TSTP Solution File: KLE010+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE010+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n028.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 12:15:27 EDT 2023
% Result : Theorem 0.20s 0.55s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 27
% Syntax : Number of formulae : 191 ( 72 unt; 0 def)
% Number of atoms : 410 ( 152 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 410 ( 191 ~; 176 |; 21 &)
% ( 19 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 19 ( 17 usr; 15 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 137 (; 132 !; 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(f17,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(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(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(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(f52,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& one != addition(addition(addition(addition(multiplication(X1,X0),multiplication(c(X1),X0)),multiplication(X0,X1)),multiplication(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(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(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(addition(addition(multiplication(sk0_2,sk0_1),multiplication(c(sk0_2),sk0_1)),multiplication(sk0_1,sk0_2)),multiplication(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(addition(addition(multiplication(addition(sk0_2,c(sk0_2)),sk0_1),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f27,f56]) ).
fof(f59,plain,
one != addition(addition(addition(multiplication(addition(c(sk0_2),sk0_2),sk0_1),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f19,f58]) ).
fof(f76,plain,
complement(sk0_1,c(sk0_1)),
inference(resolution,[status(thm)],[f57,f55]) ).
fof(f77,plain,
complement(sk0_2,c(sk0_2)),
inference(resolution,[status(thm)],[f57,f54]) ).
fof(f79,plain,
test(c(sk0_1)),
inference(resolution,[status(thm)],[f76,f38]) ).
fof(f81,plain,
test(c(sk0_2)),
inference(resolution,[status(thm)],[f77,f38]) ).
fof(f83,plain,
addition(c(sk0_2),sk0_2) = one,
inference(resolution,[status(thm)],[f43,f77]) ).
fof(f84,plain,
addition(c(sk0_1),sk0_1) = one,
inference(resolution,[status(thm)],[f43,f76]) ).
fof(f85,plain,
one != addition(addition(addition(multiplication(one,sk0_1),multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(backward_demodulation,[status(thm)],[f83,f59]) ).
fof(f86,plain,
one != addition(addition(addition(sk0_1,multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f25,f85]) ).
fof(f87,plain,
one != addition(addition(addition(multiplication(sk0_1,sk0_2),sk0_1),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f19,f86]) ).
fof(f96,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f99,plain,
! [X0,X1,X2,X3] : addition(addition(X0,X1),addition(X2,X3)) = addition(addition(X0,addition(X1,X2)),X3),
inference(paramodulation,[status(thm)],[f20,f20]) ).
fof(f102,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f104,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f114,plain,
! [X0] : addition(zero,X0) = X0,
inference(paramodulation,[status(thm)],[f19,f21]) ).
fof(f158,plain,
complement(sk0_0(sk0_1),sk0_1),
inference(resolution,[status(thm)],[f37,f55]) ).
fof(f159,plain,
complement(sk0_0(sk0_2),sk0_2),
inference(resolution,[status(thm)],[f37,f54]) ).
fof(f161,plain,
addition(sk0_1,sk0_0(sk0_1)) = one,
inference(resolution,[status(thm)],[f158,f43]) ).
fof(f162,plain,
addition(sk0_0(sk0_1),sk0_1) = one,
inference(forward_demodulation,[status(thm)],[f19,f161]) ).
fof(f164,plain,
addition(sk0_2,sk0_0(sk0_2)) = one,
inference(resolution,[status(thm)],[f159,f43]) ).
fof(f165,plain,
addition(sk0_0(sk0_2),sk0_2) = one,
inference(forward_demodulation,[status(thm)],[f19,f164]) ).
fof(f188,plain,
multiplication(sk0_1,sk0_0(sk0_1)) = zero,
inference(resolution,[status(thm)],[f41,f158]) ).
fof(f192,plain,
multiplication(sk0_0(sk0_1),sk0_1) = zero,
inference(resolution,[status(thm)],[f42,f158]) ).
fof(f221,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f222,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f221]) ).
fof(f344,plain,
( spl0_20
<=> one = one ),
introduced(split_symbol_definition) ).
fof(f346,plain,
( one != one
| spl0_20 ),
inference(component_clause,[status(thm)],[f344]) ).
fof(f383,plain,
one != addition(multiplication(c(sk0_1),c(sk0_2)),addition(addition(multiplication(sk0_1,sk0_2),sk0_1),multiplication(c(sk0_1),sk0_2))),
inference(paramodulation,[status(thm)],[f19,f87]) ).
fof(f384,plain,
one != addition(addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(sk0_1,sk0_2),sk0_1)),multiplication(c(sk0_1),sk0_2)),
inference(forward_demodulation,[status(thm)],[f20,f383]) ).
fof(f385,plain,
one != addition(addition(addition(multiplication(c(sk0_1),c(sk0_2)),multiplication(sk0_1,sk0_2)),sk0_1),multiplication(c(sk0_1),sk0_2)),
inference(forward_demodulation,[status(thm)],[f20,f384]) ).
fof(f407,plain,
( spl0_21
<=> complement(sk0_1,sk0_0(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f408,plain,
( complement(sk0_1,sk0_0(sk0_1))
| ~ spl0_21 ),
inference(component_clause,[status(thm)],[f407]) ).
fof(f410,plain,
( spl0_22
<=> multiplication(sk0_0(sk0_1),sk0_1) = zero ),
introduced(split_symbol_definition) ).
fof(f412,plain,
( multiplication(sk0_0(sk0_1),sk0_1) != zero
| spl0_22 ),
inference(component_clause,[status(thm)],[f410]) ).
fof(f413,plain,
( spl0_23
<=> multiplication(sk0_1,sk0_0(sk0_1)) = zero ),
introduced(split_symbol_definition) ).
fof(f415,plain,
( multiplication(sk0_1,sk0_0(sk0_1)) != zero
| spl0_23 ),
inference(component_clause,[status(thm)],[f413]) ).
fof(f416,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)],[f162,f44]) ).
fof(f417,plain,
( spl0_21
| ~ spl0_22
| ~ spl0_23 ),
inference(split_clause,[status(thm)],[f416,f407,f410,f413]) ).
fof(f443,plain,
( zero != zero
| spl0_23 ),
inference(forward_demodulation,[status(thm)],[f188,f415]) ).
fof(f444,plain,
( $false
| spl0_23 ),
inference(trivial_equality_resolution,[status(esa)],[f443]) ).
fof(f445,plain,
spl0_23,
inference(contradiction_clause,[status(thm)],[f444]) ).
fof(f446,plain,
( zero != zero
| spl0_22 ),
inference(forward_demodulation,[status(thm)],[f192,f412]) ).
fof(f447,plain,
( $false
| spl0_22 ),
inference(trivial_equality_resolution,[status(esa)],[f446]) ).
fof(f448,plain,
spl0_22,
inference(contradiction_clause,[status(thm)],[f447]) ).
fof(f452,plain,
( test(sk0_0(sk0_1))
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f408,f38]) ).
fof(f453,plain,
( complement(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_1))
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f452,f37]) ).
fof(f454,plain,
( complement(sk0_0(sk0_1),c(sk0_0(sk0_1)))
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f452,f57]) ).
fof(f455,plain,
( multiplication(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_1)) = zero
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f453,f42]) ).
fof(f456,plain,
( multiplication(sk0_0(sk0_1),sk0_0(sk0_0(sk0_1))) = zero
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f453,f41]) ).
fof(f457,plain,
( addition(sk0_0(sk0_1),sk0_0(sk0_0(sk0_1))) = one
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f453,f43]) ).
fof(f458,plain,
( addition(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_1)) = one
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f19,f457]) ).
fof(f462,plain,
( addition(c(sk0_0(sk0_1)),sk0_0(sk0_1)) = one
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f454,f43]) ).
fof(f470,plain,
! [X0] :
( multiplication(sk0_0(sk0_0(sk0_1)),addition(X0,sk0_0(sk0_1))) = addition(multiplication(sk0_0(sk0_0(sk0_1)),X0),zero)
| ~ spl0_21 ),
inference(paramodulation,[status(thm)],[f455,f26]) ).
fof(f471,plain,
! [X0] :
( multiplication(sk0_0(sk0_0(sk0_1)),addition(X0,sk0_0(sk0_1))) = multiplication(sk0_0(sk0_0(sk0_1)),X0)
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f21,f470]) ).
fof(f486,plain,
( spl0_27
<=> complement(sk0_0(sk0_1),sk0_0(sk0_0(sk0_1))) ),
introduced(split_symbol_definition) ).
fof(f487,plain,
( complement(sk0_0(sk0_1),sk0_0(sk0_0(sk0_1)))
| ~ spl0_27 ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,plain,
( spl0_28
<=> multiplication(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_1)) = zero ),
introduced(split_symbol_definition) ).
fof(f491,plain,
( multiplication(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_1)) != zero
| spl0_28 ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,plain,
( spl0_29
<=> multiplication(sk0_0(sk0_1),sk0_0(sk0_0(sk0_1))) = zero ),
introduced(split_symbol_definition) ).
fof(f494,plain,
( multiplication(sk0_0(sk0_1),sk0_0(sk0_0(sk0_1))) != zero
| spl0_29 ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( complement(sk0_0(sk0_1),sk0_0(sk0_0(sk0_1)))
| multiplication(sk0_0(sk0_0(sk0_1)),sk0_0(sk0_1)) != zero
| multiplication(sk0_0(sk0_1),sk0_0(sk0_0(sk0_1))) != zero
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f458,f44]) ).
fof(f496,plain,
( spl0_27
| ~ spl0_28
| ~ spl0_29
| ~ spl0_21 ),
inference(split_clause,[status(thm)],[f495,f486,f489,f492,f407]) ).
fof(f522,plain,
( zero != zero
| ~ spl0_21
| spl0_29 ),
inference(forward_demodulation,[status(thm)],[f456,f494]) ).
fof(f523,plain,
( $false
| ~ spl0_21
| spl0_29 ),
inference(trivial_equality_resolution,[status(esa)],[f522]) ).
fof(f524,plain,
( ~ spl0_21
| spl0_29 ),
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f525,plain,
( zero != zero
| ~ spl0_21
| spl0_28 ),
inference(forward_demodulation,[status(thm)],[f455,f491]) ).
fof(f526,plain,
( $false
| ~ spl0_21
| spl0_28 ),
inference(trivial_equality_resolution,[status(esa)],[f525]) ).
fof(f527,plain,
( ~ spl0_21
| spl0_28 ),
inference(contradiction_clause,[status(thm)],[f526]) ).
fof(f701,plain,
( multiplication(sk0_0(sk0_0(sk0_1)),one) = multiplication(sk0_0(sk0_0(sk0_1)),c(sk0_0(sk0_1)))
| ~ spl0_21 ),
inference(paramodulation,[status(thm)],[f462,f471]) ).
fof(f702,plain,
( sk0_0(sk0_0(sk0_1)) = multiplication(sk0_0(sk0_0(sk0_1)),c(sk0_0(sk0_1)))
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f24,f701]) ).
fof(f771,plain,
! [X0] : multiplication(sk0_1,addition(sk0_0(sk0_1),X0)) = addition(zero,multiplication(sk0_1,X0)),
inference(paramodulation,[status(thm)],[f188,f26]) ).
fof(f772,plain,
! [X0] : multiplication(sk0_1,addition(sk0_0(sk0_1),X0)) = multiplication(sk0_1,X0),
inference(forward_demodulation,[status(thm)],[f114,f771]) ).
fof(f911,plain,
( spl0_66
<=> test(sk0_0(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f913,plain,
( ~ test(sk0_0(sk0_1))
| spl0_66 ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f914,plain,
( spl0_67
<=> c(sk0_0(sk0_1)) = sk0_0(sk0_0(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f915,plain,
( c(sk0_0(sk0_1)) = sk0_0(sk0_0(sk0_1))
| ~ spl0_67 ),
inference(component_clause,[status(thm)],[f914]) ).
fof(f917,plain,
( ~ test(sk0_0(sk0_1))
| c(sk0_0(sk0_1)) = sk0_0(sk0_0(sk0_1))
| ~ spl0_27 ),
inference(resolution,[status(thm)],[f49,f487]) ).
fof(f918,plain,
( ~ spl0_66
| spl0_67
| ~ spl0_27 ),
inference(split_clause,[status(thm)],[f917,f911,f914,f486]) ).
fof(f924,plain,
( spl0_69
<=> c(sk0_0(sk0_1)) = sk0_1 ),
introduced(split_symbol_definition) ).
fof(f925,plain,
( c(sk0_0(sk0_1)) = sk0_1
| ~ spl0_69 ),
inference(component_clause,[status(thm)],[f924]) ).
fof(f927,plain,
( ~ test(sk0_0(sk0_1))
| c(sk0_0(sk0_1)) = sk0_1 ),
inference(resolution,[status(thm)],[f49,f158]) ).
fof(f928,plain,
( ~ spl0_66
| spl0_69 ),
inference(split_clause,[status(thm)],[f927,f911,f924]) ).
fof(f937,plain,
( spl0_72
<=> test(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f939,plain,
( ~ test(sk0_1)
| spl0_72 ),
inference(component_clause,[status(thm)],[f937]) ).
fof(f940,plain,
( spl0_73
<=> c(sk0_1) = sk0_0(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f941,plain,
( c(sk0_1) = sk0_0(sk0_1)
| ~ spl0_73 ),
inference(component_clause,[status(thm)],[f940]) ).
fof(f943,plain,
( ~ test(sk0_1)
| c(sk0_1) = sk0_0(sk0_1)
| ~ spl0_21 ),
inference(resolution,[status(thm)],[f49,f408]) ).
fof(f944,plain,
( ~ spl0_72
| spl0_73
| ~ spl0_21 ),
inference(split_clause,[status(thm)],[f943,f937,f940,f407]) ).
fof(f960,plain,
( $false
| spl0_72 ),
inference(forward_subsumption_resolution,[status(thm)],[f939,f55]) ).
fof(f961,plain,
spl0_72,
inference(contradiction_clause,[status(thm)],[f960]) ).
fof(f962,plain,
( $false
| ~ spl0_21
| spl0_66 ),
inference(forward_subsumption_resolution,[status(thm)],[f913,f452]) ).
fof(f963,plain,
( ~ spl0_21
| spl0_66 ),
inference(contradiction_clause,[status(thm)],[f962]) ).
fof(f964,plain,
( c(c(sk0_1)) = sk0_0(sk0_0(sk0_1))
| ~ spl0_73
| ~ spl0_67 ),
inference(forward_demodulation,[status(thm)],[f941,f915]) ).
fof(f965,plain,
( c(c(sk0_1)) = sk0_0(c(sk0_1))
| ~ spl0_73
| ~ spl0_67 ),
inference(forward_demodulation,[status(thm)],[f941,f964]) ).
fof(f966,plain,
( c(c(sk0_1)) = sk0_1
| ~ spl0_73
| ~ spl0_69 ),
inference(forward_demodulation,[status(thm)],[f941,f925]) ).
fof(f1083,plain,
! [X0] :
( multiplication(sk0_1,addition(c(sk0_1),X0)) = multiplication(sk0_1,X0)
| ~ spl0_73 ),
inference(backward_demodulation,[status(thm)],[f941,f772]) ).
fof(f1100,plain,
( sk0_0(sk0_0(sk0_1)) = multiplication(sk0_0(sk0_0(sk0_1)),c(c(sk0_1)))
| ~ spl0_73
| ~ spl0_21 ),
inference(backward_demodulation,[status(thm)],[f941,f702]) ).
fof(f1101,plain,
( sk0_0(c(sk0_1)) = multiplication(sk0_0(sk0_0(sk0_1)),c(c(sk0_1)))
| ~ spl0_73
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f941,f1100]) ).
fof(f1102,plain,
( sk0_0(c(sk0_1)) = multiplication(sk0_0(c(sk0_1)),c(c(sk0_1)))
| ~ spl0_73
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f941,f1101]) ).
fof(f1103,plain,
( sk0_0(c(sk0_1)) = multiplication(sk0_0(c(sk0_1)),sk0_1)
| ~ spl0_69
| ~ spl0_73
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f966,f1102]) ).
fof(f1290,plain,
( sk0_1 = sk0_0(c(sk0_1))
| ~ spl0_69
| ~ spl0_73
| ~ spl0_67 ),
inference(backward_demodulation,[status(thm)],[f966,f965]) ).
fof(f1333,plain,
( sk0_0(c(sk0_1)) = multiplication(sk0_1,sk0_1)
| ~ spl0_67
| ~ spl0_69
| ~ spl0_73
| ~ spl0_21 ),
inference(backward_demodulation,[status(thm)],[f1290,f1103]) ).
fof(f1334,plain,
( sk0_1 = multiplication(sk0_1,sk0_1)
| ~ spl0_67
| ~ spl0_69
| ~ spl0_73
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f1290,f1333]) ).
fof(f1394,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f104,f33]) ).
fof(f1433,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f19,f1394]) ).
fof(f1438,plain,
leq(sk0_2,one),
inference(paramodulation,[status(thm)],[f165,f1433]) ).
fof(f1450,plain,
addition(sk0_2,one) = one,
inference(resolution,[status(thm)],[f1438,f32]) ).
fof(f1451,plain,
addition(one,sk0_2) = one,
inference(forward_demodulation,[status(thm)],[f19,f1450]) ).
fof(f1490,plain,
( $false
| spl0_20 ),
inference(trivial_equality_resolution,[status(esa)],[f346]) ).
fof(f1491,plain,
spl0_20,
inference(contradiction_clause,[status(thm)],[f1490]) ).
fof(f1582,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,f96]) ).
fof(f1583,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(addition(multiplication(X1,X3),X0),multiplication(X1,X2)),
inference(forward_demodulation,[status(thm)],[f20,f1582]) ).
fof(f1797,plain,
one != addition(addition(multiplication(sk0_1,sk0_2),addition(multiplication(c(sk0_1),c(sk0_2)),sk0_1)),multiplication(c(sk0_1),sk0_2)),
inference(paramodulation,[status(thm)],[f102,f385]) ).
fof(f1798,plain,
one != addition(addition(multiplication(c(sk0_1),c(sk0_2)),sk0_1),addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),sk0_2))),
inference(forward_demodulation,[status(thm)],[f102,f1797]) ).
fof(f1799,plain,
one != addition(addition(multiplication(c(sk0_1),c(sk0_2)),addition(sk0_1,multiplication(sk0_1,sk0_2))),multiplication(c(sk0_1),sk0_2)),
inference(forward_demodulation,[status(thm)],[f99,f1798]) ).
fof(f1800,plain,
one != addition(addition(sk0_1,multiplication(sk0_1,sk0_2)),multiplication(c(sk0_1),addition(sk0_2,c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f1583,f1799]) ).
fof(f1801,plain,
one != addition(addition(multiplication(sk0_1,sk0_2),sk0_1),multiplication(c(sk0_1),addition(sk0_2,c(sk0_2)))),
inference(forward_demodulation,[status(thm)],[f19,f1800]) ).
fof(f1802,plain,
one != addition(addition(multiplication(sk0_1,sk0_2),sk0_1),multiplication(c(sk0_1),addition(c(sk0_2),sk0_2))),
inference(forward_demodulation,[status(thm)],[f222,f1801]) ).
fof(f1803,plain,
one != addition(addition(multiplication(sk0_1,sk0_2),sk0_1),multiplication(c(sk0_1),one)),
inference(forward_demodulation,[status(thm)],[f83,f1802]) ).
fof(f1804,plain,
one != addition(addition(multiplication(sk0_1,sk0_2),sk0_1),c(sk0_1)),
inference(forward_demodulation,[status(thm)],[f24,f1803]) ).
fof(f1890,plain,
( spl0_94
<=> test(c(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f1892,plain,
( ~ test(c(sk0_1))
| spl0_94 ),
inference(component_clause,[status(thm)],[f1890]) ).
fof(f1903,plain,
( $false
| spl0_94 ),
inference(forward_subsumption_resolution,[status(thm)],[f1892,f79]) ).
fof(f1904,plain,
spl0_94,
inference(contradiction_clause,[status(thm)],[f1903]) ).
fof(f1909,plain,
! [X0] :
( multiplication(sk0_1,addition(sk0_1,X0)) = addition(sk0_1,multiplication(sk0_1,X0))
| ~ spl0_67
| ~ spl0_69
| ~ spl0_73
| ~ spl0_21 ),
inference(paramodulation,[status(thm)],[f1334,f26]) ).
fof(f1910,plain,
! [X0] :
( multiplication(sk0_1,addition(sk0_1,X0)) = addition(multiplication(sk0_1,X0),sk0_1)
| ~ spl0_67
| ~ spl0_69
| ~ spl0_73
| ~ spl0_21 ),
inference(forward_demodulation,[status(thm)],[f19,f1909]) ).
fof(f1927,plain,
( spl0_98
<=> test(c(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f1929,plain,
( ~ test(c(sk0_2))
| spl0_98 ),
inference(component_clause,[status(thm)],[f1927]) ).
fof(f1940,plain,
( $false
| spl0_98 ),
inference(forward_subsumption_resolution,[status(thm)],[f1929,f81]) ).
fof(f1941,plain,
spl0_98,
inference(contradiction_clause,[status(thm)],[f1940]) ).
fof(f1955,plain,
! [X0,X1] :
( multiplication(sk0_1,addition(addition(c(sk0_1),X0),X1)) = addition(multiplication(sk0_1,X0),multiplication(sk0_1,X1))
| ~ spl0_73 ),
inference(paramodulation,[status(thm)],[f1083,f26]) ).
fof(f1956,plain,
! [X0,X1] :
( multiplication(sk0_1,addition(addition(c(sk0_1),X0),X1)) = multiplication(sk0_1,addition(X0,X1))
| ~ spl0_73 ),
inference(forward_demodulation,[status(thm)],[f26,f1955]) ).
fof(f2267,plain,
! [X0] :
( multiplication(sk0_1,addition(one,X0)) = multiplication(sk0_1,addition(sk0_1,X0))
| ~ spl0_73 ),
inference(paramodulation,[status(thm)],[f84,f1956]) ).
fof(f2268,plain,
! [X0] :
( multiplication(sk0_1,addition(one,X0)) = addition(multiplication(sk0_1,X0),sk0_1)
| ~ spl0_67
| ~ spl0_69
| ~ spl0_21
| ~ spl0_73 ),
inference(forward_demodulation,[status(thm)],[f1910,f2267]) ).
fof(f2307,plain,
( multiplication(sk0_1,one) = addition(multiplication(sk0_1,sk0_2),sk0_1)
| ~ spl0_67
| ~ spl0_69
| ~ spl0_21
| ~ spl0_73 ),
inference(paramodulation,[status(thm)],[f1451,f2268]) ).
fof(f2308,plain,
( sk0_1 = addition(multiplication(sk0_1,sk0_2),sk0_1)
| ~ spl0_67
| ~ spl0_69
| ~ spl0_21
| ~ spl0_73 ),
inference(forward_demodulation,[status(thm)],[f24,f2307]) ).
fof(f2344,plain,
( one != addition(sk0_1,c(sk0_1))
| ~ spl0_67
| ~ spl0_69
| ~ spl0_21
| ~ spl0_73 ),
inference(backward_demodulation,[status(thm)],[f2308,f1804]) ).
fof(f2345,plain,
( one != addition(c(sk0_1),sk0_1)
| ~ spl0_67
| ~ spl0_69
| ~ spl0_21
| ~ spl0_73 ),
inference(forward_demodulation,[status(thm)],[f19,f2344]) ).
fof(f2346,plain,
( one != one
| ~ spl0_67
| ~ spl0_69
| ~ spl0_21
| ~ spl0_73 ),
inference(forward_demodulation,[status(thm)],[f84,f2345]) ).
fof(f2347,plain,
( $false
| ~ spl0_67
| ~ spl0_69
| ~ spl0_21
| ~ spl0_73 ),
inference(trivial_equality_resolution,[status(esa)],[f2346]) ).
fof(f2348,plain,
( ~ spl0_67
| ~ spl0_69
| ~ spl0_21
| ~ spl0_73 ),
inference(contradiction_clause,[status(thm)],[f2347]) ).
fof(f2349,plain,
$false,
inference(sat_refutation,[status(thm)],[f417,f445,f448,f496,f524,f527,f918,f928,f944,f961,f963,f1491,f1904,f1941,f2348]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE010+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n028.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 12:01:02 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.35 % Drodi V3.5.1
% 0.20/0.55 % Refutation found
% 0.20/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.58/0.56 % Elapsed time: 0.218476 seconds
% 1.58/0.56 % CPU time: 1.604436 seconds
% 1.58/0.56 % Memory used: 80.034 MB
%------------------------------------------------------------------------------