TSTP Solution File: KLE070+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE070+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 02:15:02 EDT 2022
% Result : Theorem 0.62s 0.80s
% Output : CNFRefutation 0.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 40 unt; 0 def)
% Number of atoms : 85 ( 84 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 59 ( 32 ~; 27 |; 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; 3 con; 0-2 aty)
% Number of variables : 68 ( 2 sgn 27 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(goals,conjecture,
! [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(X0) ).
fof(subgoal_0,plain,
! [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(X0),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) = domain(X0),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] : addition(domain(X0),multiplication(domain(X0),domain(X1))) != domain(X0),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_3,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X0] : addition(domain(X0),one) = one,
inference(canonicalize,[],[domain3]) ).
fof(normalize_0_5,plain,
! [X0] : addition(domain(X0),one) = one,
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_7,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_9,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_8]) ).
cnf(refute_0_0,plain,
addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
multiplication(domain(skolemFOFtoCNF_X0),one) = domain(skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_1:[bind(A,$fot(domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_3,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_6,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_7,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_9,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_9:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_11,plain,
( addition(domain(X0),one) != addition(one,domain(X0))
| addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),one),one) ),[0],$fot(addition(one,domain(X0)))]]) ).
cnf(refute_0_12,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_3,refute_0_12]) ).
cnf(refute_0_14,plain,
addition(one,domain(skolemFOFtoCNF_X1)) = one,
inference(subst,[],[refute_0_13:[bind(X0,$fot(skolemFOFtoCNF_X1))]]) ).
cnf(refute_0_15,plain,
multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))),
introduced(tautology,[refl,[$fot(multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))))]]) ).
cnf(refute_0_16,plain,
( addition(one,domain(skolemFOFtoCNF_X1)) != one
| multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) != multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1)))
| multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))),multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_17,plain,
( addition(one,domain(skolemFOFtoCNF_X1)) != one
| multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),one) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))),multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),one),
inference(resolve,[$cnf( $equal(addition(one,domain(skolemFOFtoCNF_X1)),one) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_7,refute_0_19]) ).
cnf(refute_0_21,plain,
( multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) != multiplication(domain(skolemFOFtoCNF_X0),one)
| multiplication(domain(skolemFOFtoCNF_X0),one) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))))),bind(Y,$fot(multiplication(domain(skolemFOFtoCNF_X0),one))),bind(Z,$fot(domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_22,plain,
( multiplication(domain(skolemFOFtoCNF_X0),one) != domain(skolemFOFtoCNF_X0)
| multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))),multiplication(domain(skolemFOFtoCNF_X0),one)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),one),domain(skolemFOFtoCNF_X0)) )],[refute_0_2,refute_0_22]) ).
cnf(refute_0_24,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_25,plain,
multiplication(X_90,addition(one,X_92)) = addition(multiplication(X_90,one),multiplication(X_90,X_92)),
inference(subst,[],[refute_0_24:[bind(A,$fot(X_90)),bind(B,$fot(one)),bind(C,$fot(X_92))]]) ).
cnf(refute_0_26,plain,
multiplication(X_90,one) = X_90,
inference(subst,[],[refute_0_1:[bind(A,$fot(X_90))]]) ).
cnf(refute_0_27,plain,
( multiplication(X_90,addition(one,X_92)) != addition(multiplication(X_90,one),multiplication(X_90,X_92))
| multiplication(X_90,one) != X_90
| multiplication(X_90,addition(one,X_92)) = addition(X_90,multiplication(X_90,X_92)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(X_90,addition(one,X_92)),addition(multiplication(X_90,one),multiplication(X_90,X_92))) ),[1,0],$fot(X_90)]]) ).
cnf(refute_0_28,plain,
( multiplication(X_90,addition(one,X_92)) != addition(multiplication(X_90,one),multiplication(X_90,X_92))
| multiplication(X_90,addition(one,X_92)) = addition(X_90,multiplication(X_90,X_92)) ),
inference(resolve,[$cnf( $equal(multiplication(X_90,one),X_90) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
multiplication(X_90,addition(one,X_92)) = addition(X_90,multiplication(X_90,X_92)),
inference(resolve,[$cnf( $equal(multiplication(X_90,addition(one,X_92)),addition(multiplication(X_90,one),multiplication(X_90,X_92))) )],[refute_0_25,refute_0_28]) ).
cnf(refute_0_30,plain,
( multiplication(X_90,addition(one,X_92)) != addition(X_90,multiplication(X_90,X_92))
| addition(X_90,multiplication(X_90,X_92)) = multiplication(X_90,addition(one,X_92)) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(multiplication(X_90,addition(one,X_92)))),bind(Y,$fot(addition(X_90,multiplication(X_90,X_92))))]]) ).
cnf(refute_0_31,plain,
addition(X_90,multiplication(X_90,X_92)) = multiplication(X_90,addition(one,X_92)),
inference(resolve,[$cnf( $equal(multiplication(X_90,addition(one,X_92)),addition(X_90,multiplication(X_90,X_92))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))),
inference(subst,[],[refute_0_31:[bind(X_90,$fot(domain(skolemFOFtoCNF_X0))),bind(X_92,$fot(domain(skolemFOFtoCNF_X1)))]]) ).
cnf(refute_0_33,plain,
( addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1)))
| multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))))),bind(Y,$fot(multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))))),bind(Z,$fot(domain(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_34,plain,
( multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(multiplication(domain(skolemFOFtoCNF_X0),addition(one,domain(skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) )],[refute_0_23,refute_0_34]) ).
cnf(refute_0_36,plain,
( addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) != domain(skolemFOFtoCNF_X0)
| domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) ),[0],$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_37,plain,
( domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0)
| addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))) = domain(skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
domain(skolemFOFtoCNF_X0) != domain(skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(addition(domain(skolemFOFtoCNF_X0),multiplication(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X1))),domain(skolemFOFtoCNF_X0)) )],[refute_0_37,refute_0_0]) ).
cnf(refute_0_39,plain,
domain(skolemFOFtoCNF_X0) = domain(skolemFOFtoCNF_X0),
introduced(tautology,[refl,[$fot(domain(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_40,plain,
$false,
inference(resolve,[$cnf( $equal(domain(skolemFOFtoCNF_X0),domain(skolemFOFtoCNF_X0)) )],[refute_0_39,refute_0_38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE070+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 12:02:52 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.62/0.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.62/0.80
% 0.62/0.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.62/0.80
%------------------------------------------------------------------------------