TSTP Solution File: KLE025+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE025+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 : Timeout 290.26s 290.45s
% Output : None
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 97 ( 53 unt; 0 def)
% Number of atoms : 185 ( 141 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 162 ( 74 ~; 60 |; 17 &)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 109 ( 0 sgn 59 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(multiplicative_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ).
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(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) )
=> ( multiplication(multiplication(X1,X0),c(X2)) = zero
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( ( test(X1)
& test(X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero )
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( ( test(X1)
& test(X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero )
=> multiplication(X1,X0) = multiplication(multiplication(X1,X0),X2) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_1,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X0,X1,X2] :
( multiplication(X1,X0) != multiplication(multiplication(X1,X0),X2)
& multiplication(multiplication(X1,X0),c(X2)) = zero
& test(X1)
& test(X2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) != multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2)
& multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = zero
& test(skolemFOFtoCNF_X1_1)
& test(skolemFOFtoCNF_X2) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = zero,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_0_6,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_8,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
test(skolemFOFtoCNF_X2),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_0_11,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,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_15,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,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_15]) ).
fof(normalize_0_17,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_19,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_21,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) != multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) = addition(multiplication(skolemFOFtoCNF_X1_1,X_42),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(X_42)),bind(C,$fot(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_2,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = zero,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
X = X,
introduced(tautology,[refl,[$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( $equal(X,X) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( multiplication(A,multiplication(B,C)) != multiplication(multiplication(A,B),C)
| multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(multiplication(A,multiplication(B,C)))),bind(Y,$fot(multiplication(multiplication(A,B),C)))]]) ).
cnf(refute_0_8,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,multiplication(B,C)),multiplication(multiplication(A,B),C)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(c(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_10,plain,
( multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(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_11,plain,
( multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)) != zero
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) = zero ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) = zero,
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X2)),zero) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) != addition(multiplication(skolemFOFtoCNF_X1_1,X_42),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) != zero
| multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) = addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),addition(multiplication(skolemFOFtoCNF_X1_1,X_42),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_14,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) != addition(multiplication(skolemFOFtoCNF_X1_1,X_42),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))
| multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) = addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),zero) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) = addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),addition(multiplication(skolemFOFtoCNF_X1_1,X_42),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))))) )],[refute_0_1,refute_0_14]) ).
cnf(refute_0_16,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_17,plain,
addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero) = multiplication(skolemFOFtoCNF_X1_1,X_42),
inference(subst,[],[refute_0_16:[bind(A,$fot(multiplication(skolemFOFtoCNF_X1_1,X_42)))]]) ).
cnf(refute_0_18,plain,
( addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero) != multiplication(skolemFOFtoCNF_X1_1,X_42)
| multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) != addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero)
| multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) = multiplication(skolemFOFtoCNF_X1_1,X_42) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero)) ),[1],$fot(multiplication(skolemFOFtoCNF_X1_1,X_42))]]) ).
cnf(refute_0_19,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) != addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero)
| multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) = multiplication(skolemFOFtoCNF_X1_1,X_42) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero),multiplication(skolemFOFtoCNF_X1_1,X_42)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) = multiplication(skolemFOFtoCNF_X1_1,X_42),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(X_42,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),addition(multiplication(skolemFOFtoCNF_X1_1,X_42),zero)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,B)),
inference(subst,[],[refute_0_20:[bind(X_42,$fot(multiplication(skolemFOFtoCNF_X0,B)))]]) ).
cnf(refute_0_22,plain,
multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2))) = addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(c(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_23,plain,
( multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2))) != addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))
| addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) = multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2))) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2))))),bind(Y,$fot(addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))))]]) ).
cnf(refute_0_24,plain,
addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) = multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2))),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2))),addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
( addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))) != multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2)))
| multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,B))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2)))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,B))) ),[0,1],$fot(multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_26,plain,
( multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,B))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2)))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,B)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2))),multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2)))) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,addition(B,c(skolemFOFtoCNF_X2)))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,B)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,addition(multiplication(skolemFOFtoCNF_X0,B),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X2)))),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,B))) )],[refute_0_21,refute_0_26]) ).
cnf(refute_0_28,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)))) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_27:[bind(B,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_29,plain,
test(skolemFOFtoCNF_X2),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_30,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_31,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_30:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_32,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_33,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_32,refute_0_31]) ).
cnf(refute_0_34,plain,
( ~ test(skolemFOFtoCNF_X2)
| complement(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)) ),
inference(subst,[],[refute_0_33:[bind(X0,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_35,plain,
complement(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X2) )],[refute_0_29,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_37,plain,
( ~ complement(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2))
| addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2) = one ),
inference(subst,[],[refute_0_36:[bind(X0,$fot(c(skolemFOFtoCNF_X2))),bind(X1,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_38,plain,
addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_40,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_41,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2) = addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_41:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(c(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_43,plain,
( addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2) != addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2))
| addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2) != one
| addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2),one) ),[0],$fot(addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_44,plain,
( addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2) != one
| addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2),addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2),one) )],[refute_0_38,refute_0_44]) ).
cnf(refute_0_46,plain,
( addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)) != one
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)))) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)))),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))) ),[0,1,1],$fot(one)]]) ).
cnf(refute_0_47,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)))) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)),one) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X2,c(skolemFOFtoCNF_X2)))),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))) )],[refute_0_28,refute_0_47]) ).
cnf(refute_0_49,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_50,plain,
multiplication(skolemFOFtoCNF_X0,one) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_49:[bind(A,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_51,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)),
introduced(tautology,[refl,[$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)))]]) ).
cnf(refute_0_52,plain,
( multiplication(skolemFOFtoCNF_X0,one) != skolemFOFtoCNF_X0
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) = multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one))) ),[1,1],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_53,plain,
( multiplication(skolemFOFtoCNF_X0,one) != skolemFOFtoCNF_X0
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) = multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) = multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,one),skolemFOFtoCNF_X0) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))
| multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) != multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0)
| multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))) ),[0],$fot(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_56,plain,
( multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))
| multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)),multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,one)),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))) )],[refute_0_48,refute_0_56]) ).
cnf(refute_0_58,plain,
multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) != multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_59,plain,
multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2) = multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_60,plain,
( multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))
| multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))
| multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) = multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2)) ),[1],$fot(multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_61,plain,
( multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))
| multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) = multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0) != multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),multiplication(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),skolemFOFtoCNF_X2)) )],[refute_0_61,refute_0_58]) ).
cnf(refute_0_63,plain,
$false,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X2))) )],[refute_0_57,refute_0_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.14/0.14 % Problem : KLE025+1 : TPTP v8.1.0. Released v4.0.0.
% 0.14/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Thu Jun 16 14:11:10 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 290.26/290.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 290.26/290.45
% 290.26/290.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 290.26/290.45
%------------------------------------------------------------------------------