TSTP Solution File: KLE005+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE005+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 02:14:30 EDT 2022
% Result : Theorem 0.35s 0.60s
% Output : CNFRefutation 0.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 13
% Syntax : Number of formulae : 73 ( 25 unt; 0 def)
% Number of atoms : 152 ( 82 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 144 ( 65 ~; 61 |; 7 &)
% ( 9 <=>; 2 =>; 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; 2 con; 0-2 aty)
% Number of variables : 64 ( 1 sgn 39 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ) ).
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(test_4,axiom,
! [X0] :
( ~ test(X0)
=> c(X0) = zero ) ).
fof(goals,conjecture,
c(one) = zero ).
fof(subgoal_0,plain,
c(one) = zero,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
c(one) != zero,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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_1,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_0_5,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(canonicalize,[],[test_1]) ).
fof(normalize_0_9,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| test(X0) )
& ( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| test(X0) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(canonicalize,[],[test_4]) ).
fof(normalize_0_13,plain,
! [X0] :
( c(X0) = zero
| test(X0) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X0] :
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_15,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_16,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
c(one) != zero,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_18,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_19,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_18]) ).
cnf(refute_0_0,plain,
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ complement(one,c(one))
| multiplication(c(one),one) = zero ),
inference(subst,[],[refute_0_0:[bind(X0,$fot(c(one))),bind(X1,$fot(one))]]) ).
cnf(refute_0_2,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_2:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_4,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_5,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ test(one)
| complement(one,c(one)) ),
inference(subst,[],[refute_0_5:[bind(X0,$fot(one))]]) ).
cnf(refute_0_7,plain,
( ~ complement(X1,X0)
| test(X0) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( ~ complement(zero,one)
| test(one) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(one)),bind(X1,$fot(zero))]]) ).
cnf(refute_0_9,plain,
( c(X0) = zero
| test(X0) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_10,plain,
( c(X_11) = zero
| test(X_11) ),
inference(subst,[],[refute_0_9:[bind(X0,$fot(X_11))]]) ).
cnf(refute_0_11,plain,
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ test(X_11)
| complement(skolemFOFtoCNF_X1(X_11),X_11) ),
inference(subst,[],[refute_0_11:[bind(X0,$fot(X_11))]]) ).
cnf(refute_0_13,plain,
( c(X_11) = zero
| complement(skolemFOFtoCNF_X1(X_11),X_11) ),
inference(resolve,[$cnf( test(X_11) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( c(one) = zero
| complement(skolemFOFtoCNF_X1(one),one) ),
inference(subst,[],[refute_0_13:[bind(X_11,$fot(one))]]) ).
cnf(refute_0_15,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_16,plain,
multiplication(one,skolemFOFtoCNF_X1(one)) = skolemFOFtoCNF_X1(one),
inference(subst,[],[refute_0_15:[bind(A,$fot(skolemFOFtoCNF_X1(one)))]]) ).
cnf(refute_0_17,plain,
( c(X_99) = zero
| complement(skolemFOFtoCNF_X1(X_99),X_99) ),
inference(subst,[],[refute_0_13:[bind(X_11,$fot(X_99))]]) ).
cnf(refute_0_18,plain,
( ~ complement(skolemFOFtoCNF_X1(X_99),X_99)
| multiplication(X_99,skolemFOFtoCNF_X1(X_99)) = zero ),
inference(subst,[],[refute_0_0:[bind(X0,$fot(X_99)),bind(X1,$fot(skolemFOFtoCNF_X1(X_99)))]]) ).
cnf(refute_0_19,plain,
( c(X_99) = zero
| multiplication(X_99,skolemFOFtoCNF_X1(X_99)) = zero ),
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1(X_99),X_99) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( c(one) = zero
| multiplication(one,skolemFOFtoCNF_X1(one)) = zero ),
inference(subst,[],[refute_0_19:[bind(X_99,$fot(one))]]) ).
cnf(refute_0_21,plain,
( multiplication(one,skolemFOFtoCNF_X1(one)) != skolemFOFtoCNF_X1(one)
| multiplication(one,skolemFOFtoCNF_X1(one)) != zero
| zero = skolemFOFtoCNF_X1(one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(one)),skolemFOFtoCNF_X1(one)) ),[0],$fot(zero)]]) ).
cnf(refute_0_22,plain,
( multiplication(one,skolemFOFtoCNF_X1(one)) != skolemFOFtoCNF_X1(one)
| c(one) = zero
| zero = skolemFOFtoCNF_X1(one) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(one)),zero) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( c(one) = zero
| zero = skolemFOFtoCNF_X1(one) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(one)),skolemFOFtoCNF_X1(one)) )],[refute_0_16,refute_0_22]) ).
cnf(refute_0_24,plain,
c(one) != zero,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_25,plain,
zero = skolemFOFtoCNF_X1(one),
inference(resolve,[$cnf( $equal(c(one),zero) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( zero != skolemFOFtoCNF_X1(one)
| skolemFOFtoCNF_X1(one) = zero ),
inference(subst,[],[refute_0_28:[bind(X,$fot(zero)),bind(Y,$fot(skolemFOFtoCNF_X1(one)))]]) ).
cnf(refute_0_30,plain,
skolemFOFtoCNF_X1(one) = zero,
inference(resolve,[$cnf( $equal(zero,skolemFOFtoCNF_X1(one)) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( skolemFOFtoCNF_X1(one) != zero
| ~ complement(skolemFOFtoCNF_X1(one),one)
| complement(zero,one) ),
introduced(tautology,[equality,[$cnf( complement(skolemFOFtoCNF_X1(one),one) ),[0],$fot(zero)]]) ).
cnf(refute_0_32,plain,
( ~ complement(skolemFOFtoCNF_X1(one),one)
| complement(zero,one) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(one),zero) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( c(one) = zero
| complement(zero,one) ),
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1(one),one) )],[refute_0_14,refute_0_32]) ).
cnf(refute_0_34,plain,
complement(zero,one),
inference(resolve,[$cnf( $equal(c(one),zero) )],[refute_0_33,refute_0_24]) ).
cnf(refute_0_35,plain,
test(one),
inference(resolve,[$cnf( complement(zero,one) )],[refute_0_34,refute_0_8]) ).
cnf(refute_0_36,plain,
complement(one,c(one)),
inference(resolve,[$cnf( test(one) )],[refute_0_35,refute_0_6]) ).
cnf(refute_0_37,plain,
multiplication(c(one),one) = zero,
inference(resolve,[$cnf( complement(one,c(one)) )],[refute_0_36,refute_0_1]) ).
cnf(refute_0_38,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_39,plain,
multiplication(c(one),one) = c(one),
inference(subst,[],[refute_0_38:[bind(A,$fot(c(one)))]]) ).
cnf(refute_0_40,plain,
( multiplication(c(one),one) != c(one)
| multiplication(c(one),one) != zero
| c(one) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(one),one),zero) ),[0],$fot(c(one))]]) ).
cnf(refute_0_41,plain,
( multiplication(c(one),one) != zero
| c(one) = zero ),
inference(resolve,[$cnf( $equal(multiplication(c(one),one),c(one)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
c(one) = zero,
inference(resolve,[$cnf( $equal(multiplication(c(one),one),zero) )],[refute_0_37,refute_0_41]) ).
cnf(refute_0_43,plain,
$false,
inference(resolve,[$cnf( $equal(c(one),zero) )],[refute_0_42,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : KLE005+1 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.09 % Command : metis --show proof --show saturation %s
% 0.07/0.27 % Computer : n032.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 600
% 0.07/0.27 % DateTime : Thu Jun 16 08:21:59 EDT 2022
% 0.07/0.27 % CPUTime :
% 0.07/0.27 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.35/0.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.35/0.60
% 0.35/0.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.35/0.61
%------------------------------------------------------------------------------