TSTP Solution File: KLE017+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE017+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n020.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 02:14:39 EDT 2022
% Result : Theorem 57.63s 57.80s
% Output : CNFRefutation 57.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 76
% Syntax : Number of formulae : 473 ( 239 unt; 0 def)
% Number of atoms : 882 ( 595 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 768 ( 359 ~; 308 |; 70 &)
% ( 23 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 646 ( 15 sgn 188 !; 10 ?)
% 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_identity,axiom,
! [A] : addition(A,zero) = A ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(multiplicative_right_identity,axiom,
! [A] : multiplication(A,one) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2) )
=> ( leq(X2,multiplication(X0,X1))
<=> ( leq(X2,X0)
& leq(X2,X1) ) ) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2)
& leq(X2,multiplication(X0,X1)) )
=> leq(X2,X0) ),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2)
& leq(X2,multiplication(X0,X1))
& leq(X2,X0) )
=> leq(X2,X1) ),
inference(strip,[],[goals]) ).
fof(subgoal_2,plain,
! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2)
& leq(X2,X0)
& leq(X2,X1) )
=> leq(X2,multiplication(X0,X1)) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2)
& leq(X2,multiplication(X0,X1)) )
=> leq(X2,X0) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_1,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_0_5,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_7,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_9,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [X0,X1,X2] :
( ~ leq(X2,X0)
& leq(X2,multiplication(X0,X1))
& test(X0)
& test(X1)
& test(X2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( ~ leq(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0)
& leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))
& test(skolemFOFtoCNF_X0)
& test(skolemFOFtoCNF_X1_1)
& test(skolemFOFtoCNF_X2) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_14,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_15,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
test(skolemFOFtoCNF_X1_1),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_17,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(canonicalize,[],[test_1]) ).
fof(normalize_0_18,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| test(X0) )
& ( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X0] :
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,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_22,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,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_22]) ).
fof(normalize_0_24,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [A] : multiplication(A,one) = A,
inference(canonicalize,[],[multiplicative_right_identity]) ).
fof(normalize_0_26,plain,
! [A] : multiplication(A,one) = A,
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
~ leq(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( addition(X_41,addition(X_41,X_16)) != addition(X_41,X_16)
| leq(X_41,addition(X_41,X_16)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_41)),bind(B,$fot(addition(X_41,X_16)))]]) ).
cnf(refute_0_2,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
addition(X_15,addition(X_15,X_16)) = addition(addition(X_15,X_15),X_16),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_15)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_4,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
addition(X_15,X_15) = X_15,
inference(subst,[],[refute_0_4:[bind(A,$fot(X_15))]]) ).
cnf(refute_0_6,plain,
( addition(X_15,X_15) != X_15
| addition(X_15,addition(X_15,X_16)) != addition(addition(X_15,X_15),X_16)
| addition(X_15,addition(X_15,X_16)) = addition(X_15,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_15,addition(X_15,X_16)),addition(addition(X_15,X_15),X_16)) ),[1,0],$fot(X_15)]]) ).
cnf(refute_0_7,plain,
( addition(X_15,addition(X_15,X_16)) != addition(addition(X_15,X_15),X_16)
| addition(X_15,addition(X_15,X_16)) = addition(X_15,X_16) ),
inference(resolve,[$cnf( $equal(addition(X_15,X_15),X_15) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
addition(X_15,addition(X_15,X_16)) = addition(X_15,X_16),
inference(resolve,[$cnf( $equal(addition(X_15,addition(X_15,X_16)),addition(addition(X_15,X_15),X_16)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
addition(X_41,addition(X_41,X_16)) = addition(X_41,X_16),
inference(subst,[],[refute_0_8:[bind(X_15,$fot(X_41))]]) ).
cnf(refute_0_10,plain,
( addition(X_41,X_16) != addition(X_41,X_16)
| addition(X_41,addition(X_41,X_16)) != addition(X_41,X_16)
| addition(X_41,addition(X_41,X_16)) = addition(X_41,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_41,addition(X_41,X_16)),addition(X_41,X_16)) ),[0,1],$fot(addition(X_41,X_16))]]) ).
cnf(refute_0_11,plain,
( addition(X_41,X_16) != addition(X_41,X_16)
| addition(X_41,addition(X_41,X_16)) = addition(X_41,X_16) ),
inference(resolve,[$cnf( $equal(addition(X_41,addition(X_41,X_16)),addition(X_41,X_16)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( addition(X_41,X_16) != addition(X_41,X_16)
| leq(X_41,addition(X_41,X_16)) ),
inference(resolve,[$cnf( $equal(addition(X_41,addition(X_41,X_16)),addition(X_41,X_16)) )],[refute_0_11,refute_0_1]) ).
cnf(refute_0_13,plain,
addition(X_41,X_16) = addition(X_41,X_16),
introduced(tautology,[refl,[$fot(addition(X_41,X_16))]]) ).
cnf(refute_0_14,plain,
leq(X_41,addition(X_41,X_16)),
inference(resolve,[$cnf( $equal(addition(X_41,X_16),addition(X_41,X_16)) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
leq(X_56,addition(X_56,addition(X_14,X_16))),
inference(subst,[],[refute_0_14:[bind(X_16,$fot(addition(X_14,X_16))),bind(X_41,$fot(X_56))]]) ).
cnf(refute_0_16,plain,
addition(X_14,addition(X_15,X_16)) = addition(addition(X_14,X_15),X_16),
inference(subst,[],[refute_0_2:[bind(A,$fot(X_14)),bind(B,$fot(X_15)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_17,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_18,plain,
addition(X_15,X_14) = addition(X_14,X_15),
inference(subst,[],[refute_0_17:[bind(A,$fot(X_15)),bind(B,$fot(X_14))]]) ).
cnf(refute_0_19,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_20,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( addition(X_15,X_14) != addition(X_14,X_15)
| addition(X_14,X_15) = addition(X_15,X_14) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(X_15,X_14))),bind(Y,$fot(addition(X_14,X_15)))]]) ).
cnf(refute_0_23,plain,
addition(X_14,X_15) = addition(X_15,X_14),
inference(resolve,[$cnf( $equal(addition(X_15,X_14),addition(X_14,X_15)) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( addition(X_14,X_15) != addition(X_15,X_14)
| addition(X_14,addition(X_15,X_16)) != addition(addition(X_14,X_15),X_16)
| addition(X_14,addition(X_15,X_16)) = addition(addition(X_15,X_14),X_16) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_14,addition(X_15,X_16)),addition(addition(X_14,X_15),X_16)) ),[1,0],$fot(addition(X_15,X_14))]]) ).
cnf(refute_0_25,plain,
( addition(X_14,addition(X_15,X_16)) != addition(addition(X_14,X_15),X_16)
| addition(X_14,addition(X_15,X_16)) = addition(addition(X_15,X_14),X_16) ),
inference(resolve,[$cnf( $equal(addition(X_14,X_15),addition(X_15,X_14)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(X_14,addition(X_15,X_16)) = addition(addition(X_15,X_14),X_16),
inference(resolve,[$cnf( $equal(addition(X_14,addition(X_15,X_16)),addition(addition(X_14,X_15),X_16)) )],[refute_0_16,refute_0_25]) ).
cnf(refute_0_27,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_0_28,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_0_2,refute_0_27]) ).
cnf(refute_0_29,plain,
addition(addition(X_15,X_14),X_16) = addition(X_15,addition(X_14,X_16)),
inference(subst,[],[refute_0_28:[bind(A,$fot(X_15)),bind(B,$fot(X_14)),bind(C,$fot(X_16))]]) ).
cnf(refute_0_30,plain,
( addition(X_14,addition(X_15,X_16)) != addition(addition(X_15,X_14),X_16)
| addition(addition(X_15,X_14),X_16) != addition(X_15,addition(X_14,X_16))
| addition(X_14,addition(X_15,X_16)) = addition(X_15,addition(X_14,X_16)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_14,addition(X_15,X_16)),addition(X_15,addition(X_14,X_16))) ),[0],$fot(addition(addition(X_15,X_14),X_16))]]) ).
cnf(refute_0_31,plain,
( addition(X_14,addition(X_15,X_16)) != addition(addition(X_15,X_14),X_16)
| addition(X_14,addition(X_15,X_16)) = addition(X_15,addition(X_14,X_16)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_15,X_14),X_16),addition(X_15,addition(X_14,X_16))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
addition(X_14,addition(X_15,X_16)) = addition(X_15,addition(X_14,X_16)),
inference(resolve,[$cnf( $equal(addition(X_14,addition(X_15,X_16)),addition(addition(X_15,X_14),X_16)) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
addition(X_14,addition(X_56,X_16)) = addition(X_56,addition(X_14,X_16)),
inference(subst,[],[refute_0_32:[bind(X_15,$fot(X_56))]]) ).
cnf(refute_0_34,plain,
( addition(X_14,addition(X_56,X_16)) != addition(X_56,addition(X_14,X_16))
| addition(X_56,addition(X_14,X_16)) = addition(X_14,addition(X_56,X_16)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(X_14,addition(X_56,X_16)))),bind(Y,$fot(addition(X_56,addition(X_14,X_16))))]]) ).
cnf(refute_0_35,plain,
addition(X_56,addition(X_14,X_16)) = addition(X_14,addition(X_56,X_16)),
inference(resolve,[$cnf( $equal(addition(X_14,addition(X_56,X_16)),addition(X_56,addition(X_14,X_16))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( addition(X_56,addition(X_14,X_16)) != addition(X_14,addition(X_56,X_16))
| ~ leq(X_56,addition(X_56,addition(X_14,X_16)))
| leq(X_56,addition(X_14,addition(X_56,X_16))) ),
introduced(tautology,[equality,[$cnf( leq(X_56,addition(X_56,addition(X_14,X_16))) ),[1],$fot(addition(X_14,addition(X_56,X_16)))]]) ).
cnf(refute_0_37,plain,
( ~ leq(X_56,addition(X_56,addition(X_14,X_16)))
| leq(X_56,addition(X_14,addition(X_56,X_16))) ),
inference(resolve,[$cnf( $equal(addition(X_56,addition(X_14,X_16)),addition(X_14,addition(X_56,X_16))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
leq(X_56,addition(X_14,addition(X_56,X_16))),
inference(resolve,[$cnf( leq(X_56,addition(X_56,addition(X_14,X_16))) )],[refute_0_15,refute_0_37]) ).
cnf(refute_0_39,plain,
leq(skolemFOFtoCNF_X2,addition(X_14,addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)))),
inference(subst,[],[refute_0_38:[bind(X_16,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))),bind(X_56,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_40,plain,
leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_41,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_42,plain,
( ~ leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))
| addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)) = multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_0_41:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_43,plain,
addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)) = multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)) )],[refute_0_40,refute_0_42]) ).
cnf(refute_0_44,plain,
( addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)) != multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)
| ~ leq(skolemFOFtoCNF_X2,addition(X_14,addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))))
| leq(skolemFOFtoCNF_X2,addition(X_14,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X2,addition(X_14,addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)))) ),[1,1],$fot(multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_45,plain,
( ~ leq(skolemFOFtoCNF_X2,addition(X_14,addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))))
| leq(skolemFOFtoCNF_X2,addition(X_14,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
leq(skolemFOFtoCNF_X2,addition(X_14,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2,addition(X_14,addition(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)))) )],[refute_0_39,refute_0_45]) ).
cnf(refute_0_47,plain,
leq(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_46:[bind(X_14,$fot(multiplication(skolemFOFtoCNF_X0,X_816)))]]) ).
cnf(refute_0_48,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_49,plain,
multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1)) = addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_48:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(X_816)),bind(C,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_50,plain,
( multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1)) != addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))
| addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)) = multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1)))),bind(Y,$fot(addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_51,plain,
addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)) = multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1)),addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)) != multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1))
| ~ leq(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))) ),[1],$fot(multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_53,plain,
( ~ leq(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)),multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,addition(X_816,skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2,addition(multiplication(skolemFOFtoCNF_X0,X_816),multiplication(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1))) )],[refute_0_47,refute_0_53]) ).
cnf(refute_0_55,plain,
leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,addition(one,skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_54:[bind(X_816,$fot(one))]]) ).
cnf(refute_0_56,plain,
addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_8:[bind(X_15,$fot(skolemFOFtoCNF_X1_1)),bind(X_16,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_57,plain,
test(skolemFOFtoCNF_X1_1),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_58,plain,
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_59,plain,
( ~ test(skolemFOFtoCNF_X1_1)
| complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_0_58:[bind(X0,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_60,plain,
complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_1) )],[refute_0_57,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_62,plain,
( ~ complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1)
| addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = one ),
inference(subst,[],[refute_0_61:[bind(X0,$fot(skolemFOFtoCNF_X1_1)),bind(X1,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_63,plain,
addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) )],[refute_0_60,refute_0_62]) ).
cnf(refute_0_64,plain,
( addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != one
| addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),one) ),[0],$fot(addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_65,plain,
( addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))
| addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = one ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),one) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = one,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) )],[refute_0_56,refute_0_65]) ).
cnf(refute_0_67,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_68,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_17,refute_0_67]) ).
cnf(refute_0_69,plain,
addition(skolemFOFtoCNF_X1_1,one) = addition(one,skolemFOFtoCNF_X1_1),
inference(subst,[],[refute_0_68:[bind(A,$fot(one)),bind(B,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_70,plain,
addition(skolemFOFtoCNF_X1_1,addition(X_15,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(X_15,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_32:[bind(X_14,$fot(skolemFOFtoCNF_X1_1)),bind(X_16,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_71,plain,
( addition(skolemFOFtoCNF_X1_1,addition(X_15,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != addition(X_15,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))
| addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)) != one
| addition(skolemFOFtoCNF_X1_1,addition(X_15,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(X_15,one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,addition(X_15,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),addition(X_15,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_72,plain,
( addition(skolemFOFtoCNF_X1_1,addition(X_15,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != addition(X_15,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))
| addition(skolemFOFtoCNF_X1_1,addition(X_15,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(X_15,one) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)),one) )],[refute_0_63,refute_0_71]) ).
cnf(refute_0_73,plain,
addition(skolemFOFtoCNF_X1_1,addition(X_15,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(X_15,one),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,addition(X_15,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),addition(X_15,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1)))) )],[refute_0_70,refute_0_72]) ).
cnf(refute_0_74,plain,
addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(skolemFOFtoCNF_X1_1,one),
inference(subst,[],[refute_0_73:[bind(X_15,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_75,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_76,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_21,refute_0_75]) ).
cnf(refute_0_77,plain,
( addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != addition(skolemFOFtoCNF_X1_1,one)
| addition(skolemFOFtoCNF_X1_1,one) != addition(one,skolemFOFtoCNF_X1_1)
| addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(one,skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_0_76:[bind(X,$fot(addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(addition(skolemFOFtoCNF_X1_1,one))),bind(Z,$fot(addition(one,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_78,plain,
( addition(skolemFOFtoCNF_X1_1,one) != addition(one,skolemFOFtoCNF_X1_1)
| addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(one,skolemFOFtoCNF_X1_1) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),addition(skolemFOFtoCNF_X1_1,one)) )],[refute_0_74,refute_0_77]) ).
cnf(refute_0_79,plain,
addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) = addition(one,skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,one),addition(one,skolemFOFtoCNF_X1_1)) )],[refute_0_69,refute_0_78]) ).
cnf(refute_0_80,plain,
( addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != addition(one,skolemFOFtoCNF_X1_1)
| addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != one
| addition(one,skolemFOFtoCNF_X1_1) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),one) ),[0],$fot(addition(one,skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_81,plain,
( addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))) != one
| addition(one,skolemFOFtoCNF_X1_1) = one ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),addition(one,skolemFOFtoCNF_X1_1)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
addition(one,skolemFOFtoCNF_X1_1) = one,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1(skolemFOFtoCNF_X1_1))),one) )],[refute_0_66,refute_0_81]) ).
cnf(refute_0_83,plain,
( addition(one,skolemFOFtoCNF_X1_1) != one
| ~ leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,addition(one,skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,one)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,addition(one,skolemFOFtoCNF_X1_1))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_84,plain,
( ~ leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,addition(one,skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,one)) ),
inference(resolve,[$cnf( $equal(addition(one,skolemFOFtoCNF_X1_1),one) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,one)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,addition(one,skolemFOFtoCNF_X1_1))) )],[refute_0_55,refute_0_84]) ).
cnf(refute_0_86,plain,
multiplication(A,one) = A,
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_87,plain,
multiplication(skolemFOFtoCNF_X0,one) = skolemFOFtoCNF_X0,
inference(subst,[],[refute_0_86:[bind(A,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_88,plain,
( multiplication(skolemFOFtoCNF_X0,one) != skolemFOFtoCNF_X0
| ~ leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,one))
| leq(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,one)) ),[1],$fot(skolemFOFtoCNF_X0)]]) ).
cnf(refute_0_89,plain,
( ~ leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,one))
| leq(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0,one),skolemFOFtoCNF_X0) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
leq(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2,multiplication(skolemFOFtoCNF_X0,one)) )],[refute_0_85,refute_0_89]) ).
cnf(refute_0_91,plain,
~ leq(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_92,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2,skolemFOFtoCNF_X0) )],[refute_0_90,refute_0_91]) ).
fof(negate_1_0,plain,
~ ! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2)
& leq(X2,multiplication(X0,X1))
& leq(X2,X0) )
=> leq(X2,X1) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_1_1,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_1_5,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_1_7,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
? [X0,X1,X2] :
( ~ leq(X2,X1)
& leq(X2,X0)
& leq(X2,multiplication(X0,X1))
& test(X0)
& test(X1)
& test(X2) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_9,plain,
( ~ leq(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)
& leq(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))
& leq(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X0_1)
& test(skolemFOFtoCNF_X0_1)
& test(skolemFOFtoCNF_X1_2)
& test(skolemFOFtoCNF_X2_1) ),
inference(skolemize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
leq(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_12,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_1_13,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
test(skolemFOFtoCNF_X0_1),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_15,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_1_16,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_1_17]) ).
fof(normalize_1_19,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_20,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,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_20]) ).
fof(normalize_1_22,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_1_24,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
~ leq(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2),
inference(conjunct,[],[normalize_1_9]) ).
cnf(refute_1_0,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)
| leq(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(skolemFOFtoCNF_X2_1)),bind(B,$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)))]]) ).
cnf(refute_1_2,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_3,plain,
addition(A,addition(X_833,X_834)) = addition(addition(X_833,X_834),A),
inference(subst,[],[refute_1_2:[bind(B,$fot(addition(X_833,X_834)))]]) ).
cnf(refute_1_4,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_5,plain,
addition(X_833,addition(X_834,A)) = addition(addition(X_833,X_834),A),
inference(subst,[],[refute_1_4:[bind(A,$fot(X_833)),bind(B,$fot(X_834)),bind(C,$fot(A))]]) ).
cnf(refute_1_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_6,refute_1_7]) ).
cnf(refute_1_9,plain,
( addition(X_833,addition(X_834,A)) != addition(addition(X_833,X_834),A)
| addition(addition(X_833,X_834),A) = addition(X_833,addition(X_834,A)) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(addition(X_833,addition(X_834,A)))),bind(Y,$fot(addition(addition(X_833,X_834),A)))]]) ).
cnf(refute_1_10,plain,
addition(addition(X_833,X_834),A) = addition(X_833,addition(X_834,A)),
inference(resolve,[$cnf( $equal(addition(X_833,addition(X_834,A)),addition(addition(X_833,X_834),A)) )],[refute_1_5,refute_1_9]) ).
cnf(refute_1_11,plain,
( addition(A,addition(X_833,X_834)) != addition(addition(X_833,X_834),A)
| addition(addition(X_833,X_834),A) != addition(X_833,addition(X_834,A))
| addition(A,addition(X_833,X_834)) = addition(X_833,addition(X_834,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_833,X_834)),addition(X_833,addition(X_834,A))) ),[0],$fot(addition(addition(X_833,X_834),A))]]) ).
cnf(refute_1_12,plain,
( addition(A,addition(X_833,X_834)) != addition(addition(X_833,X_834),A)
| addition(A,addition(X_833,X_834)) = addition(X_833,addition(X_834,A)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_833,X_834),A),addition(X_833,addition(X_834,A))) )],[refute_1_10,refute_1_11]) ).
cnf(refute_1_13,plain,
addition(A,addition(X_833,X_834)) = addition(X_833,addition(X_834,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_833,X_834)),addition(addition(X_833,X_834),A)) )],[refute_1_3,refute_1_12]) ).
cnf(refute_1_14,plain,
addition(A,addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))) = addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),A)),
inference(subst,[],[refute_1_13:[bind(X_833,$fot(skolemFOFtoCNF_X2_1)),bind(X_834,$fot(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_15,plain,
leq(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_16,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_17,plain,
( ~ leq(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))
| addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) = multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2) ),
inference(subst,[],[refute_1_16:[bind(A,$fot(skolemFOFtoCNF_X2_1)),bind(B,$fot(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_18,plain,
addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) = multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) )],[refute_1_15,refute_1_17]) ).
cnf(refute_1_19,plain,
( addition(A,addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))) != addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),A))
| addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) != multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)
| addition(A,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) = addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),A)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))),addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),A))) ),[0,1],$fot(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_20,plain,
( addition(A,addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))) != addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),A))
| addition(A,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) = addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),A)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)),multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) )],[refute_1_18,refute_1_19]) ).
cnf(refute_1_21,plain,
addition(A,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) = addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),A)),
inference(resolve,[$cnf( $equal(addition(A,addition(skolemFOFtoCNF_X2_1,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))),addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),A))) )],[refute_1_14,refute_1_20]) ).
cnf(refute_1_22,plain,
addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) = addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)),
inference(subst,[],[refute_1_21:[bind(A,$fot(X_880))]]) ).
cnf(refute_1_23,plain,
( addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) != addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880))
| addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) = addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)))),bind(Y,$fot(addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880))))]]) ).
cnf(refute_1_24,plain,
addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) = addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( $equal(addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)),addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880))) )],[refute_1_22,refute_1_23]) ).
cnf(refute_1_25,plain,
( addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)
| addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) != addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))
| addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880) ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)),addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))) ),[1],$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880))]]) ).
cnf(refute_1_26,plain,
( addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)
| addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)),addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))) )],[refute_1_24,refute_1_25]) ).
cnf(refute_1_27,plain,
( addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)
| leq(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) )],[refute_1_26,refute_1_1]) ).
cnf(refute_1_28,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_1_29,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_1_2,refute_1_28]) ).
cnf(refute_1_30,plain,
addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880),
inference(subst,[],[refute_1_29:[bind(A,$fot(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2))),bind(B,$fot(X_880))]]) ).
cnf(refute_1_31,plain,
leq(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)),
inference(resolve,[$cnf( $equal(addition(X_880,multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),X_880)) )],[refute_1_30,refute_1_27]) ).
cnf(refute_1_32,plain,
leq(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2))),
inference(subst,[],[refute_1_31:[bind(X_880,$fot(multiplication(B,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_33,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_34,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2) = addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2)),
inference(subst,[],[refute_1_33:[bind(A,$fot(skolemFOFtoCNF_X0_1)),bind(C,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_35,plain,
( multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2) != addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2))
| addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2)) = multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2))),bind(Y,$fot(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_36,plain,
addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2)) = multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2),addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2))) )],[refute_1_34,refute_1_35]) ).
cnf(refute_1_37,plain,
( addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2)) != multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2)
| ~ leq(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2)))
| leq(skolemFOFtoCNF_X2_1,multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2))) ),[1],$fot(multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_38,plain,
( ~ leq(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2)))
| leq(skolemFOFtoCNF_X2_1,multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2)),multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2)) )],[refute_1_36,refute_1_37]) ).
cnf(refute_1_39,plain,
leq(skolemFOFtoCNF_X2_1,multiplication(addition(skolemFOFtoCNF_X0_1,B),skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_1,addition(multiplication(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2),multiplication(B,skolemFOFtoCNF_X1_2))) )],[refute_1_32,refute_1_38]) ).
cnf(refute_1_40,plain,
leq(skolemFOFtoCNF_X2_1,multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2)),
inference(subst,[],[refute_1_39:[bind(B,$fot(c(skolemFOFtoCNF_X0_1)))]]) ).
cnf(refute_1_41,plain,
test(skolemFOFtoCNF_X0_1),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_42,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_43,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_1_42:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_1_44,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_1_45,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_1_44,refute_1_43]) ).
cnf(refute_1_46,plain,
( ~ test(skolemFOFtoCNF_X0_1)
| complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) ),
inference(subst,[],[refute_1_45:[bind(X0,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_47,plain,
complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X0_1) )],[refute_1_41,refute_1_46]) ).
cnf(refute_1_48,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_49,plain,
( ~ complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))
| addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = one ),
inference(subst,[],[refute_1_48:[bind(X0,$fot(c(skolemFOFtoCNF_X0_1))),bind(X1,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_50,plain,
addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) )],[refute_1_47,refute_1_49]) ).
cnf(refute_1_51,plain,
addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),
inference(subst,[],[refute_1_29:[bind(A,$fot(skolemFOFtoCNF_X0_1)),bind(B,$fot(c(skolemFOFtoCNF_X0_1)))]]) ).
cnf(refute_1_52,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_53,plain,
( addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) != one
| addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))) )],[refute_1_51,refute_1_52]) ).
cnf(refute_1_54,plain,
addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),one) )],[refute_1_50,refute_1_53]) ).
cnf(refute_1_55,plain,
( addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) != one
| ~ leq(skolemFOFtoCNF_X2_1,multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2))
| leq(skolemFOFtoCNF_X2_1,multiplication(one,skolemFOFtoCNF_X1_2)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X2_1,multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2)) ),[1,0],$fot(one)]]) ).
cnf(refute_1_56,plain,
( ~ leq(skolemFOFtoCNF_X2_1,multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2))
| leq(skolemFOFtoCNF_X2_1,multiplication(one,skolemFOFtoCNF_X1_2)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),one) )],[refute_1_54,refute_1_55]) ).
cnf(refute_1_57,plain,
leq(skolemFOFtoCNF_X2_1,multiplication(one,skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_1,multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2)) )],[refute_1_40,refute_1_56]) ).
cnf(refute_1_58,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_59,plain,
multiplication(one,skolemFOFtoCNF_X1_2) = skolemFOFtoCNF_X1_2,
inference(subst,[],[refute_1_58:[bind(A,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_60,plain,
( multiplication(one,skolemFOFtoCNF_X1_2) != skolemFOFtoCNF_X1_2
| ~ leq(skolemFOFtoCNF_X2_1,multiplication(one,skolemFOFtoCNF_X1_2))
| leq(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X2_1,multiplication(one,skolemFOFtoCNF_X1_2)) ),[1],$fot(skolemFOFtoCNF_X1_2)]]) ).
cnf(refute_1_61,plain,
( ~ leq(skolemFOFtoCNF_X2_1,multiplication(one,skolemFOFtoCNF_X1_2))
| leq(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) )],[refute_1_59,refute_1_60]) ).
cnf(refute_1_62,plain,
leq(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_1,multiplication(one,skolemFOFtoCNF_X1_2)) )],[refute_1_57,refute_1_61]) ).
cnf(refute_1_63,plain,
~ leq(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_64,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2) )],[refute_1_62,refute_1_63]) ).
fof(negate_2_0,plain,
~ ! [X0,X1,X2] :
( ( test(X0)
& test(X1)
& test(X2)
& leq(X2,X0)
& leq(X2,X1) )
=> leq(X2,multiplication(X0,X1)) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_2_1,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_2_0]) ).
fof(normalize_2_2,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_2_1]) ).
fof(normalize_2_3,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_4,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_2_5,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_2_4]) ).
fof(normalize_2_6,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_2_7,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_2_6]) ).
fof(normalize_2_8,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_2_9,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_2_11,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_2_13,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_2_12]) ).
fof(normalize_2_14,plain,
? [X0,X1,X2] :
( ~ leq(X2,multiplication(X0,X1))
& leq(X2,X0)
& leq(X2,X1)
& test(X0)
& test(X1)
& test(X2) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_15,plain,
( ~ leq(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))
& leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)
& leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)
& test(skolemFOFtoCNF_X0_2)
& test(skolemFOFtoCNF_X1_3)
& test(skolemFOFtoCNF_X2_2) ),
inference(skolemize,[],[normalize_2_14]) ).
fof(normalize_2_16,plain,
test(skolemFOFtoCNF_X2_2),
inference(conjunct,[],[normalize_2_15]) ).
fof(normalize_2_17,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_2_18,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_2_17]) ).
fof(normalize_2_19,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_2_18]) ).
fof(normalize_2_20,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_2_19]) ).
fof(normalize_2_21,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(canonicalize,[],[test_2]) ).
fof(normalize_2_22,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_2_21]) ).
fof(normalize_2_23,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_2_22]) ).
fof(normalize_2_24,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(conjunct,[],[normalize_2_23]) ).
fof(normalize_2_25,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_2_26,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_2_25]) ).
fof(normalize_2_27,plain,
leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),
inference(conjunct,[],[normalize_2_15]) ).
fof(normalize_2_28,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_29,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_2_23]) ).
fof(normalize_2_30,plain,
test(skolemFOFtoCNF_X0_2),
inference(conjunct,[],[normalize_2_15]) ).
fof(normalize_2_31,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_2_32,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_2_31]) ).
fof(normalize_2_33,plain,
leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3),
inference(conjunct,[],[normalize_2_15]) ).
fof(normalize_2_34,plain,
~ leq(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)),
inference(conjunct,[],[normalize_2_15]) ).
cnf(refute_2_0,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
( addition(X_988,addition(X_949,X_988)) != addition(X_949,X_988)
| leq(X_988,addition(X_949,X_988)) ),
inference(subst,[],[refute_2_0:[bind(A,$fot(X_988)),bind(B,$fot(addition(X_949,X_988)))]]) ).
cnf(refute_2_2,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_2_5]) ).
cnf(refute_2_3,plain,
addition(addition(X_949,X_950),addition(X_949,X_950)) = addition(addition(addition(X_949,X_950),X_949),X_950),
inference(subst,[],[refute_2_2:[bind(A,$fot(addition(X_949,X_950))),bind(B,$fot(X_949)),bind(C,$fot(X_950))]]) ).
cnf(refute_2_4,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_5,plain,
addition(addition(X_949,X_950),addition(X_949,X_950)) = addition(X_949,X_950),
inference(subst,[],[refute_2_4:[bind(A,$fot(addition(X_949,X_950)))]]) ).
cnf(refute_2_6,plain,
( addition(addition(X_949,X_950),addition(X_949,X_950)) != addition(X_949,X_950)
| addition(addition(X_949,X_950),addition(X_949,X_950)) != addition(addition(addition(X_949,X_950),X_949),X_950)
| addition(X_949,X_950) = addition(addition(addition(X_949,X_950),X_949),X_950) ),
introduced(tautology,[equality,[$cnf( $equal(addition(addition(X_949,X_950),addition(X_949,X_950)),addition(addition(addition(X_949,X_950),X_949),X_950)) ),[0],$fot(addition(X_949,X_950))]]) ).
cnf(refute_2_7,plain,
( addition(addition(X_949,X_950),addition(X_949,X_950)) != addition(addition(addition(X_949,X_950),X_949),X_950)
| addition(X_949,X_950) = addition(addition(addition(X_949,X_950),X_949),X_950) ),
inference(resolve,[$cnf( $equal(addition(addition(X_949,X_950),addition(X_949,X_950)),addition(X_949,X_950)) )],[refute_2_5,refute_2_6]) ).
cnf(refute_2_8,plain,
addition(X_949,X_950) = addition(addition(addition(X_949,X_950),X_949),X_950),
inference(resolve,[$cnf( $equal(addition(addition(X_949,X_950),addition(X_949,X_950)),addition(addition(addition(X_949,X_950),X_949),X_950)) )],[refute_2_3,refute_2_7]) ).
cnf(refute_2_9,plain,
addition(X_948,addition(X_949,X_950)) = addition(addition(X_948,X_949),X_950),
inference(subst,[],[refute_2_2:[bind(A,$fot(X_948)),bind(B,$fot(X_949)),bind(C,$fot(X_950))]]) ).
cnf(refute_2_10,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_11,plain,
addition(X_950,X_949) = addition(X_949,X_950),
inference(subst,[],[refute_2_10:[bind(A,$fot(X_950)),bind(B,$fot(X_949))]]) ).
cnf(refute_2_12,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_13,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_14,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_12,refute_2_13]) ).
cnf(refute_2_15,plain,
( addition(X_950,X_949) != addition(X_949,X_950)
| addition(X_949,X_950) = addition(X_950,X_949) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(X_950,X_949))),bind(Y,$fot(addition(X_949,X_950)))]]) ).
cnf(refute_2_16,plain,
addition(X_949,X_950) = addition(X_950,X_949),
inference(resolve,[$cnf( $equal(addition(X_950,X_949),addition(X_949,X_950)) )],[refute_2_11,refute_2_15]) ).
cnf(refute_2_17,plain,
( addition(X_948,addition(X_949,X_950)) != addition(addition(X_948,X_949),X_950)
| addition(X_949,X_950) != addition(X_950,X_949)
| addition(X_948,addition(X_950,X_949)) = addition(addition(X_948,X_949),X_950) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_948,addition(X_949,X_950)),addition(addition(X_948,X_949),X_950)) ),[0,1],$fot(addition(X_950,X_949))]]) ).
cnf(refute_2_18,plain,
( addition(X_948,addition(X_949,X_950)) != addition(addition(X_948,X_949),X_950)
| addition(X_948,addition(X_950,X_949)) = addition(addition(X_948,X_949),X_950) ),
inference(resolve,[$cnf( $equal(addition(X_949,X_950),addition(X_950,X_949)) )],[refute_2_16,refute_2_17]) ).
cnf(refute_2_19,plain,
addition(X_948,addition(X_950,X_949)) = addition(addition(X_948,X_949),X_950),
inference(resolve,[$cnf( $equal(addition(X_948,addition(X_949,X_950)),addition(addition(X_948,X_949),X_950)) )],[refute_2_9,refute_2_18]) ).
cnf(refute_2_20,plain,
( addition(A,addition(B,C)) != addition(addition(A,B),C)
| addition(addition(A,B),C) = addition(A,addition(B,C)) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(A,addition(B,C)))),bind(Y,$fot(addition(addition(A,B),C)))]]) ).
cnf(refute_2_21,plain,
addition(addition(A,B),C) = addition(A,addition(B,C)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,C)),addition(addition(A,B),C)) )],[refute_2_2,refute_2_20]) ).
cnf(refute_2_22,plain,
addition(addition(X_948,X_949),X_950) = addition(X_948,addition(X_949,X_950)),
inference(subst,[],[refute_2_21:[bind(A,$fot(X_948)),bind(B,$fot(X_949)),bind(C,$fot(X_950))]]) ).
cnf(refute_2_23,plain,
( addition(X_948,addition(X_950,X_949)) != addition(addition(X_948,X_949),X_950)
| addition(addition(X_948,X_949),X_950) != addition(X_948,addition(X_949,X_950))
| addition(X_948,addition(X_950,X_949)) = addition(X_948,addition(X_949,X_950)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_948,addition(X_950,X_949)),addition(X_948,addition(X_949,X_950))) ),[0],$fot(addition(addition(X_948,X_949),X_950))]]) ).
cnf(refute_2_24,plain,
( addition(X_948,addition(X_950,X_949)) != addition(addition(X_948,X_949),X_950)
| addition(X_948,addition(X_950,X_949)) = addition(X_948,addition(X_949,X_950)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_948,X_949),X_950),addition(X_948,addition(X_949,X_950))) )],[refute_2_22,refute_2_23]) ).
cnf(refute_2_25,plain,
addition(X_948,addition(X_950,X_949)) = addition(X_948,addition(X_949,X_950)),
inference(resolve,[$cnf( $equal(addition(X_948,addition(X_950,X_949)),addition(addition(X_948,X_949),X_950)) )],[refute_2_19,refute_2_24]) ).
cnf(refute_2_26,plain,
( addition(X_948,addition(X_950,X_949)) != addition(X_948,addition(X_949,X_950))
| addition(X_948,addition(X_949,X_950)) = addition(X_948,addition(X_950,X_949)) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(X_948,addition(X_950,X_949)))),bind(Y,$fot(addition(X_948,addition(X_949,X_950))))]]) ).
cnf(refute_2_27,plain,
addition(X_948,addition(X_949,X_950)) = addition(X_948,addition(X_950,X_949)),
inference(resolve,[$cnf( $equal(addition(X_948,addition(X_950,X_949)),addition(X_948,addition(X_949,X_950))) )],[refute_2_25,refute_2_26]) ).
cnf(refute_2_28,plain,
addition(X_950,addition(addition(X_949,X_950),X_949)) = addition(X_950,addition(X_949,addition(X_949,X_950))),
inference(subst,[],[refute_2_27:[bind(X_948,$fot(X_950)),bind(X_949,$fot(addition(X_949,X_950))),bind(X_950,$fot(X_949))]]) ).
cnf(refute_2_29,plain,
addition(A,addition(X_948,X_949)) = addition(addition(X_948,X_949),A),
inference(subst,[],[refute_2_10:[bind(B,$fot(addition(X_948,X_949)))]]) ).
cnf(refute_2_30,plain,
addition(X_948,addition(X_949,A)) = addition(addition(X_948,X_949),A),
inference(subst,[],[refute_2_2:[bind(A,$fot(X_948)),bind(B,$fot(X_949)),bind(C,$fot(A))]]) ).
cnf(refute_2_31,plain,
( addition(X_948,addition(X_949,A)) != addition(addition(X_948,X_949),A)
| addition(addition(X_948,X_949),A) = addition(X_948,addition(X_949,A)) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(X_948,addition(X_949,A)))),bind(Y,$fot(addition(addition(X_948,X_949),A)))]]) ).
cnf(refute_2_32,plain,
addition(addition(X_948,X_949),A) = addition(X_948,addition(X_949,A)),
inference(resolve,[$cnf( $equal(addition(X_948,addition(X_949,A)),addition(addition(X_948,X_949),A)) )],[refute_2_30,refute_2_31]) ).
cnf(refute_2_33,plain,
( addition(A,addition(X_948,X_949)) != addition(addition(X_948,X_949),A)
| addition(addition(X_948,X_949),A) != addition(X_948,addition(X_949,A))
| addition(A,addition(X_948,X_949)) = addition(X_948,addition(X_949,A)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(A,addition(X_948,X_949)),addition(X_948,addition(X_949,A))) ),[0],$fot(addition(addition(X_948,X_949),A))]]) ).
cnf(refute_2_34,plain,
( addition(A,addition(X_948,X_949)) != addition(addition(X_948,X_949),A)
| addition(A,addition(X_948,X_949)) = addition(X_948,addition(X_949,A)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_948,X_949),A),addition(X_948,addition(X_949,A))) )],[refute_2_32,refute_2_33]) ).
cnf(refute_2_35,plain,
addition(A,addition(X_948,X_949)) = addition(X_948,addition(X_949,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_948,X_949)),addition(addition(X_948,X_949),A)) )],[refute_2_29,refute_2_34]) ).
cnf(refute_2_36,plain,
( addition(A,addition(X_948,X_949)) != addition(X_948,addition(X_949,A))
| addition(X_948,addition(X_949,A)) = addition(A,addition(X_948,X_949)) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(A,addition(X_948,X_949)))),bind(Y,$fot(addition(X_948,addition(X_949,A))))]]) ).
cnf(refute_2_37,plain,
addition(X_948,addition(X_949,A)) = addition(A,addition(X_948,X_949)),
inference(resolve,[$cnf( $equal(addition(A,addition(X_948,X_949)),addition(X_948,addition(X_949,A))) )],[refute_2_35,refute_2_36]) ).
cnf(refute_2_38,plain,
addition(addition(X_949,X_950),addition(X_949,X_950)) = addition(X_950,addition(addition(X_949,X_950),X_949)),
inference(subst,[],[refute_2_37:[bind(A,$fot(X_950)),bind(X_948,$fot(addition(X_949,X_950)))]]) ).
cnf(refute_2_39,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_2_40,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_2_14,refute_2_39]) ).
cnf(refute_2_41,plain,
( addition(X_950,addition(addition(X_949,X_950),X_949)) != addition(X_950,addition(X_949,addition(X_949,X_950)))
| addition(addition(X_949,X_950),addition(X_949,X_950)) != addition(X_950,addition(addition(X_949,X_950),X_949))
| addition(addition(X_949,X_950),addition(X_949,X_950)) = addition(X_950,addition(X_949,addition(X_949,X_950))) ),
inference(subst,[],[refute_2_40:[bind(X,$fot(addition(addition(X_949,X_950),addition(X_949,X_950)))),bind(Y,$fot(addition(X_950,addition(addition(X_949,X_950),X_949)))),bind(Z,$fot(addition(X_950,addition(X_949,addition(X_949,X_950)))))]]) ).
cnf(refute_2_42,plain,
( addition(X_950,addition(addition(X_949,X_950),X_949)) != addition(X_950,addition(X_949,addition(X_949,X_950)))
| addition(addition(X_949,X_950),addition(X_949,X_950)) = addition(X_950,addition(X_949,addition(X_949,X_950))) ),
inference(resolve,[$cnf( $equal(addition(addition(X_949,X_950),addition(X_949,X_950)),addition(X_950,addition(addition(X_949,X_950),X_949))) )],[refute_2_38,refute_2_41]) ).
cnf(refute_2_43,plain,
addition(addition(X_949,X_950),addition(X_949,X_950)) = addition(X_950,addition(X_949,addition(X_949,X_950))),
inference(resolve,[$cnf( $equal(addition(X_950,addition(addition(X_949,X_950),X_949)),addition(X_950,addition(X_949,addition(X_949,X_950)))) )],[refute_2_28,refute_2_42]) ).
cnf(refute_2_44,plain,
addition(addition(addition(X_949,X_950),X_949),X_950) = addition(addition(X_949,X_950),addition(X_949,X_950)),
inference(subst,[],[refute_2_21:[bind(A,$fot(addition(X_949,X_950))),bind(B,$fot(X_949)),bind(C,$fot(X_950))]]) ).
cnf(refute_2_45,plain,
( addition(addition(X_949,X_950),addition(X_949,X_950)) != addition(X_950,addition(X_949,addition(X_949,X_950)))
| addition(addition(addition(X_949,X_950),X_949),X_950) != addition(addition(X_949,X_950),addition(X_949,X_950))
| addition(addition(addition(X_949,X_950),X_949),X_950) = addition(X_950,addition(X_949,addition(X_949,X_950))) ),
inference(subst,[],[refute_2_40:[bind(X,$fot(addition(addition(addition(X_949,X_950),X_949),X_950))),bind(Y,$fot(addition(addition(X_949,X_950),addition(X_949,X_950)))),bind(Z,$fot(addition(X_950,addition(X_949,addition(X_949,X_950)))))]]) ).
cnf(refute_2_46,plain,
( addition(addition(X_949,X_950),addition(X_949,X_950)) != addition(X_950,addition(X_949,addition(X_949,X_950)))
| addition(addition(addition(X_949,X_950),X_949),X_950) = addition(X_950,addition(X_949,addition(X_949,X_950))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_949,X_950),X_949),X_950),addition(addition(X_949,X_950),addition(X_949,X_950))) )],[refute_2_44,refute_2_45]) ).
cnf(refute_2_47,plain,
addition(addition(addition(X_949,X_950),X_949),X_950) = addition(X_950,addition(X_949,addition(X_949,X_950))),
inference(resolve,[$cnf( $equal(addition(addition(X_949,X_950),addition(X_949,X_950)),addition(X_950,addition(X_949,addition(X_949,X_950)))) )],[refute_2_43,refute_2_46]) ).
cnf(refute_2_48,plain,
( addition(X_949,X_950) != addition(addition(addition(X_949,X_950),X_949),X_950)
| addition(addition(addition(X_949,X_950),X_949),X_950) != addition(X_950,addition(X_949,addition(X_949,X_950)))
| addition(X_949,X_950) = addition(X_950,addition(X_949,addition(X_949,X_950))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_949,X_950),addition(X_950,addition(X_949,addition(X_949,X_950)))) ),[0],$fot(addition(addition(addition(X_949,X_950),X_949),X_950))]]) ).
cnf(refute_2_49,plain,
( addition(X_949,X_950) != addition(addition(addition(X_949,X_950),X_949),X_950)
| addition(X_949,X_950) = addition(X_950,addition(X_949,addition(X_949,X_950))) ),
inference(resolve,[$cnf( $equal(addition(addition(addition(X_949,X_950),X_949),X_950),addition(X_950,addition(X_949,addition(X_949,X_950)))) )],[refute_2_47,refute_2_48]) ).
cnf(refute_2_50,plain,
addition(X_949,X_950) = addition(X_950,addition(X_949,addition(X_949,X_950))),
inference(resolve,[$cnf( $equal(addition(X_949,X_950),addition(addition(addition(X_949,X_950),X_949),X_950)) )],[refute_2_8,refute_2_49]) ).
cnf(refute_2_51,plain,
addition(X_949,addition(X_949,X_950)) = addition(addition(X_949,X_949),X_950),
inference(subst,[],[refute_2_2:[bind(A,$fot(X_949)),bind(B,$fot(X_949)),bind(C,$fot(X_950))]]) ).
cnf(refute_2_52,plain,
addition(X_949,X_949) = X_949,
inference(subst,[],[refute_2_4:[bind(A,$fot(X_949))]]) ).
cnf(refute_2_53,plain,
( addition(X_949,X_949) != X_949
| addition(X_949,addition(X_949,X_950)) != addition(addition(X_949,X_949),X_950)
| addition(X_949,addition(X_949,X_950)) = addition(X_949,X_950) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_949,addition(X_949,X_950)),addition(addition(X_949,X_949),X_950)) ),[1,0],$fot(X_949)]]) ).
cnf(refute_2_54,plain,
( addition(X_949,addition(X_949,X_950)) != addition(addition(X_949,X_949),X_950)
| addition(X_949,addition(X_949,X_950)) = addition(X_949,X_950) ),
inference(resolve,[$cnf( $equal(addition(X_949,X_949),X_949) )],[refute_2_52,refute_2_53]) ).
cnf(refute_2_55,plain,
addition(X_949,addition(X_949,X_950)) = addition(X_949,X_950),
inference(resolve,[$cnf( $equal(addition(X_949,addition(X_949,X_950)),addition(addition(X_949,X_949),X_950)) )],[refute_2_51,refute_2_54]) ).
cnf(refute_2_56,plain,
addition(X_950,addition(X_949,addition(X_949,X_950))) = addition(X_950,addition(X_949,addition(X_949,X_950))),
introduced(tautology,[refl,[$fot(addition(X_950,addition(X_949,addition(X_949,X_950))))]]) ).
cnf(refute_2_57,plain,
( addition(X_949,addition(X_949,X_950)) != addition(X_949,X_950)
| addition(X_950,addition(X_949,addition(X_949,X_950))) != addition(X_950,addition(X_949,addition(X_949,X_950)))
| addition(X_950,addition(X_949,addition(X_949,X_950))) = addition(X_950,addition(X_949,X_950)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_950,addition(X_949,addition(X_949,X_950))),addition(X_950,addition(X_949,addition(X_949,X_950)))) ),[1,1],$fot(addition(X_949,X_950))]]) ).
cnf(refute_2_58,plain,
( addition(X_949,addition(X_949,X_950)) != addition(X_949,X_950)
| addition(X_950,addition(X_949,addition(X_949,X_950))) = addition(X_950,addition(X_949,X_950)) ),
inference(resolve,[$cnf( $equal(addition(X_950,addition(X_949,addition(X_949,X_950))),addition(X_950,addition(X_949,addition(X_949,X_950)))) )],[refute_2_56,refute_2_57]) ).
cnf(refute_2_59,plain,
addition(X_950,addition(X_949,addition(X_949,X_950))) = addition(X_950,addition(X_949,X_950)),
inference(resolve,[$cnf( $equal(addition(X_949,addition(X_949,X_950)),addition(X_949,X_950)) )],[refute_2_55,refute_2_58]) ).
cnf(refute_2_60,plain,
( addition(X_949,X_950) != addition(X_950,addition(X_949,addition(X_949,X_950)))
| addition(X_950,addition(X_949,addition(X_949,X_950))) != addition(X_950,addition(X_949,X_950))
| addition(X_949,X_950) = addition(X_950,addition(X_949,X_950)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_949,X_950),addition(X_950,addition(X_949,X_950))) ),[0],$fot(addition(X_950,addition(X_949,addition(X_949,X_950))))]]) ).
cnf(refute_2_61,plain,
( addition(X_949,X_950) != addition(X_950,addition(X_949,addition(X_949,X_950)))
| addition(X_949,X_950) = addition(X_950,addition(X_949,X_950)) ),
inference(resolve,[$cnf( $equal(addition(X_950,addition(X_949,addition(X_949,X_950))),addition(X_950,addition(X_949,X_950))) )],[refute_2_59,refute_2_60]) ).
cnf(refute_2_62,plain,
addition(X_949,X_950) = addition(X_950,addition(X_949,X_950)),
inference(resolve,[$cnf( $equal(addition(X_949,X_950),addition(X_950,addition(X_949,addition(X_949,X_950)))) )],[refute_2_50,refute_2_61]) ).
cnf(refute_2_63,plain,
addition(X_949,X_988) = addition(X_988,addition(X_949,X_988)),
inference(subst,[],[refute_2_62:[bind(X_950,$fot(X_988))]]) ).
cnf(refute_2_64,plain,
( addition(X_949,X_988) != addition(X_988,addition(X_949,X_988))
| addition(X_988,addition(X_949,X_988)) = addition(X_949,X_988) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(X_949,X_988))),bind(Y,$fot(addition(X_988,addition(X_949,X_988))))]]) ).
cnf(refute_2_65,plain,
addition(X_988,addition(X_949,X_988)) = addition(X_949,X_988),
inference(resolve,[$cnf( $equal(addition(X_949,X_988),addition(X_988,addition(X_949,X_988))) )],[refute_2_63,refute_2_64]) ).
cnf(refute_2_66,plain,
( addition(X_949,X_988) != addition(X_949,X_988)
| addition(X_988,addition(X_949,X_988)) != addition(X_949,X_988)
| addition(X_988,addition(X_949,X_988)) = addition(X_949,X_988) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_988,addition(X_949,X_988)),addition(X_949,X_988)) ),[0,1],$fot(addition(X_949,X_988))]]) ).
cnf(refute_2_67,plain,
( addition(X_949,X_988) != addition(X_949,X_988)
| addition(X_988,addition(X_949,X_988)) = addition(X_949,X_988) ),
inference(resolve,[$cnf( $equal(addition(X_988,addition(X_949,X_988)),addition(X_949,X_988)) )],[refute_2_65,refute_2_66]) ).
cnf(refute_2_68,plain,
( addition(X_949,X_988) != addition(X_949,X_988)
| leq(X_988,addition(X_949,X_988)) ),
inference(resolve,[$cnf( $equal(addition(X_988,addition(X_949,X_988)),addition(X_949,X_988)) )],[refute_2_67,refute_2_1]) ).
cnf(refute_2_69,plain,
addition(X_949,X_988) = addition(X_949,X_988),
introduced(tautology,[refl,[$fot(addition(X_949,X_988))]]) ).
cnf(refute_2_70,plain,
leq(X_988,addition(X_949,X_988)),
inference(resolve,[$cnf( $equal(addition(X_949,X_988),addition(X_949,X_988)) )],[refute_2_69,refute_2_68]) ).
cnf(refute_2_71,plain,
leq(X_995,addition(X_994,X_995)),
inference(subst,[],[refute_2_70:[bind(X_949,$fot(X_994)),bind(X_988,$fot(X_995))]]) ).
cnf(refute_2_72,plain,
addition(X_995,X_994) = addition(X_994,X_995),
inference(subst,[],[refute_2_10:[bind(A,$fot(X_995)),bind(B,$fot(X_994))]]) ).
cnf(refute_2_73,plain,
( addition(X_995,X_994) != addition(X_994,X_995)
| addition(X_994,X_995) = addition(X_995,X_994) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(X_995,X_994))),bind(Y,$fot(addition(X_994,X_995)))]]) ).
cnf(refute_2_74,plain,
addition(X_994,X_995) = addition(X_995,X_994),
inference(resolve,[$cnf( $equal(addition(X_995,X_994),addition(X_994,X_995)) )],[refute_2_72,refute_2_73]) ).
cnf(refute_2_75,plain,
( addition(X_994,X_995) != addition(X_995,X_994)
| ~ leq(X_995,addition(X_994,X_995))
| leq(X_995,addition(X_995,X_994)) ),
introduced(tautology,[equality,[$cnf( leq(X_995,addition(X_994,X_995)) ),[1],$fot(addition(X_995,X_994))]]) ).
cnf(refute_2_76,plain,
( ~ leq(X_995,addition(X_994,X_995))
| leq(X_995,addition(X_995,X_994)) ),
inference(resolve,[$cnf( $equal(addition(X_994,X_995),addition(X_995,X_994)) )],[refute_2_74,refute_2_75]) ).
cnf(refute_2_77,plain,
leq(X_995,addition(X_995,X_994)),
inference(resolve,[$cnf( leq(X_995,addition(X_994,X_995)) )],[refute_2_71,refute_2_76]) ).
cnf(refute_2_78,plain,
leq(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))),
inference(subst,[],[refute_2_77:[bind(X_994,$fot(multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))),bind(X_995,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_79,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_80,plain,
multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) = addition(multiplication(skolemFOFtoCNF_X0_2,B),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)),
inference(subst,[],[refute_2_79:[bind(A,$fot(skolemFOFtoCNF_X0_2)),bind(C,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_81,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_2_13]) ).
cnf(refute_2_82,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) = addition(multiplication(A,skolemFOFtoCNF_X2_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2)),
inference(subst,[],[refute_2_81:[bind(B,$fot(c(skolemFOFtoCNF_X2_2))),bind(C,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_83,plain,
test(skolemFOFtoCNF_X2_2),
inference(canonicalize,[],[normalize_2_16]) ).
cnf(refute_2_84,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_2_20]) ).
cnf(refute_2_85,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_2_84:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_2_86,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_2_87,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_2_86,refute_2_85]) ).
cnf(refute_2_88,plain,
( ~ test(skolemFOFtoCNF_X2_2)
| complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) ),
inference(subst,[],[refute_2_87:[bind(X0,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_89,plain,
complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X2_2) )],[refute_2_83,refute_2_88]) ).
cnf(refute_2_90,plain,
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(canonicalize,[],[normalize_2_24]) ).
cnf(refute_2_91,plain,
( ~ complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2))
| multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) = zero ),
inference(subst,[],[refute_2_90:[bind(X0,$fot(c(skolemFOFtoCNF_X2_2))),bind(X1,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_92,plain,
multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) )],[refute_2_89,refute_2_91]) ).
cnf(refute_2_93,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) != addition(multiplication(A,skolemFOFtoCNF_X2_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2))
| multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) != zero
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) = addition(multiplication(A,skolemFOFtoCNF_X2_2),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2),addition(multiplication(A,skolemFOFtoCNF_X2_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2))) ),[1,1],$fot(zero)]]) ).
cnf(refute_2_94,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) != addition(multiplication(A,skolemFOFtoCNF_X2_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2))
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) = addition(multiplication(A,skolemFOFtoCNF_X2_2),zero) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2),zero) )],[refute_2_92,refute_2_93]) ).
cnf(refute_2_95,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) = addition(multiplication(A,skolemFOFtoCNF_X2_2),zero),
inference(resolve,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2),addition(multiplication(A,skolemFOFtoCNF_X2_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2))) )],[refute_2_82,refute_2_94]) ).
cnf(refute_2_96,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_2_26]) ).
cnf(refute_2_97,plain,
addition(multiplication(A,skolemFOFtoCNF_X2_2),zero) = multiplication(A,skolemFOFtoCNF_X2_2),
inference(subst,[],[refute_2_96:[bind(A,$fot(multiplication(A,skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_98,plain,
( addition(multiplication(A,skolemFOFtoCNF_X2_2),zero) != multiplication(A,skolemFOFtoCNF_X2_2)
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) != addition(multiplication(A,skolemFOFtoCNF_X2_2),zero)
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) = multiplication(A,skolemFOFtoCNF_X2_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2),addition(multiplication(A,skolemFOFtoCNF_X2_2),zero)) ),[1],$fot(multiplication(A,skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_99,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) != addition(multiplication(A,skolemFOFtoCNF_X2_2),zero)
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) = multiplication(A,skolemFOFtoCNF_X2_2) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,skolemFOFtoCNF_X2_2),zero),multiplication(A,skolemFOFtoCNF_X2_2)) )],[refute_2_97,refute_2_98]) ).
cnf(refute_2_100,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) = multiplication(A,skolemFOFtoCNF_X2_2),
inference(resolve,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2),addition(multiplication(A,skolemFOFtoCNF_X2_2),zero)) )],[refute_2_95,refute_2_99]) ).
cnf(refute_2_101,plain,
multiplication(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2),
inference(subst,[],[refute_2_100:[bind(A,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_102,plain,
addition(A,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) = addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,A)),
inference(subst,[],[refute_2_35:[bind(X_948,$fot(skolemFOFtoCNF_X0_2)),bind(X_949,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_103,plain,
leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),
inference(canonicalize,[],[normalize_2_27]) ).
cnf(refute_2_104,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_2_28]) ).
cnf(refute_2_105,plain,
( ~ leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)
| addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) = skolemFOFtoCNF_X0_2 ),
inference(subst,[],[refute_2_104:[bind(A,$fot(skolemFOFtoCNF_X2_2)),bind(B,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_106,plain,
addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) = skolemFOFtoCNF_X0_2,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) )],[refute_2_103,refute_2_105]) ).
cnf(refute_2_107,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_2_108,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_2_10,refute_2_107]) ).
cnf(refute_2_109,plain,
addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2),
inference(subst,[],[refute_2_108:[bind(A,$fot(skolemFOFtoCNF_X0_2)),bind(B,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_110,plain,
( addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) != addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)
| addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) != skolemFOFtoCNF_X0_2
| addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X0_2 ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) ),[0],$fot(addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_111,plain,
( addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) != skolemFOFtoCNF_X0_2
| addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X0_2 ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) )],[refute_2_109,refute_2_110]) ).
cnf(refute_2_112,plain,
addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X0_2,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) )],[refute_2_106,refute_2_111]) ).
cnf(refute_2_113,plain,
( addition(A,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) != addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,A))
| addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) != skolemFOFtoCNF_X0_2
| addition(A,skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,A)) ),
introduced(tautology,[equality,[$cnf( $equal(addition(A,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)),addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,A))) ),[0,1],$fot(skolemFOFtoCNF_X0_2)]]) ).
cnf(refute_2_114,plain,
( addition(A,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) != addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,A))
| addition(A,skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,A)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) )],[refute_2_112,refute_2_113]) ).
cnf(refute_2_115,plain,
addition(A,skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,A)),
inference(resolve,[$cnf( $equal(addition(A,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)),addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,A))) )],[refute_2_102,refute_2_114]) ).
cnf(refute_2_116,plain,
addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2))),
inference(subst,[],[refute_2_115:[bind(A,$fot(c(skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_117,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_2_29]) ).
cnf(refute_2_118,plain,
( ~ complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2))
| addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) = one ),
inference(subst,[],[refute_2_117:[bind(X0,$fot(c(skolemFOFtoCNF_X2_2))),bind(X1,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_119,plain,
addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) )],[refute_2_89,refute_2_118]) ).
cnf(refute_2_120,plain,
addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) = addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),
inference(subst,[],[refute_2_108:[bind(A,$fot(skolemFOFtoCNF_X2_2)),bind(B,$fot(c(skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_121,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) != addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2))
| addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) != one
| addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2),one) ),[0],$fot(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_122,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) != one
| addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2),addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2))) )],[refute_2_120,refute_2_121]) ).
cnf(refute_2_123,plain,
addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2),one) )],[refute_2_119,refute_2_122]) ).
cnf(refute_2_124,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) != addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)))
| addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) != one
| addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)))) ),[1,1],$fot(one)]]) ).
cnf(refute_2_125,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) != addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)))
| addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,one) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),one) )],[refute_2_123,refute_2_124]) ).
cnf(refute_2_126,plain,
addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,one),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)))) )],[refute_2_116,refute_2_125]) ).
cnf(refute_2_127,plain,
addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),
inference(subst,[],[refute_2_108:[bind(A,$fot(skolemFOFtoCNF_X0_2)),bind(B,$fot(c(skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_128,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) != addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2))
| addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) != addition(skolemFOFtoCNF_X0_2,one)
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) = addition(skolemFOFtoCNF_X0_2,one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),addition(skolemFOFtoCNF_X0_2,one)) ),[0],$fot(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_129,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) != addition(skolemFOFtoCNF_X0_2,one)
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) = addition(skolemFOFtoCNF_X0_2,one) ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2))) )],[refute_2_127,refute_2_128]) ).
cnf(refute_2_130,plain,
addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) = addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)),
inference(subst,[],[refute_2_55:[bind(X_949,$fot(skolemFOFtoCNF_X0_2)),bind(X_950,$fot(c(skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_131,plain,
test(skolemFOFtoCNF_X0_2),
inference(canonicalize,[],[normalize_2_30]) ).
cnf(refute_2_132,plain,
( ~ test(skolemFOFtoCNF_X0_2)
| complement(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)) ),
inference(subst,[],[refute_2_87:[bind(X0,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_133,plain,
complement(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X0_2) )],[refute_2_131,refute_2_132]) ).
cnf(refute_2_134,plain,
( ~ complement(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))
| addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) = one ),
inference(subst,[],[refute_2_117:[bind(X0,$fot(c(skolemFOFtoCNF_X0_2))),bind(X1,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_135,plain,
addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)) )],[refute_2_133,refute_2_134]) ).
cnf(refute_2_136,plain,
addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) = addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)),
inference(subst,[],[refute_2_108:[bind(A,$fot(skolemFOFtoCNF_X0_2)),bind(B,$fot(c(skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_137,plain,
( addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) != addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))
| addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) != one
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2),one) ),[0],$fot(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_138,plain,
( addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) != one
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2),addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) )],[refute_2_136,refute_2_137]) ).
cnf(refute_2_139,plain,
addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2),one) )],[refute_2_135,refute_2_138]) ).
cnf(refute_2_140,plain,
( addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) != addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)) != one
| addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))),one) ),[0],$fot(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_141,plain,
( addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) != addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))
| addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) = one ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)),one) )],[refute_2_139,refute_2_140]) ).
cnf(refute_2_142,plain,
addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) = one,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))),addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) )],[refute_2_130,refute_2_141]) ).
cnf(refute_2_143,plain,
addition(skolemFOFtoCNF_X0_2,one) = addition(one,skolemFOFtoCNF_X0_2),
inference(subst,[],[refute_2_108:[bind(A,$fot(one)),bind(B,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_144,plain,
addition(X_949,X_948) = addition(X_948,X_949),
inference(subst,[],[refute_2_10:[bind(A,$fot(X_949)),bind(B,$fot(X_948))]]) ).
cnf(refute_2_145,plain,
( addition(X_949,X_948) != addition(X_948,X_949)
| addition(X_948,X_949) = addition(X_949,X_948) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(addition(X_949,X_948))),bind(Y,$fot(addition(X_948,X_949)))]]) ).
cnf(refute_2_146,plain,
addition(X_948,X_949) = addition(X_949,X_948),
inference(resolve,[$cnf( $equal(addition(X_949,X_948),addition(X_948,X_949)) )],[refute_2_144,refute_2_145]) ).
cnf(refute_2_147,plain,
( addition(X_948,X_949) != addition(X_949,X_948)
| addition(X_948,addition(X_949,X_950)) != addition(addition(X_948,X_949),X_950)
| addition(X_948,addition(X_949,X_950)) = addition(addition(X_949,X_948),X_950) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_948,addition(X_949,X_950)),addition(addition(X_948,X_949),X_950)) ),[1,0],$fot(addition(X_949,X_948))]]) ).
cnf(refute_2_148,plain,
( addition(X_948,addition(X_949,X_950)) != addition(addition(X_948,X_949),X_950)
| addition(X_948,addition(X_949,X_950)) = addition(addition(X_949,X_948),X_950) ),
inference(resolve,[$cnf( $equal(addition(X_948,X_949),addition(X_949,X_948)) )],[refute_2_146,refute_2_147]) ).
cnf(refute_2_149,plain,
addition(X_948,addition(X_949,X_950)) = addition(addition(X_949,X_948),X_950),
inference(resolve,[$cnf( $equal(addition(X_948,addition(X_949,X_950)),addition(addition(X_948,X_949),X_950)) )],[refute_2_9,refute_2_148]) ).
cnf(refute_2_150,plain,
addition(addition(X_949,X_948),X_950) = addition(X_949,addition(X_948,X_950)),
inference(subst,[],[refute_2_21:[bind(A,$fot(X_949)),bind(B,$fot(X_948)),bind(C,$fot(X_950))]]) ).
cnf(refute_2_151,plain,
( addition(X_948,addition(X_949,X_950)) != addition(addition(X_949,X_948),X_950)
| addition(addition(X_949,X_948),X_950) != addition(X_949,addition(X_948,X_950))
| addition(X_948,addition(X_949,X_950)) = addition(X_949,addition(X_948,X_950)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(X_948,addition(X_949,X_950)),addition(X_949,addition(X_948,X_950))) ),[0],$fot(addition(addition(X_949,X_948),X_950))]]) ).
cnf(refute_2_152,plain,
( addition(X_948,addition(X_949,X_950)) != addition(addition(X_949,X_948),X_950)
| addition(X_948,addition(X_949,X_950)) = addition(X_949,addition(X_948,X_950)) ),
inference(resolve,[$cnf( $equal(addition(addition(X_949,X_948),X_950),addition(X_949,addition(X_948,X_950))) )],[refute_2_150,refute_2_151]) ).
cnf(refute_2_153,plain,
addition(X_948,addition(X_949,X_950)) = addition(X_949,addition(X_948,X_950)),
inference(resolve,[$cnf( $equal(addition(X_948,addition(X_949,X_950)),addition(addition(X_949,X_948),X_950)) )],[refute_2_149,refute_2_152]) ).
cnf(refute_2_154,plain,
addition(skolemFOFtoCNF_X0_2,addition(X_949,c(skolemFOFtoCNF_X0_2))) = addition(X_949,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))),
inference(subst,[],[refute_2_153:[bind(X_948,$fot(skolemFOFtoCNF_X0_2)),bind(X_950,$fot(c(skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_155,plain,
( addition(skolemFOFtoCNF_X0_2,addition(X_949,c(skolemFOFtoCNF_X0_2))) != addition(X_949,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)))
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)) != one
| addition(skolemFOFtoCNF_X0_2,addition(X_949,c(skolemFOFtoCNF_X0_2))) = addition(X_949,one) ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,addition(X_949,c(skolemFOFtoCNF_X0_2))),addition(X_949,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)))) ),[1,1],$fot(one)]]) ).
cnf(refute_2_156,plain,
( addition(skolemFOFtoCNF_X0_2,addition(X_949,c(skolemFOFtoCNF_X0_2))) != addition(X_949,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)))
| addition(skolemFOFtoCNF_X0_2,addition(X_949,c(skolemFOFtoCNF_X0_2))) = addition(X_949,one) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)),one) )],[refute_2_139,refute_2_155]) ).
cnf(refute_2_157,plain,
addition(skolemFOFtoCNF_X0_2,addition(X_949,c(skolemFOFtoCNF_X0_2))) = addition(X_949,one),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,addition(X_949,c(skolemFOFtoCNF_X0_2))),addition(X_949,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2)))) )],[refute_2_154,refute_2_156]) ).
cnf(refute_2_158,plain,
addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) = addition(skolemFOFtoCNF_X0_2,one),
inference(subst,[],[refute_2_157:[bind(X_949,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_159,plain,
( addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) != addition(skolemFOFtoCNF_X0_2,one)
| addition(skolemFOFtoCNF_X0_2,one) != addition(one,skolemFOFtoCNF_X0_2)
| addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) = addition(one,skolemFOFtoCNF_X0_2) ),
inference(subst,[],[refute_2_40:[bind(X,$fot(addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))))),bind(Y,$fot(addition(skolemFOFtoCNF_X0_2,one))),bind(Z,$fot(addition(one,skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_160,plain,
( addition(skolemFOFtoCNF_X0_2,one) != addition(one,skolemFOFtoCNF_X0_2)
| addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) = addition(one,skolemFOFtoCNF_X0_2) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))),addition(skolemFOFtoCNF_X0_2,one)) )],[refute_2_158,refute_2_159]) ).
cnf(refute_2_161,plain,
addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) = addition(one,skolemFOFtoCNF_X0_2),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,one),addition(one,skolemFOFtoCNF_X0_2)) )],[refute_2_143,refute_2_160]) ).
cnf(refute_2_162,plain,
( addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) != addition(one,skolemFOFtoCNF_X0_2)
| addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) != one
| addition(one,skolemFOFtoCNF_X0_2) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))),one) ),[0],$fot(addition(one,skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_163,plain,
( addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))) != one
| addition(one,skolemFOFtoCNF_X0_2) = one ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))),addition(one,skolemFOFtoCNF_X0_2)) )],[refute_2_161,refute_2_162]) ).
cnf(refute_2_164,plain,
addition(one,skolemFOFtoCNF_X0_2) = one,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X0_2))),one) )],[refute_2_142,refute_2_163]) ).
cnf(refute_2_165,plain,
( addition(one,skolemFOFtoCNF_X0_2) != one
| addition(skolemFOFtoCNF_X0_2,one) != addition(one,skolemFOFtoCNF_X0_2)
| addition(skolemFOFtoCNF_X0_2,one) = one ),
inference(subst,[],[refute_2_40:[bind(X,$fot(addition(skolemFOFtoCNF_X0_2,one))),bind(Y,$fot(addition(one,skolemFOFtoCNF_X0_2))),bind(Z,$fot(one))]]) ).
cnf(refute_2_166,plain,
( addition(one,skolemFOFtoCNF_X0_2) != one
| addition(skolemFOFtoCNF_X0_2,one) = one ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,one),addition(one,skolemFOFtoCNF_X0_2)) )],[refute_2_143,refute_2_165]) ).
cnf(refute_2_167,plain,
addition(skolemFOFtoCNF_X0_2,one) = one,
inference(resolve,[$cnf( $equal(addition(one,skolemFOFtoCNF_X0_2),one) )],[refute_2_164,refute_2_166]) ).
cnf(refute_2_168,plain,
( addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) != addition(skolemFOFtoCNF_X0_2,one)
| addition(skolemFOFtoCNF_X0_2,one) != one
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) = one ),
introduced(tautology,[equality,[$cnf( ~ $equal(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),one) ),[0],$fot(addition(skolemFOFtoCNF_X0_2,one))]]) ).
cnf(refute_2_169,plain,
( addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) != addition(skolemFOFtoCNF_X0_2,one)
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) = one ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,one),one) )],[refute_2_167,refute_2_168]) ).
cnf(refute_2_170,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) != addition(skolemFOFtoCNF_X0_2,one)
| addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) = one ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),addition(skolemFOFtoCNF_X0_2,one)) )],[refute_2_129,refute_2_169]) ).
cnf(refute_2_171,plain,
addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),addition(skolemFOFtoCNF_X0_2,one)) )],[refute_2_126,refute_2_170]) ).
cnf(refute_2_172,plain,
( addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)) != one
| multiplication(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) != multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)
| multiplication(one,skolemFOFtoCNF_X2_2) = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) ),[0,0],$fot(one)]]) ).
cnf(refute_2_173,plain,
( multiplication(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2) != multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)
| multiplication(one,skolemFOFtoCNF_X2_2) = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),one) )],[refute_2_171,refute_2_172]) ).
cnf(refute_2_174,plain,
multiplication(one,skolemFOFtoCNF_X2_2) = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X2_2),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) )],[refute_2_101,refute_2_173]) ).
cnf(refute_2_175,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_2_32]) ).
cnf(refute_2_176,plain,
multiplication(one,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X2_2,
inference(subst,[],[refute_2_175:[bind(A,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_177,plain,
( multiplication(one,skolemFOFtoCNF_X2_2) != multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)
| multiplication(one,skolemFOFtoCNF_X2_2) != skolemFOFtoCNF_X2_2
| skolemFOFtoCNF_X2_2 = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X2_2),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) ),[0],$fot(skolemFOFtoCNF_X2_2)]]) ).
cnf(refute_2_178,plain,
( multiplication(one,skolemFOFtoCNF_X2_2) != multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)
| skolemFOFtoCNF_X2_2 = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) )],[refute_2_176,refute_2_177]) ).
cnf(refute_2_179,plain,
skolemFOFtoCNF_X2_2 = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X2_2),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) )],[refute_2_174,refute_2_178]) ).
cnf(refute_2_180,plain,
( skolemFOFtoCNF_X2_2 != multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)
| multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X2_2 ),
inference(subst,[],[refute_2_14:[bind(X,$fot(skolemFOFtoCNF_X2_2)),bind(Y,$fot(multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_181,plain,
multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X2_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2)) )],[refute_2_179,refute_2_180]) ).
cnf(refute_2_182,plain,
( multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) != addition(multiplication(skolemFOFtoCNF_X0_2,B),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2))
| multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2) != skolemFOFtoCNF_X2_2
| multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) = addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)),addition(multiplication(skolemFOFtoCNF_X0_2,B),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2))) ),[1,1],$fot(skolemFOFtoCNF_X2_2)]]) ).
cnf(refute_2_183,plain,
( multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) != addition(multiplication(skolemFOFtoCNF_X0_2,B),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2))
| multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) = addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) )],[refute_2_181,refute_2_182]) ).
cnf(refute_2_184,plain,
multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) = addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)),addition(multiplication(skolemFOFtoCNF_X0_2,B),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X2_2))) )],[refute_2_80,refute_2_183]) ).
cnf(refute_2_185,plain,
addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2) = addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,B)),
inference(subst,[],[refute_2_108:[bind(A,$fot(skolemFOFtoCNF_X2_2)),bind(B,$fot(multiplication(skolemFOFtoCNF_X0_2,B)))]]) ).
cnf(refute_2_186,plain,
( addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2) != addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,B))
| multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) != addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2)
| multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) = addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,B)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)),addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2)) ),[1],$fot(addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,B)))]]) ).
cnf(refute_2_187,plain,
( multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) != addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2)
| multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) = addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,B)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2),addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,B))) )],[refute_2_185,refute_2_186]) ).
cnf(refute_2_188,plain,
multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)) = addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,B)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0_2,addition(B,skolemFOFtoCNF_X2_2)),addition(multiplication(skolemFOFtoCNF_X0_2,B),skolemFOFtoCNF_X2_2)) )],[refute_2_184,refute_2_187]) ).
cnf(refute_2_189,plain,
multiplication(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2)) = addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)),
inference(subst,[],[refute_2_188:[bind(B,$fot(skolemFOFtoCNF_X1_3))]]) ).
cnf(refute_2_190,plain,
leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3),
inference(canonicalize,[],[normalize_2_33]) ).
cnf(refute_2_191,plain,
( ~ leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)
| addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) = skolemFOFtoCNF_X1_3 ),
inference(subst,[],[refute_2_104:[bind(A,$fot(skolemFOFtoCNF_X2_2)),bind(B,$fot(skolemFOFtoCNF_X1_3))]]) ).
cnf(refute_2_192,plain,
addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) = skolemFOFtoCNF_X1_3,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) )],[refute_2_190,refute_2_191]) ).
cnf(refute_2_193,plain,
addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) = addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2),
inference(subst,[],[refute_2_108:[bind(A,$fot(skolemFOFtoCNF_X1_3)),bind(B,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_194,plain,
( addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) != addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2)
| addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) != skolemFOFtoCNF_X1_3
| addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X1_3 ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3),skolemFOFtoCNF_X1_3) ),[0],$fot(addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_195,plain,
( addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) != skolemFOFtoCNF_X1_3
| addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X1_3 ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3),addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2)) )],[refute_2_193,refute_2_194]) ).
cnf(refute_2_196,plain,
addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2) = skolemFOFtoCNF_X1_3,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3),skolemFOFtoCNF_X1_3) )],[refute_2_192,refute_2_195]) ).
cnf(refute_2_197,plain,
( addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2) != skolemFOFtoCNF_X1_3
| multiplication(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2)) != addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))
| multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) = addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2)),addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))) ),[0,1],$fot(skolemFOFtoCNF_X1_3)]]) ).
cnf(refute_2_198,plain,
( multiplication(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2)) != addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))
| multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) = addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X1_3) )],[refute_2_196,refute_2_197]) ).
cnf(refute_2_199,plain,
multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) = addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X1_3,skolemFOFtoCNF_X2_2)),addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))) )],[refute_2_189,refute_2_198]) ).
cnf(refute_2_200,plain,
( multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) != addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))
| addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) ),
inference(subst,[],[refute_2_14:[bind(X,$fot(multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))),bind(Y,$fot(addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))))]]) ).
cnf(refute_2_201,plain,
addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) = multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3),addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))) )],[refute_2_199,refute_2_200]) ).
cnf(refute_2_202,plain,
( addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) != multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)
| ~ leq(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)))
| leq(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))) ),[1],$fot(multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))]]) ).
cnf(refute_2_203,plain,
( ~ leq(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)))
| leq(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)),multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) )],[refute_2_201,refute_2_202]) ).
cnf(refute_2_204,plain,
leq(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3))) )],[refute_2_78,refute_2_203]) ).
cnf(refute_2_205,plain,
~ leq(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)),
inference(canonicalize,[],[normalize_2_34]) ).
cnf(refute_2_206,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X2_2,multiplication(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) )],[refute_2_204,refute_2_205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE017+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 10:23:04 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 57.63/57.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.63/57.80
% 57.63/57.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.63/57.83
%------------------------------------------------------------------------------