TSTP Solution File: KLE024+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE024+2 : 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 02:14:44 EDT 2022
% Result : Theorem 4.62s 4.78s
% Output : CNFRefutation 4.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 23
% Syntax : Number of formulae : 113 ( 59 unt; 0 def)
% Number of atoms : 213 ( 138 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 186 ( 86 ~; 68 |; 18 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 167 ( 6 sgn 77 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
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(goals,conjecture,
! [X0,X1,X2] :
( ( test(X1)
& test(X2) )
=> ( addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
=> multiplication(multiplication(X1,X0),c(X2)) = zero ) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( ( test(X1)
& test(X2)
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) )
=> multiplication(multiplication(X1,X0),c(X2)) = zero ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2)
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0) )
=> multiplication(multiplication(X1,X0),c(X2)) = zero ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_1,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_6,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_8,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_10,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
? [X0,X1,X2] :
( multiplication(multiplication(X1,X0),c(X2)) != zero
& addition(multiplication(X0,c(X2)),multiplication(c(X1),X0)) = multiplication(c(X1),X0)
& test(X1)
& test(X2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_12,plain,
( multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != zero
& addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)
& test(skolemFOFtoCNF_X1_1)
& test(skolemFOFtoCNF_X2) ),
inference(skolemize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_0_15,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
test(skolemFOFtoCNF_X1_1),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_17,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_0_18,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,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_22,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,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_22]) ).
fof(normalize_0_24,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| multiplication(X1,X0) = zero ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_26,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_28,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != zero,
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero)
| addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) = zero ),
inference(subst,[],[refute_0_0:[bind(A,$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))),bind(B,$fot(zero))]]) ).
cnf(refute_0_2,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( addition(X_39,addition(X_39,X_20)) != addition(X_39,X_20)
| leq(X_39,addition(X_39,X_20)) ),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_39)),bind(B,$fot(addition(X_39,X_20)))]]) ).
cnf(refute_0_4,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
addition(X_19,addition(X_19,X_20)) = addition(addition(X_19,X_19),X_20),
inference(subst,[],[refute_0_4:[bind(A,$fot(X_19)),bind(B,$fot(X_19)),bind(C,$fot(X_20))]]) ).
cnf(refute_0_6,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
addition(X_19,X_19) = X_19,
inference(subst,[],[refute_0_6:[bind(A,$fot(X_19))]]) ).
cnf(refute_0_8,plain,
( addition(X_19,X_19) != X_19
| addition(X_19,addition(X_19,X_20)) != addition(addition(X_19,X_19),X_20)
| addition(X_19,addition(X_19,X_20)) = addition(X_19,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_19,addition(X_19,X_20)),addition(addition(X_19,X_19),X_20)) ),[1,0],$fot(X_19)]]) ).
cnf(refute_0_9,plain,
( addition(X_19,addition(X_19,X_20)) != addition(addition(X_19,X_19),X_20)
| addition(X_19,addition(X_19,X_20)) = addition(X_19,X_20) ),
inference(resolve,[$cnf( $equal(addition(X_19,X_19),X_19) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
addition(X_19,addition(X_19,X_20)) = addition(X_19,X_20),
inference(resolve,[$cnf( $equal(addition(X_19,addition(X_19,X_20)),addition(addition(X_19,X_19),X_20)) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
addition(X_39,addition(X_39,X_20)) = addition(X_39,X_20),
inference(subst,[],[refute_0_10:[bind(X_19,$fot(X_39))]]) ).
cnf(refute_0_12,plain,
( addition(X_39,X_20) != addition(X_39,X_20)
| addition(X_39,addition(X_39,X_20)) != addition(X_39,X_20)
| addition(X_39,addition(X_39,X_20)) = addition(X_39,X_20) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_39,addition(X_39,X_20)),addition(X_39,X_20)) ),[0,1],$fot(addition(X_39,X_20))]]) ).
cnf(refute_0_13,plain,
( addition(X_39,X_20) != addition(X_39,X_20)
| addition(X_39,addition(X_39,X_20)) = addition(X_39,X_20) ),
inference(resolve,[$cnf( $equal(addition(X_39,addition(X_39,X_20)),addition(X_39,X_20)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( addition(X_39,X_20) != addition(X_39,X_20)
| leq(X_39,addition(X_39,X_20)) ),
inference(resolve,[$cnf( $equal(addition(X_39,addition(X_39,X_20)),addition(X_39,X_20)) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
addition(X_39,X_20) = addition(X_39,X_20),
introduced(tautology,[refl,[$fot(addition(X_39,X_20))]]) ).
cnf(refute_0_16,plain,
leq(X_39,addition(X_39,X_20)),
inference(resolve,[$cnf( $equal(addition(X_39,X_20),addition(X_39,X_20)) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C))),
inference(subst,[],[refute_0_16:[bind(X_20,$fot(multiplication(A,C))),bind(X_39,$fot(multiplication(A,B)))]]) ).
cnf(refute_0_18,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
| addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).
cnf(refute_0_23,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( addition(multiplication(A,B),multiplication(A,C)) != multiplication(A,addition(B,C))
| ~ leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C)))
| leq(multiplication(A,B),multiplication(A,addition(B,C))) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C))) ),[1],$fot(multiplication(A,addition(B,C)))]]) ).
cnf(refute_0_25,plain,
( ~ leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C)))
| leq(multiplication(A,B),multiplication(A,addition(B,C))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,B),multiplication(A,C)),multiplication(A,addition(B,C))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
leq(multiplication(A,B),multiplication(A,addition(B,C))),
inference(resolve,[$cnf( leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C))) )],[refute_0_17,refute_0_25]) ).
cnf(refute_0_27,plain,
leq(multiplication(X_75,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(X_75,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)))),
inference(subst,[],[refute_0_26:[bind(A,$fot(X_75)),bind(B,$fot(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),bind(C,$fot(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_28,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) = multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_29,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) != multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)
| ~ leq(multiplication(X_75,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(X_75,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))))
| leq(multiplication(X_75,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(X_75,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_75,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(X_75,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)))) ),[1,1],$fot(multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_30,plain,
( ~ leq(multiplication(X_75,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(X_75,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))))
| leq(multiplication(X_75,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(X_75,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
leq(multiplication(X_75,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(X_75,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))),
inference(resolve,[$cnf( leq(multiplication(X_75,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(X_75,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)),multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)))) )],[refute_0_27,refute_0_30]) ).
cnf(refute_0_32,plain,
leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))),
inference(subst,[],[refute_0_31:[bind(X_75,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_33,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_34,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = multiplication(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),C),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_35,plain,
test(skolemFOFtoCNF_X1_1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_36,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_37,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_36:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_38,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_39,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_38,refute_0_37]) ).
cnf(refute_0_40,plain,
( ~ test(skolemFOFtoCNF_X1_1)
| complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_0_39:[bind(X0,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_41,plain,
complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_1) )],[refute_0_35,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ complement(X1,X0)
| multiplication(X1,X0) = zero ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_43,plain,
( ~ complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
| multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = zero ),
inference(subst,[],[refute_0_42:[bind(X0,$fot(c(skolemFOFtoCNF_X1_1))),bind(X1,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_44,plain,
multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) )],[refute_0_41,refute_0_43]) ).
cnf(refute_0_45,plain,
( multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) != multiplication(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),C)
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = multiplication(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)),multiplication(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_46,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) != multiplication(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),C)
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = multiplication(zero,C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),zero) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = multiplication(zero,C),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)),multiplication(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),C)) )],[refute_0_34,refute_0_46]) ).
cnf(refute_0_48,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_49,plain,
multiplication(zero,C) = zero,
inference(subst,[],[refute_0_48:[bind(A,$fot(C))]]) ).
cnf(refute_0_50,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) != multiplication(zero,C)
| multiplication(zero,C) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)),zero) ),[0],$fot(multiplication(zero,C))]]) ).
cnf(refute_0_51,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) != multiplication(zero,C)
| multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(zero,C),zero) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),C)),multiplication(zero,C)) )],[refute_0_47,refute_0_51]) ).
cnf(refute_0_53,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) = zero,
inference(subst,[],[refute_0_52:[bind(C,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_54,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)) != zero
| ~ leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)))
| leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))) ),[1],$fot(zero)]]) ).
cnf(refute_0_55,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)))
| leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0)),zero) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero),
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(skolemFOFtoCNF_X1_1,multiplication(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X0))) )],[refute_0_32,refute_0_55]) ).
cnf(refute_0_57,plain,
addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) = zero,
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) )],[refute_0_56,refute_0_1]) ).
cnf(refute_0_58,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_59,plain,
addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_58:[bind(A,$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))))]]) ).
cnf(refute_0_60,plain,
( addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_61,plain,
( addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) = zero ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) = zero,
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero),zero) )],[refute_0_57,refute_0_61]) ).
cnf(refute_0_63,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != zero,
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_64,plain,
( multiplication(A,multiplication(B,C)) != multiplication(multiplication(A,B),C)
| multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiplication(A,multiplication(B,C)))),bind(Y,$fot(multiplication(multiplication(A,B),C)))]]) ).
cnf(refute_0_65,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,multiplication(B,C)),multiplication(multiplication(A,B),C)) )],[refute_0_33,refute_0_64]) ).
cnf(refute_0_66,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_65:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(c(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_67,plain,
( multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) != zero
| multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_68,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) != zero
| multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) != zero,
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)),zero) )],[refute_0_68,refute_0_63]) ).
cnf(refute_0_70,plain,
$false,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) )],[refute_0_62,refute_0_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : KLE024+2 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 13:39:17 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.15/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.62/4.78 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.62/4.78
% 4.62/4.78 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.62/4.79
%------------------------------------------------------------------------------