TSTP Solution File: PUZ133+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : PUZ133+1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 18:21:01 EDT 2022
% Result : Theorem 52.44s 52.61s
% Output : CNFRefutation 52.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 77
% Number of leaves : 59
% Syntax : Number of formulae : 327 ( 77 unt; 0 def)
% Number of atoms : 856 ( 550 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 964 ( 435 ~; 473 |; 39 &)
% ( 8 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 427 ( 0 sgn 88 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(queens_p,axiom,
( queens_p
=> ! [I,J] :
( ( le(s(n0),I)
& le(I,n)
& le(s(I),J)
& le(J,n) )
=> ( p(I) != p(J)
& plus(p(I),I) != plus(p(J),J)
& minus(p(I),I) != minus(p(J),J) ) ) ) ).
fof(queens_q,axiom,
( ! [I,J] :
( ( le(s(n0),I)
& le(I,n)
& le(s(I),J)
& le(J,n)
& ( le(s(I),J)
<=> le(s(perm(J)),perm(I)) ) )
=> ( q(I) != q(J)
& plus(q(I),I) != plus(q(J),J)
& minus(q(I),I) != minus(q(J),J) ) )
=> queens_q ) ).
fof(queens_sym,conjecture,
( ( queens_p
& ! [I] : q(I) = p(perm(I)) )
=> queens_q ) ).
fof(permutation_range,axiom,
! [I] :
( ( le(s(n0),I)
& le(I,n) )
=> ( le(s(n0),perm(I))
& le(perm(I),n) ) ) ).
fof(permutation_another_one,axiom,
! [J,I] : minus(I,J) = minus(perm(J),perm(I)) ).
fof(le_trans,axiom,
! [X,Y,Z] :
( ( le(X,Y)
& le(Y,Z) )
=> le(X,Z) ) ).
fof(succ_le,axiom,
! [X] : le(X,s(X)) ).
fof(plus1,axiom,
! [I,J,K,L] :
( plus(I,J) = plus(K,L)
<=> minus(I,K) = minus(L,J) ) ).
fof(minus1,axiom,
! [I,J,K,L] :
( minus(I,J) = minus(K,L)
<=> minus(I,K) = minus(J,L) ) ).
fof(subgoal_0,plain,
( ( queens_p
& ! [I] : q(I) = p(perm(I)) )
=> queens_q ),
inference(strip,[],[queens_sym]) ).
fof(negate_0_0,plain,
~ ( ( queens_p
& ! [I] : q(I) = p(perm(I)) )
=> queens_q ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ queens_p
| ! [I,J] :
( ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ( minus(p(I),I) != minus(p(J),J)
& p(I) != p(J)
& plus(p(I),I) != plus(p(J),J) ) ) ),
inference(canonicalize,[],[queens_p]) ).
fof(normalize_0_1,plain,
! [I,J] :
( ( minus(p(I),I) != minus(p(J),J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p )
& ( p(I) != p(J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p )
& ( plus(p(I),I) != plus(p(J),J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p ) ),
inference(clausify,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [I,J] :
( minus(p(I),I) != minus(p(J),J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( ~ queens_q
& queens_p
& ! [I] : q(I) = p(perm(I)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_4,plain,
queens_p,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [I] : q(I) = p(perm(I)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [I] : q(I) = p(perm(I)),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [I,J,K,L] :
( minus(I,J) != minus(K,L)
<=> minus(I,K) != minus(J,L) ),
inference(canonicalize,[],[minus1]) ).
fof(normalize_0_8,plain,
! [I,J,K,L] :
( minus(I,J) != minus(K,L)
<=> minus(I,K) != minus(J,L) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [I,J,K,L] :
( ( minus(I,J) != minus(K,L)
| minus(I,K) = minus(J,L) )
& ( minus(I,K) != minus(J,L)
| minus(I,J) = minus(K,L) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [I,J,K,L] :
( minus(I,J) != minus(K,L)
| minus(I,K) = minus(J,L) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [I,J] : minus(I,J) = minus(perm(J),perm(I)),
inference(canonicalize,[],[permutation_another_one]) ).
fof(normalize_0_12,plain,
! [I,J] : minus(I,J) = minus(perm(J),perm(I)),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [I,J] :
( plus(p(I),I) != plus(p(J),J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_14,plain,
! [I,J,K,L] :
( minus(I,K) != minus(L,J)
<=> plus(I,J) != plus(K,L) ),
inference(canonicalize,[],[plus1]) ).
fof(normalize_0_15,plain,
! [I,J,K,L] :
( minus(I,K) != minus(L,J)
<=> plus(I,J) != plus(K,L) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [I,J,K,L] :
( ( minus(I,K) != minus(L,J)
| plus(I,J) = plus(K,L) )
& ( plus(I,J) != plus(K,L)
| minus(I,K) = minus(L,J) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [I,J,K,L] :
( minus(I,K) != minus(L,J)
| plus(I,J) = plus(K,L) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [I,J,K,L] :
( plus(I,J) != plus(K,L)
| minus(I,K) = minus(L,J) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_19,plain,
( queens_q
| ? [I,J] :
( le(I,n)
& le(J,n)
& le(s(I),J)
& le(s(n0),I)
& ( minus(q(I),I) = minus(q(J),J)
| plus(q(I),I) = plus(q(J),J)
| q(I) = q(J) )
& ( ~ le(s(I),J)
<=> ~ le(s(perm(J)),perm(I)) ) ) ),
inference(canonicalize,[],[queens_q]) ).
fof(normalize_0_20,plain,
( ( le(s(n0),skolemFOFtoCNF_I)
| queens_q )
& ( le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J)
| queens_q )
& ( le(skolemFOFtoCNF_I,n)
| queens_q )
& ( le(skolemFOFtoCNF_J,n)
| queens_q )
& ( ~ le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I))
| le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J)
| queens_q )
& ( ~ le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J)
| le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I))
| queens_q )
& ( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J)
| queens_q ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J)
| queens_q ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
~ queens_q,
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_23,plain,
( ~ le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J)
| le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I))
| queens_q ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_24,plain,
( le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J)
| queens_q ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_25,plain,
! [I,J] :
( p(I) != p(J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_26,plain,
( le(s(n0),skolemFOFtoCNF_I)
| queens_q ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_27,plain,
! [I] :
( ~ le(I,n)
| ~ le(s(n0),I)
| ( le(perm(I),n)
& le(s(n0),perm(I)) ) ),
inference(canonicalize,[],[permutation_range]) ).
fof(normalize_0_28,plain,
! [I] :
( ~ le(I,n)
| ~ le(s(n0),I)
| ( le(perm(I),n)
& le(s(n0),perm(I)) ) ),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [I] :
( ( ~ le(I,n)
| ~ le(s(n0),I)
| le(perm(I),n) )
& ( ~ le(I,n)
| ~ le(s(n0),I)
| le(s(n0),perm(I)) ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [I] :
( ~ le(I,n)
| ~ le(s(n0),I)
| le(perm(I),n) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
( le(skolemFOFtoCNF_I,n)
| queens_q ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_32,plain,
! [X] : le(X,s(X)),
inference(canonicalize,[],[succ_le]) ).
fof(normalize_0_33,plain,
! [X] : le(X,s(X)),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [X,Y,Z] :
( ~ le(X,Y)
| ~ le(Y,Z)
| le(X,Z) ),
inference(canonicalize,[],[le_trans]) ).
fof(normalize_0_35,plain,
! [X,Y,Z] :
( ~ le(X,Y)
| ~ le(Y,Z)
| le(X,Z) ),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
( le(skolemFOFtoCNF_J,n)
| queens_q ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_37,plain,
! [I] :
( ~ le(I,n)
| ~ le(s(n0),I)
| le(s(n0),perm(I)) ),
inference(conjunct,[],[normalize_0_29]) ).
cnf(refute_0_0,plain,
( minus(p(I),I) != minus(p(J),J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
queens_p,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( minus(p(I),I) != minus(p(J),J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I) ),
inference(resolve,[$cnf( queens_p )],[refute_0_1,refute_0_0]) ).
cnf(refute_0_3,plain,
( minus(p(perm(I)),perm(I)) != minus(p(X_1303),X_1303)
| ~ le(X_1303,n)
| ~ le(perm(I),n)
| ~ le(s(n0),perm(I))
| ~ le(s(perm(I)),X_1303) ),
inference(subst,[],[refute_0_2:[bind(I,$fot(perm(I))),bind(J,$fot(X_1303))]]) ).
cnf(refute_0_4,plain,
q(I) = p(perm(I)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_6,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_7,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( q(I) != p(perm(I))
| p(perm(I)) = q(I) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(q(I))),bind(Y0,$fot(p(perm(I))))]]) ).
cnf(refute_0_9,plain,
p(perm(I)) = q(I),
inference(resolve,[$cnf( $equal(q(I),p(perm(I))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( minus(q(I),perm(I)) != minus(p(X_1303),X_1303)
| p(perm(I)) != q(I)
| minus(p(perm(I)),perm(I)) = minus(p(X_1303),X_1303) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(p(perm(I)),perm(I)),minus(p(X_1303),X_1303)) ),[0,0],$fot(q(I))]]) ).
cnf(refute_0_11,plain,
( minus(q(I),perm(I)) != minus(p(X_1303),X_1303)
| minus(p(perm(I)),perm(I)) = minus(p(X_1303),X_1303) ),
inference(resolve,[$cnf( $equal(p(perm(I)),q(I)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( minus(q(I),perm(I)) != minus(p(X_1303),X_1303)
| ~ le(X_1303,n)
| ~ le(perm(I),n)
| ~ le(s(n0),perm(I))
| ~ le(s(perm(I)),X_1303) ),
inference(resolve,[$cnf( $equal(minus(p(perm(I)),perm(I)),minus(p(X_1303),X_1303)) )],[refute_0_11,refute_0_3]) ).
cnf(refute_0_13,plain,
( minus(I,J) != minus(K,L)
| minus(I,K) = minus(J,L) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_14,plain,
( minus(X_192,X_193) != minus(perm(J),perm(I))
| minus(X_192,perm(J)) = minus(X_193,perm(I)) ),
inference(subst,[],[refute_0_13:[bind(I,$fot(X_192)),bind(J,$fot(X_193)),bind(K,$fot(perm(J))),bind(L,$fot(perm(I)))]]) ).
cnf(refute_0_15,plain,
minus(I,J) = minus(perm(J),perm(I)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
( minus(I,J) != minus(perm(J),perm(I))
| minus(perm(J),perm(I)) = minus(I,J) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(minus(I,J))),bind(Y0,$fot(minus(perm(J),perm(I))))]]) ).
cnf(refute_0_17,plain,
minus(perm(J),perm(I)) = minus(I,J),
inference(resolve,[$cnf( $equal(minus(I,J),minus(perm(J),perm(I))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( minus(X_192,X_193) != minus(I,J)
| minus(perm(J),perm(I)) != minus(I,J)
| minus(X_192,X_193) = minus(perm(J),perm(I)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(X_192,X_193),minus(perm(J),perm(I))) ),[1],$fot(minus(I,J))]]) ).
cnf(refute_0_19,plain,
( minus(X_192,X_193) != minus(I,J)
| minus(X_192,X_193) = minus(perm(J),perm(I)) ),
inference(resolve,[$cnf( $equal(minus(perm(J),perm(I)),minus(I,J)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( minus(X_192,X_193) != minus(I,J)
| minus(X_192,perm(J)) = minus(X_193,perm(I)) ),
inference(resolve,[$cnf( $equal(minus(X_192,X_193),minus(perm(J),perm(I))) )],[refute_0_19,refute_0_14]) ).
cnf(refute_0_21,plain,
( minus(I,J) != minus(I,J)
| minus(I,perm(J)) = minus(J,perm(I)) ),
inference(subst,[],[refute_0_20:[bind(X_192,$fot(I)),bind(X_193,$fot(J))]]) ).
cnf(refute_0_22,plain,
minus(I,J) = minus(I,J),
introduced(tautology,[refl,[$fot(minus(I,J))]]) ).
cnf(refute_0_23,plain,
minus(I,perm(J)) = minus(J,perm(I)),
inference(resolve,[$cnf( $equal(minus(I,J),minus(I,J)) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
( minus(I,perm(J)) != minus(J,perm(I))
| minus(J,perm(I)) = minus(I,perm(J)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(minus(I,perm(J)))),bind(Y0,$fot(minus(J,perm(I))))]]) ).
cnf(refute_0_25,plain,
minus(J,perm(I)) = minus(I,perm(J)),
inference(resolve,[$cnf( $equal(minus(I,perm(J)),minus(J,perm(I))) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
minus(q(I),perm(I)) = minus(I,perm(q(I))),
inference(subst,[],[refute_0_25:[bind(J,$fot(q(I)))]]) ).
cnf(refute_0_27,plain,
( minus(I,perm(q(I))) != minus(p(X_1303),X_1303)
| minus(q(I),perm(I)) != minus(I,perm(q(I)))
| minus(q(I),perm(I)) = minus(p(X_1303),X_1303) ),
introduced(tautology,[equality,[$cnf( $equal(minus(q(I),perm(I)),minus(I,perm(q(I)))) ),[1],$fot(minus(p(X_1303),X_1303))]]) ).
cnf(refute_0_28,plain,
( minus(I,perm(q(I))) != minus(p(X_1303),X_1303)
| minus(q(I),perm(I)) = minus(p(X_1303),X_1303) ),
inference(resolve,[$cnf( $equal(minus(q(I),perm(I)),minus(I,perm(q(I)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( minus(I,perm(q(I))) != minus(p(X_1303),X_1303)
| ~ le(X_1303,n)
| ~ le(perm(I),n)
| ~ le(s(n0),perm(I))
| ~ le(s(perm(I)),X_1303) ),
inference(resolve,[$cnf( $equal(minus(q(I),perm(I)),minus(p(X_1303),X_1303)) )],[refute_0_28,refute_0_12]) ).
cnf(refute_0_30,plain,
( minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))) != minus(p(X_3117),X_3117)
| ~ le(X_3117,n)
| ~ le(perm(skolemFOFtoCNF_J),n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J))
| ~ le(s(perm(skolemFOFtoCNF_J)),X_3117) ),
inference(subst,[],[refute_0_29:[bind(I,$fot(skolemFOFtoCNF_J)),bind(X_1303,$fot(X_3117))]]) ).
cnf(refute_0_31,plain,
( minus(X_192,X_193) != minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I))
| minus(X_192,perm(q(skolemFOFtoCNF_I))) = minus(X_193,perm(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_20:[bind(I,$fot(skolemFOFtoCNF_J)),bind(J,$fot(q(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_32,plain,
( plus(p(I),I) != plus(p(J),J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_33,plain,
( minus(I,K) != minus(L,J)
| plus(I,J) = plus(K,L) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_34,plain,
( minus(L,J) != minus(L,J)
| plus(L,J) = plus(J,L) ),
inference(subst,[],[refute_0_33:[bind(I,$fot(L)),bind(K,$fot(J))]]) ).
cnf(refute_0_35,plain,
minus(L,J) = minus(L,J),
introduced(tautology,[refl,[$fot(minus(L,J))]]) ).
cnf(refute_0_36,plain,
plus(L,J) = plus(J,L),
inference(resolve,[$cnf( $equal(minus(L,J),minus(L,J)) )],[refute_0_35,refute_0_34]) ).
cnf(refute_0_37,plain,
( plus(L,J) != plus(J,L)
| plus(J,L) = plus(L,J) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(L,J))),bind(Y0,$fot(plus(J,L)))]]) ).
cnf(refute_0_38,plain,
plus(J,L) = plus(L,J),
inference(resolve,[$cnf( $equal(plus(L,J),plus(J,L)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
plus(p(I),I) = plus(I,p(I)),
inference(subst,[],[refute_0_38:[bind(J,$fot(p(I))),bind(L,$fot(I))]]) ).
cnf(refute_0_40,plain,
( plus(I,p(I)) != plus(p(J),J)
| plus(p(I),I) != plus(I,p(I))
| plus(p(I),I) = plus(p(J),J) ),
introduced(tautology,[equality,[$cnf( $equal(plus(p(I),I),plus(I,p(I))) ),[1],$fot(plus(p(J),J))]]) ).
cnf(refute_0_41,plain,
( plus(I,p(I)) != plus(p(J),J)
| plus(p(I),I) = plus(p(J),J) ),
inference(resolve,[$cnf( $equal(plus(p(I),I),plus(I,p(I))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
plus(p(J),J) = plus(J,p(J)),
inference(subst,[],[refute_0_38:[bind(J,$fot(p(J))),bind(L,$fot(J))]]) ).
cnf(refute_0_43,plain,
( plus(I,p(I)) != plus(J,p(J))
| plus(p(J),J) != plus(J,p(J))
| plus(I,p(I)) = plus(p(J),J) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(I,p(I)),plus(p(J),J)) ),[1],$fot(plus(J,p(J)))]]) ).
cnf(refute_0_44,plain,
( plus(I,p(I)) != plus(J,p(J))
| plus(I,p(I)) = plus(p(J),J) ),
inference(resolve,[$cnf( $equal(plus(p(J),J),plus(J,p(J))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( plus(I,p(I)) != plus(J,p(J))
| plus(p(I),I) = plus(p(J),J) ),
inference(resolve,[$cnf( $equal(plus(I,p(I)),plus(p(J),J)) )],[refute_0_44,refute_0_41]) ).
cnf(refute_0_46,plain,
( plus(I,p(I)) != plus(J,p(J))
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p ),
inference(resolve,[$cnf( $equal(plus(p(I),I),plus(p(J),J)) )],[refute_0_45,refute_0_32]) ).
cnf(refute_0_47,plain,
( plus(I,p(I)) != plus(J,p(J))
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I) ),
inference(resolve,[$cnf( queens_p )],[refute_0_1,refute_0_46]) ).
cnf(refute_0_48,plain,
( plus(perm(I),p(perm(I))) != plus(X_1305,p(X_1305))
| ~ le(X_1305,n)
| ~ le(perm(I),n)
| ~ le(s(n0),perm(I))
| ~ le(s(perm(I)),X_1305) ),
inference(subst,[],[refute_0_47:[bind(I,$fot(perm(I))),bind(J,$fot(X_1305))]]) ).
cnf(refute_0_49,plain,
( p(perm(I)) != q(I)
| plus(perm(I),q(I)) != plus(X_1305,p(X_1305))
| plus(perm(I),p(perm(I))) = plus(X_1305,p(X_1305)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(perm(I),p(perm(I))),plus(X_1305,p(X_1305))) ),[0,1],$fot(q(I))]]) ).
cnf(refute_0_50,plain,
( plus(perm(I),q(I)) != plus(X_1305,p(X_1305))
| plus(perm(I),p(perm(I))) = plus(X_1305,p(X_1305)) ),
inference(resolve,[$cnf( $equal(p(perm(I)),q(I)) )],[refute_0_9,refute_0_49]) ).
cnf(refute_0_51,plain,
( plus(perm(I),q(I)) != plus(X_1305,p(X_1305))
| ~ le(X_1305,n)
| ~ le(perm(I),n)
| ~ le(s(n0),perm(I))
| ~ le(s(perm(I)),X_1305) ),
inference(resolve,[$cnf( $equal(plus(perm(I),p(perm(I))),plus(X_1305,p(X_1305))) )],[refute_0_50,refute_0_48]) ).
cnf(refute_0_52,plain,
( plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) != plus(X_2060,p(X_2060))
| ~ le(X_2060,n)
| ~ le(perm(skolemFOFtoCNF_J),n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J))
| ~ le(s(perm(skolemFOFtoCNF_J)),X_2060) ),
inference(subst,[],[refute_0_51:[bind(I,$fot(skolemFOFtoCNF_J)),bind(X_1305,$fot(X_2060))]]) ).
cnf(refute_0_53,plain,
( minus(X_179,X_181) != minus(perm(J),perm(I))
| plus(X_179,perm(I)) = plus(X_181,perm(J)) ),
inference(subst,[],[refute_0_33:[bind(I,$fot(X_179)),bind(J,$fot(perm(I))),bind(K,$fot(X_181)),bind(L,$fot(perm(J)))]]) ).
cnf(refute_0_54,plain,
( minus(X_179,X_181) != minus(I,J)
| minus(perm(J),perm(I)) != minus(I,J)
| minus(X_179,X_181) = minus(perm(J),perm(I)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(X_179,X_181),minus(perm(J),perm(I))) ),[1],$fot(minus(I,J))]]) ).
cnf(refute_0_55,plain,
( minus(X_179,X_181) != minus(I,J)
| minus(X_179,X_181) = minus(perm(J),perm(I)) ),
inference(resolve,[$cnf( $equal(minus(perm(J),perm(I)),minus(I,J)) )],[refute_0_17,refute_0_54]) ).
cnf(refute_0_56,plain,
( minus(X_179,X_181) != minus(I,J)
| plus(X_179,perm(I)) = plus(X_181,perm(J)) ),
inference(resolve,[$cnf( $equal(minus(X_179,X_181),minus(perm(J),perm(I))) )],[refute_0_55,refute_0_53]) ).
cnf(refute_0_57,plain,
( minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) != minus(I,J)
| plus(q(skolemFOFtoCNF_J),perm(I)) = plus(q(skolemFOFtoCNF_I),perm(J)) ),
inference(subst,[],[refute_0_56:[bind(X_179,$fot(q(skolemFOFtoCNF_J))),bind(X_181,$fot(q(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_58,plain,
( minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) != minus(K,L)
| minus(q(skolemFOFtoCNF_J),K) = minus(skolemFOFtoCNF_J,L) ),
inference(subst,[],[refute_0_13:[bind(I,$fot(q(skolemFOFtoCNF_J))),bind(J,$fot(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_59,plain,
( minus(I,J) != minus(perm(X_204),L)
| minus(I,perm(X_204)) = minus(J,L) ),
inference(subst,[],[refute_0_13:[bind(K,$fot(perm(X_204)))]]) ).
cnf(refute_0_60,plain,
( minus(perm(J),perm(I)) != minus(X_194,X_195)
| minus(perm(J),X_194) = minus(perm(I),X_195) ),
inference(subst,[],[refute_0_13:[bind(I,$fot(perm(J))),bind(J,$fot(perm(I))),bind(K,$fot(X_194)),bind(L,$fot(X_195))]]) ).
cnf(refute_0_61,plain,
( minus(I,J) != minus(X_194,X_195)
| minus(perm(J),perm(I)) != minus(I,J)
| minus(perm(J),perm(I)) = minus(X_194,X_195) ),
introduced(tautology,[equality,[$cnf( $equal(minus(perm(J),perm(I)),minus(I,J)) ),[1],$fot(minus(X_194,X_195))]]) ).
cnf(refute_0_62,plain,
( minus(I,J) != minus(X_194,X_195)
| minus(perm(J),perm(I)) = minus(X_194,X_195) ),
inference(resolve,[$cnf( $equal(minus(perm(J),perm(I)),minus(I,J)) )],[refute_0_17,refute_0_61]) ).
cnf(refute_0_63,plain,
( minus(I,J) != minus(X_194,X_195)
| minus(perm(J),X_194) = minus(perm(I),X_195) ),
inference(resolve,[$cnf( $equal(minus(perm(J),perm(I)),minus(X_194,X_195)) )],[refute_0_62,refute_0_60]) ).
cnf(refute_0_64,plain,
( minus(X_194,X_195) != minus(X_194,X_195)
| minus(perm(X_195),X_194) = minus(perm(X_194),X_195) ),
inference(subst,[],[refute_0_63:[bind(I,$fot(X_194)),bind(J,$fot(X_195))]]) ).
cnf(refute_0_65,plain,
minus(X_194,X_195) = minus(X_194,X_195),
introduced(tautology,[refl,[$fot(minus(X_194,X_195))]]) ).
cnf(refute_0_66,plain,
minus(perm(X_195),X_194) = minus(perm(X_194),X_195),
inference(resolve,[$cnf( $equal(minus(X_194,X_195),minus(X_194,X_195)) )],[refute_0_65,refute_0_64]) ).
cnf(refute_0_67,plain,
minus(perm(X_204),L) = minus(perm(L),X_204),
inference(subst,[],[refute_0_66:[bind(X_194,$fot(L)),bind(X_195,$fot(X_204))]]) ).
cnf(refute_0_68,plain,
( minus(I,J) != minus(perm(L),X_204)
| minus(perm(X_204),L) != minus(perm(L),X_204)
| minus(I,J) = minus(perm(X_204),L) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(I,J),minus(perm(X_204),L)) ),[1],$fot(minus(perm(L),X_204))]]) ).
cnf(refute_0_69,plain,
( minus(I,J) != minus(perm(L),X_204)
| minus(I,J) = minus(perm(X_204),L) ),
inference(resolve,[$cnf( $equal(minus(perm(X_204),L),minus(perm(L),X_204)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( minus(I,J) != minus(perm(L),X_204)
| minus(I,perm(X_204)) = minus(J,L) ),
inference(resolve,[$cnf( $equal(minus(I,J),minus(perm(X_204),L)) )],[refute_0_69,refute_0_59]) ).
cnf(refute_0_71,plain,
( minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) != minus(perm(X_1073),X_1074)
| minus(perm(skolemFOFtoCNF_J),perm(X_1074)) = minus(q(skolemFOFtoCNF_I),X_1073) ),
inference(subst,[],[refute_0_70:[bind(I,$fot(perm(skolemFOFtoCNF_J))),bind(J,$fot(q(skolemFOFtoCNF_I))),bind(L,$fot(X_1073)),bind(X_204,$fot(X_1074))]]) ).
cnf(refute_0_72,plain,
( plus(I,J) != plus(K,L)
| minus(I,K) = minus(L,J) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_73,plain,
( plus(X_188,X_189) != plus(X_190,X_191)
| minus(X_188,X_190) = minus(X_191,X_189) ),
inference(subst,[],[refute_0_72:[bind(I,$fot(X_188)),bind(J,$fot(X_189)),bind(K,$fot(X_190)),bind(L,$fot(X_191))]]) ).
cnf(refute_0_74,plain,
plus(X_189,X_188) = plus(X_188,X_189),
inference(subst,[],[refute_0_36:[bind(J,$fot(X_188)),bind(L,$fot(X_189))]]) ).
cnf(refute_0_75,plain,
( plus(X_189,X_188) != plus(X_188,X_189)
| plus(X_188,X_189) = plus(X_189,X_188) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(X_189,X_188))),bind(Y0,$fot(plus(X_188,X_189)))]]) ).
cnf(refute_0_76,plain,
plus(X_188,X_189) = plus(X_189,X_188),
inference(resolve,[$cnf( $equal(plus(X_189,X_188),plus(X_188,X_189)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( plus(X_188,X_189) != plus(X_189,X_188)
| plus(X_189,X_188) != plus(X_190,X_191)
| plus(X_188,X_189) = plus(X_190,X_191) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(X_188,X_189),plus(X_190,X_191)) ),[0],$fot(plus(X_189,X_188))]]) ).
cnf(refute_0_78,plain,
( plus(X_189,X_188) != plus(X_190,X_191)
| plus(X_188,X_189) = plus(X_190,X_191) ),
inference(resolve,[$cnf( $equal(plus(X_188,X_189),plus(X_189,X_188)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( plus(X_189,X_188) != plus(X_190,X_191)
| minus(X_188,X_190) = minus(X_191,X_189) ),
inference(resolve,[$cnf( $equal(plus(X_188,X_189),plus(X_190,X_191)) )],[refute_0_78,refute_0_73]) ).
cnf(refute_0_80,plain,
( plus(X_189,X_188) != plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))
| minus(X_188,q(skolemFOFtoCNF_I)) = minus(perm(q(skolemFOFtoCNF_J)),X_189) ),
inference(subst,[],[refute_0_79:[bind(X_190,$fot(q(skolemFOFtoCNF_I))),bind(X_191,$fot(perm(q(skolemFOFtoCNF_J))))]]) ).
cnf(refute_0_81,plain,
( minus(perm(J),perm(I)) != minus(X_182,X_180)
| plus(perm(J),X_180) = plus(perm(I),X_182) ),
inference(subst,[],[refute_0_33:[bind(I,$fot(perm(J))),bind(J,$fot(X_180)),bind(K,$fot(perm(I))),bind(L,$fot(X_182))]]) ).
cnf(refute_0_82,plain,
( minus(I,J) != minus(X_182,X_180)
| minus(perm(J),perm(I)) != minus(I,J)
| minus(perm(J),perm(I)) = minus(X_182,X_180) ),
introduced(tautology,[equality,[$cnf( $equal(minus(perm(J),perm(I)),minus(I,J)) ),[1],$fot(minus(X_182,X_180))]]) ).
cnf(refute_0_83,plain,
( minus(I,J) != minus(X_182,X_180)
| minus(perm(J),perm(I)) = minus(X_182,X_180) ),
inference(resolve,[$cnf( $equal(minus(perm(J),perm(I)),minus(I,J)) )],[refute_0_17,refute_0_82]) ).
cnf(refute_0_84,plain,
( minus(I,J) != minus(X_182,X_180)
| plus(perm(J),X_180) = plus(perm(I),X_182) ),
inference(resolve,[$cnf( $equal(minus(perm(J),perm(I)),minus(X_182,X_180)) )],[refute_0_83,refute_0_81]) ).
cnf(refute_0_85,plain,
( minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) != minus(X_614,X_613)
| plus(perm(skolemFOFtoCNF_J),X_613) = plus(perm(q(skolemFOFtoCNF_J)),X_614) ),
inference(subst,[],[refute_0_84:[bind(I,$fot(q(skolemFOFtoCNF_J))),bind(J,$fot(skolemFOFtoCNF_J)),bind(X_180,$fot(X_613)),bind(X_182,$fot(X_614))]]) ).
cnf(refute_0_86,plain,
( minus(X_192,X_193) != minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| minus(X_192,q(skolemFOFtoCNF_I)) = minus(X_193,q(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_13:[bind(I,$fot(X_192)),bind(J,$fot(X_193)),bind(K,$fot(q(skolemFOFtoCNF_I))),bind(L,$fot(q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_87,plain,
( plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) != plus(X_190,X_191)
| minus(skolemFOFtoCNF_J,X_190) = minus(X_191,q(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_72:[bind(I,$fot(skolemFOFtoCNF_J)),bind(J,$fot(q(skolemFOFtoCNF_J))),bind(K,$fot(X_190)),bind(L,$fot(X_191))]]) ).
cnf(refute_0_88,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J)
| queens_q ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_89,plain,
plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)),
inference(subst,[],[refute_0_38:[bind(J,$fot(q(skolemFOFtoCNF_I))),bind(L,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_90,plain,
( plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I))
| plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) = plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) ),
introduced(tautology,[equality,[$cnf( $equal(plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I),plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)) ),[0],$fot(plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_91,plain,
( plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) = plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I),plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I))) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)),
inference(subst,[],[refute_0_38:[bind(J,$fot(q(skolemFOFtoCNF_J))),bind(L,$fot(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_93,plain,
( plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) != plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J))
| plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) != plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) = plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) ),
introduced(tautology,[equality,[$cnf( $equal(plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)),plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)) ),[1],$fot(plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_94,plain,
( plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) != plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) = plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J),plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) = plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)),plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) = plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J)
| queens_q ),
inference(resolve,[$cnf( $equal(plus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I),plus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)) )],[refute_0_88,refute_0_95]) ).
cnf(refute_0_97,plain,
~ queens_q,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_98,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) = plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( queens_q )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
( plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) != plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J))
| plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) = plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)))),bind(Y0,$fot(plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J))))]]) ).
cnf(refute_0_100,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) = plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)),plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) != plus(X_190,X_191)
| plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) != plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I))
| plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) = plus(X_190,X_191) ),
introduced(tautology,[equality,[$cnf( $equal(plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)),plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I))) ),[1],$fot(plus(X_190,X_191))]]) ).
cnf(refute_0_102,plain,
( plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) != plus(X_190,X_191)
| minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)) = plus(X_190,X_191)
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)),plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I))) )],[refute_0_100,refute_0_101]) ).
cnf(refute_0_103,plain,
( plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) != plus(X_190,X_191)
| minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| minus(skolemFOFtoCNF_J,X_190) = minus(X_191,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_J)),plus(X_190,X_191)) )],[refute_0_102,refute_0_87]) ).
cnf(refute_0_104,plain,
( plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) != plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I))
| minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(subst,[],[refute_0_103:[bind(X_190,$fot(skolemFOFtoCNF_I)),bind(X_191,$fot(q(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_105,plain,
plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)) = plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)),
introduced(tautology,[refl,[$fot(plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_106,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I)),plus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_I))) )],[refute_0_105,refute_0_104]) ).
cnf(refute_0_107,plain,
( minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) != minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) = minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I))),bind(Y0,$fot(minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))))]]) ).
cnf(refute_0_108,plain,
( minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) = minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I),minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
( minus(X_192,X_193) != minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) != minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(X_192,X_193) = minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(X_192,X_193),minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))) ),[1],$fot(minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I))]]) ).
cnf(refute_0_110,plain,
( minus(X_192,X_193) != minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(X_192,X_193) = minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)),minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
( minus(X_192,X_193) != minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(X_192,q(skolemFOFtoCNF_I)) = minus(X_193,q(skolemFOFtoCNF_J))
| minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(X_192,X_193),minus(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))) )],[refute_0_110,refute_0_86]) ).
cnf(refute_0_112,plain,
( minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) != minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(subst,[],[refute_0_111:[bind(X_192,$fot(skolemFOFtoCNF_J)),bind(X_193,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_113,plain,
minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) = minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I),
introduced(tautology,[refl,[$fot(minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I))]]) ).
cnf(refute_0_114,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I),minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)) )],[refute_0_113,refute_0_112]) ).
cnf(refute_0_115,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)
| minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I))),bind(Y0,$fot(minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_116,plain,
( minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I),minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(X_614,X_613)
| minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) != minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)
| minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = minus(X_614,X_613) ),
introduced(tautology,[equality,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J),minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)) ),[1],$fot(minus(X_614,X_613))]]) ).
cnf(refute_0_118,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(X_614,X_613)
| minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = minus(X_614,X_613)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J),minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(X_614,X_613)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(perm(skolemFOFtoCNF_J),X_613) = plus(perm(q(skolemFOFtoCNF_J)),X_614)
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J),minus(X_614,X_613)) )],[refute_0_118,refute_0_85]) ).
cnf(refute_0_120,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I) = plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(subst,[],[refute_0_119:[bind(X_613,$fot(skolemFOFtoCNF_I)),bind(X_614,$fot(q(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_121,plain,
minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) = minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I),
introduced(tautology,[refl,[$fot(minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I))]]) ).
cnf(refute_0_122,plain,
( minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I) = plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I),minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)) )],[refute_0_121,refute_0_120]) ).
cnf(refute_0_123,plain,
plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I) = plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)),
inference(subst,[],[refute_0_38:[bind(J,$fot(perm(skolemFOFtoCNF_J))),bind(L,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_124,plain,
( plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I) != plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))
| plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I) != plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))
| plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) = plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I)) ),
introduced(tautology,[equality,[$cnf( $equal(plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I),plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))) ),[0],$fot(plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_125,plain,
( plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I) != plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))
| plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) = plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I),plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I)) = plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))),
inference(subst,[],[refute_0_38:[bind(J,$fot(perm(q(skolemFOFtoCNF_J)))),bind(L,$fot(q(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_127,plain,
( plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I)) != plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))
| plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) != plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))
| plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) = plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))) ),
introduced(tautology,[equality,[$cnf( $equal(plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)),plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))) ),[1],$fot(plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))))]]) ).
cnf(refute_0_128,plain,
( plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) != plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))
| plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) = plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))) ),
inference(resolve,[$cnf( $equal(plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I)),plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
( plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I) != plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))
| plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) = plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))) ),
inference(resolve,[$cnf( $equal(plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)),plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
( minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) = plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(perm(skolemFOFtoCNF_J),skolemFOFtoCNF_I),plus(perm(q(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_I))) )],[refute_0_122,refute_0_129]) ).
cnf(refute_0_131,plain,
( plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) != plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))
| plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))) = plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)))),bind(Y0,$fot(plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))))]]) ).
cnf(refute_0_132,plain,
( minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))) = plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)),plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
( plus(X_189,X_188) != plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))
| plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))) != plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))
| plus(X_189,X_188) = plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(X_189,X_188),plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))) ),[1],$fot(plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_134,plain,
( plus(X_189,X_188) != plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(X_189,X_188) = plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J))),plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
( plus(X_189,X_188) != plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))
| minus(X_188,q(skolemFOFtoCNF_I)) = minus(perm(q(skolemFOFtoCNF_J)),X_189)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(X_189,X_188),plus(q(skolemFOFtoCNF_I),perm(q(skolemFOFtoCNF_J)))) )],[refute_0_134,refute_0_80]) ).
cnf(refute_0_136,plain,
( plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) != plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))
| minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(subst,[],[refute_0_135:[bind(X_188,$fot(perm(skolemFOFtoCNF_J))),bind(X_189,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_137,plain,
plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)) = plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)),
introduced(tautology,[refl,[$fot(plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_138,plain,
( minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J)),plus(skolemFOFtoCNF_I,perm(skolemFOFtoCNF_J))) )],[refute_0_137,refute_0_136]) ).
cnf(refute_0_139,plain,
minus(perm(X_202),J) = minus(perm(J),perm(perm(X_202))),
inference(subst,[],[refute_0_15:[bind(I,$fot(perm(X_202)))]]) ).
cnf(refute_0_140,plain,
minus(perm(J),perm(I)) = minus(I,perm(perm(J))),
inference(subst,[],[refute_0_23:[bind(I,$fot(perm(J))),bind(J,$fot(I))]]) ).
cnf(refute_0_141,plain,
( minus(I,J) != minus(perm(J),perm(I))
| minus(perm(J),perm(I)) != minus(I,perm(perm(J)))
| minus(I,J) = minus(I,perm(perm(J))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(I,J),minus(I,perm(perm(J)))) ),[0],$fot(minus(perm(J),perm(I)))]]) ).
cnf(refute_0_142,plain,
( minus(I,J) != minus(perm(J),perm(I))
| minus(I,J) = minus(I,perm(perm(J))) ),
inference(resolve,[$cnf( $equal(minus(perm(J),perm(I)),minus(I,perm(perm(J)))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
minus(I,J) = minus(I,perm(perm(J))),
inference(resolve,[$cnf( $equal(minus(I,J),minus(perm(J),perm(I))) )],[refute_0_15,refute_0_142]) ).
cnf(refute_0_144,plain,
minus(perm(J),X_202) = minus(perm(J),perm(perm(X_202))),
inference(subst,[],[refute_0_143:[bind(I,$fot(perm(J))),bind(J,$fot(X_202))]]) ).
cnf(refute_0_145,plain,
( minus(perm(J),X_202) != minus(perm(J),perm(perm(X_202)))
| minus(perm(J),perm(perm(X_202))) = minus(perm(J),X_202) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(minus(perm(J),X_202))),bind(Y0,$fot(minus(perm(J),perm(perm(X_202)))))]]) ).
cnf(refute_0_146,plain,
minus(perm(J),perm(perm(X_202))) = minus(perm(J),X_202),
inference(resolve,[$cnf( $equal(minus(perm(J),X_202),minus(perm(J),perm(perm(X_202)))) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
( minus(perm(J),perm(perm(X_202))) != minus(perm(J),X_202)
| minus(perm(X_202),J) != minus(perm(J),perm(perm(X_202)))
| minus(perm(X_202),J) = minus(perm(J),X_202) ),
introduced(tautology,[equality,[$cnf( $equal(minus(perm(X_202),J),minus(perm(J),perm(perm(X_202)))) ),[1],$fot(minus(perm(J),X_202))]]) ).
cnf(refute_0_148,plain,
( minus(perm(X_202),J) != minus(perm(J),perm(perm(X_202)))
| minus(perm(X_202),J) = minus(perm(J),X_202) ),
inference(resolve,[$cnf( $equal(minus(perm(J),perm(perm(X_202))),minus(perm(J),X_202)) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
minus(perm(X_202),J) = minus(perm(J),X_202),
inference(resolve,[$cnf( $equal(minus(perm(X_202),J),minus(perm(J),perm(perm(X_202)))) )],[refute_0_139,refute_0_148]) ).
cnf(refute_0_150,plain,
( minus(perm(X_202),J) != minus(perm(J),X_202)
| minus(perm(J),X_202) = minus(perm(X_202),J) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(minus(perm(X_202),J))),bind(Y0,$fot(minus(perm(J),X_202)))]]) ).
cnf(refute_0_151,plain,
minus(perm(J),X_202) = minus(perm(X_202),J),
inference(resolve,[$cnf( $equal(minus(perm(X_202),J),minus(perm(J),X_202)) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I) = minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)),
inference(subst,[],[refute_0_151:[bind(J,$fot(q(skolemFOFtoCNF_J))),bind(X_202,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_153,plain,
( minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I) != minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) != minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I)
| minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) ),
introduced(tautology,[equality,[$cnf( $equal(minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)),minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I)) ),[1],$fot(minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_154,plain,
( minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) != minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I)
| minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I),minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
( minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)),minus(perm(q(skolemFOFtoCNF_J)),skolemFOFtoCNF_I)) )],[refute_0_138,refute_0_154]) ).
cnf(refute_0_156,plain,
( minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) != minus(perm(X_1073),X_1074)
| minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) != minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(perm(X_1073),X_1074) ),
introduced(tautology,[equality,[$cnf( $equal(minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)),minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))) ),[1],$fot(minus(perm(X_1073),X_1074))]]) ).
cnf(refute_0_157,plain,
( minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) != minus(perm(X_1073),X_1074)
| minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(perm(X_1073),X_1074)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)),minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
( minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) != minus(perm(X_1073),X_1074)
| minus(perm(skolemFOFtoCNF_J),perm(X_1074)) = minus(q(skolemFOFtoCNF_I),X_1073)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)),minus(perm(X_1073),X_1074)) )],[refute_0_157,refute_0_71]) ).
cnf(refute_0_159,plain,
minus(perm(skolemFOFtoCNF_J),perm(X_1074)) = minus(X_1074,skolemFOFtoCNF_J),
inference(subst,[],[refute_0_17:[bind(I,$fot(X_1074)),bind(J,$fot(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_160,plain,
( minus(perm(skolemFOFtoCNF_J),perm(X_1074)) != minus(X_1074,skolemFOFtoCNF_J)
| minus(perm(skolemFOFtoCNF_J),perm(X_1074)) != minus(q(skolemFOFtoCNF_I),X_1073)
| minus(X_1074,skolemFOFtoCNF_J) = minus(q(skolemFOFtoCNF_I),X_1073) ),
introduced(tautology,[equality,[$cnf( $equal(minus(perm(skolemFOFtoCNF_J),perm(X_1074)),minus(q(skolemFOFtoCNF_I),X_1073)) ),[0],$fot(minus(X_1074,skolemFOFtoCNF_J))]]) ).
cnf(refute_0_161,plain,
( minus(perm(skolemFOFtoCNF_J),perm(X_1074)) != minus(q(skolemFOFtoCNF_I),X_1073)
| minus(X_1074,skolemFOFtoCNF_J) = minus(q(skolemFOFtoCNF_I),X_1073) ),
inference(resolve,[$cnf( $equal(minus(perm(skolemFOFtoCNF_J),perm(X_1074)),minus(X_1074,skolemFOFtoCNF_J)) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
( minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) != minus(perm(X_1073),X_1074)
| minus(X_1074,skolemFOFtoCNF_J) = minus(q(skolemFOFtoCNF_I),X_1073)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| q(skolemFOFtoCNF_I) = q(skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( $equal(minus(perm(skolemFOFtoCNF_J),perm(X_1074)),minus(q(skolemFOFtoCNF_I),X_1073)) )],[refute_0_158,refute_0_161]) ).
cnf(refute_0_163,plain,
( ~ le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J)
| le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I))
| queens_q ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_164,plain,
( le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J)
| queens_q ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_165,plain,
le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J),
inference(resolve,[$cnf( queens_q )],[refute_0_164,refute_0_97]) ).
cnf(refute_0_166,plain,
( le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I))
| queens_q ),
inference(resolve,[$cnf( le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J) )],[refute_0_165,refute_0_163]) ).
cnf(refute_0_167,plain,
le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I)),
inference(resolve,[$cnf( queens_q )],[refute_0_166,refute_0_97]) ).
cnf(refute_0_168,plain,
( p(I) != p(J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I)
| ~ queens_p ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_169,plain,
( p(I) != p(J)
| ~ le(I,n)
| ~ le(J,n)
| ~ le(s(I),J)
| ~ le(s(n0),I) ),
inference(resolve,[$cnf( queens_p )],[refute_0_1,refute_0_168]) ).
cnf(refute_0_170,plain,
( p(perm(skolemFOFtoCNF_J)) != p(perm(skolemFOFtoCNF_I))
| ~ le(perm(skolemFOFtoCNF_I),n)
| ~ le(perm(skolemFOFtoCNF_J),n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J))
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I)) ),
inference(subst,[],[refute_0_169:[bind(I,$fot(perm(skolemFOFtoCNF_J))),bind(J,$fot(perm(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_171,plain,
( p(perm(skolemFOFtoCNF_J)) != p(perm(skolemFOFtoCNF_I))
| ~ le(perm(skolemFOFtoCNF_I),n)
| ~ le(perm(skolemFOFtoCNF_J),n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I)) )],[refute_0_167,refute_0_170]) ).
cnf(refute_0_172,plain,
p(perm(skolemFOFtoCNF_J)) = q(skolemFOFtoCNF_J),
inference(subst,[],[refute_0_9:[bind(I,$fot(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_173,plain,
( p(perm(skolemFOFtoCNF_J)) != q(skolemFOFtoCNF_J)
| q(skolemFOFtoCNF_J) != p(perm(skolemFOFtoCNF_I))
| p(perm(skolemFOFtoCNF_J)) = p(perm(skolemFOFtoCNF_I)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(p(perm(skolemFOFtoCNF_J)),p(perm(skolemFOFtoCNF_I))) ),[0],$fot(q(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_174,plain,
( q(skolemFOFtoCNF_J) != p(perm(skolemFOFtoCNF_I))
| p(perm(skolemFOFtoCNF_J)) = p(perm(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(p(perm(skolemFOFtoCNF_J)),q(skolemFOFtoCNF_J)) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
p(perm(skolemFOFtoCNF_I)) = q(skolemFOFtoCNF_I),
inference(subst,[],[refute_0_9:[bind(I,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_176,plain,
( p(perm(skolemFOFtoCNF_I)) != q(skolemFOFtoCNF_I)
| q(skolemFOFtoCNF_J) != q(skolemFOFtoCNF_I)
| q(skolemFOFtoCNF_J) = p(perm(skolemFOFtoCNF_I)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(q(skolemFOFtoCNF_J),p(perm(skolemFOFtoCNF_I))) ),[1],$fot(q(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_177,plain,
( q(skolemFOFtoCNF_J) != q(skolemFOFtoCNF_I)
| q(skolemFOFtoCNF_J) = p(perm(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(p(perm(skolemFOFtoCNF_I)),q(skolemFOFtoCNF_I)) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
( q(skolemFOFtoCNF_J) != q(skolemFOFtoCNF_I)
| p(perm(skolemFOFtoCNF_J)) = p(perm(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(q(skolemFOFtoCNF_J),p(perm(skolemFOFtoCNF_I))) )],[refute_0_177,refute_0_174]) ).
cnf(refute_0_179,plain,
( q(skolemFOFtoCNF_J) != q(skolemFOFtoCNF_I)
| ~ le(perm(skolemFOFtoCNF_I),n)
| ~ le(perm(skolemFOFtoCNF_J),n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(p(perm(skolemFOFtoCNF_J)),p(perm(skolemFOFtoCNF_I))) )],[refute_0_178,refute_0_171]) ).
cnf(refute_0_180,plain,
( le(s(n0),skolemFOFtoCNF_I)
| queens_q ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_181,plain,
le(s(n0),skolemFOFtoCNF_I),
inference(resolve,[$cnf( queens_q )],[refute_0_180,refute_0_97]) ).
cnf(refute_0_182,plain,
( ~ le(I,n)
| ~ le(s(n0),I)
| le(perm(I),n) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_183,plain,
( ~ le(s(n0),skolemFOFtoCNF_I)
| ~ le(skolemFOFtoCNF_I,n)
| le(perm(skolemFOFtoCNF_I),n) ),
inference(subst,[],[refute_0_182:[bind(I,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_184,plain,
( ~ le(skolemFOFtoCNF_I,n)
| le(perm(skolemFOFtoCNF_I),n) ),
inference(resolve,[$cnf( le(s(n0),skolemFOFtoCNF_I) )],[refute_0_181,refute_0_183]) ).
cnf(refute_0_185,plain,
( le(skolemFOFtoCNF_I,n)
| queens_q ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_186,plain,
le(skolemFOFtoCNF_I,n),
inference(resolve,[$cnf( queens_q )],[refute_0_185,refute_0_97]) ).
cnf(refute_0_187,plain,
le(perm(skolemFOFtoCNF_I),n),
inference(resolve,[$cnf( le(skolemFOFtoCNF_I,n) )],[refute_0_186,refute_0_184]) ).
cnf(refute_0_188,plain,
( q(skolemFOFtoCNF_J) != q(skolemFOFtoCNF_I)
| ~ le(perm(skolemFOFtoCNF_J),n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( le(perm(skolemFOFtoCNF_I),n) )],[refute_0_187,refute_0_179]) ).
cnf(refute_0_189,plain,
( ~ le(s(n0),skolemFOFtoCNF_J)
| ~ le(skolemFOFtoCNF_J,n)
| le(perm(skolemFOFtoCNF_J),n) ),
inference(subst,[],[refute_0_182:[bind(I,$fot(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_190,plain,
le(X,s(X)),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_191,plain,
le(skolemFOFtoCNF_I,s(skolemFOFtoCNF_I)),
inference(subst,[],[refute_0_190:[bind(X,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_192,plain,
( ~ le(X,Y)
| ~ le(Y,Z)
| le(X,Z) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_193,plain,
( ~ le(s(n0),skolemFOFtoCNF_I)
| ~ le(skolemFOFtoCNF_I,X_15)
| le(s(n0),X_15) ),
inference(subst,[],[refute_0_192:[bind(X,$fot(s(n0))),bind(Y,$fot(skolemFOFtoCNF_I)),bind(Z,$fot(X_15))]]) ).
cnf(refute_0_194,plain,
( ~ le(skolemFOFtoCNF_I,X_15)
| le(s(n0),X_15) ),
inference(resolve,[$cnf( le(s(n0),skolemFOFtoCNF_I) )],[refute_0_181,refute_0_193]) ).
cnf(refute_0_195,plain,
( ~ le(skolemFOFtoCNF_I,s(skolemFOFtoCNF_I))
| le(s(n0),s(skolemFOFtoCNF_I)) ),
inference(subst,[],[refute_0_194:[bind(X_15,$fot(s(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_196,plain,
le(s(n0),s(skolemFOFtoCNF_I)),
inference(resolve,[$cnf( le(skolemFOFtoCNF_I,s(skolemFOFtoCNF_I)) )],[refute_0_191,refute_0_195]) ).
cnf(refute_0_197,plain,
( ~ le(X_13,s(skolemFOFtoCNF_I))
| ~ le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J)
| le(X_13,skolemFOFtoCNF_J) ),
inference(subst,[],[refute_0_192:[bind(X,$fot(X_13)),bind(Y,$fot(s(skolemFOFtoCNF_I))),bind(Z,$fot(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_198,plain,
( ~ le(X_13,s(skolemFOFtoCNF_I))
| le(X_13,skolemFOFtoCNF_J) ),
inference(resolve,[$cnf( le(s(skolemFOFtoCNF_I),skolemFOFtoCNF_J) )],[refute_0_165,refute_0_197]) ).
cnf(refute_0_199,plain,
( ~ le(s(n0),s(skolemFOFtoCNF_I))
| le(s(n0),skolemFOFtoCNF_J) ),
inference(subst,[],[refute_0_198:[bind(X_13,$fot(s(n0)))]]) ).
cnf(refute_0_200,plain,
le(s(n0),skolemFOFtoCNF_J),
inference(resolve,[$cnf( le(s(n0),s(skolemFOFtoCNF_I)) )],[refute_0_196,refute_0_199]) ).
cnf(refute_0_201,plain,
( ~ le(skolemFOFtoCNF_J,n)
| le(perm(skolemFOFtoCNF_J),n) ),
inference(resolve,[$cnf( le(s(n0),skolemFOFtoCNF_J) )],[refute_0_200,refute_0_189]) ).
cnf(refute_0_202,plain,
( le(skolemFOFtoCNF_J,n)
| queens_q ),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_203,plain,
le(skolemFOFtoCNF_J,n),
inference(resolve,[$cnf( queens_q )],[refute_0_202,refute_0_97]) ).
cnf(refute_0_204,plain,
le(perm(skolemFOFtoCNF_J),n),
inference(resolve,[$cnf( le(skolemFOFtoCNF_J,n) )],[refute_0_203,refute_0_201]) ).
cnf(refute_0_205,plain,
( q(skolemFOFtoCNF_J) != q(skolemFOFtoCNF_I)
| ~ le(s(n0),perm(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( le(perm(skolemFOFtoCNF_J),n) )],[refute_0_204,refute_0_188]) ).
cnf(refute_0_206,plain,
( ~ le(I,n)
| ~ le(s(n0),I)
| le(s(n0),perm(I)) ),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_207,plain,
( ~ le(s(n0),skolemFOFtoCNF_J)
| ~ le(skolemFOFtoCNF_J,n)
| le(s(n0),perm(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_206:[bind(I,$fot(skolemFOFtoCNF_J))]]) ).
cnf(refute_0_208,plain,
( ~ le(skolemFOFtoCNF_J,n)
| le(s(n0),perm(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( le(s(n0),skolemFOFtoCNF_J) )],[refute_0_200,refute_0_207]) ).
cnf(refute_0_209,plain,
le(s(n0),perm(skolemFOFtoCNF_J)),
inference(resolve,[$cnf( le(skolemFOFtoCNF_J,n) )],[refute_0_203,refute_0_208]) ).
cnf(refute_0_210,plain,
q(skolemFOFtoCNF_J) != q(skolemFOFtoCNF_I),
inference(resolve,[$cnf( le(s(n0),perm(skolemFOFtoCNF_J)) )],[refute_0_209,refute_0_205]) ).
cnf(refute_0_211,plain,
( q(skolemFOFtoCNF_I) != q(skolemFOFtoCNF_J)
| q(skolemFOFtoCNF_J) = q(skolemFOFtoCNF_I) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(q(skolemFOFtoCNF_I))),bind(Y0,$fot(q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_212,plain,
q(skolemFOFtoCNF_I) != q(skolemFOFtoCNF_J),
inference(resolve,[$cnf( $equal(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) )],[refute_0_211,refute_0_210]) ).
cnf(refute_0_213,plain,
( minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) != minus(perm(X_1073),X_1074)
| minus(X_1074,skolemFOFtoCNF_J) = minus(q(skolemFOFtoCNF_I),X_1073)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(q(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) )],[refute_0_162,refute_0_212]) ).
cnf(refute_0_214,plain,
( minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) != minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))
| minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_213:[bind(X_1073,$fot(skolemFOFtoCNF_I)),bind(X_1074,$fot(q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_215,plain,
minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)) = minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)),
introduced(tautology,[refl,[$fot(minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_216,plain,
( minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J)),minus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_J))) )],[refute_0_215,refute_0_214]) ).
cnf(refute_0_217,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(K,L)
| minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) != minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)
| minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = minus(K,L) ),
introduced(tautology,[equality,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J),minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)) ),[1],$fot(minus(K,L))]]) ).
cnf(refute_0_218,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(K,L)
| minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J) = minus(K,L)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J),minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)) )],[refute_0_216,refute_0_217]) ).
cnf(refute_0_219,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(K,L)
| minus(q(skolemFOFtoCNF_J),K) = minus(skolemFOFtoCNF_J,L)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),skolemFOFtoCNF_J),minus(K,L)) )],[refute_0_218,refute_0_58]) ).
cnf(refute_0_220,plain,
( minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I) != minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)
| minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_219:[bind(K,$fot(q(skolemFOFtoCNF_I))),bind(L,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_221,plain,
( minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I),minus(q(skolemFOFtoCNF_I),skolemFOFtoCNF_I)) )],[refute_0_121,refute_0_220]) ).
cnf(refute_0_222,plain,
( minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) != minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) != minus(I,J)
| minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(I,J) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)),minus(I,J)) ),[0],$fot(minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I))]]) ).
cnf(refute_0_223,plain,
( minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) != minus(I,J)
| minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)) = minus(I,J)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)),minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)) )],[refute_0_221,refute_0_222]) ).
cnf(refute_0_224,plain,
( minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) != minus(I,J)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(q(skolemFOFtoCNF_J),perm(I)) = plus(q(skolemFOFtoCNF_I),perm(J)) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),q(skolemFOFtoCNF_I)),minus(I,J)) )],[refute_0_223,refute_0_57]) ).
cnf(refute_0_225,plain,
( minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I) != minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) = plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I)) ),
inference(subst,[],[refute_0_224:[bind(I,$fot(skolemFOFtoCNF_J)),bind(J,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_226,plain,
( minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) = plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I),minus(skolemFOFtoCNF_J,skolemFOFtoCNF_I)) )],[refute_0_113,refute_0_225]) ).
cnf(refute_0_227,plain,
plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) = plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)),
inference(subst,[],[refute_0_38:[bind(J,$fot(q(skolemFOFtoCNF_J))),bind(L,$fot(perm(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_228,plain,
( plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) != plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J))
| plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) != plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) = plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I)) ),
introduced(tautology,[equality,[$cnf( $equal(plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)),plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I))) ),[0],$fot(plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_229,plain,
( plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) != plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) = plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)),plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I)) = plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)),
inference(subst,[],[refute_0_38:[bind(J,$fot(q(skolemFOFtoCNF_I))),bind(L,$fot(perm(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_231,plain,
( plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) != plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I))
| plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I)) != plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) = plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)),plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I))) ),[0],$fot(plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_232,plain,
( plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) != plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) = plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I)),plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) != plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) = plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)),plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I))) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
( minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) = plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(plus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)),plus(q(skolemFOFtoCNF_I),perm(skolemFOFtoCNF_I))) )],[refute_0_226,refute_0_233]) ).
cnf(refute_0_235,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(X_2060,p(X_2060))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) != plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) = plus(X_2060,p(X_2060)) ),
introduced(tautology,[equality,[$cnf( $equal(plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)),plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I))) ),[1],$fot(plus(X_2060,p(X_2060)))]]) ).
cnf(refute_0_236,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(X_2060,p(X_2060))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)) = plus(X_2060,p(X_2060)) ),
inference(resolve,[$cnf( $equal(plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)),plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I))) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(X_2060,p(X_2060))
| ~ le(X_2060,n)
| ~ le(perm(skolemFOFtoCNF_J),n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J))
| ~ le(s(perm(skolemFOFtoCNF_J)),X_2060)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(plus(perm(skolemFOFtoCNF_J),q(skolemFOFtoCNF_J)),plus(X_2060,p(X_2060))) )],[refute_0_236,refute_0_52]) ).
cnf(refute_0_238,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(X_2060,p(X_2060))
| ~ le(X_2060,n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J))
| ~ le(s(perm(skolemFOFtoCNF_J)),X_2060)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( le(perm(skolemFOFtoCNF_J),n) )],[refute_0_204,refute_0_237]) ).
cnf(refute_0_239,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(X_2060,p(X_2060))
| ~ le(X_2060,n)
| ~ le(s(perm(skolemFOFtoCNF_J)),X_2060)
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( le(s(n0),perm(skolemFOFtoCNF_J)) )],[refute_0_209,refute_0_238]) ).
cnf(refute_0_240,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(perm(I),p(perm(I)))
| ~ le(perm(I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(I))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_239:[bind(X_2060,$fot(perm(I)))]]) ).
cnf(refute_0_241,plain,
( p(perm(I)) != q(I)
| plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(perm(I),q(I))
| plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) = plus(perm(I),p(perm(I))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)),plus(perm(I),p(perm(I)))) ),[1,1],$fot(q(I))]]) ).
cnf(refute_0_242,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(perm(I),q(I))
| plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) = plus(perm(I),p(perm(I))) ),
inference(resolve,[$cnf( $equal(p(perm(I)),q(I)) )],[refute_0_9,refute_0_241]) ).
cnf(refute_0_243,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(perm(I),q(I))
| ~ le(perm(I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(I))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)),plus(perm(I),p(perm(I)))) )],[refute_0_242,refute_0_240]) ).
cnf(refute_0_244,plain,
( plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) != plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I))
| ~ le(perm(skolemFOFtoCNF_I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_243:[bind(I,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_245,plain,
plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)) = plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)),
introduced(tautology,[refl,[$fot(plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)))]]) ).
cnf(refute_0_246,plain,
( ~ le(perm(skolemFOFtoCNF_I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I)),plus(perm(skolemFOFtoCNF_I),q(skolemFOFtoCNF_I))) )],[refute_0_245,refute_0_244]) ).
cnf(refute_0_247,plain,
( ~ le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( le(perm(skolemFOFtoCNF_I),n) )],[refute_0_187,refute_0_246]) ).
cnf(refute_0_248,plain,
minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)),
inference(resolve,[$cnf( le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I)) )],[refute_0_167,refute_0_247]) ).
cnf(refute_0_249,plain,
( minus(X_192,X_193) != minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) != minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| minus(X_192,X_193) = minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(X_192,X_193),minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I))) ),[1],$fot(minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_250,plain,
( minus(X_192,X_193) != minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| minus(X_192,X_193) = minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I)),minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))) )],[refute_0_248,refute_0_249]) ).
cnf(refute_0_251,plain,
( minus(X_192,X_193) != minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| minus(X_192,perm(q(skolemFOFtoCNF_I))) = minus(X_193,perm(skolemFOFtoCNF_J)) ),
inference(resolve,[$cnf( $equal(minus(X_192,X_193),minus(skolemFOFtoCNF_J,q(skolemFOFtoCNF_I))) )],[refute_0_250,refute_0_31]) ).
cnf(refute_0_252,plain,
( minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) != minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) ),
inference(subst,[],[refute_0_251:[bind(X_192,$fot(skolemFOFtoCNF_I)),bind(X_193,$fot(q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_253,plain,
minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)) = minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)),
introduced(tautology,[refl,[$fot(minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_254,plain,
minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J)),minus(skolemFOFtoCNF_I,q(skolemFOFtoCNF_J))) )],[refute_0_253,refute_0_252]) ).
cnf(refute_0_255,plain,
minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) = minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))),
inference(subst,[],[refute_0_25:[bind(I,$fot(skolemFOFtoCNF_J)),bind(J,$fot(q(skolemFOFtoCNF_J)))]]) ).
cnf(refute_0_256,plain,
( minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)) != minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J)))
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J))
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))) ),
introduced(tautology,[equality,[$cnf( $equal(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J))) ),[1],$fot(minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))))]]) ).
cnf(refute_0_257,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J))
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))) ),
inference(resolve,[$cnf( $equal(minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J)),minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J)))) )],[refute_0_255,refute_0_256]) ).
cnf(refute_0_258,plain,
minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),minus(q(skolemFOFtoCNF_J),perm(skolemFOFtoCNF_J))) )],[refute_0_254,refute_0_257]) ).
cnf(refute_0_259,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J)))
| minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))) = minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))))),bind(Y0,$fot(minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J)))))]]) ).
cnf(refute_0_260,plain,
minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))) = minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J)))) )],[refute_0_258,refute_0_259]) ).
cnf(refute_0_261,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(p(X_3117),X_3117)
| minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))) != minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I)))
| minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))) = minus(p(X_3117),X_3117) ),
introduced(tautology,[equality,[$cnf( $equal(minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))),minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I)))) ),[1],$fot(minus(p(X_3117),X_3117))]]) ).
cnf(refute_0_262,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(p(X_3117),X_3117)
| minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))) = minus(p(X_3117),X_3117) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))),minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(p(X_3117),X_3117)
| ~ le(X_3117,n)
| ~ le(perm(skolemFOFtoCNF_J),n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J))
| ~ le(s(perm(skolemFOFtoCNF_J)),X_3117) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_J,perm(q(skolemFOFtoCNF_J))),minus(p(X_3117),X_3117)) )],[refute_0_262,refute_0_30]) ).
cnf(refute_0_264,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(p(X_3117),X_3117)
| ~ le(X_3117,n)
| ~ le(s(n0),perm(skolemFOFtoCNF_J))
| ~ le(s(perm(skolemFOFtoCNF_J)),X_3117) ),
inference(resolve,[$cnf( le(perm(skolemFOFtoCNF_J),n) )],[refute_0_204,refute_0_263]) ).
cnf(refute_0_265,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(p(X_3117),X_3117)
| ~ le(X_3117,n)
| ~ le(s(perm(skolemFOFtoCNF_J)),X_3117) ),
inference(resolve,[$cnf( le(s(n0),perm(skolemFOFtoCNF_J)) )],[refute_0_209,refute_0_264]) ).
cnf(refute_0_266,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(p(perm(I)),perm(I))
| ~ le(perm(I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(I)) ),
inference(subst,[],[refute_0_265:[bind(X_3117,$fot(perm(I)))]]) ).
cnf(refute_0_267,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(q(I),perm(I))
| p(perm(I)) != q(I)
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(p(perm(I)),perm(I)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),minus(p(perm(I)),perm(I))) ),[1,0],$fot(q(I))]]) ).
cnf(refute_0_268,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(q(I),perm(I))
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(p(perm(I)),perm(I)) ),
inference(resolve,[$cnf( $equal(p(perm(I)),q(I)) )],[refute_0_9,refute_0_267]) ).
cnf(refute_0_269,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(q(I),perm(I))
| ~ le(perm(I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(I)) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),minus(p(perm(I)),perm(I))) )],[refute_0_268,refute_0_266]) ).
cnf(refute_0_270,plain,
( minus(q(I),perm(I)) != minus(I,perm(q(I)))
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(I,perm(q(I)))
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(q(I),perm(I)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),minus(q(I),perm(I))) ),[1],$fot(minus(I,perm(q(I))))]]) ).
cnf(refute_0_271,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(I,perm(q(I)))
| minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(q(I),perm(I)) ),
inference(resolve,[$cnf( $equal(minus(q(I),perm(I)),minus(I,perm(q(I)))) )],[refute_0_26,refute_0_270]) ).
cnf(refute_0_272,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(I,perm(q(I)))
| ~ le(perm(I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(I)) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),minus(q(I),perm(I))) )],[refute_0_271,refute_0_269]) ).
cnf(refute_0_273,plain,
( minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) != minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I)))
| ~ le(perm(skolemFOFtoCNF_I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I)) ),
inference(subst,[],[refute_0_272:[bind(I,$fot(skolemFOFtoCNF_I))]]) ).
cnf(refute_0_274,plain,
minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))) = minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),
introduced(tautology,[refl,[$fot(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))))]]) ).
cnf(refute_0_275,plain,
( ~ le(perm(skolemFOFtoCNF_I),n)
| ~ le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I)) ),
inference(resolve,[$cnf( $equal(minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I))),minus(skolemFOFtoCNF_I,perm(q(skolemFOFtoCNF_I)))) )],[refute_0_274,refute_0_273]) ).
cnf(refute_0_276,plain,
~ le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I)),
inference(resolve,[$cnf( le(perm(skolemFOFtoCNF_I),n) )],[refute_0_187,refute_0_275]) ).
cnf(refute_0_277,plain,
$false,
inference(resolve,[$cnf( le(s(perm(skolemFOFtoCNF_J)),perm(skolemFOFtoCNF_I)) )],[refute_0_167,refute_0_276]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : PUZ133+1 : TPTP v8.1.0. Released v4.1.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.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 : Sat May 28 23:00:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 52.44/52.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 52.44/52.61
% 52.44/52.61 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.44/52.63
%------------------------------------------------------------------------------