TSTP Solution File: KLE008+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE008+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 02:14:32 EDT 2022
% Result : Theorem 13.39s 13.57s
% Output : CNFRefutation 13.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 59
% Syntax : Number of formulae : 361 ( 189 unt; 0 def)
% Number of atoms : 658 ( 381 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 570 ( 273 ~; 222 |; 44 &)
% ( 23 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 1 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 : 502 ( 30 sgn 193 !; 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_associativity,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(left_distributivity,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ).
fof(left_annihilation,axiom,
! [A] : multiplication(zero,A) = zero ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(test_1,axiom,
! [X0] :
( test(X0)
<=> ? [X1] : complement(X1,X0) ) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
! [X0,X1,X2] :
( test(X2)
=> ( leq(X0,multiplication(X2,X1))
<=> ( leq(X0,X1)
& leq(multiplication(c(X2),X0),zero) ) ) ) ).
fof(subgoal_0,plain,
! [X0,X1,X2] :
( ( test(X2)
& leq(X0,multiplication(X2,X1)) )
=> leq(X0,X1) ),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1,X2] :
( ( test(X2)
& leq(X0,multiplication(X2,X1))
& leq(X0,X1) )
=> leq(multiplication(c(X2),X0),zero) ),
inference(strip,[],[goals]) ).
fof(subgoal_2,plain,
! [X0,X1,X2] :
( ( test(X2)
& leq(X0,X1)
& leq(multiplication(c(X2),X0),zero) )
=> leq(X0,multiplication(X2,X1)) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1,X2] :
( ( test(X2)
& leq(X0,multiplication(X2,X1)) )
=> leq(X0,X1) ),
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(X0,X1)
& leq(X0,multiplication(X2,X1))
& test(X2) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( ~ leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1)
& leq(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))
& test(skolemFOFtoCNF_X2) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
leq(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,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(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_0_15,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_17,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
test(skolemFOFtoCNF_X2),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_19,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(canonicalize,[],[test_1]) ).
fof(normalize_0_20,plain,
! [X0] :
( ~ test(X0)
<=> ! [X1] : ~ complement(X1,X0) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X0,X1] :
( ( ~ complement(X1,X0)
| test(X0) )
& ( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X0] :
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,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_24,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,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_24]) ).
fof(normalize_0_26,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
~ leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),
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_20,addition(X_20,X_16)) != addition(X_20,X_16)
| leq(X_20,addition(X_20,X_16)) ),
inference(subst,[],[refute_0_0:[bind(A,$fot(X_20)),bind(B,$fot(addition(X_20,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( $equal(addition(X_15,addition(X_15,X_16)),addition(addition(X_15,X_15),X_16)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
addition(X_20,addition(X_20,X_16)) = addition(X_20,X_16),
inference(subst,[],[refute_0_8:[bind(X_15,$fot(X_20))]]) ).
cnf(refute_0_10,plain,
( addition(X_20,X_16) != addition(X_20,X_16)
| addition(X_20,addition(X_20,X_16)) != addition(X_20,X_16)
| addition(X_20,addition(X_20,X_16)) = addition(X_20,X_16) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_20,addition(X_20,X_16)),addition(X_20,X_16)) ),[0,1],$fot(addition(X_20,X_16))]]) ).
cnf(refute_0_11,plain,
( addition(X_20,X_16) != addition(X_20,X_16)
| addition(X_20,addition(X_20,X_16)) = addition(X_20,X_16) ),
inference(resolve,[$cnf( $equal(addition(X_20,addition(X_20,X_16)),addition(X_20,X_16)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( addition(X_20,X_16) != addition(X_20,X_16)
| leq(X_20,addition(X_20,X_16)) ),
inference(resolve,[$cnf( $equal(addition(X_20,addition(X_20,X_16)),addition(X_20,X_16)) )],[refute_0_11,refute_0_1]) ).
cnf(refute_0_13,plain,
addition(X_20,X_16) = addition(X_20,X_16),
introduced(tautology,[refl,[$fot(addition(X_20,X_16))]]) ).
cnf(refute_0_14,plain,
leq(X_20,addition(X_20,X_16)),
inference(resolve,[$cnf( $equal(addition(X_20,X_16),addition(X_20,X_16)) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
leq(X_25,addition(X_25,X_24)),
inference(subst,[],[refute_0_14:[bind(X_16,$fot(X_24)),bind(X_20,$fot(X_25))]]) ).
cnf(refute_0_16,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_17,plain,
addition(X_24,X_25) = addition(X_25,X_24),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_24)),bind(B,$fot(X_25))]]) ).
cnf(refute_0_18,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_19,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_20,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( addition(X_24,X_25) != addition(X_25,X_24)
| addition(X_25,X_24) = addition(X_24,X_25) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_24,X_25))),bind(Y,$fot(addition(X_25,X_24)))]]) ).
cnf(refute_0_22,plain,
addition(X_25,X_24) = addition(X_24,X_25),
inference(resolve,[$cnf( $equal(addition(X_24,X_25),addition(X_25,X_24)) )],[refute_0_17,refute_0_21]) ).
cnf(refute_0_23,plain,
( addition(X_25,X_24) != addition(X_24,X_25)
| ~ leq(X_25,addition(X_25,X_24))
| leq(X_25,addition(X_24,X_25)) ),
introduced(tautology,[equality,[$cnf( leq(X_25,addition(X_25,X_24)) ),[1],$fot(addition(X_24,X_25))]]) ).
cnf(refute_0_24,plain,
( ~ leq(X_25,addition(X_25,X_24))
| leq(X_25,addition(X_24,X_25)) ),
inference(resolve,[$cnf( $equal(addition(X_25,X_24),addition(X_24,X_25)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
leq(X_25,addition(X_24,X_25)),
inference(resolve,[$cnf( leq(X_25,addition(X_25,X_24)) )],[refute_0_15,refute_0_24]) ).
cnf(refute_0_26,plain,
leq(X_27,addition(addition(A,B),X_27)),
inference(subst,[],[refute_0_25:[bind(X_24,$fot(addition(A,B))),bind(X_25,$fot(X_27))]]) ).
cnf(refute_0_27,plain,
addition(A,addition(B,X_27)) = addition(addition(A,B),X_27),
inference(subst,[],[refute_0_2:[bind(C,$fot(X_27))]]) ).
cnf(refute_0_28,plain,
( addition(A,addition(B,X_27)) != addition(addition(A,B),X_27)
| addition(addition(A,B),X_27) = addition(A,addition(B,X_27)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(A,addition(B,X_27)))),bind(Y,$fot(addition(addition(A,B),X_27)))]]) ).
cnf(refute_0_29,plain,
addition(addition(A,B),X_27) = addition(A,addition(B,X_27)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,X_27)),addition(addition(A,B),X_27)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( addition(addition(A,B),X_27) != addition(A,addition(B,X_27))
| ~ leq(X_27,addition(addition(A,B),X_27))
| leq(X_27,addition(A,addition(B,X_27))) ),
introduced(tautology,[equality,[$cnf( leq(X_27,addition(addition(A,B),X_27)) ),[1],$fot(addition(A,addition(B,X_27)))]]) ).
cnf(refute_0_31,plain,
( ~ leq(X_27,addition(addition(A,B),X_27))
| leq(X_27,addition(A,addition(B,X_27))) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),X_27),addition(A,addition(B,X_27))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
leq(X_27,addition(A,addition(B,X_27))),
inference(resolve,[$cnf( leq(X_27,addition(addition(A,B),X_27)) )],[refute_0_26,refute_0_31]) ).
cnf(refute_0_33,plain,
leq(X_30,addition(X_28,addition(X_29,X_30))),
inference(subst,[],[refute_0_32:[bind(A,$fot(X_28)),bind(B,$fot(X_29)),bind(X_27,$fot(X_30))]]) ).
cnf(refute_0_34,plain,
addition(X_30,X_29) = addition(X_29,X_30),
inference(subst,[],[refute_0_16:[bind(A,$fot(X_30)),bind(B,$fot(X_29))]]) ).
cnf(refute_0_35,plain,
( addition(X_30,X_29) != addition(X_29,X_30)
| addition(X_29,X_30) = addition(X_30,X_29) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(X_30,X_29))),bind(Y,$fot(addition(X_29,X_30)))]]) ).
cnf(refute_0_36,plain,
addition(X_29,X_30) = addition(X_30,X_29),
inference(resolve,[$cnf( $equal(addition(X_30,X_29),addition(X_29,X_30)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( addition(X_29,X_30) != addition(X_30,X_29)
| ~ leq(X_30,addition(X_28,addition(X_29,X_30)))
| leq(X_30,addition(X_28,addition(X_30,X_29))) ),
introduced(tautology,[equality,[$cnf( leq(X_30,addition(X_28,addition(X_29,X_30))) ),[1,1],$fot(addition(X_30,X_29))]]) ).
cnf(refute_0_38,plain,
( ~ leq(X_30,addition(X_28,addition(X_29,X_30)))
| leq(X_30,addition(X_28,addition(X_30,X_29))) ),
inference(resolve,[$cnf( $equal(addition(X_29,X_30),addition(X_30,X_29)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
leq(X_30,addition(X_28,addition(X_30,X_29))),
inference(resolve,[$cnf( leq(X_30,addition(X_28,addition(X_29,X_30))) )],[refute_0_33,refute_0_38]) ).
cnf(refute_0_40,plain,
leq(skolemFOFtoCNF_X0,addition(X_28,addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)))),
inference(subst,[],[refute_0_39:[bind(X_29,$fot(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))),bind(X_30,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_41,plain,
leq(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_42,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_43,plain,
( ~ leq(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))
| addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)) = multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_0_42:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_44,plain,
addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)) = multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)) )],[refute_0_41,refute_0_43]) ).
cnf(refute_0_45,plain,
( addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)) != multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)
| ~ leq(skolemFOFtoCNF_X0,addition(X_28,addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))))
| leq(skolemFOFtoCNF_X0,addition(X_28,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X0,addition(X_28,addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)))) ),[1,1],$fot(multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_46,plain,
( ~ leq(skolemFOFtoCNF_X0,addition(X_28,addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))))
| leq(skolemFOFtoCNF_X0,addition(X_28,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
leq(skolemFOFtoCNF_X0,addition(X_28,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,addition(X_28,addition(skolemFOFtoCNF_X0,multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)))) )],[refute_0_40,refute_0_46]) ).
cnf(refute_0_48,plain,
leq(skolemFOFtoCNF_X0,addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_47:[bind(X_28,$fot(multiplication(A,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_49,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_50,plain,
multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1) = addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_49:[bind(B,$fot(skolemFOFtoCNF_X2)),bind(C,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_51,plain,
( multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1) != addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))
| addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)) = multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))),bind(Y,$fot(addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_52,plain,
addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)) = multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( $equal(multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1),addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)) != multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)
| ~ leq(skolemFOFtoCNF_X0,addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X0,multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X0,addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))) ),[1],$fot(multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_54,plain,
( ~ leq(skolemFOFtoCNF_X0,addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X0,multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1)),multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
leq(skolemFOFtoCNF_X0,multiplication(addition(A,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,addition(multiplication(A,skolemFOFtoCNF_X1_1),multiplication(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1_1))) )],[refute_0_48,refute_0_54]) ).
cnf(refute_0_56,plain,
leq(skolemFOFtoCNF_X0,multiplication(addition(addition(A,B),skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_55:[bind(A,$fot(addition(A,B)))]]) ).
cnf(refute_0_57,plain,
addition(A,addition(B,skolemFOFtoCNF_X2)) = addition(addition(A,B),skolemFOFtoCNF_X2),
inference(subst,[],[refute_0_2:[bind(C,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_58,plain,
( addition(A,addition(B,skolemFOFtoCNF_X2)) != addition(addition(A,B),skolemFOFtoCNF_X2)
| addition(addition(A,B),skolemFOFtoCNF_X2) = addition(A,addition(B,skolemFOFtoCNF_X2)) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(A,addition(B,skolemFOFtoCNF_X2)))),bind(Y,$fot(addition(addition(A,B),skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_59,plain,
addition(addition(A,B),skolemFOFtoCNF_X2) = addition(A,addition(B,skolemFOFtoCNF_X2)),
inference(resolve,[$cnf( $equal(addition(A,addition(B,skolemFOFtoCNF_X2)),addition(addition(A,B),skolemFOFtoCNF_X2)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
( addition(addition(A,B),skolemFOFtoCNF_X2) != addition(A,addition(B,skolemFOFtoCNF_X2))
| ~ leq(skolemFOFtoCNF_X0,multiplication(addition(addition(A,B),skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))
| leq(skolemFOFtoCNF_X0,multiplication(addition(A,addition(B,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X0,multiplication(addition(addition(A,B),skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)) ),[1,0],$fot(addition(A,addition(B,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_61,plain,
( ~ leq(skolemFOFtoCNF_X0,multiplication(addition(addition(A,B),skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))
| leq(skolemFOFtoCNF_X0,multiplication(addition(A,addition(B,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1)) ),
inference(resolve,[$cnf( $equal(addition(addition(A,B),skolemFOFtoCNF_X2),addition(A,addition(B,skolemFOFtoCNF_X2))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
leq(skolemFOFtoCNF_X0,multiplication(addition(A,addition(B,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,multiplication(addition(addition(A,B),skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)) )],[refute_0_56,refute_0_61]) ).
cnf(refute_0_63,plain,
leq(skolemFOFtoCNF_X0,multiplication(addition(one,addition(X_107,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_62:[bind(A,$fot(one)),bind(B,$fot(X_107))]]) ).
cnf(refute_0_64,plain,
multiplication(addition(one,X_47),X_48) = addition(multiplication(one,X_48),multiplication(X_47,X_48)),
inference(subst,[],[refute_0_49:[bind(A,$fot(one)),bind(B,$fot(X_47)),bind(C,$fot(X_48))]]) ).
cnf(refute_0_65,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_66,plain,
multiplication(one,X_48) = X_48,
inference(subst,[],[refute_0_65:[bind(A,$fot(X_48))]]) ).
cnf(refute_0_67,plain,
( multiplication(addition(one,X_47),X_48) != addition(multiplication(one,X_48),multiplication(X_47,X_48))
| multiplication(one,X_48) != X_48
| multiplication(addition(one,X_47),X_48) = addition(X_48,multiplication(X_47,X_48)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(one,X_47),X_48),addition(multiplication(one,X_48),multiplication(X_47,X_48))) ),[1,0],$fot(X_48)]]) ).
cnf(refute_0_68,plain,
( multiplication(addition(one,X_47),X_48) != addition(multiplication(one,X_48),multiplication(X_47,X_48))
| multiplication(addition(one,X_47),X_48) = addition(X_48,multiplication(X_47,X_48)) ),
inference(resolve,[$cnf( $equal(multiplication(one,X_48),X_48) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
multiplication(addition(one,X_47),X_48) = addition(X_48,multiplication(X_47,X_48)),
inference(resolve,[$cnf( $equal(multiplication(addition(one,X_47),X_48),addition(multiplication(one,X_48),multiplication(X_47,X_48))) )],[refute_0_64,refute_0_68]) ).
cnf(refute_0_70,plain,
multiplication(addition(one,addition(X_107,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1) = addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_107,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_69:[bind(X_47,$fot(addition(X_107,skolemFOFtoCNF_X2))),bind(X_48,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_71,plain,
( multiplication(addition(one,addition(X_107,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1) != addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_107,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))
| ~ leq(skolemFOFtoCNF_X0,multiplication(addition(one,addition(X_107,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1))
| leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_107,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X0,multiplication(addition(one,addition(X_107,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1)) ),[1],$fot(addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_107,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_72,plain,
( ~ leq(skolemFOFtoCNF_X0,multiplication(addition(one,addition(X_107,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1))
| leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_107,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(multiplication(addition(one,addition(X_107,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_107,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_107,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,multiplication(addition(one,addition(X_107,skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1)) )],[refute_0_63,refute_0_72]) ).
cnf(refute_0_74,plain,
leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_108,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_73:[bind(X_107,$fot(X_108))]]) ).
cnf(refute_0_75,plain,
addition(skolemFOFtoCNF_X2,X_108) = addition(X_108,skolemFOFtoCNF_X2),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_X2)),bind(B,$fot(X_108))]]) ).
cnf(refute_0_76,plain,
( addition(skolemFOFtoCNF_X2,X_108) != addition(X_108,skolemFOFtoCNF_X2)
| addition(X_108,skolemFOFtoCNF_X2) = addition(skolemFOFtoCNF_X2,X_108) ),
inference(subst,[],[refute_0_20:[bind(X,$fot(addition(skolemFOFtoCNF_X2,X_108))),bind(Y,$fot(addition(X_108,skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_77,plain,
addition(X_108,skolemFOFtoCNF_X2) = addition(skolemFOFtoCNF_X2,X_108),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2,X_108),addition(X_108,skolemFOFtoCNF_X2)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( addition(X_108,skolemFOFtoCNF_X2) != addition(skolemFOFtoCNF_X2,X_108)
| ~ leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_108,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(skolemFOFtoCNF_X2,X_108),skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_108,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))) ),[1,1,0],$fot(addition(skolemFOFtoCNF_X2,X_108))]]) ).
cnf(refute_0_79,plain,
( ~ leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_108,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(skolemFOFtoCNF_X2,X_108),skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(addition(X_108,skolemFOFtoCNF_X2),addition(skolemFOFtoCNF_X2,X_108)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(skolemFOFtoCNF_X2,X_108),skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(X_108,skolemFOFtoCNF_X2),skolemFOFtoCNF_X1_1))) )],[refute_0_74,refute_0_79]) ).
cnf(refute_0_81,plain,
leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_80:[bind(X_108,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_82,plain,
test(skolemFOFtoCNF_X2),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_83,plain,
( ~ test(X0)
| complement(skolemFOFtoCNF_X1(X0),X0) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_84,plain,
( ~ test(skolemFOFtoCNF_X2)
| complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2) ),
inference(subst,[],[refute_0_83:[bind(X0,$fot(skolemFOFtoCNF_X2))]]) ).
cnf(refute_0_85,plain,
complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X2) )],[refute_0_82,refute_0_84]) ).
cnf(refute_0_86,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_87,plain,
( ~ complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2)
| addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)) = one ),
inference(subst,[],[refute_0_86:[bind(X0,$fot(skolemFOFtoCNF_X2)),bind(X1,$fot(skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)))]]) ).
cnf(refute_0_88,plain,
addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1(skolemFOFtoCNF_X2),skolemFOFtoCNF_X2) )],[refute_0_85,refute_0_87]) ).
cnf(refute_0_89,plain,
( addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)) != one
| ~ leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1))) ),[1,1,0],$fot(one)]]) ).
cnf(refute_0_90,plain,
( ~ leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)),one) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(addition(skolemFOFtoCNF_X2,skolemFOFtoCNF_X1(skolemFOFtoCNF_X2)),skolemFOFtoCNF_X1_1))) )],[refute_0_81,refute_0_90]) ).
cnf(refute_0_92,plain,
addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1) = skolemFOFtoCNF_X1_1,
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_93,plain,
multiplication(one,skolemFOFtoCNF_X1_1) = skolemFOFtoCNF_X1_1,
inference(subst,[],[refute_0_65:[bind(A,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_94,plain,
addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) = addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)),
introduced(tautology,[refl,[$fot(addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_95,plain,
( addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) != addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1))
| multiplication(one,skolemFOFtoCNF_X1_1) != skolemFOFtoCNF_X1_1
| addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) = addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1) ),
introduced(tautology,[equality,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)),addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1))) ),[1,1],$fot(skolemFOFtoCNF_X1_1)]]) ).
cnf(refute_0_96,plain,
( multiplication(one,skolemFOFtoCNF_X1_1) != skolemFOFtoCNF_X1_1
| addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) = addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)),addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) = addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) )],[refute_0_93,refute_0_96]) ).
cnf(refute_0_98,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_99,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_20,refute_0_98]) ).
cnf(refute_0_100,plain,
( addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) != addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1)
| addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1) != skolemFOFtoCNF_X1_1
| addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) = skolemFOFtoCNF_X1_1 ),
inference(subst,[],[refute_0_99:[bind(X,$fot(addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)))),bind(Y,$fot(addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1))),bind(Z,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_101,plain,
( addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1) != skolemFOFtoCNF_X1_1
| addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) = skolemFOFtoCNF_X1_1 ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)),addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1)) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) = skolemFOFtoCNF_X1_1,
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) )],[refute_0_92,refute_0_101]) ).
cnf(refute_0_103,plain,
( addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)) != skolemFOFtoCNF_X1_1
| ~ leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1))) ),[1],$fot(skolemFOFtoCNF_X1_1)]]) ).
cnf(refute_0_104,plain,
( ~ leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)))
| leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1)),skolemFOFtoCNF_X1_1) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,addition(skolemFOFtoCNF_X1_1,multiplication(one,skolemFOFtoCNF_X1_1))) )],[refute_0_91,refute_0_104]) ).
cnf(refute_0_106,plain,
~ leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_107,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0,skolemFOFtoCNF_X1_1) )],[refute_0_105,refute_0_106]) ).
fof(negate_1_0,plain,
~ ! [X0,X1,X2] :
( ( test(X2)
& leq(X0,multiplication(X2,X1))
& leq(X0,X1) )
=> leq(multiplication(c(X2),X0),zero) ),
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,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[additive_associativity]) ).
fof(normalize_1_5,plain,
! [A,B,C] : addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_1_7,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_1_9,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
? [X0,X1,X2] :
( ~ leq(multiplication(c(X2),X0),zero)
& leq(X0,X1)
& leq(X0,multiplication(X2,X1))
& test(X2) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_11,plain,
( ~ leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),zero)
& leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))
& leq(skolemFOFtoCNF_X0_1,skolemFOFtoCNF_X1_2)
& test(skolemFOFtoCNF_X2_1) ),
inference(skolemize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_14,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[multiplicative_associativity]) ).
fof(normalize_1_15,plain,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
test(skolemFOFtoCNF_X2_1),
inference(conjunct,[],[normalize_1_11]) ).
fof(normalize_1_17,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_1_18,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_19,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_1_18]) ).
fof(normalize_1_20,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_1_19]) ).
fof(normalize_1_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_1_22,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_1_21]) ).
fof(normalize_1_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_1_22]) ).
fof(normalize_1_24,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(conjunct,[],[normalize_1_23]) ).
fof(normalize_1_25,plain,
! [A] : multiplication(zero,A) = zero,
inference(canonicalize,[],[left_annihilation]) ).
fof(normalize_1_26,plain,
! [A] : multiplication(zero,A) = zero,
inference(specialize,[],[normalize_1_25]) ).
fof(normalize_1_27,plain,
~ leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),zero),
inference(conjunct,[],[normalize_1_11]) ).
cnf(refute_1_0,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( addition(X_174,addition(X_174,X_150)) != addition(X_174,X_150)
| leq(X_174,addition(X_174,X_150)) ),
inference(subst,[],[refute_1_0:[bind(A,$fot(X_174)),bind(B,$fot(addition(X_174,X_150)))]]) ).
cnf(refute_1_2,plain,
addition(A,addition(B,C)) = addition(addition(A,B),C),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_3,plain,
addition(X_149,addition(X_149,X_150)) = addition(addition(X_149,X_149),X_150),
inference(subst,[],[refute_1_2:[bind(A,$fot(X_149)),bind(B,$fot(X_149)),bind(C,$fot(X_150))]]) ).
cnf(refute_1_4,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_5,plain,
addition(X_149,X_149) = X_149,
inference(subst,[],[refute_1_4:[bind(A,$fot(X_149))]]) ).
cnf(refute_1_6,plain,
( addition(X_149,X_149) != X_149
| addition(X_149,addition(X_149,X_150)) != addition(addition(X_149,X_149),X_150)
| addition(X_149,addition(X_149,X_150)) = addition(X_149,X_150) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_149,addition(X_149,X_150)),addition(addition(X_149,X_149),X_150)) ),[1,0],$fot(X_149)]]) ).
cnf(refute_1_7,plain,
( addition(X_149,addition(X_149,X_150)) != addition(addition(X_149,X_149),X_150)
| addition(X_149,addition(X_149,X_150)) = addition(X_149,X_150) ),
inference(resolve,[$cnf( $equal(addition(X_149,X_149),X_149) )],[refute_1_5,refute_1_6]) ).
cnf(refute_1_8,plain,
addition(X_149,addition(X_149,X_150)) = addition(X_149,X_150),
inference(resolve,[$cnf( $equal(addition(X_149,addition(X_149,X_150)),addition(addition(X_149,X_149),X_150)) )],[refute_1_3,refute_1_7]) ).
cnf(refute_1_9,plain,
addition(X_174,addition(X_174,X_150)) = addition(X_174,X_150),
inference(subst,[],[refute_1_8:[bind(X_149,$fot(X_174))]]) ).
cnf(refute_1_10,plain,
( addition(X_174,X_150) != addition(X_174,X_150)
| addition(X_174,addition(X_174,X_150)) != addition(X_174,X_150)
| addition(X_174,addition(X_174,X_150)) = addition(X_174,X_150) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_174,addition(X_174,X_150)),addition(X_174,X_150)) ),[0,1],$fot(addition(X_174,X_150))]]) ).
cnf(refute_1_11,plain,
( addition(X_174,X_150) != addition(X_174,X_150)
| addition(X_174,addition(X_174,X_150)) = addition(X_174,X_150) ),
inference(resolve,[$cnf( $equal(addition(X_174,addition(X_174,X_150)),addition(X_174,X_150)) )],[refute_1_9,refute_1_10]) ).
cnf(refute_1_12,plain,
( addition(X_174,X_150) != addition(X_174,X_150)
| leq(X_174,addition(X_174,X_150)) ),
inference(resolve,[$cnf( $equal(addition(X_174,addition(X_174,X_150)),addition(X_174,X_150)) )],[refute_1_11,refute_1_1]) ).
cnf(refute_1_13,plain,
addition(X_174,X_150) = addition(X_174,X_150),
introduced(tautology,[refl,[$fot(addition(X_174,X_150))]]) ).
cnf(refute_1_14,plain,
leq(X_174,addition(X_174,X_150)),
inference(resolve,[$cnf( $equal(addition(X_174,X_150),addition(X_174,X_150)) )],[refute_1_13,refute_1_12]) ).
cnf(refute_1_15,plain,
leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C))),
inference(subst,[],[refute_1_14:[bind(X_150,$fot(multiplication(A,C))),bind(X_174,$fot(multiplication(A,B)))]]) ).
cnf(refute_1_16,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_17,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_18,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_19,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_17,refute_1_18]) ).
cnf(refute_1_20,plain,
( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
| addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
inference(subst,[],[refute_1_19:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).
cnf(refute_1_21,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_1_16,refute_1_20]) ).
cnf(refute_1_22,plain,
( addition(multiplication(A,B),multiplication(A,C)) != multiplication(A,addition(B,C))
| ~ leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C)))
| leq(multiplication(A,B),multiplication(A,addition(B,C))) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C))) ),[1],$fot(multiplication(A,addition(B,C)))]]) ).
cnf(refute_1_23,plain,
( ~ leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C)))
| leq(multiplication(A,B),multiplication(A,addition(B,C))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,B),multiplication(A,C)),multiplication(A,addition(B,C))) )],[refute_1_21,refute_1_22]) ).
cnf(refute_1_24,plain,
leq(multiplication(A,B),multiplication(A,addition(B,C))),
inference(resolve,[$cnf( leq(multiplication(A,B),addition(multiplication(A,B),multiplication(A,C))) )],[refute_1_15,refute_1_23]) ).
cnf(refute_1_25,plain,
leq(multiplication(X_738,skolemFOFtoCNF_X0_1),multiplication(X_738,addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)))),
inference(subst,[],[refute_1_24:[bind(A,$fot(X_738)),bind(B,$fot(skolemFOFtoCNF_X0_1)),bind(C,$fot(multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_26,plain,
leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_27,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_28,plain,
( ~ leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))
| addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)) = multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2) ),
inference(subst,[],[refute_1_27:[bind(A,$fot(skolemFOFtoCNF_X0_1)),bind(B,$fot(multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_29,plain,
addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)) = multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)) )],[refute_1_26,refute_1_28]) ).
cnf(refute_1_30,plain,
( addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)) != multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)
| ~ leq(multiplication(X_738,skolemFOFtoCNF_X0_1),multiplication(X_738,addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))))
| leq(multiplication(X_738,skolemFOFtoCNF_X0_1),multiplication(X_738,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(X_738,skolemFOFtoCNF_X0_1),multiplication(X_738,addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)))) ),[1,1],$fot(multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_31,plain,
( ~ leq(multiplication(X_738,skolemFOFtoCNF_X0_1),multiplication(X_738,addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))))
| leq(multiplication(X_738,skolemFOFtoCNF_X0_1),multiplication(X_738,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)) )],[refute_1_29,refute_1_30]) ).
cnf(refute_1_32,plain,
leq(multiplication(X_738,skolemFOFtoCNF_X0_1),multiplication(X_738,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))),
inference(resolve,[$cnf( leq(multiplication(X_738,skolemFOFtoCNF_X0_1),multiplication(X_738,addition(skolemFOFtoCNF_X0_1,multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)))) )],[refute_1_25,refute_1_31]) ).
cnf(refute_1_33,plain,
leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))),
inference(subst,[],[refute_1_32:[bind(X_738,$fot(c(skolemFOFtoCNF_X2_1)))]]) ).
cnf(refute_1_34,plain,
multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_35,plain,
multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) = multiplication(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1),C),
inference(subst,[],[refute_1_34:[bind(A,$fot(c(skolemFOFtoCNF_X2_1))),bind(B,$fot(skolemFOFtoCNF_X2_1))]]) ).
cnf(refute_1_36,plain,
test(skolemFOFtoCNF_X2_1),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_37,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_38,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_1_37:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_1_39,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_1_40,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_1_39,refute_1_38]) ).
cnf(refute_1_41,plain,
( ~ test(skolemFOFtoCNF_X2_1)
| complement(skolemFOFtoCNF_X2_1,c(skolemFOFtoCNF_X2_1)) ),
inference(subst,[],[refute_1_40:[bind(X0,$fot(skolemFOFtoCNF_X2_1))]]) ).
cnf(refute_1_42,plain,
complement(skolemFOFtoCNF_X2_1,c(skolemFOFtoCNF_X2_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X2_1) )],[refute_1_36,refute_1_41]) ).
cnf(refute_1_43,plain,
( ~ complement(X1,X0)
| multiplication(X0,X1) = zero ),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_44,plain,
( ~ complement(skolemFOFtoCNF_X2_1,c(skolemFOFtoCNF_X2_1))
| multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1) = zero ),
inference(subst,[],[refute_1_43:[bind(X0,$fot(c(skolemFOFtoCNF_X2_1))),bind(X1,$fot(skolemFOFtoCNF_X2_1))]]) ).
cnf(refute_1_45,plain,
multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1) = zero,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X2_1,c(skolemFOFtoCNF_X2_1)) )],[refute_1_42,refute_1_44]) ).
cnf(refute_1_46,plain,
( multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) != multiplication(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1),C)
| multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1) != zero
| multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) = multiplication(zero,C) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)),multiplication(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1),C)) ),[1,0],$fot(zero)]]) ).
cnf(refute_1_47,plain,
( multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) != multiplication(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1),C)
| multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) = multiplication(zero,C) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1),zero) )],[refute_1_45,refute_1_46]) ).
cnf(refute_1_48,plain,
multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) = multiplication(zero,C),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)),multiplication(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X2_1),C)) )],[refute_1_35,refute_1_47]) ).
cnf(refute_1_49,plain,
multiplication(zero,A) = zero,
inference(canonicalize,[],[normalize_1_26]) ).
cnf(refute_1_50,plain,
multiplication(zero,C) = zero,
inference(subst,[],[refute_1_49:[bind(A,$fot(C))]]) ).
cnf(refute_1_51,plain,
( multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) != multiplication(zero,C)
| multiplication(zero,C) != zero
| multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) = zero ),
introduced(tautology,[equality,[$cnf( ~ $equal(multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)),zero) ),[0],$fot(multiplication(zero,C))]]) ).
cnf(refute_1_52,plain,
( multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) != multiplication(zero,C)
| multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) = zero ),
inference(resolve,[$cnf( $equal(multiplication(zero,C),zero) )],[refute_1_50,refute_1_51]) ).
cnf(refute_1_53,plain,
multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)) = zero,
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,C)),multiplication(zero,C)) )],[refute_1_48,refute_1_52]) ).
cnf(refute_1_54,plain,
multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)) = zero,
inference(subst,[],[refute_1_53:[bind(C,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_55,plain,
( multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)) != zero
| ~ leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)))
| leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),zero) ),
introduced(tautology,[equality,[$cnf( leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))) ),[1],$fot(zero)]]) ).
cnf(refute_1_56,plain,
( ~ leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)))
| leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),zero) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2)),zero) )],[refute_1_54,refute_1_55]) ).
cnf(refute_1_57,plain,
leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),zero),
inference(resolve,[$cnf( leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),multiplication(c(skolemFOFtoCNF_X2_1),multiplication(skolemFOFtoCNF_X2_1,skolemFOFtoCNF_X1_2))) )],[refute_1_33,refute_1_56]) ).
cnf(refute_1_58,plain,
~ leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),zero),
inference(canonicalize,[],[normalize_1_27]) ).
cnf(refute_1_59,plain,
$false,
inference(resolve,[$cnf( leq(multiplication(c(skolemFOFtoCNF_X2_1),skolemFOFtoCNF_X0_1),zero) )],[refute_1_57,refute_1_58]) ).
fof(negate_2_0,plain,
~ ! [X0,X1,X2] :
( ( test(X2)
& leq(X0,X1)
& leq(multiplication(c(X2),X0),zero) )
=> leq(X0,multiplication(X2,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,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_2_9,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_2_8]) ).
fof(normalize_2_10,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[left_distributivity]) ).
fof(normalize_2_11,plain,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(specialize,[],[normalize_2_10]) ).
fof(normalize_2_12,plain,
? [X0,X1,X2] :
( ~ leq(X0,multiplication(X2,X1))
& leq(X0,X1)
& leq(multiplication(c(X2),X0),zero)
& test(X2) ),
inference(canonicalize,[],[negate_2_0]) ).
fof(normalize_2_13,plain,
( ~ leq(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))
& leq(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero)
& leq(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)
& test(skolemFOFtoCNF_X2_2) ),
inference(skolemize,[],[normalize_2_12]) ).
fof(normalize_2_14,plain,
leq(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero),
inference(conjunct,[],[normalize_2_13]) ).
fof(normalize_2_15,plain,
! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B ),
inference(conjunct,[],[normalize_2_2]) ).
fof(normalize_2_16,plain,
! [A] : addition(A,zero) = A,
inference(canonicalize,[],[additive_identity]) ).
fof(normalize_2_17,plain,
! [A] : addition(A,zero) = A,
inference(specialize,[],[normalize_2_16]) ).
fof(normalize_2_18,plain,
test(skolemFOFtoCNF_X2_2),
inference(conjunct,[],[normalize_2_13]) ).
fof(normalize_2_19,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_2_20,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_2_19]) ).
fof(normalize_2_21,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_2_20]) ).
fof(normalize_2_22,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_2_21]) ).
fof(normalize_2_23,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_24,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_2_23]) ).
fof(normalize_2_25,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_24]) ).
fof(normalize_2_26,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_2_25]) ).
fof(normalize_2_27,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_2_28,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_2_27]) ).
fof(normalize_2_29,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_2_30,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_2_29]) ).
fof(normalize_2_31,plain,
leq(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3),
inference(conjunct,[],[normalize_2_13]) ).
fof(normalize_2_32,plain,
~ leq(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)),
inference(conjunct,[],[normalize_2_13]) ).
cnf(refute_2_0,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_2_3]) ).
cnf(refute_2_1,plain,
( addition(X_832,addition(X_832,X_803)) != addition(X_832,X_803)
| leq(X_832,addition(X_832,X_803)) ),
inference(subst,[],[refute_2_0:[bind(A,$fot(X_832)),bind(B,$fot(addition(X_832,X_803)))]]) ).
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(X_802,addition(X_802,X_803)) = addition(addition(X_802,X_802),X_803),
inference(subst,[],[refute_2_2:[bind(A,$fot(X_802)),bind(B,$fot(X_802)),bind(C,$fot(X_803))]]) ).
cnf(refute_2_4,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_2_7]) ).
cnf(refute_2_5,plain,
addition(X_802,X_802) = X_802,
inference(subst,[],[refute_2_4:[bind(A,$fot(X_802))]]) ).
cnf(refute_2_6,plain,
( addition(X_802,X_802) != X_802
| addition(X_802,addition(X_802,X_803)) != addition(addition(X_802,X_802),X_803)
| addition(X_802,addition(X_802,X_803)) = addition(X_802,X_803) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_802,addition(X_802,X_803)),addition(addition(X_802,X_802),X_803)) ),[1,0],$fot(X_802)]]) ).
cnf(refute_2_7,plain,
( addition(X_802,addition(X_802,X_803)) != addition(addition(X_802,X_802),X_803)
| addition(X_802,addition(X_802,X_803)) = addition(X_802,X_803) ),
inference(resolve,[$cnf( $equal(addition(X_802,X_802),X_802) )],[refute_2_5,refute_2_6]) ).
cnf(refute_2_8,plain,
addition(X_802,addition(X_802,X_803)) = addition(X_802,X_803),
inference(resolve,[$cnf( $equal(addition(X_802,addition(X_802,X_803)),addition(addition(X_802,X_802),X_803)) )],[refute_2_3,refute_2_7]) ).
cnf(refute_2_9,plain,
addition(X_832,addition(X_832,X_803)) = addition(X_832,X_803),
inference(subst,[],[refute_2_8:[bind(X_802,$fot(X_832))]]) ).
cnf(refute_2_10,plain,
( addition(X_832,X_803) != addition(X_832,X_803)
| addition(X_832,addition(X_832,X_803)) != addition(X_832,X_803)
| addition(X_832,addition(X_832,X_803)) = addition(X_832,X_803) ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_832,addition(X_832,X_803)),addition(X_832,X_803)) ),[0,1],$fot(addition(X_832,X_803))]]) ).
cnf(refute_2_11,plain,
( addition(X_832,X_803) != addition(X_832,X_803)
| addition(X_832,addition(X_832,X_803)) = addition(X_832,X_803) ),
inference(resolve,[$cnf( $equal(addition(X_832,addition(X_832,X_803)),addition(X_832,X_803)) )],[refute_2_9,refute_2_10]) ).
cnf(refute_2_12,plain,
( addition(X_832,X_803) != addition(X_832,X_803)
| leq(X_832,addition(X_832,X_803)) ),
inference(resolve,[$cnf( $equal(addition(X_832,addition(X_832,X_803)),addition(X_832,X_803)) )],[refute_2_11,refute_2_1]) ).
cnf(refute_2_13,plain,
addition(X_832,X_803) = addition(X_832,X_803),
introduced(tautology,[refl,[$fot(addition(X_832,X_803))]]) ).
cnf(refute_2_14,plain,
leq(X_832,addition(X_832,X_803)),
inference(resolve,[$cnf( $equal(addition(X_832,X_803),addition(X_832,X_803)) )],[refute_2_13,refute_2_12]) ).
cnf(refute_2_15,plain,
leq(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))),
inference(subst,[],[refute_2_14:[bind(X_803,$fot(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))),bind(X_832,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_16,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_2_9]) ).
cnf(refute_2_17,plain,
multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,C)) = addition(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,C)),
inference(subst,[],[refute_2_16:[bind(A,$fot(skolemFOFtoCNF_X2_2)),bind(B,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_18,plain,
multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
inference(canonicalize,[],[normalize_2_11]) ).
cnf(refute_2_19,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) = addition(multiplication(A,skolemFOFtoCNF_X0_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2)),
inference(subst,[],[refute_2_18:[bind(B,$fot(c(skolemFOFtoCNF_X2_2))),bind(C,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_20,plain,
leq(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero),
inference(canonicalize,[],[normalize_2_14]) ).
cnf(refute_2_21,plain,
( ~ leq(A,B)
| addition(A,B) = B ),
inference(canonicalize,[],[normalize_2_15]) ).
cnf(refute_2_22,plain,
( ~ leq(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero)
| addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero) = zero ),
inference(subst,[],[refute_2_21:[bind(A,$fot(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2))),bind(B,$fot(zero))]]) ).
cnf(refute_2_23,plain,
addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero) = zero,
inference(resolve,[$cnf( leq(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero) )],[refute_2_20,refute_2_22]) ).
cnf(refute_2_24,plain,
addition(A,zero) = A,
inference(canonicalize,[],[normalize_2_17]) ).
cnf(refute_2_25,plain,
addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero) = multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),
inference(subst,[],[refute_2_24:[bind(A,$fot(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_26,plain,
( addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero) != multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2)
| addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero) != zero
| multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) = zero ),
introduced(tautology,[equality,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero),zero) ),[0],$fot(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_27,plain,
( addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero) != zero
| multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) = zero ),
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2)) )],[refute_2_25,refute_2_26]) ).
cnf(refute_2_28,plain,
multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) = zero,
inference(resolve,[$cnf( $equal(addition(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero),zero) )],[refute_2_23,refute_2_27]) ).
cnf(refute_2_29,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) != addition(multiplication(A,skolemFOFtoCNF_X0_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2))
| multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2) != zero
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) = addition(multiplication(A,skolemFOFtoCNF_X0_2),zero) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2),addition(multiplication(A,skolemFOFtoCNF_X0_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2))) ),[1,1],$fot(zero)]]) ).
cnf(refute_2_30,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) != addition(multiplication(A,skolemFOFtoCNF_X0_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2))
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) = addition(multiplication(A,skolemFOFtoCNF_X0_2),zero) ),
inference(resolve,[$cnf( $equal(multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2),zero) )],[refute_2_28,refute_2_29]) ).
cnf(refute_2_31,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) = addition(multiplication(A,skolemFOFtoCNF_X0_2),zero),
inference(resolve,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2),addition(multiplication(A,skolemFOFtoCNF_X0_2),multiplication(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X0_2))) )],[refute_2_19,refute_2_30]) ).
cnf(refute_2_32,plain,
addition(multiplication(A,skolemFOFtoCNF_X0_2),zero) = multiplication(A,skolemFOFtoCNF_X0_2),
inference(subst,[],[refute_2_24:[bind(A,$fot(multiplication(A,skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_33,plain,
( addition(multiplication(A,skolemFOFtoCNF_X0_2),zero) != multiplication(A,skolemFOFtoCNF_X0_2)
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) != addition(multiplication(A,skolemFOFtoCNF_X0_2),zero)
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) = multiplication(A,skolemFOFtoCNF_X0_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2),addition(multiplication(A,skolemFOFtoCNF_X0_2),zero)) ),[1],$fot(multiplication(A,skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_34,plain,
( multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) != addition(multiplication(A,skolemFOFtoCNF_X0_2),zero)
| multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) = multiplication(A,skolemFOFtoCNF_X0_2) ),
inference(resolve,[$cnf( $equal(addition(multiplication(A,skolemFOFtoCNF_X0_2),zero),multiplication(A,skolemFOFtoCNF_X0_2)) )],[refute_2_32,refute_2_33]) ).
cnf(refute_2_35,plain,
multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) = multiplication(A,skolemFOFtoCNF_X0_2),
inference(resolve,[$cnf( $equal(multiplication(addition(A,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2),addition(multiplication(A,skolemFOFtoCNF_X0_2),zero)) )],[refute_2_31,refute_2_34]) ).
cnf(refute_2_36,plain,
multiplication(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),
inference(subst,[],[refute_2_35:[bind(A,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_37,plain,
test(skolemFOFtoCNF_X2_2),
inference(canonicalize,[],[normalize_2_18]) ).
cnf(refute_2_38,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_2_22]) ).
cnf(refute_2_39,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_2_38:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_2_40,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_2_41,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_2_40,refute_2_39]) ).
cnf(refute_2_42,plain,
( ~ test(skolemFOFtoCNF_X2_2)
| complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) ),
inference(subst,[],[refute_2_41:[bind(X0,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_43,plain,
complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X2_2) )],[refute_2_37,refute_2_42]) ).
cnf(refute_2_44,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_2_26]) ).
cnf(refute_2_45,plain,
( ~ complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2))
| addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) = one ),
inference(subst,[],[refute_2_44:[bind(X0,$fot(c(skolemFOFtoCNF_X2_2))),bind(X1,$fot(skolemFOFtoCNF_X2_2))]]) ).
cnf(refute_2_46,plain,
addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) )],[refute_2_43,refute_2_45]) ).
cnf(refute_2_47,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_2_28]) ).
cnf(refute_2_48,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_2_49,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_2_50,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_2_48,refute_2_49]) ).
cnf(refute_2_51,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_2_50:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_2_52,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_2_47,refute_2_51]) ).
cnf(refute_2_53,plain,
addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) = addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),
inference(subst,[],[refute_2_52:[bind(A,$fot(skolemFOFtoCNF_X2_2)),bind(B,$fot(c(skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_54,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) != addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2))
| addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) != one
| addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2),one) ),[0],$fot(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)))]]) ).
cnf(refute_2_55,plain,
( addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2) != one
| addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2),addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2))) )],[refute_2_53,refute_2_54]) ).
cnf(refute_2_56,plain,
addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X2_2),skolemFOFtoCNF_X2_2),one) )],[refute_2_46,refute_2_55]) ).
cnf(refute_2_57,plain,
( addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)) != one
| multiplication(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) != multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)
| multiplication(one,skolemFOFtoCNF_X0_2) = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)) ),[0,0],$fot(one)]]) ).
cnf(refute_2_58,plain,
( multiplication(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2) != multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)
| multiplication(one,skolemFOFtoCNF_X0_2) = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),one) )],[refute_2_56,refute_2_57]) ).
cnf(refute_2_59,plain,
multiplication(one,skolemFOFtoCNF_X0_2) = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X2_2,c(skolemFOFtoCNF_X2_2)),skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)) )],[refute_2_36,refute_2_58]) ).
cnf(refute_2_60,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_2_30]) ).
cnf(refute_2_61,plain,
multiplication(one,skolemFOFtoCNF_X0_2) = skolemFOFtoCNF_X0_2,
inference(subst,[],[refute_2_60:[bind(A,$fot(skolemFOFtoCNF_X0_2))]]) ).
cnf(refute_2_62,plain,
( multiplication(one,skolemFOFtoCNF_X0_2) != multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)
| multiplication(one,skolemFOFtoCNF_X0_2) != skolemFOFtoCNF_X0_2
| skolemFOFtoCNF_X0_2 = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)) ),[0],$fot(skolemFOFtoCNF_X0_2)]]) ).
cnf(refute_2_63,plain,
( multiplication(one,skolemFOFtoCNF_X0_2) != multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)
| skolemFOFtoCNF_X0_2 = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) ),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) )],[refute_2_61,refute_2_62]) ).
cnf(refute_2_64,plain,
skolemFOFtoCNF_X0_2 = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),
inference(resolve,[$cnf( $equal(multiplication(one,skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)) )],[refute_2_59,refute_2_63]) ).
cnf(refute_2_65,plain,
( skolemFOFtoCNF_X0_2 != multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)
| multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) = skolemFOFtoCNF_X0_2 ),
inference(subst,[],[refute_2_50:[bind(X,$fot(skolemFOFtoCNF_X0_2)),bind(Y,$fot(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)))]]) ).
cnf(refute_2_66,plain,
multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) = skolemFOFtoCNF_X0_2,
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2)) )],[refute_2_64,refute_2_65]) ).
cnf(refute_2_67,plain,
( multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,C)) != addition(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,C))
| multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2) != skolemFOFtoCNF_X0_2
| multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,C)) = addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,C)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,C)),addition(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,C))) ),[1,0],$fot(skolemFOFtoCNF_X0_2)]]) ).
cnf(refute_2_68,plain,
( multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,C)) != addition(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,C))
| multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,C)) = addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,C)) ),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),skolemFOFtoCNF_X0_2) )],[refute_2_66,refute_2_67]) ).
cnf(refute_2_69,plain,
multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,C)) = addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,C)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,C)),addition(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X0_2),multiplication(skolemFOFtoCNF_X2_2,C))) )],[refute_2_17,refute_2_68]) ).
cnf(refute_2_70,plain,
multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) = addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)),
inference(subst,[],[refute_2_69:[bind(C,$fot(skolemFOFtoCNF_X1_3))]]) ).
cnf(refute_2_71,plain,
leq(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3),
inference(canonicalize,[],[normalize_2_31]) ).
cnf(refute_2_72,plain,
( ~ leq(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)
| addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) = skolemFOFtoCNF_X1_3 ),
inference(subst,[],[refute_2_21:[bind(A,$fot(skolemFOFtoCNF_X0_2)),bind(B,$fot(skolemFOFtoCNF_X1_3))]]) ).
cnf(refute_2_73,plain,
addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) = skolemFOFtoCNF_X1_3,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) )],[refute_2_71,refute_2_72]) ).
cnf(refute_2_74,plain,
( addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3) != skolemFOFtoCNF_X1_3
| multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) != addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))
| multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) = addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)),addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))) ),[0,1],$fot(skolemFOFtoCNF_X1_3)]]) ).
cnf(refute_2_75,plain,
( multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)) != addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))
| multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) = addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3),skolemFOFtoCNF_X1_3) )],[refute_2_73,refute_2_74]) ).
cnf(refute_2_76,plain,
multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) = addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2_2,addition(skolemFOFtoCNF_X0_2,skolemFOFtoCNF_X1_3)),addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))) )],[refute_2_70,refute_2_75]) ).
cnf(refute_2_77,plain,
( multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) != addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))
| addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3) ),
inference(subst,[],[refute_2_50:[bind(X,$fot(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))),bind(Y,$fot(addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))))]]) ).
cnf(refute_2_78,plain,
addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) = multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3),
inference(resolve,[$cnf( $equal(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3),addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))) )],[refute_2_76,refute_2_77]) ).
cnf(refute_2_79,plain,
( addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) != multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)
| ~ leq(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)))
| leq(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))) ),[1],$fot(multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))]]) ).
cnf(refute_2_80,plain,
( ~ leq(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)))
| leq(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) ),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)),multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) )],[refute_2_78,refute_2_79]) ).
cnf(refute_2_81,plain,
leq(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0_2,addition(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3))) )],[refute_2_15,refute_2_80]) ).
cnf(refute_2_82,plain,
~ leq(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)),
inference(canonicalize,[],[normalize_2_32]) ).
cnf(refute_2_83,plain,
$false,
inference(resolve,[$cnf( leq(skolemFOFtoCNF_X0_2,multiplication(skolemFOFtoCNF_X2_2,skolemFOFtoCNF_X1_3)) )],[refute_2_81,refute_2_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : KLE008+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.15/0.36 % Computer : n010.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 600
% 0.15/0.36 % DateTime : Thu Jun 16 13:12:38 EDT 2022
% 0.15/0.36 % CPUTime :
% 0.21/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 13.39/13.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.39/13.57
% 13.39/13.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.41/13.60
%------------------------------------------------------------------------------