TSTP Solution File: KLE034+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE034+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 02:14:49 EDT 2022
% Result : Theorem 0.98s 1.15s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 35
% Syntax : Number of formulae : 163 ( 84 unt; 0 def)
% Number of atoms : 310 ( 205 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 271 ( 124 ~; 105 |; 29 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 167 ( 3 sgn 83 !; 5 ?)
% 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(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,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,X3,X4] :
( ( test(X3)
& test(X2)
& test(X4)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero) )
=> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X2)
& test(X4)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero) )
=> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X2)
& test(X4)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero) )
=> leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1,X2,X3,X4] :
( ~ leq(multiplication(multiplication(multiplication(X2,X0),X1),c(X4)),zero)
& leq(multiplication(multiplication(X2,X0),c(X3)),zero)
& leq(multiplication(multiplication(X3,X1),c(X4)),zero)
& test(X2)
& test(X3)
& test(X4) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ leq(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero)
& leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero)
& leq(multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero)
& test(skolemFOFtoCNF_X2)
& test(skolemFOFtoCNF_X3)
& test(skolemFOFtoCNF_X4) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ leq(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),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_X0),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] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_13,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_15,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
leq(multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_17,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_18,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
test(skolemFOFtoCNF_X3),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_20,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_0_21,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,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_25,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_29,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_31,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_32,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_31]) ).
cnf(refute_0_0,plain,
~ leq(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),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( $equal(multiplication(A,multiplication(B,C)),multiplication(multiplication(A,B),C)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))]]) ).
cnf(refute_0_8,plain,
multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)) = multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),
inference(subst,[],[refute_0_6:[bind(A,$fot(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0))),bind(B,$fot(skolemFOFtoCNF_X1_1)),bind(C,$fot(c(skolemFOFtoCNF_X4)))]]) ).
cnf(refute_0_9,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_9]) ).
cnf(refute_0_11,plain,
( multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)) != multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))
| multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)))),bind(Y,$fot(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))),bind(Z,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))))]]) ).
cnf(refute_0_12,plain,
( multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))
| multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) )],[refute_0_8,refute_0_11]) ).
cnf(refute_0_13,plain,
multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) )],[refute_0_7,refute_0_12]) ).
cnf(refute_0_14,plain,
( multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))
| ~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),zero)
| leq(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero) ),
introduced(tautology,[equality,[$cnf( ~ leq(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))))]]) ).
cnf(refute_0_15,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),zero)
| leq(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),zero),
inference(resolve,[$cnf( leq(multiplication(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero) )],[refute_0_15,refute_0_0]) ).
cnf(refute_0_17,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),C),
inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_18,plain,
leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_19,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,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_20,plain,
( multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))
| ~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_21,plain,
( ~ leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero),
inference(resolve,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X3)),zero) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_24,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_23:[bind(A,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))))),bind(B,$fot(zero))]]) ).
cnf(refute_0_25,plain,
addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) = zero,
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_27,plain,
addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_26:[bind(A,$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))))]]) ).
cnf(refute_0_28,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_29,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( $equal(addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))) = zero,
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero),zero) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != multiplication(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),C)
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),multiplication(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_32,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != multiplication(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),C)
| multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(zero,C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),zero) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(zero,C),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),multiplication(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3))),C)) )],[refute_0_17,refute_0_32]) ).
cnf(refute_0_34,plain,
multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C) = multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C)),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_35,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),
introduced(tautology,[refl,[$fot(multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)))]]) ).
cnf(refute_0_36,plain,
( multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C) != multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))
| multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C))
| multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C))) ),[1,1],$fot(multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C)))]]) ).
cnf(refute_0_37,plain,
( multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C) != multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))
| multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) = multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C),multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C)))
| multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != multiplication(zero,C)
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) = multiplication(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),multiplication(zero,C)) ),[0],$fot(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))))]]) ).
cnf(refute_0_40,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != multiplication(zero,C)
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) = multiplication(zero,C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C)))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_42,plain,
multiplication(zero,C) = zero,
inference(subst,[],[refute_0_41:[bind(A,$fot(C))]]) ).
cnf(refute_0_43,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) != multiplication(zero,C)
| multiplication(zero,C) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))),zero) ),[0],$fot(multiplication(zero,C))]]) ).
cnf(refute_0_44,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) != multiplication(zero,C)
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) = zero ),
inference(resolve,[$cnf( $equal(multiplication(zero,C),zero) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)) != multiplication(zero,C)
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) = zero ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))),multiplication(zero,C)) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),C))) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X3)),C)),multiplication(zero,C)) )],[refute_0_33,refute_0_45]) ).
cnf(refute_0_47,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) = zero,
inference(subst,[],[refute_0_46:[bind(C,$fot(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))]]) ).
cnf(refute_0_48,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_49,plain,
multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),
inference(subst,[],[refute_0_48:[bind(A,$fot(skolemFOFtoCNF_X3)),bind(C,$fot(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))]]) ).
cnf(refute_0_50,plain,
leq(multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_51,plain,
multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)) = multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X3)),bind(B,$fot(skolemFOFtoCNF_X1_1)),bind(C,$fot(c(skolemFOFtoCNF_X4)))]]) ).
cnf(refute_0_52,plain,
( multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)) != multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| ~ leq(multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero)
| leq(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))]]) ).
cnf(refute_0_53,plain,
( ~ leq(multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero)
| leq(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) ),
inference(resolve,[$cnf( $equal(multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
leq(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero),
inference(resolve,[$cnf( leq(multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1_1),c(skolemFOFtoCNF_X4)),zero) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ leq(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero)
| addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) = zero ),
inference(subst,[],[refute_0_23:[bind(A,$fot(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))),bind(B,$fot(zero))]]) ).
cnf(refute_0_56,plain,
addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) = zero,
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) = multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),
inference(subst,[],[refute_0_26:[bind(A,$fot(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))))]]) ).
cnf(refute_0_58,plain,
( addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) != multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) != zero
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero),zero) ),[0],$fot(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))]]) ).
cnf(refute_0_59,plain,
( addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) != zero
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = zero ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero),multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = zero,
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero),zero) )],[refute_0_56,refute_0_59]) ).
cnf(refute_0_61,plain,
( multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != zero
| multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_62,plain,
( multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))
| multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),zero) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),addition(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) )],[refute_0_49,refute_0_62]) ).
cnf(refute_0_64,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_65,plain,
addition(A,zero) = addition(zero,A),
inference(subst,[],[refute_0_64:[bind(B,$fot(zero))]]) ).
cnf(refute_0_66,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_67,plain,
( addition(A,zero) != A
| addition(zero,A) = A ),
inference(resolve,[$cnf( $equal(addition(A,zero),addition(zero,A)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
addition(zero,A) = A,
inference(resolve,[$cnf( $equal(addition(A,zero),A) )],[refute_0_26,refute_0_67]) ).
cnf(refute_0_69,plain,
addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) = multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),
inference(subst,[],[refute_0_68:[bind(A,$fot(multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))))]]) ).
cnf(refute_0_70,plain,
( addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) != multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))
| multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) ),[1],$fot(multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))]]) ).
cnf(refute_0_71,plain,
( multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))
| multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) ),
inference(resolve,[$cnf( $equal(addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),addition(zero,multiplication(B,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) )],[refute_0_63,refute_0_71]) ).
cnf(refute_0_73,plain,
multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),
inference(subst,[],[refute_0_72:[bind(B,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_74,plain,
test(skolemFOFtoCNF_X3),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_75,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_76,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_75:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_77,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_78,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_77,refute_0_76]) ).
cnf(refute_0_79,plain,
( ~ test(skolemFOFtoCNF_X3)
| complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) ),
inference(subst,[],[refute_0_78:[bind(X0,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_80,plain,
complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X3) )],[refute_0_74,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_82,plain,
( ~ complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3))
| addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) = one ),
inference(subst,[],[refute_0_81:[bind(X0,$fot(c(skolemFOFtoCNF_X3))),bind(X1,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_83,plain,
addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) )],[refute_0_80,refute_0_82]) ).
cnf(refute_0_84,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_85,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_64,refute_0_84]) ).
cnf(refute_0_86,plain,
addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) = addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),
inference(subst,[],[refute_0_85:[bind(A,$fot(skolemFOFtoCNF_X3)),bind(B,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_87,plain,
( addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) != addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3))
| addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) != one
| addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),one) ),[0],$fot(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_88,plain,
( addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) != one
| addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),one) )],[refute_0_83,refute_0_88]) ).
cnf(refute_0_90,plain,
( addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) != one
| multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) ),[0,0],$fot(one)]]) ).
cnf(refute_0_91,plain,
( multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),one) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) )],[refute_0_73,refute_0_91]) ).
cnf(refute_0_93,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_94,plain,
multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)),
inference(subst,[],[refute_0_93:[bind(A,$fot(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))]]) ).
cnf(refute_0_95,plain,
( multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))
| multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)) = multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) ),[0],$fot(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))]]) ).
cnf(refute_0_96,plain,
( multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)) = multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) ),
inference(resolve,[$cnf( $equal(multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)) = multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),
inference(resolve,[$cnf( $equal(multiplication(one,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) )],[refute_0_92,refute_0_96]) ).
cnf(refute_0_98,plain,
( multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)) != multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))
| multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),bind(Y,$fot(multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))))]]) ).
cnf(refute_0_99,plain,
multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) = multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)),multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
( multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) != multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) = zero ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))),zero) ),[0,1,1],$fot(multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))]]) ).
cnf(refute_0_101,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))) != zero
| multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) = zero ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(c(skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4))))),zero) )],[refute_0_47,refute_0_101]) ).
cnf(refute_0_103,plain,
( multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))) != zero
| ~ leq(zero,zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),zero) ),
introduced(tautology,[equality,[$cnf( ~ leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),zero) ),[0],$fot(zero)]]) ).
cnf(refute_0_104,plain,
( ~ leq(zero,zero)
| leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),zero) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),zero) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
~ leq(zero,zero),
inference(resolve,[$cnf( leq(multiplication(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X4)))),zero) )],[refute_0_104,refute_0_16]) ).
cnf(refute_0_106,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_107,plain,
( addition(X_20,X_20) != X_20
| leq(X_20,X_20) ),
inference(subst,[],[refute_0_106:[bind(A,$fot(X_20)),bind(B,$fot(X_20))]]) ).
cnf(refute_0_108,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_109,plain,
addition(X_20,X_20) = X_20,
inference(subst,[],[refute_0_108:[bind(A,$fot(X_20))]]) ).
cnf(refute_0_110,plain,
( X_20 != X_20
| addition(X_20,X_20) != X_20
| addition(X_20,X_20) = X_20 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_20,X_20),X_20) ),[0,0],$fot(X_20)]]) ).
cnf(refute_0_111,plain,
( X_20 != X_20
| addition(X_20,X_20) = X_20 ),
inference(resolve,[$cnf( $equal(addition(X_20,X_20),X_20) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
( X_20 != X_20
| leq(X_20,X_20) ),
inference(resolve,[$cnf( $equal(addition(X_20,X_20),X_20) )],[refute_0_111,refute_0_107]) ).
cnf(refute_0_113,plain,
X_20 = X_20,
introduced(tautology,[refl,[$fot(X_20)]]) ).
cnf(refute_0_114,plain,
leq(X_20,X_20),
inference(resolve,[$cnf( $equal(X_20,X_20) )],[refute_0_113,refute_0_112]) ).
cnf(refute_0_115,plain,
leq(zero,zero),
inference(subst,[],[refute_0_114:[bind(X_20,$fot(zero))]]) ).
cnf(refute_0_116,plain,
$false,
inference(resolve,[$cnf( leq(zero,zero) )],[refute_0_115,refute_0_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE034+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 12:39:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.98/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.98/1.15
% 0.98/1.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.98/1.16
%------------------------------------------------------------------------------