TSTP Solution File: KLE007+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE007+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:15:26 EDT 2023
% Result : Theorem 0.11s 0.34s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 15 unt; 0 def)
% Number of atoms : 130 ( 45 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 124 ( 49 ~; 46 |; 20 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 54 (; 52 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = 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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
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) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
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(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(f33,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
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(f43,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| 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(f52,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& ( ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
| ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f53,plain,
( test(sk0_2)
& test(sk0_1)
& ( ~ leq(one,addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))))
| ~ leq(addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))),one) ) ),
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,
( ~ leq(one,addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))))
| ~ leq(addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))),one) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
( spl0_0
<=> leq(one,addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2)))) ),
introduced(split_symbol_definition) ).
fof(f59,plain,
( ~ leq(one,addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))))
| spl0_0 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( spl0_1
<=> leq(addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))),one) ),
introduced(split_symbol_definition) ).
fof(f62,plain,
( ~ leq(addition(multiplication(addition(sk0_1,c(sk0_1)),sk0_2),multiplication(addition(sk0_1,c(sk0_1)),c(sk0_2))),one)
| spl0_1 ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f56,f57,f60]) ).
fof(f64,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f48]) ).
fof(f66,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f43,f64]) ).
fof(f67,plain,
! [X0] :
( addition(X0,c(X0)) = one
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f19,f66]) ).
fof(f69,plain,
addition(sk0_1,c(sk0_1)) = one,
inference(resolution,[status(thm)],[f67,f55]) ).
fof(f70,plain,
addition(sk0_2,c(sk0_2)) = one,
inference(resolution,[status(thm)],[f67,f54]) ).
fof(f230,plain,
( ~ leq(one,multiplication(addition(sk0_1,c(sk0_1)),addition(sk0_2,c(sk0_2))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f26,f59]) ).
fof(f231,plain,
( ~ leq(one,multiplication(one,addition(sk0_2,c(sk0_2))))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f69,f230]) ).
fof(f232,plain,
( ~ leq(one,addition(sk0_2,c(sk0_2)))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f25,f231]) ).
fof(f233,plain,
( ~ leq(one,one)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f70,f232]) ).
fof(f234,plain,
( addition(one,one) != one
| spl0_0 ),
inference(resolution,[status(thm)],[f233,f33]) ).
fof(f235,plain,
( one != one
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f22,f234]) ).
fof(f236,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f235]) ).
fof(f237,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f238,plain,
( ~ leq(multiplication(addition(sk0_1,c(sk0_1)),addition(sk0_2,c(sk0_2))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f26,f62]) ).
fof(f239,plain,
( ~ leq(multiplication(one,addition(sk0_2,c(sk0_2))),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f69,f238]) ).
fof(f240,plain,
( ~ leq(addition(sk0_2,c(sk0_2)),one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f25,f239]) ).
fof(f241,plain,
( ~ leq(one,one)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f70,f240]) ).
fof(f246,plain,
( addition(one,one) != one
| spl0_1 ),
inference(resolution,[status(thm)],[f241,f33]) ).
fof(f247,plain,
( one != one
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f22,f246]) ).
fof(f248,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f247]) ).
fof(f249,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f250,plain,
$false,
inference(sat_refutation,[status(thm)],[f63,f237,f249]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE007+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n013.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue May 30 11:42:35 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.5.1
% 0.11/0.34 % Refutation found
% 0.11/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.55 % Elapsed time: 0.018687 seconds
% 0.17/0.55 % CPU time: 0.017324 seconds
% 0.17/0.55 % Memory used: 3.772 MB
%------------------------------------------------------------------------------