%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE009+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 02:14:33 EDT 2022
% Result : Theorem 1.02s 1.21s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 53
% Syntax : Number of formulae : 297 ( 150 unt; 0 def)
% Number of atoms : 548 ( 384 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 491 ( 240 ~; 200 |; 30 &)
% ( 15 <=>; 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 : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 327 ( 0 sgn 129 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_associativity,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = 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(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ) ) ).
fof(subgoal_0,plain,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1] :
( ( test(X1)
& test(X0)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
=> leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] :
( ~ leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& test(X0)
& test(X1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ leq(one,addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))
& test(skolemFOFtoCNF_X0)
& test(skolemFOFtoCNF_X1_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ leq(one,addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_4,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_6,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_8,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_10,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_12,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
test(skolemFOFtoCNF_X1_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_14,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_0_15,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,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_19,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,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_19]) ).
fof(normalize_0_21,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
test(skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_23,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_24,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_28,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_27]) ).
cnf(refute_0_0,plain,
~ leq(one,addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
| addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).
cnf(refute_0_6,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) = multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_6:[bind(A,$fot(c(skolemFOFtoCNF_X0))),bind(B,$fot(skolemFOFtoCNF_X1_1)),bind(C,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_8,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) = addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))),
introduced(tautology,[refl,[$fot(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_0_9,plain,
( addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) != multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) != addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) = addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) ),[1,1],$fot(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_10,plain,
( addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) != multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) = addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) = addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))),
introduced(tautology,[refl,[$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))))]]) ).
cnf(refute_0_13,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) != addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))) ),[1,1],$fot(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_0_14,plain,
( addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) != addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_17,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_18,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_16,refute_0_17]) ).
cnf(refute_0_19,plain,
addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))),
inference(subst,[],[refute_0_18:[bind(A,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))),bind(B,$fot(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)))),bind(C,$fot(addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_0_20,plain,
addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) = addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))),
inference(subst,[],[refute_0_18:[bind(A,$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))))),bind(B,$fot(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1))),bind(C,$fot(multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_21,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_22,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_21]) ).
cnf(refute_0_23,plain,
( addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) != addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))
| addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))
| addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))),bind(Z,$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))))]]) ).
cnf(refute_0_24,plain,
( addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))
| addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))),addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))),
inference(resolve,[$cnf( $equal(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))) )],[refute_0_19,refute_0_24]) ).
cnf(refute_0_26,plain,
( addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))
| addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))))),bind(Z,$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))))]]) ).
cnf(refute_0_27,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))
| addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) = addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),addition(multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))) )],[refute_0_15,refute_0_27]) ).
cnf(refute_0_29,plain,
( addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))) != addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))
| ~ leq(one,addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))))
| leq(one,addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) ),
introduced(tautology,[equality,[$cnf( ~ leq(one,addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) ),[1],$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))))]]) ).
cnf(refute_0_30,plain,
( ~ leq(one,addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))))
| leq(one,addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1))),addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
~ leq(one,addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))),
inference(resolve,[$cnf( leq(one,addition(addition(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1))),multiplication(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),c(skolemFOFtoCNF_X1_1)))) )],[refute_0_30,refute_0_0]) ).
cnf(refute_0_32,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_33,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_34,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_34:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(c(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_36,plain,
multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
introduced(tautology,[refl,[$fot(multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_37,plain,
( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
| multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1,0],$fot(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_38,plain,
( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
| multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))) )],[refute_0_35,refute_0_38]) ).
cnf(refute_0_40,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_41,plain,
( multiplication(addition(A,B),C) != addition(multiplication(A,C),multiplication(B,C))
| addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(addition(A,B),C))),bind(Y,$fot(addition(multiplication(A,C),multiplication(B,C))))]]) ).
cnf(refute_0_42,plain,
addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C),
inference(resolve,[$cnf( $equal(multiplication(addition(A,B),C),addition(multiplication(A,C),multiplication(B,C))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
addition(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) = multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_42:[bind(A,$fot(c(skolemFOFtoCNF_X0))),bind(B,$fot(skolemFOFtoCNF_X0)),bind(C,$fot(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_44,plain,
addition(A,addition(X_14,X_15)) = addition(addition(X_14,X_15),A),
inference(subst,[],[refute_0_32:[bind(B,$fot(addition(X_14,X_15)))]]) ).
cnf(refute_0_45,plain,
addition(X_14,addition(X_15,A)) = addition(addition(X_14,X_15),A),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(A))]]) ).
cnf(refute_0_46,plain,
( addition(X_14,addition(X_15,A)) != addition(addition(X_14,X_15),A)
| addition(addition(X_14,X_15),A) = addition(X_14,addition(X_15,A)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(X_14,addition(X_15,A)))),bind(Y,$fot(addition(addition(X_14,X_15),A)))]]) ).
cnf(refute_0_47,plain,
addition(addition(X_14,X_15),A) = addition(X_14,addition(X_15,A)),
inference(resolve,[$cnf( $equal(addition(X_14,addition(X_15,A)),addition(addition(X_14,X_15),A)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( addition(A,addition(X_14,X_15)) != addition(addition(X_14,X_15),A)
| addition(addition(X_14,X_15),A) != addition(X_14,addition(X_15,A))
| addition(A,addition(X_14,X_15)) = addition(X_14,addition(X_15,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_14,X_15)),addition(X_14,addition(X_15,A))) ),[0],$fot(addition(addition(X_14,X_15),A))]]) ).
cnf(refute_0_49,plain,
( addition(A,addition(X_14,X_15)) != addition(addition(X_14,X_15),A)
| addition(A,addition(X_14,X_15)) = addition(X_14,addition(X_15,A)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_14,X_15),A),addition(X_14,addition(X_15,A))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
addition(A,addition(X_14,X_15)) = addition(X_14,addition(X_15,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_14,X_15)),addition(addition(X_14,X_15),A)) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
addition(A,addition(multiplication(X_28,X_29),multiplication(X_28,X_30))) = addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A)),
inference(subst,[],[refute_0_50:[bind(X_14,$fot(multiplication(X_28,X_29))),bind(X_15,$fot(multiplication(X_28,X_30)))]]) ).
cnf(refute_0_52,plain,
multiplication(X_28,addition(X_29,X_30)) = addition(multiplication(X_28,X_29),multiplication(X_28,X_30)),
inference(subst,[],[refute_0_1:[bind(A,$fot(X_28)),bind(B,$fot(X_29)),bind(C,$fot(X_30))]]) ).
cnf(refute_0_53,plain,
( multiplication(X_28,addition(X_29,X_30)) != addition(multiplication(X_28,X_29),multiplication(X_28,X_30))
| addition(multiplication(X_28,X_29),multiplication(X_28,X_30)) = multiplication(X_28,addition(X_29,X_30)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(X_28,addition(X_29,X_30)))),bind(Y,$fot(addition(multiplication(X_28,X_29),multiplication(X_28,X_30))))]]) ).
cnf(refute_0_54,plain,
addition(multiplication(X_28,X_29),multiplication(X_28,X_30)) = multiplication(X_28,addition(X_29,X_30)),
inference(resolve,[$cnf( $equal(multiplication(X_28,addition(X_29,X_30)),addition(multiplication(X_28,X_29),multiplication(X_28,X_30))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( addition(A,addition(multiplication(X_28,X_29),multiplication(X_28,X_30))) != addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A))
| addition(multiplication(X_28,X_29),multiplication(X_28,X_30)) != multiplication(X_28,addition(X_29,X_30))
| addition(A,multiplication(X_28,addition(X_29,X_30))) = addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(multiplication(X_28,X_29),multiplication(X_28,X_30))),addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A))) ),[0,1],$fot(multiplication(X_28,addition(X_29,X_30)))]]) ).
cnf(refute_0_56,plain,
( addition(A,addition(multiplication(X_28,X_29),multiplication(X_28,X_30))) != addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A))
| addition(A,multiplication(X_28,addition(X_29,X_30))) = addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(X_28,X_29),multiplication(X_28,X_30)),multiplication(X_28,addition(X_29,X_30))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
addition(A,multiplication(X_28,addition(X_29,X_30))) = addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A)),
inference(resolve,[$cnf( $equal(addition(A,addition(multiplication(X_28,X_29),multiplication(X_28,X_30))),addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A))) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
( addition(A,multiplication(X_28,addition(X_29,X_30))) != addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A))
| addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A)) = addition(A,multiplication(X_28,addition(X_29,X_30))) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,multiplication(X_28,addition(X_29,X_30))))),bind(Y,$fot(addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A))))]]) ).
cnf(refute_0_59,plain,
addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A)) = addition(A,multiplication(X_28,addition(X_29,X_30))),
inference(resolve,[$cnf( $equal(addition(A,multiplication(X_28,addition(X_29,X_30))),addition(multiplication(X_28,X_29),addition(multiplication(X_28,X_30),A))) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) = addition(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))),
inference(subst,[],[refute_0_59:[bind(A,$fot(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(X_28,$fot(skolemFOFtoCNF_X0)),bind(X_29,$fot(skolemFOFtoCNF_X1_1)),bind(X_30,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_61,plain,
( addition(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) != multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) != addition(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) = multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))))),bind(Y,$fot(addition(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))),bind(Z,$fot(multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_0_62,plain,
( addition(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) != multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) = multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),addition(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) = multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))),multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_43,refute_0_62]) ).
cnf(refute_0_64,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) != multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))))),bind(Y,$fot(multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Z,$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))]]) ).
cnf(refute_0_65,plain,
( multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( $equal(multiplication(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_39,refute_0_65]) ).
cnf(refute_0_67,plain,
( addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))) != multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
| leq(one,addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))) ),
introduced(tautology,[equality,[$cnf( ~ leq(one,addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))) ),[1],$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_68,plain,
( ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
| leq(one,addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))),
inference(resolve,[$cnf( leq(one,addition(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),addition(multiplication(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X1_1)),multiplication(c(skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))))) )],[refute_0_68,refute_0_31]) ).
cnf(refute_0_70,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_71,plain,
multiplication(one,one) = one,
inference(subst,[],[refute_0_70:[bind(A,$fot(one))]]) ).
cnf(refute_0_72,plain,
test(skolemFOFtoCNF_X1_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_73,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_74,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_73:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_75,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_76,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_75,refute_0_74]) ).
cnf(refute_0_77,plain,
( ~ test(skolemFOFtoCNF_X1_1)
| complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_78,plain,
complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_1) )],[refute_0_72,refute_0_77]) ).
cnf(refute_0_79,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_80,plain,
( ~ complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
| addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = one ),
inference(subst,[],[refute_0_79:[bind(X0,$fot(c(skolemFOFtoCNF_X1_1))),bind(X1,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_81,plain,
addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) )],[refute_0_78,refute_0_80]) ).
cnf(refute_0_82,plain,
addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_34:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_83,plain,
( addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
| addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != one
| addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),one) ),[0],$fot(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_84,plain,
( addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != one
| addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),one) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
introduced(tautology,[refl,[$fot(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_87,plain,
( addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) != one
| multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_88,plain,
( addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) != one
| multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),one) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
test(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_91,plain,
( ~ test(skolemFOFtoCNF_X0)
| complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) ),
inference(subst,[],[refute_0_76:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_92,plain,
complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X0) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( ~ complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
| addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = one ),
inference(subst,[],[refute_0_79:[bind(X0,$fot(c(skolemFOFtoCNF_X0))),bind(X1,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_94,plain,
addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
| addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != one
| addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),one) ),[0],$fot(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_96,plain,
( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != one
| addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))) )],[refute_0_35,refute_0_95]) ).
cnf(refute_0_97,plain,
addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),one) )],[refute_0_94,refute_0_96]) ).
cnf(refute_0_98,plain,
multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
introduced(tautology,[refl,[$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_99,plain,
( addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) != one
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_100,plain,
( addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) != one
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),one) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Z,$fot(multiplication(one,one)))]]) ).
cnf(refute_0_103,plain,
( multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one),
inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,one)) )],[refute_0_89,refute_0_103]) ).
cnf(refute_0_105,plain,
( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
| multiplication(one,one) != one
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one ),
inference(subst,[],[refute_0_22:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(multiplication(one,one))),bind(Z,$fot(one))]]) ).
cnf(refute_0_106,plain,
( multiplication(one,one) != one
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,one)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one,
inference(resolve,[$cnf( $equal(multiplication(one,one),one) )],[refute_0_71,refute_0_106]) ).
cnf(refute_0_108,plain,
( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != one
| ~ leq(one,one)
| leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),
introduced(tautology,[equality,[$cnf( ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1],$fot(one)]]) ).
cnf(refute_0_109,plain,
( ~ leq(one,one)
| leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),one) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
~ leq(one,one),
inference(resolve,[$cnf( leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_109,refute_0_69]) ).
cnf(refute_0_111,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_112,plain,
( addition(X_46,X_46) != X_46
| leq(X_46,X_46) ),
inference(subst,[],[refute_0_111:[bind(A,$fot(X_46)),bind(B,$fot(X_46))]]) ).
cnf(refute_0_113,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_114,plain,
addition(X_46,X_46) = X_46,
inference(subst,[],[refute_0_113:[bind(A,$fot(X_46))]]) ).
cnf(refute_0_115,plain,
( X_46 != X_46
| addition(X_46,X_46) != X_46
| addition(X_46,X_46) = X_46 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_46,X_46),X_46) ),[0,0],$fot(X_46)]]) ).
cnf(refute_0_116,plain,
( X_46 != X_46
| addition(X_46,X_46) = X_46 ),
inference(resolve,[$cnf( $equal(addition(X_46,X_46),X_46) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( X_46 != X_46
| leq(X_46,X_46) ),
inference(resolve,[$cnf( $equal(addition(X_46,X_46),X_46) )],[refute_0_116,refute_0_112]) ).
cnf(refute_0_118,plain,
X_46 = X_46,
introduced(tautology,[refl,[$fot(X_46)]]) ).
cnf(refute_0_119,plain,
leq(X_46,X_46),
inference(resolve,[$cnf( $equal(X_46,X_46) )],[refute_0_118,refute_0_117]) ).
cnf(refute_0_120,plain,
leq(one,one),
inference(subst,[],[refute_0_119:[bind(X_46,$fot(one))]]) ).
cnf(refute_0_121,plain,
$false,
inference(resolve,[$cnf( leq(one,one) )],[refute_0_120,refute_0_110]) ).
fof(negate_1_0,plain,
~ ! [X0,X1] :
( ( test(X1)
& test(X0)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1)))) )
=> leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0,X1] :
( ~ leq(addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))),one)
& leq(one,addition(addition(addition(multiplication(X0,X1),multiplication(X0,c(X1))),multiplication(c(X0),X1)),multiplication(c(X0),c(X1))))
& test(X0)
& test(X1) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ leq(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),one)
& leq(one,addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))
& test(skolemFOFtoCNF_X0_1)
& test(skolemFOFtoCNF_X1_2) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ leq(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),one),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_1_4,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_1_6,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_1_8,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_1_10,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
test(skolemFOFtoCNF_X1_2),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_12,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_1_13,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_1_13]) ).
fof(normalize_1_15,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_16,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_17,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,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_17]) ).
fof(normalize_1_19,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_1_21,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
test(skolemFOFtoCNF_X0_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_23,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_1_24,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_1_24]) ).
fof(normalize_1_26,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_1_25]) ).
fof(normalize_1_27,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_1_28,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_1_27]) ).
cnf(refute_1_0,plain,
~ leq(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),one),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
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( $equal(X,X) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
| addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).
cnf(refute_1_6,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_1_1,refute_1_5]) ).
cnf(refute_1_7,plain,
addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) = multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
inference(subst,[],[refute_1_6:[bind(A,$fot(c(skolemFOFtoCNF_X0_1))),bind(B,$fot(skolemFOFtoCNF_X1_2)),bind(C,$fot(c(skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_8,plain,
addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) = addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))),
introduced(tautology,[refl,[$fot(addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))]]) ).
cnf(refute_1_9,plain,
( addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) != multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) != addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))
| addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) = addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) ),[1,1],$fot(multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_10,plain,
( addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) != multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) = addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) )],[refute_1_8,refute_1_9]) ).
cnf(refute_1_11,plain,
addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) = addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_7,refute_1_10]) ).
cnf(refute_1_12,plain,
addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))),
introduced(tautology,[refl,[$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))))]]) ).
cnf(refute_1_13,plain,
( addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) != addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))
| addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))
| addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))) ),[1,1],$fot(addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))]]) ).
cnf(refute_1_14,plain,
( addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) != addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))
| addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) )],[refute_1_11,refute_1_14]) ).
cnf(refute_1_16,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_17,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_1_18,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_1_16,refute_1_17]) ).
cnf(refute_1_19,plain,
addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))),
inference(subst,[],[refute_1_18:[bind(A,$fot(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))),bind(B,$fot(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)))),bind(C,$fot(addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))]]) ).
cnf(refute_1_20,plain,
addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) = addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))),
inference(subst,[],[refute_1_18:[bind(A,$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))))),bind(B,$fot(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2))),bind(C,$fot(multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_21,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_22,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_4,refute_1_21]) ).
cnf(refute_1_23,plain,
( addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) != addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))
| addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))
| addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) ),
inference(subst,[],[refute_1_22:[bind(X,$fot(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))),bind(Y,$fot(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))),bind(Z,$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))))]]) ).
cnf(refute_1_24,plain,
( addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))
| addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) )],[refute_1_20,refute_1_23]) ).
cnf(refute_1_25,plain,
addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))),
inference(resolve,[$cnf( $equal(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))) )],[refute_1_19,refute_1_24]) ).
cnf(refute_1_26,plain,
( addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))
| addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))
| addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) ),
inference(subst,[],[refute_1_22:[bind(X,$fot(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))),bind(Y,$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))))),bind(Z,$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))))]]) ).
cnf(refute_1_27,plain,
( addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))
| addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2)))))) )],[refute_1_25,refute_1_26]) ).
cnf(refute_1_28,plain,
addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),addition(multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))))),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))) )],[refute_1_15,refute_1_27]) ).
cnf(refute_1_29,plain,
( addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))
| ~ leq(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),one)
| leq(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),one) ),
introduced(tautology,[equality,[$cnf( ~ leq(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),one) ),[0],$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))))]]) ).
cnf(refute_1_30,plain,
( ~ leq(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),one)
| leq(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),one) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))) )],[refute_1_28,refute_1_29]) ).
cnf(refute_1_31,plain,
~ leq(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),one),
inference(resolve,[$cnf( leq(addition(addition(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_30,refute_1_0]) ).
cnf(refute_1_32,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_33,plain,
( multiplication(addition(A,B),C) != addition(multiplication(A,C),multiplication(B,C))
| addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(multiplication(addition(A,B),C))),bind(Y,$fot(addition(multiplication(A,C),multiplication(B,C))))]]) ).
cnf(refute_1_34,plain,
addition(multiplication(A,C),multiplication(B,C)) = multiplication(addition(A,B),C),
inference(resolve,[$cnf( $equal(multiplication(addition(A,B),C),addition(multiplication(A,C),multiplication(B,C))) )],[refute_1_32,refute_1_33]) ).
cnf(refute_1_35,plain,
addition(multiplication(skolemFOFtoCNF_X0_1,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
inference(subst,[],[refute_1_34:[bind(A,$fot(skolemFOFtoCNF_X0_1)),bind(B,$fot(c(skolemFOFtoCNF_X0_1))),bind(C,$fot(addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_36,plain,
addition(multiplication(A,B),addition(multiplication(A,C),X_118)) = addition(addition(multiplication(A,B),multiplication(A,C)),X_118),
inference(subst,[],[refute_1_16:[bind(A,$fot(multiplication(A,B))),bind(B,$fot(multiplication(A,C))),bind(C,$fot(X_118))]]) ).
cnf(refute_1_37,plain,
( addition(multiplication(A,B),addition(multiplication(A,C),X_118)) != addition(addition(multiplication(A,B),multiplication(A,C)),X_118)
| addition(multiplication(A,B),multiplication(A,C)) != multiplication(A,addition(B,C))
| addition(multiplication(A,B),addition(multiplication(A,C),X_118)) = addition(multiplication(A,addition(B,C)),X_118) ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(A,B),addition(multiplication(A,C),X_118)),addition(addition(multiplication(A,B),multiplication(A,C)),X_118)) ),[1,0],$fot(multiplication(A,addition(B,C)))]]) ).
cnf(refute_1_38,plain,
( addition(multiplication(A,B),addition(multiplication(A,C),X_118)) != addition(addition(multiplication(A,B),multiplication(A,C)),X_118)
| addition(multiplication(A,B),addition(multiplication(A,C),X_118)) = addition(multiplication(A,addition(B,C)),X_118) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,B),multiplication(A,C)),multiplication(A,addition(B,C))) )],[refute_1_6,refute_1_37]) ).
cnf(refute_1_39,plain,
addition(multiplication(A,B),addition(multiplication(A,C),X_118)) = addition(multiplication(A,addition(B,C)),X_118),
inference(resolve,[$cnf( $equal(addition(multiplication(A,B),addition(multiplication(A,C),X_118)),addition(addition(multiplication(A,B),multiplication(A,C)),X_118)) )],[refute_1_36,refute_1_38]) ).
cnf(refute_1_40,plain,
addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) = addition(multiplication(skolemFOFtoCNF_X0_1,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))),
inference(subst,[],[refute_1_39:[bind(A,$fot(skolemFOFtoCNF_X0_1)),bind(B,$fot(skolemFOFtoCNF_X1_2)),bind(C,$fot(c(skolemFOFtoCNF_X1_2))),bind(X_118,$fot(multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))]]) ).
cnf(refute_1_41,plain,
( addition(multiplication(skolemFOFtoCNF_X0_1,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) != multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) != addition(multiplication(skolemFOFtoCNF_X0_1,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))
| addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) ),
inference(subst,[],[refute_1_22:[bind(X,$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))))),bind(Y,$fot(addition(multiplication(skolemFOFtoCNF_X0_1,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))),bind(Z,$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))))]]) ).
cnf(refute_1_42,plain,
( addition(multiplication(skolemFOFtoCNF_X0_1,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) != multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),addition(multiplication(skolemFOFtoCNF_X0_1,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) )],[refute_1_40,refute_1_41]) ).
cnf(refute_1_43,plain,
addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_35,refute_1_42]) ).
cnf(refute_1_44,plain,
( addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))) != multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one)
| leq(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),one) ),
introduced(tautology,[equality,[$cnf( ~ leq(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),one) ),[0],$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_45,plain,
( ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one)
| leq(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),one) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_43,refute_1_44]) ).
cnf(refute_1_46,plain,
~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one),
inference(resolve,[$cnf( leq(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X1_2)),multiplication(c(skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),one) )],[refute_1_45,refute_1_31]) ).
cnf(refute_1_47,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_48,plain,
multiplication(one,one) = one,
inference(subst,[],[refute_1_47:[bind(A,$fot(one))]]) ).
cnf(refute_1_49,plain,
test(skolemFOFtoCNF_X1_2),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_50,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_51,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_1_50:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_1_52,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_1_53,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_1_52,refute_1_51]) ).
cnf(refute_1_54,plain,
( ~ test(skolemFOFtoCNF_X1_2)
| complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) ),
inference(subst,[],[refute_1_53:[bind(X0,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_55,plain,
complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_2) )],[refute_1_49,refute_1_54]) ).
cnf(refute_1_56,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_1_19]) ).
cnf(refute_1_57,plain,
( ~ complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))
| addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = one ),
inference(subst,[],[refute_1_56:[bind(X0,$fot(c(skolemFOFtoCNF_X1_2))),bind(X1,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_58,plain,
addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) )],[refute_1_55,refute_1_57]) ).
cnf(refute_1_59,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_60,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_61,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_1_59,refute_1_60]) ).
cnf(refute_1_62,plain,
addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),
inference(subst,[],[refute_1_61:[bind(A,$fot(skolemFOFtoCNF_X1_2)),bind(B,$fot(c(skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_63,plain,
( addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))
| addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != one
| addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),one) ),[0],$fot(addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_64,plain,
( addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != one
| addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) )],[refute_1_62,refute_1_63]) ).
cnf(refute_1_65,plain,
addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),one) )],[refute_1_58,refute_1_64]) ).
cnf(refute_1_66,plain,
multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
introduced(tautology,[refl,[$fot(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_67,plain,
( addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) != one
| multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) ),[1,1],$fot(one)]]) ).
cnf(refute_1_68,plain,
( addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) != one
| multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_66,refute_1_67]) ).
cnf(refute_1_69,plain,
multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),one) )],[refute_1_65,refute_1_68]) ).
cnf(refute_1_70,plain,
test(skolemFOFtoCNF_X0_1),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_71,plain,
( ~ test(skolemFOFtoCNF_X0_1)
| complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) ),
inference(subst,[],[refute_1_53:[bind(X0,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_72,plain,
complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X0_1) )],[refute_1_70,refute_1_71]) ).
cnf(refute_1_73,plain,
( ~ complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))
| addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = one ),
inference(subst,[],[refute_1_56:[bind(X0,$fot(c(skolemFOFtoCNF_X0_1))),bind(X1,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_74,plain,
addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) )],[refute_1_72,refute_1_73]) ).
cnf(refute_1_75,plain,
addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),
inference(subst,[],[refute_1_61:[bind(A,$fot(skolemFOFtoCNF_X0_1)),bind(B,$fot(c(skolemFOFtoCNF_X0_1)))]]) ).
cnf(refute_1_76,plain,
( addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) != addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))
| addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) != one
| addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),one) ),[0],$fot(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)))]]) ).
cnf(refute_1_77,plain,
( addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) != one
| addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))) )],[refute_1_75,refute_1_76]) ).
cnf(refute_1_78,plain,
addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),one) )],[refute_1_74,refute_1_77]) ).
cnf(refute_1_79,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
introduced(tautology,[refl,[$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_80,plain,
( addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) != one
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) ),[1,0],$fot(one)]]) ).
cnf(refute_1_81,plain,
( addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) != one
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_79,refute_1_80]) ).
cnf(refute_1_82,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),one) )],[refute_1_78,refute_1_81]) ).
cnf(refute_1_83,plain,
( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
inference(subst,[],[refute_1_22:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Y,$fot(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Z,$fot(multiplication(one,one)))]]) ).
cnf(refute_1_84,plain,
( multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_82,refute_1_83]) ).
cnf(refute_1_85,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one),
inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,one)) )],[refute_1_69,refute_1_84]) ).
cnf(refute_1_86,plain,
( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
| multiplication(one,one) != one
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one ),
inference(subst,[],[refute_1_22:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Y,$fot(multiplication(one,one))),bind(Z,$fot(one))]]) ).
cnf(refute_1_87,plain,
( multiplication(one,one) != one
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,one)) )],[refute_1_85,refute_1_86]) ).
cnf(refute_1_88,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one,
inference(resolve,[$cnf( $equal(multiplication(one,one),one) )],[refute_1_48,refute_1_87]) ).
cnf(refute_1_89,plain,
( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != one
| ~ leq(one,one)
| leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),
introduced(tautology,[equality,[$cnf( ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),[0],$fot(one)]]) ).
cnf(refute_1_90,plain,
( ~ leq(one,one)
| leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_88,refute_1_89]) ).
cnf(refute_1_91,plain,
~ leq(one,one),
inference(resolve,[$cnf( leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_90,refute_1_46]) ).
cnf(refute_1_92,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_1_26]) ).
cnf(refute_1_93,plain,
( addition(X_96,X_96) != X_96
| leq(X_96,X_96) ),
inference(subst,[],[refute_1_92:[bind(A,$fot(X_96)),bind(B,$fot(X_96))]]) ).
cnf(refute_1_94,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_1_28]) ).
cnf(refute_1_95,plain,
addition(X_96,X_96) = X_96,
inference(subst,[],[refute_1_94:[bind(A,$fot(X_96))]]) ).
cnf(refute_1_96,plain,
( X_96 != X_96
| addition(X_96,X_96) != X_96
| addition(X_96,X_96) = X_96 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_96,X_96),X_96) ),[0,0],$fot(X_96)]]) ).
cnf(refute_1_97,plain,
( X_96 != X_96
| addition(X_96,X_96) = X_96 ),
inference(resolve,[$cnf( $equal(addition(X_96,X_96),X_96) )],[refute_1_95,refute_1_96]) ).
cnf(refute_1_98,plain,
( X_96 != X_96
| leq(X_96,X_96) ),
inference(resolve,[$cnf( $equal(addition(X_96,X_96),X_96) )],[refute_1_97,refute_1_93]) ).
cnf(refute_1_99,plain,
X_96 = X_96,
introduced(tautology,[refl,[$fot(X_96)]]) ).
cnf(refute_1_100,plain,
leq(X_96,X_96),
inference(resolve,[$cnf( $equal(X_96,X_96) )],[refute_1_99,refute_1_98]) ).
cnf(refute_1_101,plain,
leq(one,one),
inference(subst,[],[refute_1_100:[bind(X_96,$fot(one))]]) ).
cnf(refute_1_102,plain,
$false,
inference(resolve,[$cnf( leq(one,one) )],[refute_1_101,refute_1_91]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : KLE009+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 08:49:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.02/1.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.02/1.21
% 1.02/1.21 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.08/1.24
%------------------------------------------------------------------------------