TSTP Solution File: KLE006+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE006+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 : 600s
% DateTime : Sun Jul 17 02:14:31 EDT 2022
% Result : Theorem 0.18s 0.54s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 44 ( 17 unt; 0 def)
% Number of atoms : 97 ( 58 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 102 ( 49 ~; 35 |; 8 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 29 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
! [X0] :
( test(X0)
=> one = addition(X0,c(X0)) ) ).
fof(subgoal_0,plain,
! [X0] :
( test(X0)
=> one = addition(X0,c(X0)) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] :
( test(X0)
=> one = addition(X0,c(X0)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] :
( one != addition(X0,c(X0))
& test(X0) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( one != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
& test(skolemFOFtoCNF_X0) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
test(skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_0_4,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(canonicalize,[],[test_2]) ).
fof(normalize_0_8,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| addition(X0,X1) = one )
& ( ~ complement(X1,X0)
| multiplication(X0,X1) = zero )
& ( ~ complement(X1,X0)
| multiplication(X1,X0) = zero )
& ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero
| complement(X1,X0) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_12,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
one != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
test(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_1:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_3,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_4,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_3,refute_0_2]) ).
cnf(refute_0_5,plain,
( ~ test(skolemFOFtoCNF_X0)
| complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_6,plain,
complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X0) )],[refute_0_0,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
| addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = one ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(c(skolemFOFtoCNF_X0))),bind(X1,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_9,plain,
addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_13,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_15,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(c(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_17,plain,
( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
| addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != one
| addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),one) ),[0],$fot(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_18,plain,
( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != one
| addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),one) )],[refute_0_9,refute_0_18]) ).
cnf(refute_0_20,plain,
one != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_21,plain,
( addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) != one
| one = addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)))),bind(Y,$fot(one))]]) ).
cnf(refute_0_22,plain,
addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) != one,
inference(resolve,[$cnf( $equal(one,addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),one) )],[refute_0_19,refute_0_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : KLE006+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 10:31:03 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.54 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.54
% 0.18/0.54 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.54
%------------------------------------------------------------------------------