TSTP Solution File: KLE058+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE058+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 02:14:58 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 45 ( 32 unt; 0 def)
% Number of atoms : 63 ( 62 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 22 ~; 18 |; 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 : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 33 ( 2 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(domain1,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0) ).
fof(domain3,axiom,
! [X0] : addition(domain(X0),one) = one ).
fof(goals,conjecture,
domain(one) = one ).
fof(subgoal_0,plain,
domain(one) = one,
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
domain(one) != one,
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[domain1]) ).
fof(normalize_0_1,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(specialize,[],[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,
domain(one) != one,
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
addition(one,multiplication(domain(one),one)) = multiplication(domain(one),one),
inference(subst,[],[refute_0_0:[bind(X0,$fot(one))]]) ).
cnf(refute_0_2,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
multiplication(domain(one),one) = domain(one),
inference(subst,[],[refute_0_2:[bind(A,$fot(domain(one)))]]) ).
cnf(refute_0_4,plain,
( addition(one,multiplication(domain(one),one)) != multiplication(domain(one),one)
| multiplication(domain(one),one) != domain(one)
| addition(one,domain(one)) = multiplication(domain(one),one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,multiplication(domain(one),one)),multiplication(domain(one),one)) ),[0,1],$fot(domain(one))]]) ).
cnf(refute_0_5,plain,
( addition(one,multiplication(domain(one),one)) != multiplication(domain(one),one)
| addition(one,domain(one)) = multiplication(domain(one),one) ),
inference(resolve,[$cnf( $equal(multiplication(domain(one),one),domain(one)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
addition(one,domain(one)) = multiplication(domain(one),one),
inference(resolve,[$cnf( $equal(addition(one,multiplication(domain(one),one)),multiplication(domain(one),one)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(domain(X0),one) = one,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_8,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_10,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_11,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_13,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
addition(domain(X0),one) = addition(one,domain(X0)),
inference(subst,[],[refute_0_13:[bind(A,$fot(one)),bind(B,$fot(domain(X0)))]]) ).
cnf(refute_0_15,plain,
( addition(domain(X0),one) != addition(one,domain(X0))
| addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(domain(X0),one),one) ),[0],$fot(addition(one,domain(X0)))]]) ).
cnf(refute_0_16,plain,
( addition(domain(X0),one) != one
| addition(one,domain(X0)) = one ),
inference(resolve,[$cnf( $equal(addition(domain(X0),one),addition(one,domain(X0))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
addition(one,domain(X0)) = one,
inference(resolve,[$cnf( $equal(addition(domain(X0),one),one) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
addition(one,domain(one)) = one,
inference(subst,[],[refute_0_17:[bind(X0,$fot(one))]]) ).
cnf(refute_0_19,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| addition(one,domain(one)) != one
| one = multiplication(domain(one),one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(one,domain(one)),multiplication(domain(one),one)) ),[0],$fot(one)]]) ).
cnf(refute_0_20,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| one = multiplication(domain(one),one) ),
inference(resolve,[$cnf( $equal(addition(one,domain(one)),one) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( multiplication(domain(one),one) != domain(one)
| one != multiplication(domain(one),one)
| one = domain(one) ),
introduced(tautology,[equality,[$cnf( $equal(one,multiplication(domain(one),one)) ),[1],$fot(domain(one))]]) ).
cnf(refute_0_22,plain,
( one != multiplication(domain(one),one)
| one = domain(one) ),
inference(resolve,[$cnf( $equal(multiplication(domain(one),one),domain(one)) )],[refute_0_3,refute_0_21]) ).
cnf(refute_0_23,plain,
( addition(one,domain(one)) != multiplication(domain(one),one)
| one = domain(one) ),
inference(resolve,[$cnf( $equal(one,multiplication(domain(one),one)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
one = domain(one),
inference(resolve,[$cnf( $equal(addition(one,domain(one)),multiplication(domain(one),one)) )],[refute_0_6,refute_0_23]) ).
cnf(refute_0_25,plain,
domain(one) != one,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_26,plain,
( one != domain(one)
| domain(one) = one ),
inference(subst,[],[refute_0_11:[bind(X,$fot(one)),bind(Y,$fot(domain(one)))]]) ).
cnf(refute_0_27,plain,
one != domain(one),
inference(resolve,[$cnf( $equal(domain(one),one) )],[refute_0_26,refute_0_25]) ).
cnf(refute_0_28,plain,
$false,
inference(resolve,[$cnf( $equal(one,domain(one)) )],[refute_0_24,refute_0_27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE058+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n022.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 14:24:17 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------