TSTP Solution File: KLE007+4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 1.31s 1.48s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 36
% Syntax : Number of formulae : 200 ( 94 unt; 0 def)
% Number of atoms : 393 ( 239 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 373 ( 180 ~; 142 |; 30 &)
% ( 15 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 191 ( 0 sgn 99 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(additive_commutativity,axiom,
! [A,B] : addition(A,B) = addition(B,A) ).
fof(additive_idempotence,axiom,
! [A] : addition(A,A) = A ).
fof(multiplicative_left_identity,axiom,
! [A] : multiplication(one,A) = A ).
fof(right_distributivity,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ).
fof(order,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ) ).
fof(test_2,axiom,
! [X0,X1] :
( complement(X1,X0)
<=> ( multiplication(X0,X1) = zero
& multiplication(X1,X0) = zero
& addition(X0,X1) = one ) ) ).
fof(test_3,axiom,
! [X0,X1] :
( test(X0)
=> ( c(X0) = X1
<=> complement(X0,X1) ) ) ).
fof(goals,conjecture,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> ( leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ) ) ).
fof(subgoal_0,plain,
! [X0,X1] :
( ( test(X1)
& test(X0) )
=> leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ),
inference(strip,[],[goals]) ).
fof(subgoal_1,plain,
! [X0,X1] :
( ( test(X1)
& test(X0)
& leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
=> leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ),
inference(strip,[],[goals]) ).
fof(negate_0_0,plain,
~ ! [X0,X1] :
( ( test(X1)
& test(X0) )
=> leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [X0,X1] :
( ~ leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& test(X0)
& test(X1) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1))))
& test(skolemFOFtoCNF_X0)
& test(skolemFOFtoCNF_X1_1) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_0_4,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_0_6,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
test(skolemFOFtoCNF_X1_1),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_0_9,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,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_13,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,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_13]) ).
fof(normalize_0_15,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_0_17,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
test(skolemFOFtoCNF_X0),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_19,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_0_20,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_0_24,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_0_23]) ).
cnf(refute_0_0,plain,
~ leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
| addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).
cnf(refute_0_6,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
inference(subst,[],[refute_0_6:[bind(A,$fot(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)))),bind(B,$fot(skolemFOFtoCNF_X1_1)),bind(C,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_8,plain,
( addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1))) != multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
| leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))) ),
introduced(tautology,[equality,[$cnf( ~ leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))) ),[1],$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_9,plain,
( ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))
| leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))) ),
inference(resolve,[$cnf( $equal(addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))),
inference(resolve,[$cnf( leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),skolemFOFtoCNF_X1_1),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),c(skolemFOFtoCNF_X1_1)))) )],[refute_0_9,refute_0_0]) ).
cnf(refute_0_11,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_12,plain,
multiplication(one,one) = one,
inference(subst,[],[refute_0_11:[bind(A,$fot(one))]]) ).
cnf(refute_0_13,plain,
test(skolemFOFtoCNF_X1_1),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_14,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_15,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_0_14:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_0_16,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_0_17,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
( ~ test(skolemFOFtoCNF_X1_1)
| complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_19,plain,
complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_1) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_21,plain,
( ~ complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
| addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = one ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(c(skolemFOFtoCNF_X1_1))),bind(X1,$fot(skolemFOFtoCNF_X1_1))]]) ).
cnf(refute_0_22,plain,
addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_24,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_0_25,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) = addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_X1_1)),bind(B,$fot(c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_27,plain,
( addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))
| addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != one
| addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),one) ),[0],$fot(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))]]) ).
cnf(refute_0_28,plain,
( addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1) != one
| addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_1),skolemFOFtoCNF_X1_1),one) )],[refute_0_22,refute_0_28]) ).
cnf(refute_0_30,plain,
multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
introduced(tautology,[refl,[$fot(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_31,plain,
( addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) != one
| multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1,1],$fot(one)]]) ).
cnf(refute_0_32,plain,
( addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)) != one
| multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)),one) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
test(skolemFOFtoCNF_X0),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_35,plain,
( ~ test(skolemFOFtoCNF_X0)
| complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_36,plain,
complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X0) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
| addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = one ),
inference(subst,[],[refute_0_20:[bind(X0,$fot(c(skolemFOFtoCNF_X0))),bind(X1,$fot(skolemFOFtoCNF_X0))]]) ).
cnf(refute_0_38,plain,
addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) = addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),
inference(subst,[],[refute_0_25:[bind(A,$fot(skolemFOFtoCNF_X0)),bind(B,$fot(c(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_40,plain,
( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))
| addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != one
| addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),one) ),[0],$fot(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)))]]) ).
cnf(refute_0_41,plain,
( addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0) != one
| addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0),skolemFOFtoCNF_X0),one) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
introduced(tautology,[refl,[$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))]]) ).
cnf(refute_0_44,plain,
( addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) != one
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1,0],$fot(one)]]) ).
cnf(refute_0_45,plain,
( addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)) != one
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),one) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_48,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_47]) ).
cnf(refute_0_49,plain,
( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))
| multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Z,$fot(multiplication(one,one)))]]) ).
cnf(refute_0_50,plain,
( multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = multiplication(one,one),
inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,one)) )],[refute_0_33,refute_0_50]) ).
cnf(refute_0_52,plain,
( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != multiplication(one,one)
| multiplication(one,one) != one
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one ),
inference(subst,[],[refute_0_48:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))))),bind(Y,$fot(multiplication(one,one))),bind(Z,$fot(one))]]) ).
cnf(refute_0_53,plain,
( multiplication(one,one) != one
| multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),multiplication(one,one)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) = one,
inference(resolve,[$cnf( $equal(multiplication(one,one),one) )],[refute_0_12,refute_0_53]) ).
cnf(refute_0_55,plain,
( multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))) != one
| ~ leq(one,one)
| leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),
introduced(tautology,[equality,[$cnf( ~ leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),[1],$fot(one)]]) ).
cnf(refute_0_56,plain,
( ~ leq(one,one)
| leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1))),one) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
~ leq(one,one),
inference(resolve,[$cnf( leq(one,multiplication(addition(skolemFOFtoCNF_X0,c(skolemFOFtoCNF_X0)),addition(skolemFOFtoCNF_X1_1,c(skolemFOFtoCNF_X1_1)))) )],[refute_0_56,refute_0_10]) ).
cnf(refute_0_58,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_59,plain,
( addition(X_57,X_57) != X_57
| leq(X_57,X_57) ),
inference(subst,[],[refute_0_58:[bind(A,$fot(X_57)),bind(B,$fot(X_57))]]) ).
cnf(refute_0_60,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_61,plain,
addition(X_57,X_57) = X_57,
inference(subst,[],[refute_0_60:[bind(A,$fot(X_57))]]) ).
cnf(refute_0_62,plain,
( X_57 != X_57
| addition(X_57,X_57) != X_57
| addition(X_57,X_57) = X_57 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_57,X_57),X_57) ),[0,0],$fot(X_57)]]) ).
cnf(refute_0_63,plain,
( X_57 != X_57
| addition(X_57,X_57) = X_57 ),
inference(resolve,[$cnf( $equal(addition(X_57,X_57),X_57) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
( X_57 != X_57
| leq(X_57,X_57) ),
inference(resolve,[$cnf( $equal(addition(X_57,X_57),X_57) )],[refute_0_63,refute_0_59]) ).
cnf(refute_0_65,plain,
X_57 = X_57,
introduced(tautology,[refl,[$fot(X_57)]]) ).
cnf(refute_0_66,plain,
leq(X_57,X_57),
inference(resolve,[$cnf( $equal(X_57,X_57) )],[refute_0_65,refute_0_64]) ).
cnf(refute_0_67,plain,
leq(one,one),
inference(subst,[],[refute_0_66:[bind(X_57,$fot(one))]]) ).
cnf(refute_0_68,plain,
$false,
inference(resolve,[$cnf( leq(one,one) )],[refute_0_67,refute_0_57]) ).
fof(negate_1_0,plain,
~ ! [X0,X1] :
( ( test(X1)
& test(X0)
& leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1)))) )
=> leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [X0,X1] :
( ~ leq(addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))),one)
& leq(one,addition(multiplication(addition(X0,c(X0)),X1),multiplication(addition(X0,c(X0)),c(X1))))
& test(X0)
& test(X1) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one)
& leq(one,addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))))
& test(skolemFOFtoCNF_X0_1)
& test(skolemFOFtoCNF_X1_2) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[right_distributivity]) ).
fof(normalize_1_4,plain,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [A] : multiplication(one,A) = A,
inference(canonicalize,[],[multiplicative_left_identity]) ).
fof(normalize_1_6,plain,
! [A] : multiplication(one,A) = A,
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
test(skolemFOFtoCNF_X1_2),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_8,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(canonicalize,[],[test_3]) ).
fof(normalize_1_9,plain,
! [X0] :
( ~ test(X0)
| ! [X1] :
( c(X0) != X1
<=> ~ complement(X0,X1) ) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [X0,X1] :
( ( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) )
& ( ~ complement(X0,X1)
| ~ test(X0)
| c(X0) = X1 ) ),
inference(clausify,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [X0,X1] :
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(conjunct,[],[normalize_1_10]) ).
fof(normalize_1_12,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_13,plain,
! [X0,X1] :
( ~ complement(X1,X0)
<=> ( addition(X0,X1) != one
| multiplication(X0,X1) != zero
| multiplication(X1,X0) != zero ) ),
inference(specialize,[],[normalize_1_12]) ).
fof(normalize_1_14,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_13]) ).
fof(normalize_1_15,plain,
! [X0,X1] :
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(conjunct,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(canonicalize,[],[additive_commutativity]) ).
fof(normalize_1_17,plain,
! [A,B] : addition(A,B) = addition(B,A),
inference(specialize,[],[normalize_1_16]) ).
fof(normalize_1_18,plain,
test(skolemFOFtoCNF_X0_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_19,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(canonicalize,[],[order]) ).
fof(normalize_1_20,plain,
! [A,B] :
( addition(A,B) != B
<=> ~ leq(A,B) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
! [A,B] :
( ( addition(A,B) != B
| leq(A,B) )
& ( ~ leq(A,B)
| addition(A,B) = B ) ),
inference(clausify,[],[normalize_1_20]) ).
fof(normalize_1_22,plain,
! [A,B] :
( addition(A,B) != B
| leq(A,B) ),
inference(conjunct,[],[normalize_1_21]) ).
fof(normalize_1_23,plain,
! [A] : addition(A,A) = A,
inference(canonicalize,[],[additive_idempotence]) ).
fof(normalize_1_24,plain,
! [A] : addition(A,A) = A,
inference(specialize,[],[normalize_1_23]) ).
cnf(refute_1_0,plain,
~ leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_1_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_1_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_1_2,refute_1_3]) ).
cnf(refute_1_5,plain,
( multiplication(A,addition(B,C)) != addition(multiplication(A,B),multiplication(A,C))
| addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(multiplication(A,addition(B,C)))),bind(Y,$fot(addition(multiplication(A,B),multiplication(A,C))))]]) ).
cnf(refute_1_6,plain,
addition(multiplication(A,B),multiplication(A,C)) = multiplication(A,addition(B,C)),
inference(resolve,[$cnf( $equal(multiplication(A,addition(B,C)),addition(multiplication(A,B),multiplication(A,C))) )],[refute_1_1,refute_1_5]) ).
cnf(refute_1_7,plain,
addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
inference(subst,[],[refute_1_6:[bind(A,$fot(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)))),bind(B,$fot(skolemFOFtoCNF_X1_2)),bind(C,$fot(c(skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_8,plain,
( addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))) != multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one)
| leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one) ),
introduced(tautology,[equality,[$cnf( ~ leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one) ),[0],$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_9,plain,
( ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one)
| leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one) ),
inference(resolve,[$cnf( $equal(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_7,refute_1_8]) ).
cnf(refute_1_10,plain,
~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one),
inference(resolve,[$cnf( leq(addition(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),skolemFOFtoCNF_X1_2),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_9,refute_1_0]) ).
cnf(refute_1_11,plain,
multiplication(one,A) = A,
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_12,plain,
multiplication(one,one) = one,
inference(subst,[],[refute_1_11:[bind(A,$fot(one))]]) ).
cnf(refute_1_13,plain,
test(skolemFOFtoCNF_X1_2),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_14,plain,
( c(X0) != X1
| ~ test(X0)
| complement(X0,X1) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_15,plain,
( c(X0) != c(X0)
| ~ test(X0)
| complement(X0,c(X0)) ),
inference(subst,[],[refute_1_14:[bind(X1,$fot(c(X0)))]]) ).
cnf(refute_1_16,plain,
c(X0) = c(X0),
introduced(tautology,[refl,[$fot(c(X0))]]) ).
cnf(refute_1_17,plain,
( ~ test(X0)
| complement(X0,c(X0)) ),
inference(resolve,[$cnf( $equal(c(X0),c(X0)) )],[refute_1_16,refute_1_15]) ).
cnf(refute_1_18,plain,
( ~ test(skolemFOFtoCNF_X1_2)
| complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) ),
inference(subst,[],[refute_1_17:[bind(X0,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_19,plain,
complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X1_2) )],[refute_1_13,refute_1_18]) ).
cnf(refute_1_20,plain,
( ~ complement(X1,X0)
| addition(X0,X1) = one ),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_21,plain,
( ~ complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))
| addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = one ),
inference(subst,[],[refute_1_20:[bind(X0,$fot(c(skolemFOFtoCNF_X1_2))),bind(X1,$fot(skolemFOFtoCNF_X1_2))]]) ).
cnf(refute_1_22,plain,
addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) )],[refute_1_19,refute_1_21]) ).
cnf(refute_1_23,plain,
addition(A,B) = addition(B,A),
inference(canonicalize,[],[normalize_1_17]) ).
cnf(refute_1_24,plain,
( addition(A,B) != addition(B,A)
| addition(B,A) = addition(A,B) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(addition(A,B))),bind(Y,$fot(addition(B,A)))]]) ).
cnf(refute_1_25,plain,
addition(B,A) = addition(A,B),
inference(resolve,[$cnf( $equal(addition(A,B),addition(B,A)) )],[refute_1_23,refute_1_24]) ).
cnf(refute_1_26,plain,
addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) = addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),
inference(subst,[],[refute_1_25:[bind(A,$fot(skolemFOFtoCNF_X1_2)),bind(B,$fot(c(skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_27,plain,
( addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))
| addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != one
| addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one ),
introduced(tautology,[equality,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),one) ),[0],$fot(addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))]]) ).
cnf(refute_1_28,plain,
( addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2) != one
| addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) )],[refute_1_26,refute_1_27]) ).
cnf(refute_1_29,plain,
addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X1_2),skolemFOFtoCNF_X1_2),one) )],[refute_1_22,refute_1_28]) ).
cnf(refute_1_30,plain,
multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
introduced(tautology,[refl,[$fot(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_31,plain,
( addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) != one
| multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) ),[1,1],$fot(one)]]) ).
cnf(refute_1_32,plain,
( addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)) != one
| multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_30,refute_1_31]) ).
cnf(refute_1_33,plain,
multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)),one) )],[refute_1_29,refute_1_32]) ).
cnf(refute_1_34,plain,
test(skolemFOFtoCNF_X0_1),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_35,plain,
( ~ test(skolemFOFtoCNF_X0_1)
| complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) ),
inference(subst,[],[refute_1_17:[bind(X0,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_36,plain,
complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),
inference(resolve,[$cnf( test(skolemFOFtoCNF_X0_1) )],[refute_1_34,refute_1_35]) ).
cnf(refute_1_37,plain,
( ~ complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))
| addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = one ),
inference(subst,[],[refute_1_20:[bind(X0,$fot(c(skolemFOFtoCNF_X0_1))),bind(X1,$fot(skolemFOFtoCNF_X0_1))]]) ).
cnf(refute_1_38,plain,
addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = one,
inference(resolve,[$cnf( complement(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) )],[refute_1_36,refute_1_37]) ).
cnf(refute_1_39,plain,
addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) = addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),
inference(subst,[],[refute_1_25:[bind(A,$fot(skolemFOFtoCNF_X0_1)),bind(B,$fot(c(skolemFOFtoCNF_X0_1)))]]) ).
cnf(refute_1_40,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_41,plain,
( addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1) != one
| addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one ),
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1))) )],[refute_1_39,refute_1_40]) ).
cnf(refute_1_42,plain,
addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) = one,
inference(resolve,[$cnf( $equal(addition(c(skolemFOFtoCNF_X0_1),skolemFOFtoCNF_X0_1),one) )],[refute_1_38,refute_1_41]) ).
cnf(refute_1_43,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
introduced(tautology,[refl,[$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))]]) ).
cnf(refute_1_44,plain,
( addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) != one
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) ),
introduced(tautology,[equality,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) ),[1,0],$fot(one)]]) ).
cnf(refute_1_45,plain,
( addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)) != one
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_43,refute_1_44]) ).
cnf(refute_1_46,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),
inference(resolve,[$cnf( $equal(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),one) )],[refute_1_42,refute_1_45]) ).
cnf(refute_1_47,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_1_48,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_1_4,refute_1_47]) ).
cnf(refute_1_49,plain,
( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))
| multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
inference(subst,[],[refute_1_48:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Y,$fot(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Z,$fot(multiplication(one,one)))]]) ).
cnf(refute_1_50,plain,
( multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2)))) )],[refute_1_46,refute_1_49]) ).
cnf(refute_1_51,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = multiplication(one,one),
inference(resolve,[$cnf( $equal(multiplication(one,addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,one)) )],[refute_1_33,refute_1_50]) ).
cnf(refute_1_52,plain,
( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != multiplication(one,one)
| multiplication(one,one) != one
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one ),
inference(subst,[],[refute_1_48:[bind(X,$fot(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))))),bind(Y,$fot(multiplication(one,one))),bind(Z,$fot(one))]]) ).
cnf(refute_1_53,plain,
( multiplication(one,one) != one
| multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),multiplication(one,one)) )],[refute_1_51,refute_1_52]) ).
cnf(refute_1_54,plain,
multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) = one,
inference(resolve,[$cnf( $equal(multiplication(one,one),one) )],[refute_1_12,refute_1_53]) ).
cnf(refute_1_55,plain,
( multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))) != one
| ~ leq(one,one)
| leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),
introduced(tautology,[equality,[$cnf( ~ leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),[0],$fot(one)]]) ).
cnf(refute_1_56,plain,
( ~ leq(one,one)
| leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) ),
inference(resolve,[$cnf( $equal(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_54,refute_1_55]) ).
cnf(refute_1_57,plain,
~ leq(one,one),
inference(resolve,[$cnf( leq(multiplication(addition(skolemFOFtoCNF_X0_1,c(skolemFOFtoCNF_X0_1)),addition(skolemFOFtoCNF_X1_2,c(skolemFOFtoCNF_X1_2))),one) )],[refute_1_56,refute_1_10]) ).
cnf(refute_1_58,plain,
( addition(A,B) != B
| leq(A,B) ),
inference(canonicalize,[],[normalize_1_22]) ).
cnf(refute_1_59,plain,
( addition(X_141,X_141) != X_141
| leq(X_141,X_141) ),
inference(subst,[],[refute_1_58:[bind(A,$fot(X_141)),bind(B,$fot(X_141))]]) ).
cnf(refute_1_60,plain,
addition(A,A) = A,
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_61,plain,
addition(X_141,X_141) = X_141,
inference(subst,[],[refute_1_60:[bind(A,$fot(X_141))]]) ).
cnf(refute_1_62,plain,
( X_141 != X_141
| addition(X_141,X_141) != X_141
| addition(X_141,X_141) = X_141 ),
introduced(tautology,[equality,[$cnf( $equal(addition(X_141,X_141),X_141) ),[0,0],$fot(X_141)]]) ).
cnf(refute_1_63,plain,
( X_141 != X_141
| addition(X_141,X_141) = X_141 ),
inference(resolve,[$cnf( $equal(addition(X_141,X_141),X_141) )],[refute_1_61,refute_1_62]) ).
cnf(refute_1_64,plain,
( X_141 != X_141
| leq(X_141,X_141) ),
inference(resolve,[$cnf( $equal(addition(X_141,X_141),X_141) )],[refute_1_63,refute_1_59]) ).
cnf(refute_1_65,plain,
X_141 = X_141,
introduced(tautology,[refl,[$fot(X_141)]]) ).
cnf(refute_1_66,plain,
leq(X_141,X_141),
inference(resolve,[$cnf( $equal(X_141,X_141) )],[refute_1_65,refute_1_64]) ).
cnf(refute_1_67,plain,
leq(one,one),
inference(subst,[],[refute_1_66:[bind(X_141,$fot(one))]]) ).
cnf(refute_1_68,plain,
$false,
inference(resolve,[$cnf( leq(one,one) )],[refute_1_67,refute_1_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE007+4 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 16 13:04:37 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.31/1.48 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.31/1.48
% 1.31/1.48 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.31/1.49
%------------------------------------------------------------------------------