TSTP Solution File: KLE027+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE027+2 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 02:14:46 EDT 2022
% Result : Theorem 17.46s 17.62s
% Output : CNFRefutation 17.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 73
% Syntax : Number of formulae : 373 ( 189 unt; 0 def)
% Number of atoms : 676 ( 506 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 593 ( 290 ~; 248 |; 31 &)
% ( 18 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 423 ( 12 sgn 171 !; 13 ?)
% 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_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
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(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ) ).
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(X4) )
=> ( leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2)))
& leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))) ) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X4) )
=> leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) ),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X4)
& leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) )
=> leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X4) )
=> leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1,X2,X3] :
( ~ leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2)))
& test(X3)
& ? [X4] : test(X4) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ leq(addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)))
& test(skolemFOFtoCNF_X3)
& ? [X4] : test(X4) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ leq(addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_4,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[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,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_8,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
test(skolemFOFtoCNF_X3),
inference(conjunct,[],[normalize_0_1]) ).
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)
| multiplication(X0,X1) = zero ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_0_19,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_21,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_22,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_24,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(canonicalize,[],[test_1]) ).
fof(normalize_0_26,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| test(X0) )
& ( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ) ),
inference(clausify,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X0] :
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_0_30,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_32,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_34,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_38,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_37]) ).
cnf(refute_0_0,plain,
~ leq(addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
addition(A,B) = addition(B,A),
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( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_6,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)) = addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),
inference(subst,[],[refute_0_6:[bind(A,$fot(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))),bind(B,$fot(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_0_8,plain,
( addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)) != addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))))
| ~ leq(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)))
| leq(addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) ),
introduced(tautology,[equality,[$cnf( ~ leq(addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) ),[0],$fot(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_0_9,plain,
( ~ leq(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)))
| leq(addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
~ leq(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))),
inference(resolve,[$cnf( leq(addition(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) = addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),
inference(subst,[],[refute_0_6:[bind(A,$fot(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0))),bind(B,$fot(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_12,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_13,plain,
multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,C)) = multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),C),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_X3)),bind(B,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_14,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_15,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) = addition(multiplication(A,skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3)),
inference(subst,[],[refute_0_14:[bind(B,$fot(c(skolemFOFtoCNF_X3))),bind(C,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_16,plain,
test(skolemFOFtoCNF_X3),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_17,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_17:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_19,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_20,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
( ~ test(skolemFOFtoCNF_X3)
| complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_22,plain,
complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X3) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_24,plain,
( ~ complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3))
| multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) = zero ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(c(skolemFOFtoCNF_X3))),bind(X1,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_25,plain,
multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) != addition(multiplication(A,skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3))
| multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) != zero
| multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) = addition(multiplication(A,skolemFOFtoCNF_X3),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3),addition(multiplication(A,skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_27,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) != addition(multiplication(A,skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3))
| multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) = addition(multiplication(A,skolemFOFtoCNF_X3),zero) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),zero) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) = addition(multiplication(A,skolemFOFtoCNF_X3),zero),
inference(resolve,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3),addition(multiplication(A,skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3))) )],[refute_0_15,refute_0_27]) ).
cnf(refute_0_29,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_30,plain,
addition(multiplication(A,skolemFOFtoCNF_X3),zero) = multiplication(A,skolemFOFtoCNF_X3),
inference(subst,[],[refute_0_29:[bind(A,$fot(multiplication(A,skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_31,plain,
( addition(multiplication(A,skolemFOFtoCNF_X3),zero) != multiplication(A,skolemFOFtoCNF_X3)
| multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) != addition(multiplication(A,skolemFOFtoCNF_X3),zero)
| multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) = multiplication(A,skolemFOFtoCNF_X3) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3),addition(multiplication(A,skolemFOFtoCNF_X3),zero)) ),[1],$fot(multiplication(A,skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_32,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) != addition(multiplication(A,skolemFOFtoCNF_X3),zero)
| multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) = multiplication(A,skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,skolemFOFtoCNF_X3),zero),multiplication(A,skolemFOFtoCNF_X3)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) = multiplication(A,skolemFOFtoCNF_X3),
inference(resolve,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3),addition(multiplication(A,skolemFOFtoCNF_X3),zero)) )],[refute_0_28,refute_0_32]) ).
cnf(refute_0_34,plain,
multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),
inference(subst,[],[refute_0_33:[bind(A,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_35,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_36,plain,
( ~ complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3))
| addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) = one ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(c(skolemFOFtoCNF_X3))),bind(X1,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_37,plain,
addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) )],[refute_0_22,refute_0_36]) ).
cnf(refute_0_38,plain,
addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) = addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),
inference(subst,[],[refute_0_6:[bind(A,$fot(skolemFOFtoCNF_X3)),bind(B,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_39,plain,
( addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) != addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3))
| addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) != one
| addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),one) ),[0],$fot(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_40,plain,
( addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) != one
| addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3))) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),one) )],[refute_0_37,refute_0_40]) ).
cnf(refute_0_42,plain,
( addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) != one
| multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)
| multiplication(one,skolemFOFtoCNF_X3) = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)) ),[0,0],$fot(one)]]) ).
cnf(refute_0_43,plain,
( multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3) != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)
| multiplication(one,skolemFOFtoCNF_X3) = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),one) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
multiplication(one,skolemFOFtoCNF_X3) = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)) )],[refute_0_34,refute_0_43]) ).
cnf(refute_0_45,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_46,plain,
multiplication(one,skolemFOFtoCNF_X3) = skolemFOFtoCNF_X3,
inference(subst,[],[refute_0_45:[bind(A,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_47,plain,
( multiplication(one,skolemFOFtoCNF_X3) != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)
| multiplication(one,skolemFOFtoCNF_X3) != skolemFOFtoCNF_X3
| skolemFOFtoCNF_X3 = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)) ),[0],$fot(skolemFOFtoCNF_X3)]]) ).
cnf(refute_0_48,plain,
( multiplication(one,skolemFOFtoCNF_X3) != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)
| skolemFOFtoCNF_X3 = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
skolemFOFtoCNF_X3 = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X3),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)) )],[refute_0_44,refute_0_48]) ).
cnf(refute_0_50,plain,
( skolemFOFtoCNF_X3 != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)
| multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3) = skolemFOFtoCNF_X3 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X3)),bind(Y,$fot(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_51,plain,
multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3) = skolemFOFtoCNF_X3,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3)) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,C)) != multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),C)
| multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3) != skolemFOFtoCNF_X3
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,C)) = multiplication(skolemFOFtoCNF_X3,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,C)),multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),C)) ),[1,0],$fot(skolemFOFtoCNF_X3)]]) ).
cnf(refute_0_53,plain,
( multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,C)) != multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),C)
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,C)) = multiplication(skolemFOFtoCNF_X3,C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,C)) = multiplication(skolemFOFtoCNF_X3,C),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,C)),multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X3),C)) )],[refute_0_13,refute_0_53]) ).
cnf(refute_0_55,plain,
multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),
inference(subst,[],[refute_0_54:[bind(C,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_56,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_57,plain,
multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = addition(multiplication(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),
inference(subst,[],[refute_0_56:[bind(A,$fot(skolemFOFtoCNF_X3)),bind(C,$fot(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))]]) ).
cnf(refute_0_58,plain,
multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) = multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),C),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_X3)),bind(B,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_59,plain,
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_60,plain,
( ~ test(skolemFOFtoCNF_X3)
| complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) ),
inference(subst,[],[refute_0_59:[bind(X0,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_61,plain,
complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X3) )],[refute_0_16,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3)
| multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = zero ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(skolemFOFtoCNF_X3)),bind(X1,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_63,plain,
multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) != multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),C)
| multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != zero
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) = multiplication(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)),multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_65,plain,
( multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) != multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),C)
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) = multiplication(zero,C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),zero) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) = multiplication(zero,C),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)),multiplication(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),C)) )],[refute_0_58,refute_0_65]) ).
cnf(refute_0_67,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_68,plain,
multiplication(zero,C) = zero,
inference(subst,[],[refute_0_67:[bind(A,$fot(C))]]) ).
cnf(refute_0_69,plain,
( multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) != multiplication(zero,C)
| multiplication(zero,C) != zero
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)),zero) ),[0],$fot(multiplication(zero,C))]]) ).
cnf(refute_0_70,plain,
( multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) != multiplication(zero,C)
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(zero,C),zero) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),C)),multiplication(zero,C)) )],[refute_0_66,refute_0_70]) ).
cnf(refute_0_72,plain,
multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) = zero,
inference(subst,[],[refute_0_71:[bind(C,$fot(X_310))]]) ).
cnf(refute_0_73,plain,
( multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) != addition(multiplication(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) != zero
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = addition(multiplication(skolemFOFtoCNF_X3,B),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),addition(multiplication(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_0_74,plain,
( multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) != addition(multiplication(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = addition(multiplication(skolemFOFtoCNF_X3,B),zero) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)),zero) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = addition(multiplication(skolemFOFtoCNF_X3,B),zero),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),addition(multiplication(skolemFOFtoCNF_X3,B),multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))) )],[refute_0_57,refute_0_74]) ).
cnf(refute_0_76,plain,
addition(multiplication(skolemFOFtoCNF_X3,B),zero) = multiplication(skolemFOFtoCNF_X3,B),
inference(subst,[],[refute_0_29:[bind(A,$fot(multiplication(skolemFOFtoCNF_X3,B)))]]) ).
cnf(refute_0_77,plain,
( addition(multiplication(skolemFOFtoCNF_X3,B),zero) != multiplication(skolemFOFtoCNF_X3,B)
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) != addition(multiplication(skolemFOFtoCNF_X3,B),zero)
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,B) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),addition(multiplication(skolemFOFtoCNF_X3,B),zero)) ),[1],$fot(multiplication(skolemFOFtoCNF_X3,B))]]) ).
cnf(refute_0_78,plain,
( multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) != addition(multiplication(skolemFOFtoCNF_X3,B),zero)
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,B) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X3,B),zero),multiplication(skolemFOFtoCNF_X3,B)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,B),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),addition(multiplication(skolemFOFtoCNF_X3,B),zero)) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) = addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),C)),
inference(subst,[],[refute_0_56:[bind(A,$fot(c(skolemFOFtoCNF_X3))),bind(B,$fot(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_81,plain,
( multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) != addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),C))
| multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) != zero
| multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) = addition(zero,multiplication(c(skolemFOFtoCNF_X3),C)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)),addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),C))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_82,plain,
( multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) != addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),C))
| multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) = addition(zero,multiplication(c(skolemFOFtoCNF_X3),C)) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),zero) )],[refute_0_25,refute_0_81]) ).
cnf(refute_0_83,plain,
multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) = addition(zero,multiplication(c(skolemFOFtoCNF_X3),C)),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)),addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),C))) )],[refute_0_80,refute_0_82]) ).
cnf(refute_0_84,plain,
addition(A,zero) = addition(zero,A),
inference(subst,[],[refute_0_1:[bind(B,$fot(zero))]]) ).
cnf(refute_0_85,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_86,plain,
( addition(A,zero) != A
| addition(zero,A) = A ),
inference(resolve,[$cnf( $equal(addition(A,zero),addition(zero,A)) )],[refute_0_84,refute_0_85]) ).
cnf(refute_0_87,plain,
addition(zero,A) = A,
inference(resolve,[$cnf( $equal(addition(A,zero),A) )],[refute_0_29,refute_0_86]) ).
cnf(refute_0_88,plain,
addition(zero,multiplication(c(skolemFOFtoCNF_X3),C)) = multiplication(c(skolemFOFtoCNF_X3),C),
inference(subst,[],[refute_0_87:[bind(A,$fot(multiplication(c(skolemFOFtoCNF_X3),C)))]]) ).
cnf(refute_0_89,plain,
( addition(zero,multiplication(c(skolemFOFtoCNF_X3),C)) != multiplication(c(skolemFOFtoCNF_X3),C)
| multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) != addition(zero,multiplication(c(skolemFOFtoCNF_X3),C))
| multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) = multiplication(c(skolemFOFtoCNF_X3),C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)),addition(zero,multiplication(c(skolemFOFtoCNF_X3),C))) ),[1],$fot(multiplication(c(skolemFOFtoCNF_X3),C))]]) ).
cnf(refute_0_90,plain,
( multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) != addition(zero,multiplication(c(skolemFOFtoCNF_X3),C))
| multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) = multiplication(c(skolemFOFtoCNF_X3),C) ),
inference(resolve,[$cnf( $equal(addition(zero,multiplication(c(skolemFOFtoCNF_X3),C)),multiplication(c(skolemFOFtoCNF_X3),C)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)) = multiplication(c(skolemFOFtoCNF_X3),C),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,C)),addition(zero,multiplication(c(skolemFOFtoCNF_X3),C))) )],[refute_0_83,refute_0_90]) ).
cnf(refute_0_92,plain,
multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),
inference(subst,[],[refute_0_91:[bind(C,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_93,plain,
( ~ complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3)
| addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = one ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(skolemFOFtoCNF_X3)),bind(X1,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_94,plain,
addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),skolemFOFtoCNF_X3) )],[refute_0_61,refute_0_93]) ).
cnf(refute_0_95,plain,
( addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != one
| multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| multiplication(c(skolemFOFtoCNF_X3),one) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) ),[0,1],$fot(one)]]) ).
cnf(refute_0_96,plain,
( multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| multiplication(c(skolemFOFtoCNF_X3),one) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),one) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
multiplication(c(skolemFOFtoCNF_X3),one) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),addition(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) )],[refute_0_92,refute_0_96]) ).
cnf(refute_0_98,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_99,plain,
multiplication(c(skolemFOFtoCNF_X3),one) = c(skolemFOFtoCNF_X3),
inference(subst,[],[refute_0_98:[bind(A,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_100,plain,
( multiplication(c(skolemFOFtoCNF_X3),one) != c(skolemFOFtoCNF_X3)
| multiplication(c(skolemFOFtoCNF_X3),one) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| c(skolemFOFtoCNF_X3) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),one),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) ),[0],$fot(c(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_101,plain,
( multiplication(c(skolemFOFtoCNF_X3),one) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| c(skolemFOFtoCNF_X3) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),one),c(skolemFOFtoCNF_X3)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_X3)),bind(C,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_103,plain,
( multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))
| multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != zero
| multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_104,plain,
( multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))
| multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),zero) )],[refute_0_63,refute_0_103]) ).
cnf(refute_0_105,plain,
multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))) )],[refute_0_102,refute_0_104]) ).
cnf(refute_0_106,plain,
addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) = multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),
inference(subst,[],[refute_0_87:[bind(A,$fot(multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_107,plain,
( addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) != multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))
| multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))) ),[1],$fot(multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_108,plain,
( multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))
| multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))),multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,B),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),addition(zero,multiplication(B,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),
inference(subst,[],[refute_0_109:[bind(B,$fot(c(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_111,plain,
( addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)) != one
| multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) ),[0,0],$fot(one)]]) ).
cnf(refute_0_112,plain,
( multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),one) )],[refute_0_41,refute_0_111]) ).
cnf(refute_0_113,plain,
multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3,c(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) )],[refute_0_110,refute_0_112]) ).
cnf(refute_0_114,plain,
multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),
inference(subst,[],[refute_0_45:[bind(A,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_115,plain,
( multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) ),[0],$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_116,plain,
( multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) = multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
( skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))),bind(Y,$fot(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))))]]) ).
cnf(refute_0_119,plain,
multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
( c(skolemFOFtoCNF_X3) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) != skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)
| c(skolemFOFtoCNF_X3) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) ),
introduced(tautology,[equality,[$cnf( ~ $equal(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) ),[0],$fot(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_121,plain,
( c(skolemFOFtoCNF_X3) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| c(skolemFOFtoCNF_X3) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
( multiplication(c(skolemFOFtoCNF_X3),one) != multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))
| c(skolemFOFtoCNF_X3) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) ),
inference(resolve,[$cnf( $equal(c(skolemFOFtoCNF_X3),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) )],[refute_0_101,refute_0_121]) ).
cnf(refute_0_123,plain,
c(skolemFOFtoCNF_X3) = skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3),one),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3))) )],[refute_0_97,refute_0_122]) ).
cnf(refute_0_124,plain,
( c(skolemFOFtoCNF_X3) != skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) = c(skolemFOFtoCNF_X3) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(c(skolemFOFtoCNF_X3))),bind(Y,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)))]]) ).
cnf(refute_0_125,plain,
skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) = c(skolemFOFtoCNF_X3),
inference(resolve,[$cnf( $equal(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1(skolemFOFtoCNF_X3)) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310) = multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310),
introduced(tautology,[refl,[$fot(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))]]) ).
cnf(refute_0_127,plain,
( multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310) != multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)
| skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) != c(skolemFOFtoCNF_X3)
| multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310) = multiplication(c(skolemFOFtoCNF_X3),X_310) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310),multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) ),[1,0],$fot(c(skolemFOFtoCNF_X3))]]) ).
cnf(refute_0_128,plain,
( skolemFOFtoCNF_X1(skolemFOFtoCNF_X3) != c(skolemFOFtoCNF_X3)
| multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310) = multiplication(c(skolemFOFtoCNF_X3),X_310) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310),multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310) = multiplication(c(skolemFOFtoCNF_X3),X_310),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),c(skolemFOFtoCNF_X3)) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) = addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)),
introduced(tautology,[refl,[$fot(addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))]]) ).
cnf(refute_0_131,plain,
( addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) != addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))
| multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310) != multiplication(c(skolemFOFtoCNF_X3),X_310)
| addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) = addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)),addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) ),[1,1],$fot(multiplication(c(skolemFOFtoCNF_X3),X_310))]]) ).
cnf(refute_0_132,plain,
( multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310) != multiplication(c(skolemFOFtoCNF_X3),X_310)
| addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) = addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310)) ),
inference(resolve,[$cnf( $equal(addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)),addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) = addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310),multiplication(c(skolemFOFtoCNF_X3),X_310)) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),
introduced(tautology,[refl,[$fot(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))))]]) ).
cnf(refute_0_135,plain,
( addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) != addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) != multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))) ),[1,1],$fot(addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310)))]]) ).
cnf(refute_0_136,plain,
( addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)) != addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))),
inference(resolve,[$cnf( $equal(addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310)),addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
( multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) != multiplication(skolemFOFtoCNF_X3,B)
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) != multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310)))
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,B) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),multiplication(skolemFOFtoCNF_X3,B)) ),[0],$fot(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))))]]) ).
cnf(refute_0_139,plain,
( multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))) != multiplication(skolemFOFtoCNF_X3,B)
| multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,B) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310)))) )],[refute_0_137,refute_0_138]) ).
cnf(refute_0_140,plain,
multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(c(skolemFOFtoCNF_X3),X_310))) = multiplication(skolemFOFtoCNF_X3,B),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(B,multiplication(skolemFOFtoCNF_X1(skolemFOFtoCNF_X3),X_310))),multiplication(skolemFOFtoCNF_X3,B)) )],[refute_0_79,refute_0_139]) ).
cnf(refute_0_141,plain,
multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))) = multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_140:[bind(B,$fot(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0))),bind(X_310,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_142,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_143,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_142]) ).
cnf(refute_0_144,plain,
( multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))) != multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0))
| multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)
| multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))) = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0) ),
inference(subst,[],[refute_0_143:[bind(X,$fot(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))))),bind(Y,$fot(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)))),bind(Z,$fot(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_145,plain,
( multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)
| multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))) = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0))) )],[refute_0_141,refute_0_144]) ).
cnf(refute_0_146,plain,
multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))) = multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) )],[refute_0_55,refute_0_145]) ).
cnf(refute_0_147,plain,
addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) = addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),
introduced(tautology,[refl,[$fot(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_0_148,plain,
( addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) != addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))))
| multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))) != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)
| addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) = addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))))) ),[1,1],$fot(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_149,plain,
( multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))) != multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)
| addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) = addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) = addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) != addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0))
| addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) != addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))
| addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) = addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)) ),
inference(subst,[],[refute_0_143:[bind(X,$fot(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))))),bind(Y,$fot(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)))),bind(Z,$fot(addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_152,plain,
( addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)) != addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))
| addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) = addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) = addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) )],[refute_0_11,refute_0_152]) ).
cnf(refute_0_154,plain,
( addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))) != addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))
| ~ leq(addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)))
| leq(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) ),
introduced(tautology,[equality,[$cnf( ~ leq(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) ),[0],$fot(addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_155,plain,
( ~ leq(addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)))
| leq(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) )],[refute_0_153,refute_0_154]) ).
cnf(refute_0_156,plain,
~ leq(addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))),
inference(resolve,[$cnf( leq(addition(multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2),multiplication(skolemFOFtoCNF_X3,addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) )],[refute_0_155,refute_0_10]) ).
cnf(refute_0_157,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_158,plain,
( addition(X_52,X_52) != X_52
| leq(X_52,X_52) ),
inference(subst,[],[refute_0_157:[bind(A,$fot(X_52)),bind(B,$fot(X_52))]]) ).
cnf(refute_0_159,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_160,plain,
addition(X_52,X_52) = X_52,
inference(subst,[],[refute_0_159:[bind(A,$fot(X_52))]]) ).
cnf(refute_0_161,plain,
( X_52 != X_52
| addition(X_52,X_52) != X_52
| addition(X_52,X_52) = X_52 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_52,X_52),X_52) ),[0,0],$fot(X_52)]]) ).
cnf(refute_0_162,plain,
( X_52 != X_52
| addition(X_52,X_52) = X_52 ),
inference(resolve,[$cnf( $equal(addition(X_52,X_52),X_52) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
( X_52 != X_52
| leq(X_52,X_52) ),
inference(resolve,[$cnf( $equal(addition(X_52,X_52),X_52) )],[refute_0_162,refute_0_158]) ).
cnf(refute_0_164,plain,
X_52 = X_52,
introduced(tautology,[refl,[$fot(X_52)]]) ).
cnf(refute_0_165,plain,
leq(X_52,X_52),
inference(resolve,[$cnf( $equal(X_52,X_52) )],[refute_0_164,refute_0_163]) ).
cnf(refute_0_166,plain,
leq(addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))),
inference(subst,[],[refute_0_165:[bind(X_52,$fot(addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))))]]) ).
cnf(refute_0_167,plain,
$false,
inference(resolve,[$cnf( leq(addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2)),addition(multiplication(skolemFOFtoCNF_X3,skolemFOFtoCNF_X0),multiplication(c(skolemFOFtoCNF_X3),skolemFOFtoCNF_X2))) )],[refute_0_166,refute_0_156]) ).
fof(negate_1_0,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( test(X3)
& test(X4)
& leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2))) )
=> leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2))) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0,X1,X2,X3] :
( ~ leq(addition(multiplication(X3,X0),multiplication(c(X3),X2)),addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)))
& leq(addition(multiplication(X3,addition(multiplication(X3,X0),multiplication(c(X3),X1))),multiplication(c(X3),X2)),addition(multiplication(X3,X0),multiplication(c(X3),X2)))
& test(X3)
& ? [X4] : test(X4) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)))
& leq(addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)))
& test(skolemFOFtoCNF_X3_1)
& ? [X4] : test(X4) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_1_4,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_1_6,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_1_8,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
test(skolemFOFtoCNF_X3_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_10,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_1_11,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_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_1_15,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_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_1_15]) ).
fof(normalize_1_17,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| multiplication(X1,X0) = zero ),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_1_19,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_1_21,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_1_23,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_1_22]) ).
fof(normalize_1_24,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_25,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_1_16]) ).
fof(normalize_1_26,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_1_27,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_1_26]) ).
fof(normalize_1_28,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_1_29,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_1_28]) ).
fof(normalize_1_30,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_1_29]) ).
fof(normalize_1_31,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_1_30]) ).
fof(normalize_1_32,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_1_33,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_1_32]) ).
cnf(refute_1_0,plain,
~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_1_6,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_1_1,refute_1_5]) ).
cnf(refute_1_7,plain,
addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)) = addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))),
inference(subst,[],[refute_1_6:[bind(A,$fot(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))),bind(B,$fot(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))))]]) ).
cnf(refute_1_8,plain,
( addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)) != addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))
| ~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))))
| leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))) ),
introduced(tautology,[equality,[$cnf( ~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))) ),[1],$fot(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))))]]) ).
cnf(refute_1_9,plain,
( ~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))))
| leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))),
inference(resolve,[$cnf( leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))) )],[refute_1_9,refute_1_0]) ).
cnf(refute_1_11,plain,
addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)) = addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),
inference(subst,[],[refute_1_6:[bind(A,$fot(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1))),bind(B,$fot(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)))]]) ).
cnf(refute_1_12,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_13,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) = addition(multiplication(skolemFOFtoCNF_X3_1,X_950),multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C))),
inference(subst,[],[refute_1_12:[bind(A,$fot(skolemFOFtoCNF_X3_1)),bind(B,$fot(X_950)),bind(C,$fot(multiplication(c(skolemFOFtoCNF_X3_1),C)))]]) ).
cnf(refute_1_14,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_15,plain,
multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) = multiplication(multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),C),
inference(subst,[],[refute_1_14:[bind(A,$fot(skolemFOFtoCNF_X3_1)),bind(B,$fot(c(skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_16,plain,
test(skolemFOFtoCNF_X3_1),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_17,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_18,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_1_17:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_1_19,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_1_20,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_1_19,refute_1_18]) ).
cnf(refute_1_21,plain,
( ~ test(skolemFOFtoCNF_X3_1)
| complement(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) ),
inference(subst,[],[refute_1_20:[bind(X0,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_22,plain,
complement(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X3_1) )],[refute_1_16,refute_1_21]) ).
cnf(refute_1_23,plain,
( ~ complement(X1,X0)
| multiplication(X1,X0) = zero ),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_24,plain,
( ~ complement(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1))
| multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) = zero ),
inference(subst,[],[refute_1_23:[bind(X0,$fot(c(skolemFOFtoCNF_X3_1))),bind(X1,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_25,plain,
multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) )],[refute_1_22,refute_1_24]) ).
cnf(refute_1_26,plain,
( multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) != zero
| multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) != multiplication(multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),C)
| multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) = multiplication(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)),multiplication(multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_27,plain,
( multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) != multiplication(multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),C)
| multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) = multiplication(zero,C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),zero) )],[refute_1_25,refute_1_26]) ).
cnf(refute_1_28,plain,
multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) = multiplication(zero,C),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)),multiplication(multiplication(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),C)) )],[refute_1_15,refute_1_27]) ).
cnf(refute_1_29,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_30,plain,
multiplication(zero,C) = zero,
inference(subst,[],[refute_1_29:[bind(A,$fot(C))]]) ).
cnf(refute_1_31,plain,
( multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) != multiplication(zero,C)
| multiplication(zero,C) != zero
| multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)),zero) ),[0],$fot(multiplication(zero,C))]]) ).
cnf(refute_1_32,plain,
( multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) != multiplication(zero,C)
| multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(zero,C),zero) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) = zero,
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)),multiplication(zero,C)) )],[refute_1_28,refute_1_32]) ).
cnf(refute_1_34,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) != addition(multiplication(skolemFOFtoCNF_X3_1,X_950),multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)))
| multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)) != zero
| multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) = addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))),addition(multiplication(skolemFOFtoCNF_X3_1,X_950),multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_35,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) != addition(multiplication(skolemFOFtoCNF_X3_1,X_950),multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)))
| multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) = addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)),zero) )],[refute_1_33,refute_1_34]) ).
cnf(refute_1_36,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) = addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))),addition(multiplication(skolemFOFtoCNF_X3_1,X_950),multiplication(skolemFOFtoCNF_X3_1,multiplication(c(skolemFOFtoCNF_X3_1),C)))) )],[refute_1_13,refute_1_35]) ).
cnf(refute_1_37,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_38,plain,
addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero) = multiplication(skolemFOFtoCNF_X3_1,X_950),
inference(subst,[],[refute_1_37:[bind(A,$fot(multiplication(skolemFOFtoCNF_X3_1,X_950)))]]) ).
cnf(refute_1_39,plain,
( addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero) != multiplication(skolemFOFtoCNF_X3_1,X_950)
| multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) != addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero)
| multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) = multiplication(skolemFOFtoCNF_X3_1,X_950) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))),addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero)) ),[1],$fot(multiplication(skolemFOFtoCNF_X3_1,X_950))]]) ).
cnf(refute_1_40,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) != addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero)
| multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) = multiplication(skolemFOFtoCNF_X3_1,X_950) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero),multiplication(skolemFOFtoCNF_X3_1,X_950)) )],[refute_1_38,refute_1_39]) ).
cnf(refute_1_41,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))) = multiplication(skolemFOFtoCNF_X3_1,X_950),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(X_950,multiplication(c(skolemFOFtoCNF_X3_1),C))),addition(multiplication(skolemFOFtoCNF_X3_1,X_950),zero)) )],[refute_1_36,refute_1_40]) ).
cnf(refute_1_42,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(skolemFOFtoCNF_X0_1,multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),
inference(subst,[],[refute_1_41:[bind(C,$fot(skolemFOFtoCNF_X1_2)),bind(X_950,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_43,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) = addition(multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)),multiplication(skolemFOFtoCNF_X3_1,X_951)),
inference(subst,[],[refute_1_12:[bind(A,$fot(skolemFOFtoCNF_X3_1)),bind(B,$fot(multiplication(skolemFOFtoCNF_X3_1,C))),bind(C,$fot(X_951))]]) ).
cnf(refute_1_44,plain,
multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)) = multiplication(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),C),
inference(subst,[],[refute_1_14:[bind(A,$fot(skolemFOFtoCNF_X3_1)),bind(B,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_45,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_46,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) = addition(multiplication(A,skolemFOFtoCNF_X3_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1)),
inference(subst,[],[refute_1_45:[bind(B,$fot(c(skolemFOFtoCNF_X3_1))),bind(C,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_47,plain,
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_48,plain,
( ~ complement(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1))
| multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) = zero ),
inference(subst,[],[refute_1_47:[bind(X0,$fot(c(skolemFOFtoCNF_X3_1))),bind(X1,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_49,plain,
multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) )],[refute_1_22,refute_1_48]) ).
cnf(refute_1_50,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) != addition(multiplication(A,skolemFOFtoCNF_X3_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1))
| multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) != zero
| multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) = addition(multiplication(A,skolemFOFtoCNF_X3_1),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1),addition(multiplication(A,skolemFOFtoCNF_X3_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1))) ),[1,1],$fot(zero)]]) ).
cnf(refute_1_51,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) != addition(multiplication(A,skolemFOFtoCNF_X3_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1))
| multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) = addition(multiplication(A,skolemFOFtoCNF_X3_1),zero) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1),zero) )],[refute_1_49,refute_1_50]) ).
cnf(refute_1_52,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) = addition(multiplication(A,skolemFOFtoCNF_X3_1),zero),
inference(resolve,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1),addition(multiplication(A,skolemFOFtoCNF_X3_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1))) )],[refute_1_46,refute_1_51]) ).
cnf(refute_1_53,plain,
addition(multiplication(A,skolemFOFtoCNF_X3_1),zero) = multiplication(A,skolemFOFtoCNF_X3_1),
inference(subst,[],[refute_1_37:[bind(A,$fot(multiplication(A,skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_54,plain,
( addition(multiplication(A,skolemFOFtoCNF_X3_1),zero) != multiplication(A,skolemFOFtoCNF_X3_1)
| multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) != addition(multiplication(A,skolemFOFtoCNF_X3_1),zero)
| multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) = multiplication(A,skolemFOFtoCNF_X3_1) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1),addition(multiplication(A,skolemFOFtoCNF_X3_1),zero)) ),[1],$fot(multiplication(A,skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_55,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) != addition(multiplication(A,skolemFOFtoCNF_X3_1),zero)
| multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) = multiplication(A,skolemFOFtoCNF_X3_1) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,skolemFOFtoCNF_X3_1),zero),multiplication(A,skolemFOFtoCNF_X3_1)) )],[refute_1_53,refute_1_54]) ).
cnf(refute_1_56,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) = multiplication(A,skolemFOFtoCNF_X3_1),
inference(resolve,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1),addition(multiplication(A,skolemFOFtoCNF_X3_1),zero)) )],[refute_1_52,refute_1_55]) ).
cnf(refute_1_57,plain,
multiplication(addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),
inference(subst,[],[refute_1_56:[bind(A,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_58,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_59,plain,
( ~ complement(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1))
| addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) = one ),
inference(subst,[],[refute_1_58:[bind(X0,$fot(c(skolemFOFtoCNF_X3_1))),bind(X1,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_60,plain,
addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) )],[refute_1_22,refute_1_59]) ).
cnf(refute_1_61,plain,
addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) = addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),
inference(subst,[],[refute_1_6:[bind(A,$fot(skolemFOFtoCNF_X3_1)),bind(B,$fot(c(skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_62,plain,
( addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) != addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1))
| addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) != one
| addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1),one) ),[0],$fot(addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_63,plain,
( addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) != one
| addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1),addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1))) )],[refute_1_61,refute_1_62]) ).
cnf(refute_1_64,plain,
addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1),one) )],[refute_1_60,refute_1_63]) ).
cnf(refute_1_65,plain,
( addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)) != one
| multiplication(addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)
| multiplication(one,skolemFOFtoCNF_X3_1) = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)) ),[0,0],$fot(one)]]) ).
cnf(refute_1_66,plain,
( multiplication(addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1) != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)
| multiplication(one,skolemFOFtoCNF_X3_1) = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),one) )],[refute_1_64,refute_1_65]) ).
cnf(refute_1_67,plain,
multiplication(one,skolemFOFtoCNF_X3_1) = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X3_1,c(skolemFOFtoCNF_X3_1)),skolemFOFtoCNF_X3_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)) )],[refute_1_57,refute_1_66]) ).
cnf(refute_1_68,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_1_27]) ).
cnf(refute_1_69,plain,
multiplication(one,skolemFOFtoCNF_X3_1) = skolemFOFtoCNF_X3_1,
inference(subst,[],[refute_1_68:[bind(A,$fot(skolemFOFtoCNF_X3_1))]]) ).
cnf(refute_1_70,plain,
( multiplication(one,skolemFOFtoCNF_X3_1) != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)
| multiplication(one,skolemFOFtoCNF_X3_1) != skolemFOFtoCNF_X3_1
| skolemFOFtoCNF_X3_1 = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X3_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)) ),[0],$fot(skolemFOFtoCNF_X3_1)]]) ).
cnf(refute_1_71,plain,
( multiplication(one,skolemFOFtoCNF_X3_1) != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)
| skolemFOFtoCNF_X3_1 = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) )],[refute_1_69,refute_1_70]) ).
cnf(refute_1_72,plain,
skolemFOFtoCNF_X3_1 = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X3_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)) )],[refute_1_67,refute_1_71]) ).
cnf(refute_1_73,plain,
( skolemFOFtoCNF_X3_1 != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)
| multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1) = skolemFOFtoCNF_X3_1 ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_X3_1)),bind(Y,$fot(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)))]]) ).
cnf(refute_1_74,plain,
multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1) = skolemFOFtoCNF_X3_1,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1)) )],[refute_1_72,refute_1_73]) ).
cnf(refute_1_75,plain,
( multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)) != multiplication(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),C)
| multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1) != skolemFOFtoCNF_X3_1
| multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)) = multiplication(skolemFOFtoCNF_X3_1,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)),multiplication(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),C)) ),[1,0],$fot(skolemFOFtoCNF_X3_1)]]) ).
cnf(refute_1_76,plain,
( multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)) != multiplication(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),C)
| multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)) = multiplication(skolemFOFtoCNF_X3_1,C) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X3_1) )],[refute_1_74,refute_1_75]) ).
cnf(refute_1_77,plain,
multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)) = multiplication(skolemFOFtoCNF_X3_1,C),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)),multiplication(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X3_1),C)) )],[refute_1_44,refute_1_76]) ).
cnf(refute_1_78,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) != addition(multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)),multiplication(skolemFOFtoCNF_X3_1,X_951))
| multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)) != multiplication(skolemFOFtoCNF_X3_1,C)
| multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) = addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)),addition(multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)),multiplication(skolemFOFtoCNF_X3_1,X_951))) ),[1,0],$fot(multiplication(skolemFOFtoCNF_X3_1,C))]]) ).
cnf(refute_1_79,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) != addition(multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)),multiplication(skolemFOFtoCNF_X3_1,X_951))
| multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) = addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951)) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)),multiplication(skolemFOFtoCNF_X3_1,C)) )],[refute_1_77,refute_1_78]) ).
cnf(refute_1_80,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) = addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)),addition(multiplication(skolemFOFtoCNF_X3_1,multiplication(skolemFOFtoCNF_X3_1,C)),multiplication(skolemFOFtoCNF_X3_1,X_951))) )],[refute_1_43,refute_1_79]) ).
cnf(refute_1_81,plain,
( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
| addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).
cnf(refute_1_82,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_1_12,refute_1_81]) ).
cnf(refute_1_83,plain,
addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951)) = multiplication(skolemFOFtoCNF_X3_1,addition(C,X_951)),
inference(subst,[],[refute_1_82:[bind(A,$fot(skolemFOFtoCNF_X3_1)),bind(B,$fot(C)),bind(C,$fot(X_951))]]) ).
cnf(refute_1_84,plain,
( addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951)) != multiplication(skolemFOFtoCNF_X3_1,addition(C,X_951))
| multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) != addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951))
| multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) = multiplication(skolemFOFtoCNF_X3_1,addition(C,X_951)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)),addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951))) ),[1],$fot(multiplication(skolemFOFtoCNF_X3_1,addition(C,X_951)))]]) ).
cnf(refute_1_85,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) != addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951))
| multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) = multiplication(skolemFOFtoCNF_X3_1,addition(C,X_951)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951)),multiplication(skolemFOFtoCNF_X3_1,addition(C,X_951))) )],[refute_1_83,refute_1_84]) ).
cnf(refute_1_86,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)) = multiplication(skolemFOFtoCNF_X3_1,addition(C,X_951)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,C),X_951)),addition(multiplication(skolemFOFtoCNF_X3_1,C),multiplication(skolemFOFtoCNF_X3_1,X_951))) )],[refute_1_80,refute_1_85]) ).
cnf(refute_1_87,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) = multiplication(skolemFOFtoCNF_X3_1,addition(skolemFOFtoCNF_X0_1,multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),
inference(subst,[],[refute_1_86:[bind(C,$fot(skolemFOFtoCNF_X0_1)),bind(X_951,$fot(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_88,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_89,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_4,refute_1_88]) ).
cnf(refute_1_90,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) != multiplication(skolemFOFtoCNF_X3_1,addition(skolemFOFtoCNF_X0_1,multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))
| multiplication(skolemFOFtoCNF_X3_1,addition(skolemFOFtoCNF_X0_1,multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)
| multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1) ),
inference(subst,[],[refute_1_89:[bind(X,$fot(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))),bind(Y,$fot(multiplication(skolemFOFtoCNF_X3_1,addition(skolemFOFtoCNF_X0_1,multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))),bind(Z,$fot(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)))]]) ).
cnf(refute_1_91,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(skolemFOFtoCNF_X0_1,multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)
| multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(skolemFOFtoCNF_X3_1,addition(skolemFOFtoCNF_X0_1,multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) )],[refute_1_87,refute_1_90]) ).
cnf(refute_1_92,plain,
multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) = multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(skolemFOFtoCNF_X0_1,multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)) )],[refute_1_42,refute_1_91]) ).
cnf(refute_1_93,plain,
addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) = addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))),
introduced(tautology,[refl,[$fot(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))))]]) ).
cnf(refute_1_94,plain,
( addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) != addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))
| multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)
| addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) = addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))) ),[1,1],$fot(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_95,plain,
( multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))) != multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)
| addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) = addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))) )],[refute_1_93,refute_1_94]) ).
cnf(refute_1_96,plain,
addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) = addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)) )],[refute_1_92,refute_1_95]) ).
cnf(refute_1_97,plain,
( addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) != addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1))
| addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)) != addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))
| addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) = addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)) ),
inference(subst,[],[refute_1_89:[bind(X,$fot(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))))),bind(Y,$fot(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)))),bind(Z,$fot(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))))]]) ).
cnf(refute_1_98,plain,
( addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)) != addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))
| addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) = addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1))) )],[refute_1_96,refute_1_97]) ).
cnf(refute_1_99,plain,
addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) = addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1)),addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))) )],[refute_1_11,refute_1_98]) ).
cnf(refute_1_100,plain,
( addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))) != addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))
| ~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)))
| leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))) ),
introduced(tautology,[equality,[$cnf( ~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))) ),[1],$fot(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)))]]) ).
cnf(refute_1_101,plain,
( ~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)))
| leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2)))),addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))) )],[refute_1_99,refute_1_100]) ).
cnf(refute_1_102,plain,
~ leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))),
inference(resolve,[$cnf( leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X3_1,addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X1_2))))) )],[refute_1_101,refute_1_10]) ).
cnf(refute_1_103,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_1_31]) ).
cnf(refute_1_104,plain,
( addition(X_376,X_376) != X_376
| leq(X_376,X_376) ),
inference(subst,[],[refute_1_103:[bind(A,$fot(X_376)),bind(B,$fot(X_376))]]) ).
cnf(refute_1_105,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_1_33]) ).
cnf(refute_1_106,plain,
addition(X_376,X_376) = X_376,
inference(subst,[],[refute_1_105:[bind(A,$fot(X_376))]]) ).
cnf(refute_1_107,plain,
( X_376 != X_376
| addition(X_376,X_376) != X_376
| addition(X_376,X_376) = X_376 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_376,X_376),X_376) ),[0,0],$fot(X_376)]]) ).
cnf(refute_1_108,plain,
( X_376 != X_376
| addition(X_376,X_376) = X_376 ),
inference(resolve,[$cnf( $equal(addition(X_376,X_376),X_376) )],[refute_1_106,refute_1_107]) ).
cnf(refute_1_109,plain,
( X_376 != X_376
| leq(X_376,X_376) ),
inference(resolve,[$cnf( $equal(addition(X_376,X_376),X_376) )],[refute_1_108,refute_1_104]) ).
cnf(refute_1_110,plain,
X_376 = X_376,
introduced(tautology,[refl,[$fot(X_376)]]) ).
cnf(refute_1_111,plain,
leq(X_376,X_376),
inference(resolve,[$cnf( $equal(X_376,X_376) )],[refute_1_110,refute_1_109]) ).
cnf(refute_1_112,plain,
leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))),
inference(subst,[],[refute_1_111:[bind(X_376,$fot(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))))]]) ).
cnf(refute_1_113,plain,
$false,
inference(resolve,[$cnf( leq(addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1)),addition(multiplication(skolemFOFtoCNF_X3_1,skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X3_1),skolemFOFtoCNF_X2_1))) )],[refute_1_112,refute_1_102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE027+2 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n007.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 09:02:41 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 17.46/17.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.46/17.62
% 17.46/17.62 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.46/17.64
%------------------------------------------------------------------------------