TSTP Solution File: KLE009+2 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : KLE009+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 : Tue Apr 30 20:24:08 EDT 2024
% Result : Theorem 0.20s 0.41s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 19
% Syntax : Number of formulae : 108 ( 33 unt; 0 def)
% Number of atoms : 228 ( 88 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 213 ( 93 ~; 83 |; 19 &)
% ( 15 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 15 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 62 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> one = addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f36,plain,
! [X0] :
( ( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f37,plain,
( ! [X0] :
( ~ test(X0)
| ? [X1] : complement(X1,X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(miniscoping,[status(esa)],[f36]) ).
fof(f38,plain,
( ! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) )
& ! [X0] :
( test(X0)
| ! [X1] : ~ complement(X1,X0) ) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0] :
( ~ test(X0)
| complement(sk0_0(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,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(f42,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)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X1,X0) = zero ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| multiplication(X0,X1) = zero ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| addition(X1,X0) = one ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,plain,
! [X0,X1] :
( complement(X0,X1)
| multiplication(X1,X0) != zero
| multiplication(X0,X1) != zero
| addition(X1,X0) != one ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ~ test(X0)
| ( c(X0) = X1
<=> complement(X0,X1) ) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f48,plain,
! [X0,X1] :
( ~ test(X0)
| ( ( c(X0) != X1
| complement(X0,X1) )
& ( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(NNF_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
! [X0] :
( ~ test(X0)
| ( ! [X1] :
( c(X0) != X1
| complement(X0,X1) )
& ! [X1] :
( c(X0) = X1
| ~ complement(X0,X1) ) ) ),
inference(miniscoping,[status(esa)],[f48]) ).
fof(f51,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) = X1
| ~ complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f58,plain,
? [X0,X1] :
( test(X1)
& test(X0)
& one != addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f59,plain,
( test(sk0_2)
& test(sk0_1)
& one != addition(addition(addition(multiplication(sk0_1,sk0_2),multiplication(sk0_1,c(sk0_2))),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))) ),
inference(skolemization,[status(esa)],[f58]) ).
fof(f60,plain,
test(sk0_2),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f62,plain,
one != addition(addition(addition(multiplication(sk0_1,sk0_2),multiplication(sk0_1,c(sk0_2))),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f80,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f158,plain,
one != addition(addition(multiplication(sk0_1,addition(sk0_2,c(sk0_2))),multiplication(c(sk0_1),sk0_2)),multiplication(c(sk0_1),c(sk0_2))),
inference(backward_demodulation,[status(thm)],[f28,f62]) ).
fof(f159,plain,
one != addition(addition(multiplication(c(sk0_1),sk0_2),multiplication(sk0_1,addition(sk0_2,c(sk0_2)))),multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f21,f158]) ).
fof(f160,plain,
one != addition(addition(multiplication(c(sk0_1),sk0_2),multiplication(sk0_1,addition(c(sk0_2),sk0_2))),multiplication(c(sk0_1),c(sk0_2))),
inference(forward_demodulation,[status(thm)],[f21,f159]) ).
fof(f312,plain,
complement(sk0_0(sk0_1),sk0_1),
inference(resolution,[status(thm)],[f39,f61]) ).
fof(f313,plain,
complement(sk0_0(sk0_2),sk0_2),
inference(resolution,[status(thm)],[f39,f60]) ).
fof(f315,plain,
multiplication(sk0_0(sk0_1),sk0_1) = zero,
inference(resolution,[status(thm)],[f312,f44]) ).
fof(f316,plain,
multiplication(sk0_1,sk0_0(sk0_1)) = zero,
inference(resolution,[status(thm)],[f312,f43]) ).
fof(f318,plain,
addition(sk0_1,sk0_0(sk0_1)) = one,
inference(resolution,[status(thm)],[f312,f45]) ).
fof(f319,plain,
addition(sk0_0(sk0_1),sk0_1) = one,
inference(forward_demodulation,[status(thm)],[f21,f318]) ).
fof(f320,plain,
multiplication(sk0_0(sk0_2),sk0_2) = zero,
inference(resolution,[status(thm)],[f313,f44]) ).
fof(f321,plain,
multiplication(sk0_2,sk0_0(sk0_2)) = zero,
inference(resolution,[status(thm)],[f313,f43]) ).
fof(f323,plain,
addition(sk0_2,sk0_0(sk0_2)) = one,
inference(resolution,[status(thm)],[f313,f45]) ).
fof(f324,plain,
addition(sk0_0(sk0_2),sk0_2) = one,
inference(forward_demodulation,[status(thm)],[f21,f323]) ).
fof(f705,plain,
( spl0_16
<=> complement(sk0_2,sk0_0(sk0_2)) ),
introduced(split_symbol_definition) ).
fof(f706,plain,
( complement(sk0_2,sk0_0(sk0_2))
| ~ spl0_16 ),
inference(component_clause,[status(thm)],[f705]) ).
fof(f708,plain,
( spl0_17
<=> multiplication(sk0_2,sk0_0(sk0_2)) = zero ),
introduced(split_symbol_definition) ).
fof(f710,plain,
( multiplication(sk0_2,sk0_0(sk0_2)) != zero
| spl0_17 ),
inference(component_clause,[status(thm)],[f708]) ).
fof(f711,plain,
( spl0_18
<=> addition(sk0_0(sk0_2),sk0_2) = one ),
introduced(split_symbol_definition) ).
fof(f713,plain,
( addition(sk0_0(sk0_2),sk0_2) != one
| spl0_18 ),
inference(component_clause,[status(thm)],[f711]) ).
fof(f714,plain,
( complement(sk0_2,sk0_0(sk0_2))
| multiplication(sk0_2,sk0_0(sk0_2)) != zero
| addition(sk0_0(sk0_2),sk0_2) != one ),
inference(resolution,[status(thm)],[f46,f320]) ).
fof(f715,plain,
( spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(split_clause,[status(thm)],[f714,f705,f708,f711]) ).
fof(f716,plain,
( spl0_19
<=> complement(sk0_1,sk0_0(sk0_1)) ),
introduced(split_symbol_definition) ).
fof(f717,plain,
( complement(sk0_1,sk0_0(sk0_1))
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f716]) ).
fof(f719,plain,
( spl0_20
<=> multiplication(sk0_1,sk0_0(sk0_1)) = zero ),
introduced(split_symbol_definition) ).
fof(f721,plain,
( multiplication(sk0_1,sk0_0(sk0_1)) != zero
| spl0_20 ),
inference(component_clause,[status(thm)],[f719]) ).
fof(f722,plain,
( spl0_21
<=> addition(sk0_0(sk0_1),sk0_1) = one ),
introduced(split_symbol_definition) ).
fof(f724,plain,
( addition(sk0_0(sk0_1),sk0_1) != one
| spl0_21 ),
inference(component_clause,[status(thm)],[f722]) ).
fof(f725,plain,
( complement(sk0_1,sk0_0(sk0_1))
| multiplication(sk0_1,sk0_0(sk0_1)) != zero
| addition(sk0_0(sk0_1),sk0_1) != one ),
inference(resolution,[status(thm)],[f46,f315]) ).
fof(f726,plain,
( spl0_19
| ~ spl0_20
| ~ spl0_21 ),
inference(split_clause,[status(thm)],[f725,f716,f719,f722]) ).
fof(f857,plain,
( one != one
| spl0_21 ),
inference(forward_demodulation,[status(thm)],[f319,f724]) ).
fof(f858,plain,
( $false
| spl0_21 ),
inference(trivial_equality_resolution,[status(esa)],[f857]) ).
fof(f859,plain,
spl0_21,
inference(contradiction_clause,[status(thm)],[f858]) ).
fof(f860,plain,
( zero != zero
| spl0_20 ),
inference(forward_demodulation,[status(thm)],[f316,f721]) ).
fof(f861,plain,
( $false
| spl0_20 ),
inference(trivial_equality_resolution,[status(esa)],[f860]) ).
fof(f862,plain,
spl0_20,
inference(contradiction_clause,[status(thm)],[f861]) ).
fof(f863,plain,
( one != one
| spl0_18 ),
inference(forward_demodulation,[status(thm)],[f324,f713]) ).
fof(f864,plain,
( $false
| spl0_18 ),
inference(trivial_equality_resolution,[status(esa)],[f863]) ).
fof(f865,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f864]) ).
fof(f866,plain,
( zero != zero
| spl0_17 ),
inference(forward_demodulation,[status(thm)],[f321,f710]) ).
fof(f867,plain,
( $false
| spl0_17 ),
inference(trivial_equality_resolution,[status(esa)],[f866]) ).
fof(f868,plain,
spl0_17,
inference(contradiction_clause,[status(thm)],[f867]) ).
fof(f965,plain,
( spl0_47
<=> test(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f967,plain,
( ~ test(sk0_1)
| spl0_47 ),
inference(component_clause,[status(thm)],[f965]) ).
fof(f968,plain,
( spl0_48
<=> c(sk0_1) = sk0_0(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f969,plain,
( c(sk0_1) = sk0_0(sk0_1)
| ~ spl0_48 ),
inference(component_clause,[status(thm)],[f968]) ).
fof(f971,plain,
( ~ test(sk0_1)
| c(sk0_1) = sk0_0(sk0_1)
| ~ spl0_19 ),
inference(resolution,[status(thm)],[f717,f51]) ).
fof(f972,plain,
( ~ spl0_47
| spl0_48
| ~ spl0_19 ),
inference(split_clause,[status(thm)],[f971,f965,f968,f716]) ).
fof(f979,plain,
( $false
| spl0_47 ),
inference(forward_subsumption_resolution,[status(thm)],[f967,f61]) ).
fof(f980,plain,
spl0_47,
inference(contradiction_clause,[status(thm)],[f979]) ).
fof(f989,plain,
( spl0_49
<=> test(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f991,plain,
( ~ test(sk0_2)
| spl0_49 ),
inference(component_clause,[status(thm)],[f989]) ).
fof(f992,plain,
( spl0_50
<=> c(sk0_2) = sk0_0(sk0_2) ),
introduced(split_symbol_definition) ).
fof(f993,plain,
( c(sk0_2) = sk0_0(sk0_2)
| ~ spl0_50 ),
inference(component_clause,[status(thm)],[f992]) ).
fof(f995,plain,
( ~ test(sk0_2)
| c(sk0_2) = sk0_0(sk0_2)
| ~ spl0_16 ),
inference(resolution,[status(thm)],[f706,f51]) ).
fof(f996,plain,
( ~ spl0_49
| spl0_50
| ~ spl0_16 ),
inference(split_clause,[status(thm)],[f995,f989,f992,f705]) ).
fof(f1003,plain,
( $false
| spl0_49 ),
inference(forward_subsumption_resolution,[status(thm)],[f991,f60]) ).
fof(f1004,plain,
spl0_49,
inference(contradiction_clause,[status(thm)],[f1003]) ).
fof(f1019,plain,
( addition(c(sk0_1),sk0_1) = one
| ~ spl0_48 ),
inference(backward_demodulation,[status(thm)],[f969,f319]) ).
fof(f1037,plain,
( addition(c(sk0_2),sk0_2) = one
| ~ spl0_50 ),
inference(backward_demodulation,[status(thm)],[f993,f324]) ).
fof(f1267,plain,
( spl0_72
<=> one = one ),
introduced(split_symbol_definition) ).
fof(f1269,plain,
( one != one
| spl0_72 ),
inference(component_clause,[status(thm)],[f1267]) ).
fof(f1298,plain,
( $false
| spl0_72 ),
inference(trivial_equality_resolution,[status(esa)],[f1269]) ).
fof(f1299,plain,
spl0_72,
inference(contradiction_clause,[status(thm)],[f1298]) ).
fof(f1831,plain,
( one != addition(addition(multiplication(c(sk0_1),sk0_2),multiplication(sk0_1,one)),multiplication(c(sk0_1),c(sk0_2)))
| ~ spl0_50 ),
inference(backward_demodulation,[status(thm)],[f1037,f160]) ).
fof(f1832,plain,
( one != addition(addition(multiplication(c(sk0_1),sk0_2),sk0_1),multiplication(c(sk0_1),c(sk0_2)))
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f26,f1831]) ).
fof(f1950,plain,
( one != addition(multiplication(c(sk0_1),c(sk0_2)),addition(multiplication(c(sk0_1),sk0_2),sk0_1))
| ~ spl0_50 ),
inference(paramodulation,[status(thm)],[f21,f1832]) ).
fof(f1951,plain,
( one != addition(addition(multiplication(c(sk0_1),sk0_2),multiplication(c(sk0_1),c(sk0_2))),sk0_1)
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f80,f1950]) ).
fof(f1952,plain,
( one != addition(multiplication(c(sk0_1),addition(sk0_2,c(sk0_2))),sk0_1)
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f28,f1951]) ).
fof(f1953,plain,
( one != addition(multiplication(c(sk0_1),addition(c(sk0_2),sk0_2)),sk0_1)
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f21,f1952]) ).
fof(f1954,plain,
( one != addition(multiplication(c(sk0_1),one),sk0_1)
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f1037,f1953]) ).
fof(f1955,plain,
( one != addition(c(sk0_1),sk0_1)
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f26,f1954]) ).
fof(f1956,plain,
( one != one
| ~ spl0_48
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f1019,f1955]) ).
fof(f1957,plain,
( $false
| ~ spl0_48
| ~ spl0_50 ),
inference(trivial_equality_resolution,[status(esa)],[f1956]) ).
fof(f1958,plain,
( ~ spl0_48
| ~ spl0_50 ),
inference(contradiction_clause,[status(thm)],[f1957]) ).
fof(f1959,plain,
$false,
inference(sat_refutation,[status(thm)],[f715,f726,f859,f862,f865,f868,f972,f980,f996,f1004,f1299,f1958]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE009+2 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Apr 30 01:38:25 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 0.20/0.41 % Refutation found
% 0.20/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.43 % Elapsed time: 0.087801 seconds
% 0.20/0.43 % CPU time: 0.567443 seconds
% 0.20/0.43 % Total memory used: 66.982 MB
% 0.20/0.43 % Net memory used: 66.682 MB
%------------------------------------------------------------------------------