TSTP Solution File: KLE083+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 02:15:08 EDT 2022
% Result : Theorem 0.60s 0.81s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 82 ( 59 unt; 0 def)
% Number of atoms : 115 ( 114 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 71 ( 38 ~; 33 |; 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 : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 98 ( 0 sgn 33 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
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,
! [X0] : X0 = multiplication(domain(X0),X0) ).
fof(subgoal_0,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0] : X0 = multiplication(domain(X0),X0),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0] : X0 != multiplication(domain(X0),X0),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
skolemFOFtoCNF_X0 != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_3,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_5,plain,
! [X0] : multiplication(antidomain(X0),X0) = zero,
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_7,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_9,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_11,plain,
! [X0] : addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[domain4]) ).
fof(normalize_0_13,plain,
! [X0] : domain(X0) = antidomain(antidomain(X0)),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_15,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
skolemFOFtoCNF_X0 != multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
multiplication(addition(antidomain(X_115),X_114),X_115) = addition(multiplication(antidomain(X_115),X_115),multiplication(X_114,X_115)),
inference(subst,[],[refute_0_1:[bind(A,$fot(antidomain(X_115))),bind(B,$fot(X_114)),bind(C,$fot(X_115))]]) ).
cnf(refute_0_3,plain,
multiplication(antidomain(X0),X0) = zero,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
multiplication(antidomain(X_115),X_115) = zero,
inference(subst,[],[refute_0_3:[bind(X0,$fot(X_115))]]) ).
cnf(refute_0_5,plain,
( multiplication(addition(antidomain(X_115),X_114),X_115) != addition(multiplication(antidomain(X_115),X_115),multiplication(X_114,X_115))
| multiplication(antidomain(X_115),X_115) != zero
| multiplication(addition(antidomain(X_115),X_114),X_115) = addition(zero,multiplication(X_114,X_115)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(antidomain(X_115),X_114),X_115),addition(multiplication(antidomain(X_115),X_115),multiplication(X_114,X_115))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_6,plain,
( multiplication(addition(antidomain(X_115),X_114),X_115) != addition(multiplication(antidomain(X_115),X_115),multiplication(X_114,X_115))
| multiplication(addition(antidomain(X_115),X_114),X_115) = addition(zero,multiplication(X_114,X_115)) ),
inference(resolve,[$cnf( $equal(multiplication(antidomain(X_115),X_115),zero) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
multiplication(addition(antidomain(X_115),X_114),X_115) = addition(zero,multiplication(X_114,X_115)),
inference(resolve,[$cnf( $equal(multiplication(addition(antidomain(X_115),X_114),X_115),addition(multiplication(antidomain(X_115),X_115),multiplication(X_114,X_115))) )],[refute_0_2,refute_0_6]) ).
cnf(refute_0_8,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
addition(A,zero) = addition(zero,A),
inference(subst,[],[refute_0_9:[bind(B,$fot(zero))]]) ).
cnf(refute_0_11,plain,
( addition(A,zero) != A
| addition(A,zero) != addition(zero,A)
| addition(zero,A) = A ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,zero),A) ),[0],$fot(addition(zero,A))]]) ).
cnf(refute_0_12,plain,
( addition(A,zero) != A
| addition(zero,A) = A ),
inference(resolve,[$cnf( $equal(addition(A,zero),addition(zero,A)) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
addition(zero,A) = A,
inference(resolve,[$cnf( $equal(addition(A,zero),A) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
addition(zero,multiplication(X_114,X_115)) = multiplication(X_114,X_115),
inference(subst,[],[refute_0_13:[bind(A,$fot(multiplication(X_114,X_115)))]]) ).
cnf(refute_0_15,plain,
( addition(zero,multiplication(X_114,X_115)) != multiplication(X_114,X_115)
| multiplication(addition(antidomain(X_115),X_114),X_115) != addition(zero,multiplication(X_114,X_115))
| multiplication(addition(antidomain(X_115),X_114),X_115) = multiplication(X_114,X_115) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(antidomain(X_115),X_114),X_115),addition(zero,multiplication(X_114,X_115))) ),[1],$fot(multiplication(X_114,X_115))]]) ).
cnf(refute_0_16,plain,
( multiplication(addition(antidomain(X_115),X_114),X_115) != addition(zero,multiplication(X_114,X_115))
| multiplication(addition(antidomain(X_115),X_114),X_115) = multiplication(X_114,X_115) ),
inference(resolve,[$cnf( $equal(addition(zero,multiplication(X_114,X_115)),multiplication(X_114,X_115)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
multiplication(addition(antidomain(X_115),X_114),X_115) = multiplication(X_114,X_115),
inference(resolve,[$cnf( $equal(multiplication(addition(antidomain(X_115),X_114),X_115),addition(zero,multiplication(X_114,X_115))) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
multiplication(addition(antidomain(X_166),domain(X_166)),X_166) = multiplication(domain(X_166),X_166),
inference(subst,[],[refute_0_17:[bind(X_114,$fot(domain(X_166))),bind(X_115,$fot(X_166))]]) ).
cnf(refute_0_19,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = one,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_20,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_21,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_22,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_24,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_9,refute_0_23]) ).
cnf(refute_0_25,plain,
addition(antidomain(antidomain(X0)),antidomain(X0)) = addition(antidomain(X0),antidomain(antidomain(X0))),
inference(subst,[],[refute_0_24:[bind(A,$fot(antidomain(X0))),bind(B,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_26,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != addition(antidomain(X0),antidomain(antidomain(X0)))
| addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) ),[0],$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_27,plain,
( addition(antidomain(antidomain(X0)),antidomain(X0)) != one
| addition(antidomain(X0),antidomain(antidomain(X0))) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(antidomain(X0)),antidomain(X0)),one) )],[refute_0_19,refute_0_27]) ).
cnf(refute_0_29,plain,
domain(X0) = antidomain(antidomain(X0)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_30,plain,
( domain(X0) != antidomain(antidomain(X0))
| antidomain(antidomain(X0)) = domain(X0) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(domain(X0))),bind(Y,$fot(antidomain(antidomain(X0))))]]) ).
cnf(refute_0_31,plain,
antidomain(antidomain(X0)) = domain(X0),
inference(resolve,[$cnf( $equal(domain(X0),antidomain(antidomain(X0))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),antidomain(antidomain(X0))),
introduced(tautology,[refl,[$fot(addition(antidomain(X0),antidomain(antidomain(X0))))]]) ).
cnf(refute_0_33,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_34,plain,
( antidomain(antidomain(X0)) != domain(X0)
| addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),antidomain(antidomain(X0)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
addition(antidomain(X0),antidomain(antidomain(X0))) = addition(antidomain(X0),domain(X0)),
inference(resolve,[$cnf( $equal(antidomain(antidomain(X0)),domain(X0)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != addition(antidomain(X0),domain(X0))
| addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) ),[0],$fot(addition(antidomain(X0),domain(X0)))]]) ).
cnf(refute_0_37,plain,
( addition(antidomain(X0),antidomain(antidomain(X0))) != one
| addition(antidomain(X0),domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),addition(antidomain(X0),domain(X0))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
addition(antidomain(X0),domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(antidomain(X0),antidomain(antidomain(X0))),one) )],[refute_0_28,refute_0_37]) ).
cnf(refute_0_39,plain,
addition(antidomain(X_166),domain(X_166)) = one,
inference(subst,[],[refute_0_38:[bind(X0,$fot(X_166))]]) ).
cnf(refute_0_40,plain,
( addition(antidomain(X_166),domain(X_166)) != one
| multiplication(addition(antidomain(X_166),domain(X_166)),X_166) != multiplication(domain(X_166),X_166)
| multiplication(one,X_166) = multiplication(domain(X_166),X_166) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(antidomain(X_166),domain(X_166)),X_166),multiplication(domain(X_166),X_166)) ),[0,0],$fot(one)]]) ).
cnf(refute_0_41,plain,
( multiplication(addition(antidomain(X_166),domain(X_166)),X_166) != multiplication(domain(X_166),X_166)
| multiplication(one,X_166) = multiplication(domain(X_166),X_166) ),
inference(resolve,[$cnf( $equal(addition(antidomain(X_166),domain(X_166)),one) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
multiplication(one,X_166) = multiplication(domain(X_166),X_166),
inference(resolve,[$cnf( $equal(multiplication(addition(antidomain(X_166),domain(X_166)),X_166),multiplication(domain(X_166),X_166)) )],[refute_0_18,refute_0_41]) ).
cnf(refute_0_43,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_44,plain,
multiplication(one,X_166) = X_166,
inference(subst,[],[refute_0_43:[bind(A,$fot(X_166))]]) ).
cnf(refute_0_45,plain,
( multiplication(one,X_166) != X_166
| multiplication(one,X_166) != multiplication(domain(X_166),X_166)
| X_166 = multiplication(domain(X_166),X_166) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,X_166),multiplication(domain(X_166),X_166)) ),[0],$fot(X_166)]]) ).
cnf(refute_0_46,plain,
( multiplication(one,X_166) != multiplication(domain(X_166),X_166)
| X_166 = multiplication(domain(X_166),X_166) ),
inference(resolve,[$cnf( $equal(multiplication(one,X_166),X_166) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
X_166 = multiplication(domain(X_166),X_166),
inference(resolve,[$cnf( $equal(multiplication(one,X_166),multiplication(domain(X_166),X_166)) )],[refute_0_42,refute_0_46]) ).
cnf(refute_0_48,plain,
( X_166 != multiplication(domain(X_166),X_166)
| multiplication(domain(X_166),X_166) = X_166 ),
inference(subst,[],[refute_0_22:[bind(X,$fot(X_166)),bind(Y,$fot(multiplication(domain(X_166),X_166)))]]) ).
cnf(refute_0_49,plain,
multiplication(domain(X_166),X_166) = X_166,
inference(resolve,[$cnf( $equal(X_166,multiplication(domain(X_166),X_166)) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_49:[bind(X_166,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_51,plain,
( multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) ),[1],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_52,plain,
( skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0
| skolemFOFtoCNF_X0 = multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
skolemFOFtoCNF_X0 != skolemFOFtoCNF_X0,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,multiplication(domain(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0)) )],[refute_0_52,refute_0_0]) ).
cnf(refute_0_54,plain,
skolemFOFtoCNF_X0 = skolemFOFtoCNF_X0,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0,skolemFOFtoCNF_X0) )],[refute_0_54,refute_0_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE083+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 15:34:08 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.60/0.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.60/0.81
% 0.60/0.81 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.60/0.81
%------------------------------------------------------------------------------