ).
fof(f9925,plain,
( spl0_223
| ~ spl0_306 ),
inference(contradiction_clause,[status(thm)],[f9924]) ).
fof(f10353,plain,
( spl0_350
<=> multiplication(sk0_0(zero),c(c(sk0_2))) = zero ),
introduced(split_symbol_definition) ).
fof(f10354,plain,
( multiplication(sk0_0(zero),c(c(sk0_2))) = zero
| ~ spl0_350 ),
inference(component_clause,[status(thm)],[f10353]) ).
fof(f10355,plain,
( multiplication(sk0_0(zero),c(c(sk0_2))) != zero
| spl0_350 ),
inference(component_clause,[status(thm)],[f10353]) ).
fof(f10356,plain,
( spl0_351
<=> multiplication(c(c(sk0_2)),sk0_0(zero)) = zero ),
introduced(split_symbol_definition) ).
fof(f10357,plain,
( multiplication(c(c(sk0_2)),sk0_0(zero)) = zero
| ~ spl0_351 ),
inference(component_clause,[status(thm)],[f10356]) ).
fof(f10358,plain,
( multiplication(c(c(sk0_2)),sk0_0(zero)) != zero
| spl0_351 ),
inference(component_clause,[status(thm)],[f10356]) ).
fof(f10366,plain,
( spl0_353
<=> addition(sk0_0(zero),c(zero)) = one ),
introduced(split_symbol_definition) ).
fof(f10367,plain,
( addition(sk0_0(zero),c(zero)) = one
| ~ spl0_353 ),
inference(component_clause,[status(thm)],[f10366]) ).
fof(f10368,plain,
( addition(sk0_0(zero),c(zero)) != one
| spl0_353 ),
inference(component_clause,[status(thm)],[f10366]) ).
fof(f10449,plain,
( addition(c(zero),sk0_0(zero)) = one
| ~ spl0_353 ),
inference(forward_demodulation,[status(thm)],[f19,f10367]) ).
fof(f10496,plain,
( spl0_362
<=> addition(sk0_0(zero),c(zero)) = sk0_0(zero) ),
introduced(split_symbol_definition) ).
fof(f10497,plain,
( addition(sk0_0(zero),c(zero)) = sk0_0(zero)
| ~ spl0_362 ),
inference(component_clause,[status(thm)],[f10496]) ).
fof(f10498,plain,
( addition(sk0_0(zero),c(zero)) != sk0_0(zero)
| spl0_362 ),
inference(component_clause,[status(thm)],[f10496]) ).
fof(f10507,plain,
( spl0_363
<=> addition(sk0_0(zero),c(zero)) = c(zero) ),
introduced(split_symbol_definition) ).
fof(f10508,plain,
( addition(sk0_0(zero),c(zero)) = c(zero)
| ~ spl0_363 ),
inference(component_clause,[status(thm)],[f10507]) ).
fof(f10510,plain,
( one != c(zero)
| addition(sk0_0(zero),c(zero)) = c(zero)
| ~ spl0_353 ),
inference(paramodulation,[status(thm)],[f10449,f375]) ).
fof(f10511,plain,
( ~ spl0_179
| spl0_363
| ~ spl0_353 ),
inference(split_clause,[status(thm)],[f10510,f4634,f10507,f10366]) ).
fof(f10514,plain,
( spl0_364
<=> addition(c(zero),sk0_0(zero)) = c(zero) ),
introduced(split_symbol_definition) ).
fof(f10515,plain,
( addition(c(zero),sk0_0(zero)) = c(zero)
| ~ spl0_364 ),
inference(component_clause,[status(thm)],[f10514]) ).
fof(f10516,plain,
( addition(c(zero),sk0_0(zero)) != c(zero)
| spl0_364 ),
inference(component_clause,[status(thm)],[f10514]) ).
fof(f10540,plain,
( addition(c(zero),sk0_0(zero)) = c(zero)
| ~ spl0_363 ),
inference(forward_demodulation,[status(thm)],[f19,f10508]) ).
fof(f10541,plain,
( $false
| spl0_364
| ~ spl0_363 ),
inference(forward_subsumption_resolution,[status(thm)],[f10540,f10516]) ).
fof(f10542,plain,
( spl0_364
| ~ spl0_363 ),
inference(contradiction_clause,[status(thm)],[f10541]) ).
fof(f10543,plain,
( addition(c(zero),sk0_0(zero)) != one
| spl0_353 ),
inference(forward_demodulation,[status(thm)],[f19,f10368]) ).
fof(f10569,plain,
( c(c(sk0_1)) = zero
| ~ spl0_88 ),
inference(forward_demodulation,[status(thm)],[f24,f2839]) ).
fof(f10577,plain,
( c(c(sk0_2)) = zero
| ~ spl0_104 ),
inference(forward_demodulation,[status(thm)],[f25,f2957]) ).
fof(f10593,plain,
( addition(c(sk0_1),zero) = one
| ~ spl0_88 ),
inference(backward_demodulation,[status(thm)],[f10569,f2768]) ).
fof(f10594,plain,
( spl0_171
| ~ spl0_88 ),
inference(split_clause,[status(thm)],[f10593,f4588,f2838]) ).
fof(f11117,plain,
( addition(one,c(zero)) = c(zero)
| ~ spl0_222 ),
inference(forward_demodulation,[status(thm)],[f19,f6460]) ).
fof(f11125,plain,
( c(zero) = one
| ~ spl0_222
| ~ spl0_168 ),
inference(forward_demodulation,[status(thm)],[f11117,f4574]) ).
fof(f15204,plain,
multiplication(sk0_1,sk0_0(sk0_1)) = zero,
inference(resolution,[status(thm)],[f3603,f55]) ).
fof(f15205,plain,
( $false
| spl0_129 ),
inference(forward_subsumption_resolution,[status(thm)],[f15204,f4116]) ).
fof(f15206,plain,
spl0_129,
inference(contradiction_clause,[status(thm)],[f15205]) ).
fof(f15210,plain,
multiplication(sk0_2,sk0_0(sk0_2)) = zero,
inference(resolution,[status(thm)],[f3603,f54]) ).
fof(f15211,plain,
( $false
| spl0_139 ),
inference(forward_subsumption_resolution,[status(thm)],[f15210,f4189]) ).
fof(f15212,plain,
spl0_139,
inference(contradiction_clause,[status(thm)],[f15211]) ).
fof(f15215,plain,
multiplication(c(sk0_1),sk0_1) = zero,
inference(resolution,[status(thm)],[f3604,f55]) ).
fof(f18441,plain,
( spl0_452
<=> c(sk0_0(sk0_1)) = zero ),
introduced(split_symbol_definition) ).
fof(f18442,plain,
( c(sk0_0(sk0_1)) = zero
| ~ spl0_452 ),
inference(component_clause,[status(thm)],[f18441]) ).
fof(f18444,plain,
( spl0_453
<=> c(sk0_0(sk0_1)) = sk0_1 ),
introduced(split_symbol_definition) ).
fof(f18445,plain,
( c(sk0_0(sk0_1)) = sk0_1
| ~ spl0_453 ),
inference(component_clause,[status(thm)],[f18444]) ).
fof(f18447,plain,
( c(sk0_0(sk0_1)) = zero
| c(sk0_0(sk0_1)) = sk0_1
| ~ spl0_128 ),
inference(resolution,[status(thm)],[f4534,f4112]) ).
fof(f18448,plain,
( spl0_452
| spl0_453
| ~ spl0_128 ),
inference(split_clause,[status(thm)],[f18447,f18441,f18444,f4111]) ).
fof(f18603,plain,
( addition(one,sk0_0(zero)) != one
| ~ spl0_222
| ~ spl0_168
| spl0_353 ),
inference(backward_demodulation,[status(thm)],[f11125,f10543]) ).
fof(f18629,plain,
( c(zero) != one
| spl0_290 ),
inference(forward_demodulation,[status(thm)],[f22,f9558]) ).
fof(f18630,plain,
( ~ spl0_179
| spl0_290 ),
inference(split_clause,[status(thm)],[f18629,f4634,f9556]) ).
fof(f20815,plain,
multiplication(c(sk0_2),sk0_2) = zero,
inference(resolution,[status(thm)],[f54,f3604]) ).
fof(f20828,plain,
addition(sk0_2,c(sk0_2)) = one,
inference(resolution,[status(thm)],[f54,f61]) ).
fof(f20831,plain,
addition(sk0_2,sk0_0(sk0_2)) = one,
inference(resolution,[status(thm)],[f54,f3602]) ).
fof(f20833,plain,
! [X0] :
( c(sk0_2) = X0
| ~ complement(sk0_2,X0) ),
inference(resolution,[status(thm)],[f54,f49]) ).
fof(f21102,plain,
( addition(c(sk0_1),one) != one
| ~ spl0_217
| spl0_197 ),
inference(forward_demodulation,[status(thm)],[f6416,f5076]) ).
fof(f21103,plain,
( addition(one,c(sk0_1)) != one
| ~ spl0_217
| spl0_197 ),
inference(forward_demodulation,[status(thm)],[f19,f21102]) ).
fof(f21104,plain,
( one != one
| ~ spl0_18
| ~ spl0_217
| spl0_197 ),
inference(forward_demodulation,[status(thm)],[f330,f21103]) ).
fof(f21105,plain,
( $false
| ~ spl0_18
| ~ spl0_217
| spl0_197 ),
inference(trivial_equality_resolution,[status(esa)],[f21104]) ).
fof(f21106,plain,
( ~ spl0_18
| ~ spl0_217
| spl0_197 ),
inference(contradiction_clause,[status(thm)],[f21105]) ).
fof(f21111,plain,
( addition(c(sk0_2),sk0_0(zero)) = sk0_0(zero)
| ~ spl0_267 ),
inference(forward_demodulation,[status(thm)],[f19,f7201]) ).
fof(f21124,plain,
( addition(c(zero),sk0_0(zero)) = sk0_0(zero)
| ~ spl0_362 ),
inference(forward_demodulation,[status(thm)],[f19,f10497]) ).
fof(f21153,plain,
( addition(c(sk0_1),sk0_0(zero)) = sk0_0(zero)
| ~ spl0_230 ),
inference(forward_demodulation,[status(thm)],[f19,f6612]) ).
fof(f22460,plain,
multiplication(sk0_0(sk0_2),sk0_2) = zero,
inference(resolution,[status(thm)],[f5743,f54]) ).
fof(f22461,plain,
( $false
| spl0_140 ),
inference(forward_subsumption_resolution,[status(thm)],[f22460,f4192]) ).
fof(f22462,plain,
spl0_140,
inference(contradiction_clause,[status(thm)],[f22461]) ).
fof(f22463,plain,
multiplication(sk0_0(sk0_1),sk0_1) = zero,
inference(resolution,[status(thm)],[f5743,f55]) ).
fof(f22466,plain,
multiplication(sk0_2,c(sk0_2)) = zero,
inference(resolution,[status(thm)],[f5744,f54]) ).
fof(f22468,plain,
multiplication(sk0_1,c(sk0_1)) = zero,
inference(resolution,[status(thm)],[f5744,f55]) ).
fof(f22469,plain,
( $false
| spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f22468,f2639]) ).
fof(f22470,plain,
spl0_54,
inference(contradiction_clause,[status(thm)],[f22469]) ).
fof(f22508,plain,
( spl0_465
<=> complement(one,zero) ),
introduced(split_symbol_definition) ).
fof(f22509,plain,
( complement(one,zero)
| ~ spl0_465 ),
inference(component_clause,[status(thm)],[f22508]) ).
fof(f22511,plain,
( complement(one,zero)
| multiplication(zero,one) != zero
| multiplication(one,zero) != zero ),
inference(resolution,[status(thm)],[f2752,f21]) ).
fof(f22512,plain,
( spl0_465
| ~ spl0_73
| ~ spl0_72 ),
inference(split_clause,[status(thm)],[f22511,f22508,f2706,f2703]) ).
fof(f22570,plain,
( spl0_466
<=> test(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f22572,plain,
( ~ test(sk0_2)
| spl0_466 ),
inference(component_clause,[status(thm)],[f22570]) ).
fof(f22759,plain,
( zero != zero
| spl0_130 ),
inference(forward_demodulation,[status(thm)],[f22463,f4119]) ).
fof(f22760,plain,
( $false
| spl0_130 ),
inference(trivial_equality_resolution,[status(esa)],[f22759]) ).
fof(f22761,plain,
spl0_130,
inference(contradiction_clause,[status(thm)],[f22760]) ).
fof(f23681,plain,
( addition(c(sk0_2),sk0_0(zero)) != sk0_0(zero)
| spl0_267 ),
inference(forward_demodulation,[status(thm)],[f19,f7202]) ).
fof(f23721,plain,
( one = sk0_0(zero)
| ~ spl0_197
| ~ spl0_230 ),
inference(forward_demodulation,[status(thm)],[f5075,f21153]) ).
fof(f23724,plain,
( sk0_0(zero) = c(zero)
| ~ spl0_362
| ~ spl0_364 ),
inference(forward_demodulation,[status(thm)],[f21124,f10515]) ).
fof(f23798,plain,
( addition(c(zero),sk0_0(zero)) != sk0_0(zero)
| spl0_362 ),
inference(forward_demodulation,[status(thm)],[f19,f10498]) ).
fof(f23864,plain,
( sk0_0(zero) = one
| ~ spl0_267
| ~ spl0_259 ),
inference(forward_demodulation,[status(thm)],[f21111,f6873]) ).
fof(f23865,plain,
( $false
| spl0_217
| ~ spl0_267
| ~ spl0_259 ),
inference(forward_subsumption_resolution,[status(thm)],[f23864,f6417]) ).
fof(f23866,plain,
( spl0_217
| ~ spl0_267
| ~ spl0_259 ),
inference(contradiction_clause,[status(thm)],[f23865]) ).
fof(f23921,plain,
( addition(one,one) != one
| ~ spl0_197
| ~ spl0_230
| spl0_208 ),
inference(forward_demodulation,[status(thm)],[f23721,f5187]) ).
fof(f23922,plain,
( one != one
| ~ spl0_197
| ~ spl0_230
| spl0_208 ),
inference(forward_demodulation,[status(thm)],[f22,f23921]) ).
fof(f23923,plain,
( $false
| ~ spl0_197
| ~ spl0_230
| spl0_208 ),
inference(trivial_equality_resolution,[status(esa)],[f23922]) ).
fof(f23924,plain,
( ~ spl0_197
| ~ spl0_230
| spl0_208 ),
inference(contradiction_clause,[status(thm)],[f23923]) ).
fof(f23949,plain,
( multiplication(one,c(c(sk0_2))) = zero
| ~ spl0_197
| ~ spl0_230
| ~ spl0_350 ),
inference(backward_demodulation,[status(thm)],[f23721,f10354]) ).
fof(f23950,plain,
( spl0_104
| ~ spl0_197
| ~ spl0_230
| ~ spl0_350 ),
inference(split_clause,[status(thm)],[f23949,f2956,f5074,f6611,f10353]) ).
fof(f24223,plain,
( addition(c(zero),c(c(zero))) = one
| ~ spl0_465 ),
inference(resolution,[status(thm)],[f22509,f2770]) ).
fof(f24224,plain,
( spl0_306
| ~ spl0_465 ),
inference(split_clause,[status(thm)],[f24223,f9749,f22508]) ).
fof(f24225,plain,
( addition(zero,c(zero)) = one
| ~ spl0_465 ),
inference(resolution,[status(thm)],[f22509,f2633]) ).
fof(f24226,plain,
( spl0_221
| ~ spl0_465 ),
inference(split_clause,[status(thm)],[f24225,f6434,f22508]) ).
fof(f24227,plain,
( addition(zero,sk0_0(zero)) = one
| ~ spl0_465 ),
inference(resolution,[status(thm)],[f22509,f4110]) ).
fof(f24228,plain,
( sk0_0(zero) = one
| ~ spl0_465 ),
inference(forward_demodulation,[status(thm)],[f584,f24227]) ).
fof(f24250,plain,
( ~ spl0_208
| ~ spl0_222
| ~ spl0_168
| spl0_353 ),
inference(split_clause,[status(thm)],[f18603,f5185,f6459,f4573,f10366]) ).
fof(f24369,plain,
( multiplication(one,c(c(sk0_2))) != zero
| ~ spl0_465
| spl0_350 ),
inference(forward_demodulation,[status(thm)],[f24228,f10355]) ).
fof(f24699,plain,
( multiplication(c(c(sk0_2)),c(zero)) != zero
| ~ spl0_362
| ~ spl0_364
| spl0_351 ),
inference(backward_demodulation,[status(thm)],[f23724,f10358]) ).
fof(f24896,plain,
( addition(one,c(sk0_2)) = c(zero)
| ~ spl0_222
| ~ spl0_168
| ~ spl0_252 ),
inference(forward_demodulation,[status(thm)],[f11125,f6825]) ).
fof(f25722,plain,
( addition(one,sk0_0(zero)) != sk0_0(zero)
| ~ spl0_222
| ~ spl0_168
| spl0_362 ),
inference(forward_demodulation,[status(thm)],[f11125,f23798]) ).
fof(f25723,plain,
( addition(one,one) != sk0_0(zero)
| ~ spl0_465
| ~ spl0_222
| ~ spl0_168
| spl0_362 ),
inference(forward_demodulation,[status(thm)],[f24228,f25722]) ).
fof(f25724,plain,
( one != sk0_0(zero)
| ~ spl0_465
| ~ spl0_222
| ~ spl0_168
| spl0_362 ),
inference(forward_demodulation,[status(thm)],[f22,f25723]) ).
fof(f25725,plain,
( one != one
| ~ spl0_465
| ~ spl0_222
| ~ spl0_168
| spl0_362 ),
inference(forward_demodulation,[status(thm)],[f24228,f25724]) ).
fof(f25726,plain,
( $false
| ~ spl0_465
| ~ spl0_222
| ~ spl0_168
| spl0_362 ),
inference(trivial_equality_resolution,[status(esa)],[f25725]) ).
fof(f25727,plain,
( ~ spl0_465
| ~ spl0_222
| ~ spl0_168
| spl0_362 ),
inference(contradiction_clause,[status(thm)],[f25726]) ).
fof(f25745,plain,
( addition(one,c(sk0_2)) = one
| ~ spl0_222
| ~ spl0_168
| ~ spl0_252 ),
inference(forward_demodulation,[status(thm)],[f11125,f24896]) ).
fof(f25794,plain,
( addition(c(sk0_2),one) != sk0_0(zero)
| ~ spl0_465
| spl0_267 ),
inference(forward_demodulation,[status(thm)],[f24228,f23681]) ).
fof(f25795,plain,
( addition(one,c(sk0_2)) != sk0_0(zero)
| ~ spl0_465
| spl0_267 ),
inference(forward_demodulation,[status(thm)],[f19,f25794]) ).
fof(f25796,plain,
( one != sk0_0(zero)
| ~ spl0_222
| ~ spl0_168
| ~ spl0_252
| ~ spl0_465
| spl0_267 ),
inference(forward_demodulation,[status(thm)],[f25745,f25795]) ).
fof(f25797,plain,
( one != one
| ~ spl0_222
| ~ spl0_168
| ~ spl0_252
| ~ spl0_465
| spl0_267 ),
inference(forward_demodulation,[status(thm)],[f24228,f25796]) ).
fof(f25798,plain,
( $false
| ~ spl0_222
| ~ spl0_168
| ~ spl0_252
| ~ spl0_465
| spl0_267 ),
inference(trivial_equality_resolution,[status(esa)],[f25797]) ).
fof(f25799,plain,
( ~ spl0_222
| ~ spl0_168
| ~ spl0_252
| ~ spl0_465
| spl0_267 ),
inference(contradiction_clause,[status(thm)],[f25798]) ).
fof(f25800,plain,
( addition(c(sk0_2),one) != one
| ~ spl0_465
| spl0_259 ),
inference(forward_demodulation,[status(thm)],[f24228,f6874]) ).
fof(f25801,plain,
( addition(one,c(sk0_2)) != one
| ~ spl0_465
| spl0_259 ),
inference(forward_demodulation,[status(thm)],[f19,f25800]) ).
fof(f25802,plain,
( one != one
| ~ spl0_222
| ~ spl0_168
| ~ spl0_252
| ~ spl0_465
| spl0_259 ),
inference(forward_demodulation,[status(thm)],[f25745,f25801]) ).
fof(f25803,plain,
( $false
| ~ spl0_222
| ~ spl0_168
| ~ spl0_252
| ~ spl0_465
| spl0_259 ),
inference(trivial_equality_resolution,[status(esa)],[f25802]) ).
fof(f25804,plain,
( ~ spl0_222
| ~ spl0_168
| ~ spl0_252
| ~ spl0_465
| spl0_259 ),
inference(contradiction_clause,[status(thm)],[f25803]) ).
fof(f25805,plain,
( addition(one,c(sk0_2)) != one
| ~ spl0_290
| spl0_182 ),
inference(backward_demodulation,[status(thm)],[f9636,f6855]) ).
fof(f25806,plain,
( ~ spl0_19
| ~ spl0_290
| spl0_182 ),
inference(split_clause,[status(thm)],[f25805,f334,f9556,f4653]) ).
fof(f25870,plain,
( multiplication(c(c(sk0_2)),one) != zero
| ~ spl0_222
| ~ spl0_168
| ~ spl0_362
| ~ spl0_364
| spl0_351 ),
inference(forward_demodulation,[status(thm)],[f11125,f24699]) ).
fof(f26517,plain,
( spl0_486
<=> c(c(sk0_1)) = zero ),
introduced(split_symbol_definition) ).
fof(f26518,plain,
( c(c(sk0_1)) = zero
| ~ spl0_486 ),
inference(component_clause,[status(thm)],[f26517]) ).
fof(f26535,plain,
( $false
| spl0_88
| ~ spl0_486 ),
inference(forward_subsumption_resolution,[status(thm)],[f26518,f2885]) ).
fof(f26536,plain,
( spl0_88
| ~ spl0_486 ),
inference(contradiction_clause,[status(thm)],[f26535]) ).
fof(f27227,plain,
addition(sk0_1,c(sk0_1)) = one,
inference(resolution,[status(thm)],[f55,f61]) ).
fof(f27229,plain,
addition(sk0_1,sk0_0(sk0_1)) = one,
inference(resolution,[status(thm)],[f55,f3602]) ).
fof(f27237,plain,
addition(c(sk0_2),sk0_0(c(sk0_2))) = one,
inference(resolution,[status(thm)],[f54,f4435]) ).
fof(f27593,plain,
( spl0_494
<=> complement(sk0_2,sk0_0(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f27594,plain,
( complement(sk0_2,sk0_0(sk0_2))
| ~ spl0_494 ),
inference(component_clause,[status(thm)],[f27593]) ).
fof(f27596,plain,
( complement(sk0_2,sk0_0(sk0_2))
| multiplication(sk0_0(sk0_2),sk0_2) != zero
| multiplication(sk0_2,sk0_0(sk0_2)) != zero ),
inference(resolution,[status(thm)],[f20831,f2752]) ).
fof(f27597,plain,
( spl0_494
| ~ spl0_140
| ~ spl0_139 ),
inference(split_clause,[status(thm)],[f27596,f27593,f4190,f4187]) ).
fof(f27676,plain,
( spl0_495
<=> complement(sk0_1,sk0_0(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f27677,plain,
( complement(sk0_1,sk0_0(sk0_1))
| ~ spl0_495 ),
inference(component_clause,[status(thm)],[f27676]) ).
fof(f27679,plain,
( complement(sk0_1,sk0_0(sk0_1))
| multiplication(sk0_0(sk0_1),sk0_1) != zero
| multiplication(sk0_1,sk0_0(sk0_1)) != zero ),
inference(resolution,[status(thm)],[f27229,f2752]) ).
fof(f27680,plain,
( spl0_495
| ~ spl0_130
| ~ spl0_129 ),
inference(split_clause,[status(thm)],[f27679,f27676,f4117,f4114]) ).
fof(f27759,plain,
( spl0_496
<=> complement(sk0_1,c(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f27760,plain,
( complement(sk0_1,c(sk0_1))
| ~ spl0_496 ),
inference(component_clause,[status(thm)],[f27759]) ).
fof(f27762,plain,
( complement(sk0_1,c(sk0_1))
| multiplication(c(sk0_1),sk0_1) != zero
| multiplication(sk0_1,c(sk0_1)) != zero ),
inference(resolution,[status(thm)],[f27227,f2752]) ).
fof(f27763,plain,
( spl0_496
| ~ spl0_55
| ~ spl0_54 ),
inference(split_clause,[status(thm)],[f27762,f27759,f2640,f2637]) ).
fof(f27853,plain,
( zero != zero
| spl0_55 ),
inference(forward_demodulation,[status(thm)],[f15215,f2642]) ).
fof(f27854,plain,
( $false
| spl0_55 ),
inference(trivial_equality_resolution,[status(esa)],[f27853]) ).
fof(f27855,plain,
spl0_55,
inference(contradiction_clause,[status(thm)],[f27854]) ).
fof(f28171,plain,
( addition(c(sk0_2),zero) = one
| ~ spl0_104 ),
inference(backward_demodulation,[status(thm)],[f10577,f2769]) ).
fof(f28172,plain,
( spl0_165
| ~ spl0_104 ),
inference(split_clause,[status(thm)],[f28171,f4556,f2956]) ).
fof(f28187,plain,
( c(c(sk0_2)) != zero
| ~ spl0_222
| ~ spl0_168
| ~ spl0_362
| ~ spl0_364
| spl0_351 ),
inference(forward_demodulation,[status(thm)],[f24,f25870]) ).
fof(f31575,plain,
( spl0_556
<=> c(c(sk0_2)) = zero ),
introduced(split_symbol_definition) ).
fof(f31576,plain,
( c(c(sk0_2)) = zero
| ~ spl0_556 ),
inference(component_clause,[status(thm)],[f31575]) ).
fof(f31617,plain,
( $false
| ~ spl0_222
| ~ spl0_168
| ~ spl0_362
| ~ spl0_364
| spl0_351
| ~ spl0_556 ),
inference(forward_subsumption_resolution,[status(thm)],[f31576,f28187]) ).
fof(f31618,plain,
( ~ spl0_222
| ~ spl0_168
| ~ spl0_362
| ~ spl0_364
| spl0_351
| ~ spl0_556 ),
inference(contradiction_clause,[status(thm)],[f31617]) ).
fof(f31629,plain,
( multiplication(c(c(sk0_2)),one) = zero
| ~ spl0_465
| ~ spl0_351 ),
inference(forward_demodulation,[status(thm)],[f24228,f10357]) ).
fof(f31630,plain,
( c(c(sk0_2)) = zero
| ~ spl0_465
| ~ spl0_351 ),
inference(forward_demodulation,[status(thm)],[f24,f31629]) ).
fof(f31663,plain,
( c(c(sk0_2)) != zero
| ~ spl0_465
| spl0_350 ),
inference(forward_demodulation,[status(thm)],[f25,f24369]) ).
fof(f31664,plain,
( zero != zero
| ~ spl0_351
| ~ spl0_465
| spl0_350 ),
inference(forward_demodulation,[status(thm)],[f31630,f31663]) ).
fof(f31665,plain,
( $false
| ~ spl0_351
| ~ spl0_465
| spl0_350 ),
inference(trivial_equality_resolution,[status(esa)],[f31664]) ).
fof(f31666,plain,
( ~ spl0_351
| ~ spl0_465
| spl0_350 ),
inference(contradiction_clause,[status(thm)],[f31665]) ).
fof(f35702,plain,
! [X0] : addition(sk0_2,multiplication(addition(one,X0),c(sk0_2))) = addition(one,multiplication(X0,c(sk0_2))),
inference(paramodulation,[status(thm)],[f623,f75]) ).
fof(f40218,plain,
! [X0] : multiplication(X0,one) = addition(X0,multiplication(X0,c(c(sk0_2)))),
inference(paramodulation,[status(thm)],[f2900,f130]) ).
fof(f40219,plain,
! [X0] : X0 = addition(X0,multiplication(X0,c(c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f24,f40218]) ).
fof(f44244,plain,
! [X0,X1] : addition(X0,addition(multiplication(X0,c(c(sk0_2))),X1)) = addition(X1,X0),
inference(paramodulation,[status(thm)],[f40219,f69]) ).
fof(f48027,plain,
addition(multiplication(sk0_1,c(c(sk0_2))),one) = addition(sk0_0(sk0_1),sk0_1),
inference(paramodulation,[status(thm)],[f6034,f44244]) ).
fof(f48028,plain,
addition(one,multiplication(sk0_1,c(c(sk0_2)))) = addition(sk0_0(sk0_1),sk0_1),
inference(forward_demodulation,[status(thm)],[f19,f48027]) ).
fof(f48029,plain,
addition(one,multiplication(sk0_1,c(c(sk0_2)))) = addition(sk0_1,sk0_0(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f48028]) ).
fof(f48030,plain,
addition(one,multiplication(sk0_1,c(c(sk0_2)))) = one,
inference(forward_demodulation,[status(thm)],[f27229,f48029]) ).
fof(f52201,plain,
( spl0_1022
<=> c(c(sk0_2)) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f52202,plain,
( c(c(sk0_2)) = sk0_2
| ~ spl0_1022 ),
inference(component_clause,[status(thm)],[f52201]) ).
fof(f52204,plain,
( c(c(sk0_2)) = zero
| c(c(sk0_2)) = sk0_2
| ~ spl0_56 ),
inference(resolution,[status(thm)],[f2646,f4534]) ).
fof(f52205,plain,
( spl0_556
| spl0_1022
| ~ spl0_56 ),
inference(split_clause,[status(thm)],[f52204,f31575,f52201,f2645]) ).
fof(f52231,plain,
( addition(one,multiplication(sk0_1,sk0_2)) = one
| ~ spl0_1022 ),
inference(backward_demodulation,[status(thm)],[f52202,f48030]) ).
fof(f53216,plain,
( c(sk0_1) = sk0_0(sk0_1)
| ~ spl0_495 ),
inference(resolution,[status(thm)],[f27677,f4531]) ).
fof(f53361,plain,
( c(c(sk0_1)) = zero
| ~ spl0_495
| ~ spl0_452 ),
inference(backward_demodulation,[status(thm)],[f53216,f18442]) ).
fof(f53362,plain,
( spl0_486
| ~ spl0_495
| ~ spl0_452 ),
inference(split_clause,[status(thm)],[f53361,f26517,f27676,f18441]) ).
fof(f53394,plain,
( c(c(sk0_1)) = sk0_1
| ~ spl0_495
| ~ spl0_453 ),
inference(forward_demodulation,[status(thm)],[f53216,f18445]) ).
fof(f54103,plain,
( ~ complement(sk0_1,c(sk0_1))
| ~ spl0_495
| ~ spl0_453
| spl0_76 ),
inference(backward_demodulation,[status(thm)],[f53394,f2773]) ).
fof(f54104,plain,
( $false
| ~ spl0_496
| ~ spl0_495
| ~ spl0_453
| spl0_76 ),
inference(forward_subsumption_resolution,[status(thm)],[f54103,f27760]) ).
fof(f54105,plain,
( ~ spl0_496
| ~ spl0_495
| ~ spl0_453
| spl0_76 ),
inference(contradiction_clause,[status(thm)],[f54104]) ).
fof(f54155,plain,
( addition(c(sk0_1),c(c(sk0_1))) = one
| ~ spl0_76 ),
inference(resolution,[status(thm)],[f2772,f2633]) ).
fof(f54261,plain,
( addition(c(sk0_1),sk0_1) = one
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(backward_demodulation,[status(thm)],[f53394,f54155]) ).
fof(f54262,plain,
( addition(sk0_1,c(sk0_1)) = one
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(forward_demodulation,[status(thm)],[f19,f54261]) ).
fof(f62491,plain,
( c(sk0_2) = sk0_0(sk0_2)
| ~ spl0_494 ),
inference(resolution,[status(thm)],[f27594,f20833]) ).
fof(f62601,plain,
( ~ test(sk0_2)
| complement(c(sk0_2),sk0_2)
| ~ spl0_494 ),
inference(paramodulation,[status(thm)],[f62491,f37]) ).
fof(f62602,plain,
( ~ spl0_466
| spl0_56
| ~ spl0_494 ),
inference(split_clause,[status(thm)],[f62601,f22570,f2645,f27593]) ).
fof(f62603,plain,
( $false
| spl0_466 ),
inference(forward_subsumption_resolution,[status(thm)],[f22572,f54]) ).
fof(f62604,plain,
spl0_466,
inference(contradiction_clause,[status(thm)],[f62603]) ).
fof(f63422,plain,
( spl0_1134
<=> multiplication(one,multiplication(sk0_2,multiplication(one,c(sk0_2)))) = zero ),
introduced(split_symbol_definition) ).
fof(f63424,plain,
( multiplication(one,multiplication(sk0_2,multiplication(one,c(sk0_2)))) != zero
| spl0_1134 ),
inference(component_clause,[status(thm)],[f63422]) ).
fof(f63656,plain,
( multiplication(sk0_2,multiplication(one,c(sk0_2))) != zero
| spl0_1134 ),
inference(forward_demodulation,[status(thm)],[f25,f63424]) ).
fof(f63657,plain,
( multiplication(sk0_2,c(sk0_2)) != zero
| spl0_1134 ),
inference(forward_demodulation,[status(thm)],[f25,f63656]) ).
fof(f63658,plain,
( zero != zero
| spl0_1134 ),
inference(forward_demodulation,[status(thm)],[f22466,f63657]) ).
fof(f63659,plain,
( $false
| spl0_1134 ),
inference(trivial_equality_resolution,[status(esa)],[f63658]) ).
fof(f63660,plain,
spl0_1134,
inference(contradiction_clause,[status(thm)],[f63659]) ).
fof(f63687,plain,
( spl0_1141
<=> multiplication(one,multiplication(c(sk0_2),multiplication(one,sk0_2))) = zero ),
introduced(split_symbol_definition) ).
fof(f63689,plain,
( multiplication(one,multiplication(c(sk0_2),multiplication(one,sk0_2))) != zero
| spl0_1141 ),
inference(component_clause,[status(thm)],[f63687]) ).
fof(f63941,plain,
( multiplication(c(sk0_2),multiplication(one,sk0_2)) != zero
| spl0_1141 ),
inference(forward_demodulation,[status(thm)],[f25,f63689]) ).
fof(f63942,plain,
( multiplication(c(sk0_2),sk0_2) != zero
| spl0_1141 ),
inference(forward_demodulation,[status(thm)],[f25,f63941]) ).
fof(f63943,plain,
( zero != zero
| spl0_1141 ),
inference(forward_demodulation,[status(thm)],[f20815,f63942]) ).
fof(f63944,plain,
( $false
| spl0_1141 ),
inference(trivial_equality_resolution,[status(esa)],[f63943]) ).
fof(f63945,plain,
spl0_1141,
inference(contradiction_clause,[status(thm)],[f63944]) ).
fof(f65148,plain,
( spl0_1161
<=> sk0_2 = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f65150,plain,
( sk0_2 != sk0_2
| spl0_1161 ),
inference(component_clause,[status(thm)],[f65148]) ).
fof(f65173,plain,
( $false
| spl0_1161 ),
inference(trivial_equality_resolution,[status(esa)],[f65150]) ).
fof(f65174,plain,
spl0_1161,
inference(contradiction_clause,[status(thm)],[f65173]) ).
fof(f65722,plain,
! [X0] : multiplication(addition(c(sk0_2),X0),sk0_2) = addition(zero,multiplication(X0,sk0_2)),
inference(paramodulation,[status(thm)],[f20815,f27]) ).
fof(f65723,plain,
! [X0] : multiplication(addition(c(sk0_2),X0),sk0_2) = multiplication(X0,sk0_2),
inference(forward_demodulation,[status(thm)],[f584,f65722]) ).
fof(f65758,plain,
! [X0,X1] : multiplication(addition(X0,addition(X1,c(sk0_2))),sk0_2) = multiplication(addition(X0,X1),sk0_2),
inference(paramodulation,[status(thm)],[f2369,f65723]) ).
fof(f65769,plain,
multiplication(one,sk0_2) = multiplication(sk0_0(c(sk0_2)),sk0_2),
inference(paramodulation,[status(thm)],[f27237,f65723]) ).
fof(f65770,plain,
sk0_2 = multiplication(sk0_0(c(sk0_2)),sk0_2),
inference(forward_demodulation,[status(thm)],[f25,f65769]) ).
fof(f65851,plain,
( spl0_1178
<=> multiplication(one,sk0_2) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f65853,plain,
( multiplication(one,sk0_2) != sk0_2
| spl0_1178 ),
inference(component_clause,[status(thm)],[f65851]) ).
fof(f65977,plain,
( sk0_2 != sk0_2
| spl0_1178 ),
inference(forward_demodulation,[status(thm)],[f25,f65853]) ).
fof(f65978,plain,
( $false
| spl0_1178 ),
inference(trivial_equality_resolution,[status(esa)],[f65977]) ).
fof(f65979,plain,
spl0_1178,
inference(contradiction_clause,[status(thm)],[f65978]) ).
fof(f66016,plain,
multiplication(sk0_0(c(sk0_2)),addition(one,sk0_2)) = addition(sk0_0(c(sk0_2)),sk0_2),
inference(paramodulation,[status(thm)],[f65770,f130]) ).
fof(f66017,plain,
multiplication(sk0_0(c(sk0_2)),one) = addition(sk0_0(c(sk0_2)),sk0_2),
inference(forward_demodulation,[status(thm)],[f93,f66016]) ).
fof(f66018,plain,
sk0_0(c(sk0_2)) = addition(sk0_0(c(sk0_2)),sk0_2),
inference(forward_demodulation,[status(thm)],[f24,f66017]) ).
fof(f66019,plain,
sk0_0(c(sk0_2)) = addition(sk0_2,sk0_0(c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f19,f66018]) ).
fof(f66028,plain,
( spl0_1184
<=> multiplication(addition(one,sk0_0(c(sk0_2))),sk0_2) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f66030,plain,
( multiplication(addition(one,sk0_0(c(sk0_2))),sk0_2) != sk0_2
| spl0_1184 ),
inference(component_clause,[status(thm)],[f66028]) ).
fof(f66046,plain,
( spl0_1185
<=> multiplication(addition(sk0_0(c(sk0_2)),one),sk0_2) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f66048,plain,
( multiplication(addition(sk0_0(c(sk0_2)),one),sk0_2) != sk0_2
| spl0_1185 ),
inference(component_clause,[status(thm)],[f66046]) ).
fof(f66054,plain,
( spl0_1187
<=> multiplication(sk0_0(c(sk0_2)),addition(sk0_2,one)) = sk0_0(c(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f66056,plain,
( multiplication(sk0_0(c(sk0_2)),addition(sk0_2,one)) != sk0_0(c(sk0_2))
| spl0_1187 ),
inference(component_clause,[status(thm)],[f66054]) ).
fof(f66077,plain,
! [X0] : multiplication(addition(X0,sk0_0(c(sk0_2))),sk0_2) = addition(multiplication(X0,sk0_2),sk0_2),
inference(paramodulation,[status(thm)],[f65770,f27]) ).
fof(f66078,plain,
! [X0] : multiplication(addition(X0,sk0_0(c(sk0_2))),sk0_2) = addition(sk0_2,multiplication(X0,sk0_2)),
inference(forward_demodulation,[status(thm)],[f19,f66077]) ).
fof(f66080,plain,
! [X0] : multiplication(sk0_0(c(sk0_2)),addition(X0,sk0_2)) = addition(multiplication(sk0_0(c(sk0_2)),X0),sk0_2),
inference(paramodulation,[status(thm)],[f65770,f26]) ).
fof(f66081,plain,
! [X0] : multiplication(sk0_0(c(sk0_2)),addition(X0,sk0_2)) = addition(sk0_2,multiplication(sk0_0(c(sk0_2)),X0)),
inference(forward_demodulation,[status(thm)],[f19,f66080]) ).
fof(f66111,plain,
( multiplication(sk0_0(c(sk0_2)),addition(one,sk0_2)) != sk0_0(c(sk0_2))
| spl0_1187 ),
inference(forward_demodulation,[status(thm)],[f120,f66056]) ).
fof(f66112,plain,
( addition(sk0_2,multiplication(sk0_0(c(sk0_2)),one)) != sk0_0(c(sk0_2))
| spl0_1187 ),
inference(forward_demodulation,[status(thm)],[f66081,f66111]) ).
fof(f66113,plain,
( addition(sk0_2,sk0_0(c(sk0_2))) != sk0_0(c(sk0_2))
| spl0_1187 ),
inference(forward_demodulation,[status(thm)],[f24,f66112]) ).
fof(f66114,plain,
( sk0_0(c(sk0_2)) != sk0_0(c(sk0_2))
| spl0_1187 ),
inference(forward_demodulation,[status(thm)],[f66019,f66113]) ).
fof(f66115,plain,
( $false
| spl0_1187 ),
inference(trivial_equality_resolution,[status(esa)],[f66114]) ).
fof(f66116,plain,
spl0_1187,
inference(contradiction_clause,[status(thm)],[f66115]) ).
fof(f66117,plain,
( multiplication(addition(one,sk0_0(c(sk0_2))),sk0_2) != sk0_2
| spl0_1185 ),
inference(forward_demodulation,[status(thm)],[f618,f66048]) ).
fof(f66118,plain,
( addition(sk0_2,multiplication(one,sk0_2)) != sk0_2
| spl0_1185 ),
inference(forward_demodulation,[status(thm)],[f66078,f66117]) ).
fof(f66119,plain,
( addition(sk0_2,sk0_2) != sk0_2
| spl0_1185 ),
inference(forward_demodulation,[status(thm)],[f25,f66118]) ).
fof(f66120,plain,
( sk0_2 != sk0_2
| spl0_1185 ),
inference(forward_demodulation,[status(thm)],[f22,f66119]) ).
fof(f66121,plain,
( $false
| spl0_1185 ),
inference(trivial_equality_resolution,[status(esa)],[f66120]) ).
fof(f66122,plain,
spl0_1185,
inference(contradiction_clause,[status(thm)],[f66121]) ).
fof(f66123,plain,
( addition(sk0_2,multiplication(one,sk0_2)) != sk0_2
| spl0_1184 ),
inference(forward_demodulation,[status(thm)],[f66078,f66030]) ).
fof(f66124,plain,
( addition(sk0_2,sk0_2) != sk0_2
| spl0_1184 ),
inference(forward_demodulation,[status(thm)],[f25,f66123]) ).
fof(f66125,plain,
( sk0_2 != sk0_2
| spl0_1184 ),
inference(forward_demodulation,[status(thm)],[f22,f66124]) ).
fof(f66126,plain,
( $false
| spl0_1184 ),
inference(trivial_equality_resolution,[status(esa)],[f66125]) ).
fof(f66127,plain,
spl0_1184,
inference(contradiction_clause,[status(thm)],[f66126]) ).
fof(f66191,plain,
( spl0_1191
<=> addition(sk0_2,sk0_0(c(sk0_2))) = sk0_0(c(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f66193,plain,
( addition(sk0_2,sk0_0(c(sk0_2))) != sk0_0(c(sk0_2))
| spl0_1191 ),
inference(component_clause,[status(thm)],[f66191]) ).
fof(f66281,plain,
( spl0_1196
<=> sk0_0(c(sk0_2)) = sk0_0(c(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f66283,plain,
( sk0_0(c(sk0_2)) != sk0_0(c(sk0_2))
| spl0_1196 ),
inference(component_clause,[status(thm)],[f66281]) ).
fof(f66330,plain,
( $false
| spl0_1196 ),
inference(trivial_equality_resolution,[status(esa)],[f66283]) ).
fof(f66331,plain,
spl0_1196,
inference(contradiction_clause,[status(thm)],[f66330]) ).
fof(f66337,plain,
( $false
| spl0_1191 ),
inference(forward_subsumption_resolution,[status(thm)],[f66019,f66193]) ).
fof(f66338,plain,
spl0_1191,
inference(contradiction_clause,[status(thm)],[f66337]) ).
fof(f67157,plain,
! [X0] : multiplication(addition(one,X0),sk0_2) = multiplication(addition(sk0_2,X0),sk0_2),
inference(paramodulation,[status(thm)],[f547,f65758]) ).
fof(f67513,plain,
( spl0_1202
<=> multiplication(addition(one,one),sk0_2) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f67515,plain,
( multiplication(addition(one,one),sk0_2) != sk0_2
| spl0_1202 ),
inference(component_clause,[status(thm)],[f67513]) ).
fof(f67650,plain,
( multiplication(one,sk0_2) != sk0_2
| spl0_1202 ),
inference(forward_demodulation,[status(thm)],[f22,f67515]) ).
fof(f67651,plain,
( sk0_2 != sk0_2
| spl0_1202 ),
inference(forward_demodulation,[status(thm)],[f25,f67650]) ).
fof(f67652,plain,
( $false
| spl0_1202 ),
inference(trivial_equality_resolution,[status(esa)],[f67651]) ).
fof(f67653,plain,
spl0_1202,
inference(contradiction_clause,[status(thm)],[f67652]) ).
fof(f69862,plain,
( spl0_1208
<=> addition(sk0_2,multiplication(one,sk0_2)) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f69864,plain,
( addition(sk0_2,multiplication(one,sk0_2)) != sk0_2
| spl0_1208 ),
inference(component_clause,[status(thm)],[f69862]) ).
fof(f70012,plain,
( addition(sk0_2,sk0_2) != sk0_2
| spl0_1208 ),
inference(forward_demodulation,[status(thm)],[f25,f69864]) ).
fof(f70013,plain,
( sk0_2 != sk0_2
| spl0_1208 ),
inference(forward_demodulation,[status(thm)],[f22,f70012]) ).
fof(f70014,plain,
( $false
| spl0_1208 ),
inference(trivial_equality_resolution,[status(esa)],[f70013]) ).
fof(f70015,plain,
spl0_1208,
inference(contradiction_clause,[status(thm)],[f70014]) ).
fof(f74515,plain,
! [X0,X1,X2,X3] : addition(multiplication(X0,X1),multiplication(addition(X2,X0),X3)) = addition(multiplication(X0,addition(X3,X1)),multiplication(X2,X3)),
inference(paramodulation,[status(thm)],[f142,f5808]) ).
fof(f75689,plain,
( spl0_1216
<=> multiplication(addition(sk0_2,one),sk0_2) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f75691,plain,
( multiplication(addition(sk0_2,one),sk0_2) != sk0_2
| spl0_1216 ),
inference(component_clause,[status(thm)],[f75689]) ).
fof(f75791,plain,
( multiplication(addition(one,one),sk0_2) != sk0_2
| spl0_1216 ),
inference(forward_demodulation,[status(thm)],[f67157,f75691]) ).
fof(f75792,plain,
( multiplication(one,sk0_2) != sk0_2
| spl0_1216 ),
inference(forward_demodulation,[status(thm)],[f22,f75791]) ).
fof(f75793,plain,
( sk0_2 != sk0_2
| spl0_1216 ),
inference(forward_demodulation,[status(thm)],[f25,f75792]) ).
fof(f75794,plain,
( $false
| spl0_1216 ),
inference(trivial_equality_resolution,[status(esa)],[f75793]) ).
fof(f75795,plain,
spl0_1216,
inference(contradiction_clause,[status(thm)],[f75794]) ).
fof(f81495,plain,
( spl0_1281
<=> sk0_0(c(sk0_1)) = sk0_0(c(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f81497,plain,
( sk0_0(c(sk0_1)) != sk0_0(c(sk0_1))
| spl0_1281 ),
inference(component_clause,[status(thm)],[f81495]) ).
fof(f81538,plain,
( $false
| spl0_1281 ),
inference(trivial_equality_resolution,[status(esa)],[f81497]) ).
fof(f81539,plain,
spl0_1281,
inference(contradiction_clause,[status(thm)],[f81538]) ).
fof(f83825,plain,
( spl0_1293
<=> multiplication(sk0_2,addition(c(sk0_2),one)) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f83827,plain,
( multiplication(sk0_2,addition(c(sk0_2),one)) != sk0_2
| spl0_1293 ),
inference(component_clause,[status(thm)],[f83825]) ).
fof(f83861,plain,
! [X0] : multiplication(sk0_2,addition(X0,c(sk0_2))) = addition(multiplication(sk0_2,X0),zero),
inference(paramodulation,[status(thm)],[f22466,f26]) ).
fof(f83862,plain,
! [X0] : multiplication(sk0_2,addition(X0,c(sk0_2))) = multiplication(sk0_2,X0),
inference(forward_demodulation,[status(thm)],[f21,f83861]) ).
fof(f83863,plain,
! [X0] : multiplication(sk0_2,addition(c(sk0_2),X0)) = addition(zero,multiplication(sk0_2,X0)),
inference(paramodulation,[status(thm)],[f22466,f26]) ).
fof(f83864,plain,
! [X0] : multiplication(sk0_2,addition(c(sk0_2),X0)) = multiplication(sk0_2,X0),
inference(forward_demodulation,[status(thm)],[f584,f83863]) ).
fof(f83877,plain,
( multiplication(sk0_2,addition(one,c(sk0_2))) != sk0_2
| spl0_1293 ),
inference(forward_demodulation,[status(thm)],[f120,f83827]) ).
fof(f83878,plain,
( multiplication(sk0_2,one) != sk0_2
| spl0_1293 ),
inference(forward_demodulation,[status(thm)],[f83862,f83877]) ).
fof(f83879,plain,
( sk0_2 != sk0_2
| spl0_1293 ),
inference(forward_demodulation,[status(thm)],[f24,f83878]) ).
fof(f83880,plain,
( $false
| spl0_1293 ),
inference(trivial_equality_resolution,[status(esa)],[f83879]) ).
fof(f83881,plain,
spl0_1293,
inference(contradiction_clause,[status(thm)],[f83880]) ).
fof(f84046,plain,
multiplication(sk0_2,one) = multiplication(sk0_2,sk0_0(c(sk0_2))),
inference(paramodulation,[status(thm)],[f27237,f83864]) ).
fof(f84047,plain,
sk0_2 = multiplication(sk0_2,sk0_0(c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f24,f84046]) ).
fof(f84120,plain,
( spl0_1296
<=> multiplication(sk0_2,one) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f84122,plain,
( multiplication(sk0_2,one) != sk0_2
| spl0_1296 ),
inference(component_clause,[status(thm)],[f84120]) ).
fof(f84244,plain,
( sk0_2 != sk0_2
| spl0_1296 ),
inference(forward_demodulation,[status(thm)],[f24,f84122]) ).
fof(f84245,plain,
( $false
| spl0_1296 ),
inference(trivial_equality_resolution,[status(esa)],[f84244]) ).
fof(f84246,plain,
spl0_1296,
inference(contradiction_clause,[status(thm)],[f84245]) ).
fof(f84322,plain,
( spl0_1301
<=> multiplication(sk0_2,addition(sk0_0(c(sk0_2)),one)) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f84324,plain,
( multiplication(sk0_2,addition(sk0_0(c(sk0_2)),one)) != sk0_2
| spl0_1301 ),
inference(component_clause,[status(thm)],[f84322]) ).
fof(f84345,plain,
! [X0] : multiplication(sk0_2,addition(X0,sk0_0(c(sk0_2)))) = addition(multiplication(sk0_2,X0),sk0_2),
inference(paramodulation,[status(thm)],[f84047,f26]) ).
fof(f84346,plain,
! [X0] : multiplication(sk0_2,addition(X0,sk0_0(c(sk0_2)))) = addition(sk0_2,multiplication(sk0_2,X0)),
inference(forward_demodulation,[status(thm)],[f19,f84345]) ).
fof(f84383,plain,
( multiplication(sk0_2,addition(one,sk0_0(c(sk0_2)))) != sk0_2
| spl0_1301 ),
inference(forward_demodulation,[status(thm)],[f120,f84324]) ).
fof(f84384,plain,
( addition(sk0_2,multiplication(sk0_2,one)) != sk0_2
| spl0_1301 ),
inference(forward_demodulation,[status(thm)],[f84346,f84383]) ).
fof(f84385,plain,
( addition(sk0_2,sk0_2) != sk0_2
| spl0_1301 ),
inference(forward_demodulation,[status(thm)],[f24,f84384]) ).
fof(f84386,plain,
( sk0_2 != sk0_2
| spl0_1301 ),
inference(forward_demodulation,[status(thm)],[f22,f84385]) ).
fof(f84387,plain,
( $false
| spl0_1301 ),
inference(trivial_equality_resolution,[status(esa)],[f84386]) ).
fof(f84388,plain,
spl0_1301,
inference(contradiction_clause,[status(thm)],[f84387]) ).
fof(f85861,plain,
( spl0_1309
<=> addition(sk0_2,multiplication(sk0_2,one)) = sk0_2 ),
introduced(split_symbol_definition) ).
fof(f85863,plain,
( addition(sk0_2,multiplication(sk0_2,one)) != sk0_2
| spl0_1309 ),
inference(component_clause,[status(thm)],[f85861]) ).
fof(f86010,plain,
( addition(sk0_2,sk0_2) != sk0_2
| spl0_1309 ),
inference(forward_demodulation,[status(thm)],[f24,f85863]) ).
fof(f86011,plain,
( sk0_2 != sk0_2
| spl0_1309 ),
inference(forward_demodulation,[status(thm)],[f22,f86010]) ).
fof(f86012,plain,
( $false
| spl0_1309 ),
inference(trivial_equality_resolution,[status(esa)],[f86011]) ).
fof(f86013,plain,
spl0_1309,
inference(contradiction_clause,[status(thm)],[f86012]) ).
fof(f92400,plain,
addition(sk0_2,multiplication(one,c(sk0_2))) = addition(one,multiplication(sk0_0(c(sk0_1)),c(sk0_2))),
inference(paramodulation,[status(thm)],[f5120,f35702]) ).
fof(f92401,plain,
addition(sk0_2,c(sk0_2)) = addition(one,multiplication(sk0_0(c(sk0_1)),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f25,f92400]) ).
fof(f92402,plain,
one = addition(one,multiplication(sk0_0(c(sk0_1)),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f20828,f92401]) ).
fof(f92975,plain,
( spl0_1330
<=> addition(one,multiplication(sk0_0(c(sk0_1)),c(sk0_2))) = one ),
introduced(split_symbol_definition) ).
fof(f92977,plain,
( addition(one,multiplication(sk0_0(c(sk0_1)),c(sk0_2))) != one
| spl0_1330 ),
inference(component_clause,[status(thm)],[f92975]) ).
fof(f92997,plain,
( one != one
| spl0_1330 ),
inference(forward_demodulation,[status(thm)],[f92402,f92977]) ).
fof(f92998,plain,
( $false
| spl0_1330 ),
inference(trivial_equality_resolution,[status(esa)],[f92997]) ).
fof(f92999,plain,
spl0_1330,
inference(contradiction_clause,[status(thm)],[f92998]) ).
fof(f95688,plain,
! [X0,X1] : addition(multiplication(X0,c(sk0_2)),multiplication(addition(X1,X0),sk0_2)) = addition(multiplication(X0,one),multiplication(X1,sk0_2)),
inference(paramodulation,[status(thm)],[f20828,f74515]) ).
fof(f95689,plain,
! [X0,X1] : addition(multiplication(X0,c(sk0_2)),multiplication(addition(X1,X0),sk0_2)) = addition(X0,multiplication(X1,sk0_2)),
inference(forward_demodulation,[status(thm)],[f24,f95688]) ).
fof(f114370,plain,
( addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(one,sk0_2)) = addition(c(sk0_1),multiplication(sk0_1,sk0_2))
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(paramodulation,[status(thm)],[f54262,f95689]) ).
fof(f114371,plain,
( addition(multiplication(one,sk0_2),multiplication(c(sk0_1),c(sk0_2))) = addition(c(sk0_1),multiplication(sk0_1,sk0_2))
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(forward_demodulation,[status(thm)],[f19,f114370]) ).
fof(f114372,plain,
( addition(sk0_2,multiplication(c(sk0_1),c(sk0_2))) = addition(c(sk0_1),multiplication(sk0_1,sk0_2))
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(forward_demodulation,[status(thm)],[f25,f114371]) ).
fof(f115159,plain,
( one != addition(sk0_1,addition(c(sk0_1),multiplication(sk0_1,sk0_2)))
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(backward_demodulation,[status(thm)],[f114372,f68]) ).
fof(f115160,plain,
( one != addition(one,multiplication(sk0_1,sk0_2))
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(forward_demodulation,[status(thm)],[f76,f115159]) ).
fof(f115161,plain,
( one != one
| ~ spl0_1022
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(forward_demodulation,[status(thm)],[f52231,f115160]) ).
fof(f115162,plain,
( $false
| ~ spl0_1022
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(trivial_equality_resolution,[status(esa)],[f115161]) ).
fof(f115163,plain,
( ~ spl0_1022
| ~ spl0_495
| ~ spl0_453
| ~ spl0_76 ),
inference(contradiction_clause,[status(thm)],[f115162]) ).
fof(f115164,plain,
$false,
inference(sat_refutation,[status(thm)],[f2759,f2762,f2800,f2921,f3642,f3688,f4121,f4742,f4745,f4765,f4772,f6463,f6498,f6501,f6615,f6821,f6851,f9925,f10511,f10542,f10594,f15206,f15212,f18448,f18630,f21106,f22462,f22470,f22512,f22761,f23866,f23924,f23950,f24224,f24226,f24250,f25727,f25799,f25804,f25806,f26536,f27597,f27680,f27763,f27855,f28172,f31618,f31666,f52205,f53362,f54105,f62602,f62604,f63660,f63945,f65174,f65979,f66116,f66122,f66127,f66331,f66338,f67653,f70015,f75795,f81539,f83881,f84246,f84388,f86013,f92999,f115163]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE011+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 11:44:51 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 69.92/9.31 % Refutation found
% 69.92/9.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 69.92/9.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 71.11/9.49 % Elapsed time: 9.116990 seconds
% 71.11/9.49 % CPU time: 70.919450 seconds
% 71.11/9.49 % Memory used: 515.317 MB
%------------------------------------------------------------------------------