TSTP Solution File: KLE035+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE035+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 02:14:50 EDT 2022
% Result : Theorem 0.68s 0.92s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 23
% Syntax : Number of formulae : 109 ( 62 unt; 0 def)
% Number of atoms : 188 ( 121 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 145 ( 66 ~; 55 |; 18 &)
% ( 3 <=>; 3 =>; 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 : 127 ( 0 sgn 63 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
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_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(goals,conjecture,
! [X0,X1,X2,X3] :
( ( test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2,X3] :
( ( test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2,X3] :
( ( test(X3)
& test(X2)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero) )
=> leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1,X2,X3] :
( ~ leq(multiplication(multiplication(X2,addition(X0,X1)),c(X3)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X2,X1),c(X3)),zero)
& test(X2)
& test(X3) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)),zero)
& leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero)
& leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)),zero)
& test(skolemFOFtoCNF_X2)
& test(skolemFOFtoCNF_X3) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)),zero),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_0_4,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)),zero),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_7,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_11,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_13,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_15,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_16,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_18,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_20,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_21,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_20]) ).
cnf(refute_0_0,plain,
~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)),zero),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( multiplication(A,multiplication(B,C)) != multiplication(multiplication(A,B),C)
| multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(A,multiplication(B,C)))),bind(Y,$fot(multiplication(multiplication(A,B),C)))]]) ).
cnf(refute_0_6,plain,
multiplication(multiplication(A,B),C) = multiplication(A,multiplication(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,multiplication(B,C)),multiplication(multiplication(A,B),C)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)) = multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))),bind(C,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_8,plain,
( multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)) != multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)))
| ~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),zero)
| leq(multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)),zero) ),
introduced(tautology,[equality,[$cnf( ~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_9,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),zero)
| leq(multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)),zero) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),zero),
inference(resolve,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X2,addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),c(skolemFOFtoCNF_X3)),zero) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)),zero),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_12,plain,
multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(skolemFOFtoCNF_X1_1)),bind(C,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_13,plain,
( multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3)))
| ~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)),zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_14,plain,
( ~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)),zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3)))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero),
inference(resolve,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3)),zero) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_17,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero)
| addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) = zero ),
inference(subst,[],[refute_0_16:[bind(A,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))))),bind(B,$fot(zero))]]) ).
cnf(refute_0_18,plain,
addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) = zero,
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_20,plain,
addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_19:[bind(A,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3)))))]]) ).
cnf(refute_0_21,plain,
( addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3)))
| addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_22,plain,
( addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))) = zero ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3)))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))) = zero,
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero),zero) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_25,plain,
multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),multiplication(skolemFOFtoCNF_X2,C)),
inference(subst,[],[refute_0_24:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_26,plain,
leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_27,plain,
multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_28,plain,
( multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))
| ~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_29,plain,
( ~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero),
inference(resolve,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero)
| addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) = zero ),
inference(subst,[],[refute_0_16:[bind(A,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))))),bind(B,$fot(zero))]]) ).
cnf(refute_0_32,plain,
addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) = zero,
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_19:[bind(A,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))))]]) ).
cnf(refute_0_34,plain,
( addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))
| addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_35,plain,
( addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))) = zero ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))) = zero,
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero),zero) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),multiplication(skolemFOFtoCNF_X2,C))
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))) != zero
| multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = addition(zero,multiplication(skolemFOFtoCNF_X2,C)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),multiplication(skolemFOFtoCNF_X2,C))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_38,plain,
( multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),multiplication(skolemFOFtoCNF_X2,C))
| multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = addition(zero,multiplication(skolemFOFtoCNF_X2,C)) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = addition(zero,multiplication(skolemFOFtoCNF_X2,C)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),multiplication(skolemFOFtoCNF_X2,C))) )],[refute_0_25,refute_0_38]) ).
cnf(refute_0_40,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_41,plain,
addition(A,zero) = addition(zero,A),
inference(subst,[],[refute_0_40:[bind(B,$fot(zero))]]) ).
cnf(refute_0_42,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_43,plain,
( addition(A,zero) != A
| addition(zero,A) = A ),
inference(resolve,[$cnf( $equal(addition(A,zero),addition(zero,A)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
addition(zero,A) = A,
inference(resolve,[$cnf( $equal(addition(A,zero),A) )],[refute_0_19,refute_0_43]) ).
cnf(refute_0_45,plain,
addition(zero,multiplication(skolemFOFtoCNF_X2,C)) = multiplication(skolemFOFtoCNF_X2,C),
inference(subst,[],[refute_0_44:[bind(A,$fot(multiplication(skolemFOFtoCNF_X2,C)))]]) ).
cnf(refute_0_46,plain,
( addition(zero,multiplication(skolemFOFtoCNF_X2,C)) != multiplication(skolemFOFtoCNF_X2,C)
| multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != addition(zero,multiplication(skolemFOFtoCNF_X2,C))
| multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(skolemFOFtoCNF_X2,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),addition(zero,multiplication(skolemFOFtoCNF_X2,C))) ),[1],$fot(multiplication(skolemFOFtoCNF_X2,C))]]) ).
cnf(refute_0_47,plain,
( multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != addition(zero,multiplication(skolemFOFtoCNF_X2,C))
| multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(skolemFOFtoCNF_X2,C) ),
inference(resolve,[$cnf( $equal(addition(zero,multiplication(skolemFOFtoCNF_X2,C)),multiplication(skolemFOFtoCNF_X2,C)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(skolemFOFtoCNF_X2,C),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),addition(zero,multiplication(skolemFOFtoCNF_X2,C))) )],[refute_0_39,refute_0_47]) ).
cnf(refute_0_49,plain,
multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3)))) = multiplication(skolemFOFtoCNF_X2,multiplication(B,c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_48:[bind(C,$fot(multiplication(B,c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_50,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_51,plain,
multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3)) = addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_50:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_52,plain,
( multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3)) != addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3)))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3))) = multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3)))),bind(Y,$fot(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3)))))]]) ).
cnf(refute_0_53,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3))) = multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3)),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3))) != multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3))
| multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3)))) != multiplication(skolemFOFtoCNF_X2,multiplication(B,c(skolemFOFtoCNF_X3)))
| multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3))) = multiplication(skolemFOFtoCNF_X2,multiplication(B,c(skolemFOFtoCNF_X3))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3)))),multiplication(skolemFOFtoCNF_X2,multiplication(B,c(skolemFOFtoCNF_X3)))) ),[0,1],$fot(multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_55,plain,
( multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3)))) != multiplication(skolemFOFtoCNF_X2,multiplication(B,c(skolemFOFtoCNF_X3)))
| multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3))) = multiplication(skolemFOFtoCNF_X2,multiplication(B,c(skolemFOFtoCNF_X3))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3))),multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,B),c(skolemFOFtoCNF_X3))) = multiplication(skolemFOFtoCNF_X2,multiplication(B,c(skolemFOFtoCNF_X3))),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),multiplication(B,c(skolemFOFtoCNF_X3)))),multiplication(skolemFOFtoCNF_X2,multiplication(B,c(skolemFOFtoCNF_X3)))) )],[refute_0_49,refute_0_55]) ).
cnf(refute_0_57,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_56:[bind(B,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_58,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_59,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_58]) ).
cnf(refute_0_60,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3)))
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))) = zero ),
inference(subst,[],[refute_0_59:[bind(X,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))))),bind(Y,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))))),bind(Z,$fot(zero))]]) ).
cnf(refute_0_61,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))) = zero ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3)))) )],[refute_0_57,refute_0_60]) ).
cnf(refute_0_62,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X3))),zero) )],[refute_0_23,refute_0_61]) ).
cnf(refute_0_63,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))) != zero
| ~ leq(zero,zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),zero) ),
introduced(tautology,[equality,[$cnf( ~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_64,plain,
( ~ leq(zero,zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),zero) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),zero) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
~ leq(zero,zero),
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X2,multiplication(addition(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X3))),zero) )],[refute_0_64,refute_0_10]) ).
cnf(refute_0_66,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_67,plain,
( addition(X_58,X_58) != X_58
| leq(X_58,X_58) ),
inference(subst,[],[refute_0_66:[bind(A,$fot(X_58)),bind(B,$fot(X_58))]]) ).
cnf(refute_0_68,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_69,plain,
addition(X_58,X_58) = X_58,
inference(subst,[],[refute_0_68:[bind(A,$fot(X_58))]]) ).
cnf(refute_0_70,plain,
( X_58 != X_58
| addition(X_58,X_58) != X_58
| addition(X_58,X_58) = X_58 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_58,X_58),X_58) ),[0,0],$fot(X_58)]]) ).
cnf(refute_0_71,plain,
( X_58 != X_58
| addition(X_58,X_58) = X_58 ),
inference(resolve,[$cnf( $equal(addition(X_58,X_58),X_58) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( X_58 != X_58
| leq(X_58,X_58) ),
inference(resolve,[$cnf( $equal(addition(X_58,X_58),X_58) )],[refute_0_71,refute_0_67]) ).
cnf(refute_0_73,plain,
X_58 = X_58,
introduced(tautology,[refl,[$fot(X_58)]]) ).
cnf(refute_0_74,plain,
leq(X_58,X_58),
inference(resolve,[$cnf( $equal(X_58,X_58) )],[refute_0_73,refute_0_72]) ).
cnf(refute_0_75,plain,
leq(zero,zero),
inference(subst,[],[refute_0_74:[bind(X_58,$fot(zero))]]) ).
cnf(refute_0_76,plain,
$false,
inference(resolve,[$cnf( leq(zero,zero) )],[refute_0_75,refute_0_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE035+2 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 10:50:05 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.68/0.92 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.68/0.92
% 0.68/0.92 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.68/0.93
%------------------------------------------------------------------------------