TSTP Solution File: KLE086+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE086+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 02:15:09 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 24
% Syntax : Number of formulae : 93 ( 61 unt; 0 def)
% Number of atoms : 139 ( 138 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 95 ( 49 ~; 46 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 57 ( 0 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(domain1,axiom,
! [X0] : multiplication(antidomain(X0),X0) = zero ).
fof(domain3,axiom,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one ).
fof(domain4,axiom,
! [X0] : domain(X0) = antidomain(antidomain(X0)) ).
fof(goals,conjecture,
domain(zero) = zero ).
fof(subgoal_0,plain,
domain(zero) = zero,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
domain(zero) != zero,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_1,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[domain4]) ).
fof(normalize_0_3,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_5,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_7,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_9,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_11,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
domain(zero) != zero,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
multiplication(antidomain(antidomain(X_5)),antidomain(X_5)) = zero,
inference(subst,[],[refute_0_0:[bind(X0,$fot(antidomain(X_5)))]]) ).
cnf(refute_0_2,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
domain(X_5) = antidomain(antidomain(X_5)),
inference(subst,[],[refute_0_2:[bind(X0,$fot(X_5))]]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_5,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_6,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( domain(X_5) != antidomain(antidomain(X_5))
| antidomain(antidomain(X_5)) = domain(X_5) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(domain(X_5))),bind(Y,$fot(antidomain(antidomain(X_5))))]]) ).
cnf(refute_0_8,plain,
antidomain(antidomain(X_5)) = domain(X_5),
inference(resolve,[$cnf( $equal(domain(X_5),antidomain(antidomain(X_5))) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( antidomain(antidomain(X_5)) != domain(X_5)
| multiplication(antidomain(antidomain(X_5)),antidomain(X_5)) != zero
| multiplication(domain(X_5),antidomain(X_5)) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(antidomain(X_5)),antidomain(X_5)),zero) ),[0,0],$fot(domain(X_5))]]) ).
cnf(refute_0_10,plain,
( multiplication(antidomain(antidomain(X_5)),antidomain(X_5)) != zero
| multiplication(domain(X_5),antidomain(X_5)) = zero ),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X_5)),domain(X_5)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
multiplication(domain(X_5),antidomain(X_5)) = zero,
inference(resolve,[$cnf( $equal(multiplication(antidomain(antidomain(X_5)),antidomain(X_5)),zero) )],[refute_0_1,refute_0_10]) ).
cnf(refute_0_12,plain,
multiplication(domain(zero),antidomain(zero)) = zero,
inference(subst,[],[refute_0_11:[bind(X_5,$fot(zero))]]) ).
cnf(refute_0_13,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_14,plain,
addition(zero,antidomain(zero)) = addition(antidomain(zero),zero),
inference(subst,[],[refute_0_13:[bind(A,$fot(zero)),bind(B,$fot(antidomain(zero)))]]) ).
cnf(refute_0_15,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_16,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_17,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(subst,[],[refute_0_17:[bind(A,$fot(antidomain(X0))),bind(B,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_19,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != addition(antidomain(X0),antidomain(antidomain(X0)))
| addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) ),[0],$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_20,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) )],[refute_0_15,refute_0_20]) ).
cnf(refute_0_22,plain,
( domain(X0) != antidomain(antidomain(X0))
| antidomain(antidomain(X0)) = domain(X0) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(domain(X0))),bind(Y,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_23,plain,
antidomain(antidomain(X0)) = domain(X0),
inference(resolve,[$cnf( $equal(domain(X0),antidomain(antidomain(X0))) )],[refute_0_2,refute_0_22]) ).
cnf(refute_0_24,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),antidomain(antidomain(X0))),
introduced(tautology,[refl,[$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_25,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != addition(antidomain(X0),antidomain(antidomain(X0)))
| antidomain(antidomain(X0)) != domain(X0)
| addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),antidomain(antidomain(X0)))) ),[1,1],$fot(domain(X0))]]) ).
cnf(refute_0_26,plain,
( antidomain(antidomain(X0)) != domain(X0)
| addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X0)),domain(X0)) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != addition(antidomain(X0),domain(X0))
| addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) ),[0],$fot(addition(antidomain(X0),domain(X0)))]]) ).
cnf(refute_0_29,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),domain(X0))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) )],[refute_0_21,refute_0_29]) ).
cnf(refute_0_31,plain,
addition(antidomain(one),domain(one)) = one,
inference(subst,[],[refute_0_30:[bind(X0,$fot(one))]]) ).
cnf(refute_0_32,plain,
multiplication(antidomain(one),one) = zero,
inference(subst,[],[refute_0_0:[bind(X0,$fot(one))]]) ).
cnf(refute_0_33,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_34,plain,
multiplication(antidomain(one),one) = antidomain(one),
inference(subst,[],[refute_0_33:[bind(A,$fot(antidomain(one)))]]) ).
cnf(refute_0_35,plain,
( multiplication(antidomain(one),one) != antidomain(one)
| multiplication(antidomain(one),one) != zero
| antidomain(one) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(antidomain(one),one),zero) ),[0],$fot(antidomain(one))]]) ).
cnf(refute_0_36,plain,
( multiplication(antidomain(one),one) != zero
| antidomain(one) = zero ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(one),one),antidomain(one)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
antidomain(one) = zero,
inference(resolve,[$cnf( $equal(multiplication(antidomain(one),one),zero) )],[refute_0_32,refute_0_36]) ).
cnf(refute_0_38,plain,
( addition(antidomain(one),domain(one)) != one
| antidomain(one) != zero
| addition(zero,domain(one)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(one),domain(one)),one) ),[0,0],$fot(zero)]]) ).
cnf(refute_0_39,plain,
( addition(antidomain(one),domain(one)) != one
| addition(zero,domain(one)) = one ),
inference(resolve,[$cnf( $equal(antidomain(one),zero) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
addition(zero,domain(one)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(one),domain(one)),one) )],[refute_0_31,refute_0_39]) ).
cnf(refute_0_41,plain,
domain(one) = antidomain(antidomain(one)),
inference(subst,[],[refute_0_2:[bind(X0,$fot(one))]]) ).
cnf(refute_0_42,plain,
( antidomain(one) != zero
| domain(one) != antidomain(antidomain(one))
| domain(one) = antidomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(domain(one),antidomain(antidomain(one))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_43,plain,
( domain(one) != antidomain(antidomain(one))
| domain(one) = antidomain(zero) ),
inference(resolve,[$cnf( $equal(antidomain(one),zero) )],[refute_0_37,refute_0_42]) ).
cnf(refute_0_44,plain,
domain(one) = antidomain(zero),
inference(resolve,[$cnf( $equal(domain(one),antidomain(antidomain(one))) )],[refute_0_41,refute_0_43]) ).
cnf(refute_0_45,plain,
addition(zero,domain(one)) = addition(zero,domain(one)),
introduced(tautology,[refl,[$fot(addition(zero,domain(one)))]]) ).
cnf(refute_0_46,plain,
( addition(zero,domain(one)) != addition(zero,domain(one))
| domain(one) != antidomain(zero)
| addition(zero,domain(one)) = addition(zero,antidomain(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(zero,domain(one)),addition(zero,domain(one))) ),[1,1],$fot(antidomain(zero))]]) ).
cnf(refute_0_47,plain,
( domain(one) != antidomain(zero)
| addition(zero,domain(one)) = addition(zero,antidomain(zero)) ),
inference(resolve,[$cnf( $equal(addition(zero,domain(one)),addition(zero,domain(one))) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
addition(zero,domain(one)) = addition(zero,antidomain(zero)),
inference(resolve,[$cnf( $equal(domain(one),antidomain(zero)) )],[refute_0_44,refute_0_47]) ).
cnf(refute_0_49,plain,
( addition(zero,domain(one)) != addition(zero,antidomain(zero))
| addition(zero,domain(one)) != one
| addition(zero,antidomain(zero)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(zero,domain(one)),one) ),[0],$fot(addition(zero,antidomain(zero)))]]) ).
cnf(refute_0_50,plain,
( addition(zero,domain(one)) != one
| addition(zero,antidomain(zero)) = one ),
inference(resolve,[$cnf( $equal(addition(zero,domain(one)),addition(zero,antidomain(zero))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
addition(zero,antidomain(zero)) = one,
inference(resolve,[$cnf( $equal(addition(zero,domain(one)),one) )],[refute_0_40,refute_0_50]) ).
cnf(refute_0_52,plain,
( addition(zero,antidomain(zero)) != addition(antidomain(zero),zero)
| addition(zero,antidomain(zero)) != one
| one = addition(antidomain(zero),zero) ),
introduced(tautology,[equality,[$cnf( $equal(addition(zero,antidomain(zero)),addition(antidomain(zero),zero)) ),[0],$fot(one)]]) ).
cnf(refute_0_53,plain,
( addition(zero,antidomain(zero)) != addition(antidomain(zero),zero)
| one = addition(antidomain(zero),zero) ),
inference(resolve,[$cnf( $equal(addition(zero,antidomain(zero)),one) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
one = addition(antidomain(zero),zero),
inference(resolve,[$cnf( $equal(addition(zero,antidomain(zero)),addition(antidomain(zero),zero)) )],[refute_0_14,refute_0_53]) ).
cnf(refute_0_55,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_56,plain,
addition(antidomain(zero),zero) = antidomain(zero),
inference(subst,[],[refute_0_55:[bind(A,$fot(antidomain(zero)))]]) ).
cnf(refute_0_57,plain,
( addition(antidomain(zero),zero) != antidomain(zero)
| one != addition(antidomain(zero),zero)
| one = antidomain(zero) ),
introduced(tautology,[equality,[$cnf( $equal(one,addition(antidomain(zero),zero)) ),[1],$fot(antidomain(zero))]]) ).
cnf(refute_0_58,plain,
( one != addition(antidomain(zero),zero)
| one = antidomain(zero) ),
inference(resolve,[$cnf( $equal(addition(antidomain(zero),zero),antidomain(zero)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
one = antidomain(zero),
inference(resolve,[$cnf( $equal(one,addition(antidomain(zero),zero)) )],[refute_0_54,refute_0_58]) ).
cnf(refute_0_60,plain,
( one != antidomain(zero)
| antidomain(zero) = one ),
inference(subst,[],[refute_0_6:[bind(X,$fot(one)),bind(Y,$fot(antidomain(zero)))]]) ).
cnf(refute_0_61,plain,
antidomain(zero) = one,
inference(resolve,[$cnf( $equal(one,antidomain(zero)) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( antidomain(zero) != one
| multiplication(domain(zero),antidomain(zero)) != zero
| multiplication(domain(zero),one) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(zero),antidomain(zero)),zero) ),[0,1],$fot(one)]]) ).
cnf(refute_0_63,plain,
( multiplication(domain(zero),antidomain(zero)) != zero
| multiplication(domain(zero),one) = zero ),
inference(resolve,[$cnf( $equal(antidomain(zero),one) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
multiplication(domain(zero),one) = zero,
inference(resolve,[$cnf( $equal(multiplication(domain(zero),antidomain(zero)),zero) )],[refute_0_12,refute_0_63]) ).
cnf(refute_0_65,plain,
multiplication(domain(zero),one) = domain(zero),
inference(subst,[],[refute_0_33:[bind(A,$fot(domain(zero)))]]) ).
cnf(refute_0_66,plain,
( multiplication(domain(zero),one) != domain(zero)
| multiplication(domain(zero),one) != zero
| domain(zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(zero),one),zero) ),[0],$fot(domain(zero))]]) ).
cnf(refute_0_67,plain,
( multiplication(domain(zero),one) != zero
| domain(zero) = zero ),
inference(resolve,[$cnf( $equal(multiplication(domain(zero),one),domain(zero)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
domain(zero) = zero,
inference(resolve,[$cnf( $equal(multiplication(domain(zero),one),zero) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
domain(zero) != zero,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_70,plain,
$false,
inference(resolve,[$cnf( $equal(domain(zero),zero) )],[refute_0_68,refute_0_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE086+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n029.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 07:54:27 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.40
% 0.20/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.40
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