TSTP Solution File: KLE021+4 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE021+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 12:15:31 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 : 54 ( 13 unt; 0 def)
% Number of atoms : 127 ( 48 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 124 ( 51 ~; 47 |; 17 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 57 (; 52 !; 5 ?)
% 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(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(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(f19,conjecture,
! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
& leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( test(X1)
=> ( leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
& leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f32,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f33,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f32]) ).
fof(f35,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f33]) ).
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(f45,plain,
! [X0,X1] :
( ~ complement(X0,X1)
| 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(f50,plain,
! [X0,X1] :
( ~ test(X0)
| c(X0) != X1
| complement(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f58,plain,
? [X0,X1] :
( test(X1)
& ( ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
| ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f59,plain,
? [X1] :
( test(X1)
& ( ? [X0] : ~ leq(X0,addition(multiplication(X1,X0),multiplication(c(X1),X0)))
| ? [X0] : ~ leq(addition(multiplication(X1,X0),multiplication(c(X1),X0)),X0) ) ),
inference(miniscoping,[status(esa)],[f58]) ).
fof(f60,plain,
( test(sk0_1)
& ( ~ leq(sk0_2,addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),sk0_2)))
| ~ leq(addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_3)),sk0_3) ) ),
inference(skolemization,[status(esa)],[f59]) ).
fof(f61,plain,
test(sk0_1),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f62,plain,
( ~ leq(sk0_2,addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),sk0_2)))
| ~ leq(addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_3)),sk0_3) ),
inference(cnf_transformation,[status(esa)],[f60]) ).
fof(f63,plain,
( spl0_0
<=> leq(sk0_2,addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),sk0_2))) ),
introduced(split_symbol_definition) ).
fof(f65,plain,
( ~ leq(sk0_2,addition(multiplication(sk0_1,sk0_2),multiplication(c(sk0_1),sk0_2)))
| spl0_0 ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( spl0_1
<=> leq(addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_3)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f68,plain,
( ~ leq(addition(multiplication(sk0_1,sk0_3),multiplication(c(sk0_1),sk0_3)),sk0_3)
| spl0_1 ),
inference(component_clause,[status(thm)],[f66]) ).
fof(f69,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f62,f63,f66]) ).
fof(f70,plain,
! [X0] :
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(destructive_equality_resolution,[status(esa)],[f50]) ).
fof(f464,plain,
! [X0] :
( addition(c(X0),X0) = one
| ~ test(X0) ),
inference(resolution,[status(thm)],[f45,f70]) ).
fof(f465,plain,
! [X0] :
( addition(X0,c(X0)) = one
| ~ test(X0) ),
inference(forward_demodulation,[status(thm)],[f21,f464]) ).
fof(f470,plain,
( ~ leq(sk0_2,multiplication(addition(sk0_1,c(sk0_1)),sk0_2))
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f29,f65]) ).
fof(f471,plain,
( addition(sk0_2,multiplication(addition(sk0_1,c(sk0_1)),sk0_2)) != multiplication(addition(sk0_1,c(sk0_1)),sk0_2)
| spl0_0 ),
inference(resolution,[status(thm)],[f470,f35]) ).
fof(f516,plain,
addition(sk0_1,c(sk0_1)) = one,
inference(resolution,[status(thm)],[f465,f61]) ).
fof(f518,plain,
( addition(sk0_2,multiplication(addition(sk0_1,c(sk0_1)),sk0_2)) != multiplication(one,sk0_2)
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f516,f471]) ).
fof(f519,plain,
( addition(sk0_2,multiplication(one,sk0_2)) != multiplication(one,sk0_2)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f516,f518]) ).
fof(f520,plain,
( addition(sk0_2,sk0_2) != multiplication(one,sk0_2)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f27,f519]) ).
fof(f521,plain,
( sk0_2 != multiplication(one,sk0_2)
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f24,f520]) ).
fof(f522,plain,
( sk0_2 != sk0_2
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f27,f521]) ).
fof(f523,plain,
( $false
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f522]) ).
fof(f524,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f523]) ).
fof(f540,plain,
( ~ leq(multiplication(addition(sk0_1,c(sk0_1)),sk0_3),sk0_3)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f29,f68]) ).
fof(f541,plain,
( ~ leq(multiplication(one,sk0_3),sk0_3)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f516,f540]) ).
fof(f542,plain,
( ~ leq(sk0_3,sk0_3)
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f27,f541]) ).
fof(f546,plain,
( addition(sk0_3,sk0_3) != sk0_3
| spl0_1 ),
inference(resolution,[status(thm)],[f542,f35]) ).
fof(f547,plain,
( sk0_3 != sk0_3
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f24,f546]) ).
fof(f548,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f547]) ).
fof(f549,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f550,plain,
$false,
inference(sat_refutation,[status(thm)],[f69,f524,f549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : KLE021+4 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n014.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 11:42:33 EDT 2023
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % 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
% 0.19/0.56 % Elapsed time: 0.025851 seconds
% 0.19/0.56 % CPU time: 0.026676 seconds
% 0.19/0.56 % Memory used: 3.963 MB
%------------------------------------------------------------------------------