TSTP Solution File: SWV181+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV181+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:30:23 EDT 2022
% Result : Theorem 32.87s 33.07s
% Output : CNFRefutation 32.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 64
% Syntax : Number of formulae : 263 ( 118 unt; 0 def)
% Number of atoms : 559 ( 345 equ)
% Maximal formula atoms : 26 ( 2 avg)
% Number of connectives : 509 ( 213 ~; 199 |; 55 &)
% ( 6 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 17 con; 0-3 aty)
% Number of variables : 199 ( 0 sgn 83 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X) ).
fof(leq_gt1,axiom,
! [X,Y] :
( gt(Y,X)
=> leq(X,Y) ) ).
fof(gt_succ,axiom,
! [X] : gt(succ(X),X) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0 ).
fof(succ_plus_1_r,axiom,
! [X] : plus(X,n1) = succ(X) ).
fof(succ_plus_2_r,axiom,
! [X] : plus(X,n2) = succ(succ(X)) ).
fof(succ_plus_3_r,axiom,
! [X] : plus(X,n3) = succ(succ(succ(X))) ).
fof(pred_succ,axiom,
! [X] : pred(succ(X)) = X ).
fof(succ_pred,axiom,
! [X] : succ(pred(X)) = X ).
fof(leq_succ_succ,axiom,
! [X,Y] :
( leq(succ(X),succ(Y))
<=> leq(X,Y) ) ).
fof(leq_succ_gt,axiom,
! [X,Y] :
( leq(succ(X),Y)
=> gt(Y,X) ) ).
fof(cl5_nebula_init_0081,conjecture,
( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [A] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,n4) )
=> a_select3(q_init,A,B) = init ) )
& ! [C] :
( ( leq(n0,C)
& leq(C,n4) )
=> a_select3(center_init,C,n0) = init )
& ( gt(loopcounter,n0)
=> ! [D] :
( ( leq(n0,D)
& leq(D,n4) )
=> a_select2(mu_init,D) = init ) )
& ( gt(loopcounter,n0)
=> ! [E] :
( ( leq(n0,E)
& leq(E,n4) )
=> a_select2(rho_init,E) = init ) )
& ( gt(loopcounter,n0)
=> ! [F] :
( ( leq(n0,F)
& leq(F,n4) )
=> a_select2(sigma_init,F) = init ) ) )
=> ! [G] :
( ( leq(n0,G)
& leq(G,n4) )
=> a_select2(muold_init,G) = init ) ) ).
fof(finite_domain_0,axiom,
! [X] :
( ( leq(n0,X)
& leq(X,n0) )
=> X = n0 ) ).
fof(successor_1,axiom,
succ(n0) = n1 ).
fof(successor_2,axiom,
succ(succ(n0)) = n2 ).
fof(successor_3,axiom,
succ(succ(succ(n0))) = n3 ).
fof(subgoal_0,plain,
( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [A] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,n4) )
=> a_select3(q_init,A,B) = init ) )
& ! [C] :
( ( leq(n0,C)
& leq(C,n4) )
=> a_select3(center_init,C,n0) = init )
& ( gt(loopcounter,n0)
=> ! [D] :
( ( leq(n0,D)
& leq(D,n4) )
=> a_select2(mu_init,D) = init ) )
& ( gt(loopcounter,n0)
=> ! [E] :
( ( leq(n0,E)
& leq(E,n4) )
=> a_select2(rho_init,E) = init ) )
& ( gt(loopcounter,n0)
=> ! [F] :
( ( leq(n0,F)
& leq(F,n4) )
=> a_select2(sigma_init,F) = init ) ) )
=> ! [G] :
( ( leq(n0,G)
& leq(G,n4) )
=> a_select2(muold_init,G) = init ) ),
inference(strip,[],[cl5_nebula_init_0081]) ).
fof(negate_0_0,plain,
~ ( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [A] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B] :
( ( leq(n0,B)
& leq(B,n4) )
=> a_select3(q_init,A,B) = init ) )
& ! [C] :
( ( leq(n0,C)
& leq(C,n4) )
=> a_select3(center_init,C,n0) = init )
& ( gt(loopcounter,n0)
=> ! [D] :
( ( leq(n0,D)
& leq(D,n4) )
=> a_select2(mu_init,D) = init ) )
& ( gt(loopcounter,n0)
=> ! [E] :
( ( leq(n0,E)
& leq(E,n4) )
=> a_select2(rho_init,E) = init ) )
& ( gt(loopcounter,n0)
=> ! [F] :
( ( leq(n0,F)
& leq(F,n4) )
=> a_select2(sigma_init,F) = init ) ) )
=> ! [G] :
( ( leq(n0,G)
& leq(G,n4) )
=> a_select2(muold_init,G) = init ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : gt(succ(X),X),
inference(canonicalize,[],[gt_succ]) ).
fof(normalize_0_1,plain,
! [X] : gt(succ(X),X),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] : pred(succ(X)) = X,
inference(canonicalize,[],[pred_succ]) ).
fof(normalize_0_3,plain,
! [X] : pred(succ(X)) = X,
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : plus(X,n3) = succ(succ(succ(X))),
inference(canonicalize,[],[succ_plus_3_r]) ).
fof(normalize_0_5,plain,
! [X] : plus(X,n3) = succ(succ(succ(X))),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] : plus(X,n1) = succ(X),
inference(canonicalize,[],[succ_plus_1_r]) ).
fof(normalize_0_7,plain,
! [X] : plus(X,n1) = succ(X),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
succ(tptp_minus_1) = n0,
inference(canonicalize,[],[succ_tptp_minus_1]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(canonicalize,[],[leq_gt1]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& ( ~ gt(loopcounter,n0)
| ! [D] :
( ~ leq(D,n4)
| ~ leq(n0,D)
| a_select2(mu_init,D) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [E] :
( ~ leq(E,n4)
| ~ leq(n0,E)
| a_select2(rho_init,E) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [F] :
( ~ leq(F,n4)
| ~ leq(n0,F)
| a_select2(sigma_init,F) = init ) )
& ? [G] :
( a_select2(muold_init,G) != init
& leq(G,n4)
& leq(n0,G) )
& ! [A] :
( ~ leq(A,n135299)
| ~ leq(n0,A)
| ! [B] :
( ~ leq(B,n4)
| ~ leq(n0,B)
| a_select3(q_init,A,B) = init ) )
& ! [C] :
( ~ leq(C,n4)
| ~ leq(n0,C)
| a_select3(center_init,C,n0) = init ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_12,plain,
leq(n1,loopcounter),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(canonicalize,[],[leq_succ_gt]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
succ(n0) = n1,
inference(canonicalize,[],[successor_1]) ).
fof(normalize_0_16,plain,
! [X] :
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(canonicalize,[],[finite_domain_0]) ).
fof(normalize_0_17,plain,
! [X] :
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
gt(n1,loopcounter),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(canonicalize,[],[leq_succ_gt_equiv]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( ~ leq(X,Y)
| gt(succ(Y),X) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(canonicalize,[],[leq_succ_succ]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ( ~ leq(X,Y)
| leq(succ(X),succ(Y)) )
& ( ~ leq(succ(X),succ(Y))
| leq(X,Y) ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X] : succ(pred(X)) = X,
inference(canonicalize,[],[succ_pred]) ).
fof(normalize_0_28,plain,
! [X] : succ(pred(X)) = X,
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
succ(succ(succ(n0))) = n3,
inference(canonicalize,[],[successor_3]) ).
fof(normalize_0_30,plain,
! [X] : plus(X,n2) = succ(succ(X)),
inference(canonicalize,[],[succ_plus_2_r]) ).
fof(normalize_0_31,plain,
! [X] : plus(X,n2) = succ(succ(X)),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[successor_2]) ).
fof(normalize_0_33,plain,
! [X] : ~ gt(X,X),
inference(canonicalize,[],[irreflexivity_gt]) ).
fof(normalize_0_34,plain,
! [X] : ~ gt(X,X),
inference(specialize,[],[normalize_0_33]) ).
cnf(refute_0_0,plain,
gt(succ(X),X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
pred(succ(X)) = X,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
pred(succ(succ(succ(X_12)))) = succ(succ(X_12)),
inference(subst,[],[refute_0_1:[bind(X,$fot(succ(succ(X_12))))]]) ).
cnf(refute_0_3,plain,
plus(X,n3) = succ(succ(succ(X))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
plus(X_12,n3) = succ(succ(succ(X_12))),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_12))]]) ).
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( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( plus(X_12,n3) != succ(succ(succ(X_12)))
| succ(succ(succ(X_12))) = plus(X_12,n3) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(X_12,n3))),bind(Y0,$fot(succ(succ(succ(X_12)))))]]) ).
cnf(refute_0_9,plain,
succ(succ(succ(X_12))) = plus(X_12,n3),
inference(resolve,[$cnf( $equal(plus(X_12,n3),succ(succ(succ(X_12)))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( pred(succ(succ(succ(X_12)))) != succ(succ(X_12))
| succ(succ(succ(X_12))) != plus(X_12,n3)
| pred(plus(X_12,n3)) = succ(succ(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(pred(succ(succ(succ(X_12)))),succ(succ(X_12))) ),[0,0],$fot(plus(X_12,n3))]]) ).
cnf(refute_0_11,plain,
( pred(succ(succ(succ(X_12)))) != succ(succ(X_12))
| pred(plus(X_12,n3)) = succ(succ(X_12)) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(X_12))),plus(X_12,n3)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
pred(plus(X_12,n3)) = succ(succ(X_12)),
inference(resolve,[$cnf( $equal(pred(succ(succ(succ(X_12)))),succ(succ(X_12))) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
pred(succ(X_12)) = X_12,
inference(subst,[],[refute_0_1:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_14,plain,
plus(X,n1) = succ(X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_15,plain,
succ(tptp_minus_1) = n0,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_16,plain,
( ~ gt(Y,X)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_17,plain,
( ~ gt(loopcounter,n0)
| leq(n0,loopcounter) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(n0)),bind(Y,$fot(loopcounter))]]) ).
cnf(refute_0_18,plain,
leq(n1,loopcounter),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_19,plain,
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_20,plain,
( ~ leq(succ(n0),X_1013)
| gt(X_1013,n0) ),
inference(subst,[],[refute_0_19:[bind(X,$fot(n0)),bind(Y,$fot(X_1013))]]) ).
cnf(refute_0_21,plain,
succ(n0) = n1,
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_22,plain,
( succ(n0) != n1
| ~ leq(n1,X_1013)
| leq(succ(n0),X_1013) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(n0),X_1013) ),[0],$fot(n1)]]) ).
cnf(refute_0_23,plain,
( ~ leq(n1,X_1013)
| leq(succ(n0),X_1013) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ leq(n1,X_1013)
| gt(X_1013,n0) ),
inference(resolve,[$cnf( leq(succ(n0),X_1013) )],[refute_0_23,refute_0_20]) ).
cnf(refute_0_25,plain,
( ~ leq(n1,loopcounter)
| gt(loopcounter,n0) ),
inference(subst,[],[refute_0_24:[bind(X_1013,$fot(loopcounter))]]) ).
cnf(refute_0_26,plain,
gt(loopcounter,n0),
inference(resolve,[$cnf( leq(n1,loopcounter) )],[refute_0_18,refute_0_25]) ).
cnf(refute_0_27,plain,
leq(n0,loopcounter),
inference(resolve,[$cnf( gt(loopcounter,n0) )],[refute_0_26,refute_0_17]) ).
cnf(refute_0_28,plain,
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_29,plain,
( ~ leq(loopcounter,n0)
| ~ leq(n0,loopcounter)
| loopcounter = n0 ),
inference(subst,[],[refute_0_28:[bind(X,$fot(loopcounter))]]) ).
cnf(refute_0_30,plain,
( ~ leq(loopcounter,n0)
| loopcounter = n0 ),
inference(resolve,[$cnf( leq(n0,loopcounter) )],[refute_0_27,refute_0_29]) ).
cnf(refute_0_31,plain,
gt(n1,loopcounter),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_32,plain,
( ~ gt(succ(Y),X)
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_33,plain,
( ~ gt(succ(n0),X_68)
| leq(X_68,n0) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_68)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_34,plain,
( succ(n0) != n1
| ~ gt(n1,X_68)
| gt(succ(n0),X_68) ),
introduced(tautology,[equality,[$cnf( ~ gt(succ(n0),X_68) ),[0],$fot(n1)]]) ).
cnf(refute_0_35,plain,
( ~ gt(n1,X_68)
| gt(succ(n0),X_68) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_21,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ gt(n1,X_68)
| leq(X_68,n0) ),
inference(resolve,[$cnf( gt(succ(n0),X_68) )],[refute_0_35,refute_0_33]) ).
cnf(refute_0_37,plain,
( ~ gt(n1,loopcounter)
| leq(loopcounter,n0) ),
inference(subst,[],[refute_0_36:[bind(X_68,$fot(loopcounter))]]) ).
cnf(refute_0_38,plain,
leq(loopcounter,n0),
inference(resolve,[$cnf( gt(n1,loopcounter) )],[refute_0_31,refute_0_37]) ).
cnf(refute_0_39,plain,
loopcounter = n0,
inference(resolve,[$cnf( leq(loopcounter,n0) )],[refute_0_38,refute_0_30]) ).
cnf(refute_0_40,plain,
( loopcounter != n0
| n0 = loopcounter ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(loopcounter)),bind(Y0,$fot(n0))]]) ).
cnf(refute_0_41,plain,
n0 = loopcounter,
inference(resolve,[$cnf( $equal(loopcounter,n0) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
( n0 != loopcounter
| succ(tptp_minus_1) != n0
| succ(tptp_minus_1) = loopcounter ),
introduced(tautology,[equality,[$cnf( $equal(succ(tptp_minus_1),n0) ),[1],$fot(loopcounter)]]) ).
cnf(refute_0_43,plain,
( succ(tptp_minus_1) != n0
| succ(tptp_minus_1) = loopcounter ),
inference(resolve,[$cnf( $equal(n0,loopcounter) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
succ(tptp_minus_1) = loopcounter,
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n0) )],[refute_0_15,refute_0_43]) ).
cnf(refute_0_45,plain,
succ(n0) = succ(n0),
introduced(tautology,[refl,[$fot(succ(n0))]]) ).
cnf(refute_0_46,plain,
( n0 != loopcounter
| succ(n0) != succ(n0)
| succ(n0) = succ(loopcounter) ),
introduced(tautology,[equality,[$cnf( $equal(succ(n0),succ(n0)) ),[1,0],$fot(loopcounter)]]) ).
cnf(refute_0_47,plain,
( n0 != loopcounter
| succ(n0) = succ(loopcounter) ),
inference(resolve,[$cnf( $equal(succ(n0),succ(n0)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
succ(n0) = succ(loopcounter),
inference(resolve,[$cnf( $equal(n0,loopcounter) )],[refute_0_41,refute_0_47]) ).
cnf(refute_0_49,plain,
( succ(n0) != n1
| succ(n0) != succ(loopcounter)
| succ(loopcounter) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(succ(n0),n1) ),[0],$fot(succ(loopcounter))]]) ).
cnf(refute_0_50,plain,
( succ(n0) != n1
| succ(loopcounter) = n1 ),
inference(resolve,[$cnf( $equal(succ(n0),succ(loopcounter)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
succ(loopcounter) = n1,
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_21,refute_0_50]) ).
cnf(refute_0_52,plain,
pred(succ(tptp_minus_1)) = tptp_minus_1,
inference(subst,[],[refute_0_1:[bind(X,$fot(tptp_minus_1))]]) ).
cnf(refute_0_53,plain,
( pred(succ(tptp_minus_1)) != tptp_minus_1
| succ(tptp_minus_1) != n0
| pred(n0) = tptp_minus_1 ),
introduced(tautology,[equality,[$cnf( $equal(pred(succ(tptp_minus_1)),tptp_minus_1) ),[0,0],$fot(n0)]]) ).
cnf(refute_0_54,plain,
( pred(succ(tptp_minus_1)) != tptp_minus_1
| pred(n0) = tptp_minus_1 ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n0) )],[refute_0_15,refute_0_53]) ).
cnf(refute_0_55,plain,
pred(n0) = tptp_minus_1,
inference(resolve,[$cnf( $equal(pred(succ(tptp_minus_1)),tptp_minus_1) )],[refute_0_52,refute_0_54]) ).
cnf(refute_0_56,plain,
( ~ gt(n1,loopcounter)
| leq(loopcounter,n1) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(loopcounter)),bind(Y,$fot(n1))]]) ).
cnf(refute_0_57,plain,
leq(loopcounter,n1),
inference(resolve,[$cnf( gt(n1,loopcounter) )],[refute_0_31,refute_0_56]) ).
cnf(refute_0_58,plain,
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_59,plain,
( ~ leq(succ(X_7665),succ(n0))
| leq(X_7665,n0) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(X_7665)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_60,plain,
( succ(n0) != n1
| ~ leq(succ(X_7665),n1)
| leq(succ(X_7665),succ(n0)) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(X_7665),succ(n0)) ),[1],$fot(n1)]]) ).
cnf(refute_0_61,plain,
( ~ leq(succ(X_7665),n1)
| leq(succ(X_7665),succ(n0)) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_21,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ leq(succ(X_7665),n1)
| leq(X_7665,n0) ),
inference(resolve,[$cnf( leq(succ(X_7665),succ(n0)) )],[refute_0_61,refute_0_59]) ).
cnf(refute_0_63,plain,
( ~ leq(succ(pred(X)),n1)
| leq(pred(X),n0) ),
inference(subst,[],[refute_0_62:[bind(X_7665,$fot(pred(X)))]]) ).
cnf(refute_0_64,plain,
succ(pred(X)) = X,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_65,plain,
( succ(pred(X)) != X
| ~ leq(X,n1)
| leq(succ(pred(X)),n1) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(pred(X)),n1) ),[0],$fot(X)]]) ).
cnf(refute_0_66,plain,
( ~ leq(X,n1)
| leq(succ(pred(X)),n1) ),
inference(resolve,[$cnf( $equal(succ(pred(X)),X) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
( ~ leq(X,n1)
| leq(pred(X),n0) ),
inference(resolve,[$cnf( leq(succ(pred(X)),n1) )],[refute_0_66,refute_0_63]) ).
cnf(refute_0_68,plain,
( ~ leq(loopcounter,n1)
| leq(pred(loopcounter),n0) ),
inference(subst,[],[refute_0_67:[bind(X,$fot(loopcounter))]]) ).
cnf(refute_0_69,plain,
leq(pred(loopcounter),n0),
inference(resolve,[$cnf( leq(loopcounter,n1) )],[refute_0_57,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ leq(n0,pred(loopcounter))
| ~ leq(pred(loopcounter),n0)
| pred(loopcounter) = n0 ),
inference(subst,[],[refute_0_28:[bind(X,$fot(pred(loopcounter)))]]) ).
cnf(refute_0_71,plain,
( ~ leq(n0,pred(loopcounter))
| pred(loopcounter) = n0 ),
inference(resolve,[$cnf( leq(pred(loopcounter),n0) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( ~ gt(succ(pred(X)),X_68)
| leq(X_68,pred(X)) ),
inference(subst,[],[refute_0_32:[bind(X,$fot(X_68)),bind(Y,$fot(pred(X)))]]) ).
cnf(refute_0_73,plain,
( succ(pred(X)) != X
| ~ gt(X,X_68)
| gt(succ(pred(X)),X_68) ),
introduced(tautology,[equality,[$cnf( ~ gt(succ(pred(X)),X_68) ),[0],$fot(X)]]) ).
cnf(refute_0_74,plain,
( ~ gt(X,X_68)
| gt(succ(pred(X)),X_68) ),
inference(resolve,[$cnf( $equal(succ(pred(X)),X) )],[refute_0_64,refute_0_73]) ).
cnf(refute_0_75,plain,
( ~ gt(X,X_68)
| leq(X_68,pred(X)) ),
inference(resolve,[$cnf( gt(succ(pred(X)),X_68) )],[refute_0_74,refute_0_72]) ).
cnf(refute_0_76,plain,
( ~ gt(loopcounter,n0)
| leq(n0,pred(loopcounter)) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(loopcounter)),bind(X_68,$fot(n0))]]) ).
cnf(refute_0_77,plain,
leq(n0,pred(loopcounter)),
inference(resolve,[$cnf( gt(loopcounter,n0) )],[refute_0_26,refute_0_76]) ).
cnf(refute_0_78,plain,
pred(loopcounter) = n0,
inference(resolve,[$cnf( leq(n0,pred(loopcounter)) )],[refute_0_77,refute_0_71]) ).
cnf(refute_0_79,plain,
( n0 != loopcounter
| pred(loopcounter) != n0
| pred(loopcounter) = loopcounter ),
introduced(tautology,[equality,[$cnf( $equal(pred(loopcounter),n0) ),[1],$fot(loopcounter)]]) ).
cnf(refute_0_80,plain,
( pred(loopcounter) != n0
| pred(loopcounter) = loopcounter ),
inference(resolve,[$cnf( $equal(n0,loopcounter) )],[refute_0_41,refute_0_79]) ).
cnf(refute_0_81,plain,
pred(loopcounter) = loopcounter,
inference(resolve,[$cnf( $equal(pred(loopcounter),n0) )],[refute_0_78,refute_0_80]) ).
cnf(refute_0_82,plain,
pred(n0) = pred(n0),
introduced(tautology,[refl,[$fot(pred(n0))]]) ).
cnf(refute_0_83,plain,
( n0 != loopcounter
| pred(n0) != pred(n0)
| pred(n0) = pred(loopcounter) ),
introduced(tautology,[equality,[$cnf( $equal(pred(n0),pred(n0)) ),[1,0],$fot(loopcounter)]]) ).
cnf(refute_0_84,plain,
( n0 != loopcounter
| pred(n0) = pred(loopcounter) ),
inference(resolve,[$cnf( $equal(pred(n0),pred(n0)) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
pred(n0) = pred(loopcounter),
inference(resolve,[$cnf( $equal(n0,loopcounter) )],[refute_0_41,refute_0_84]) ).
cnf(refute_0_86,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_87,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_86]) ).
cnf(refute_0_88,plain,
( pred(loopcounter) != loopcounter
| pred(n0) != pred(loopcounter)
| pred(n0) = loopcounter ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(pred(n0))),bind(Y0,$fot(pred(loopcounter))),bind(Z,$fot(loopcounter))]]) ).
cnf(refute_0_89,plain,
( pred(loopcounter) != loopcounter
| pred(n0) = loopcounter ),
inference(resolve,[$cnf( $equal(pred(n0),pred(loopcounter)) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
pred(n0) = loopcounter,
inference(resolve,[$cnf( $equal(pred(loopcounter),loopcounter) )],[refute_0_81,refute_0_89]) ).
cnf(refute_0_91,plain,
( pred(n0) != loopcounter
| pred(n0) != tptp_minus_1
| loopcounter = tptp_minus_1 ),
introduced(tautology,[equality,[$cnf( $equal(pred(n0),tptp_minus_1) ),[0],$fot(loopcounter)]]) ).
cnf(refute_0_92,plain,
( pred(n0) != tptp_minus_1
| loopcounter = tptp_minus_1 ),
inference(resolve,[$cnf( $equal(pred(n0),loopcounter) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
loopcounter = tptp_minus_1,
inference(resolve,[$cnf( $equal(pred(n0),tptp_minus_1) )],[refute_0_55,refute_0_92]) ).
cnf(refute_0_94,plain,
( loopcounter != tptp_minus_1
| tptp_minus_1 = loopcounter ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(loopcounter)),bind(Y0,$fot(tptp_minus_1))]]) ).
cnf(refute_0_95,plain,
tptp_minus_1 = loopcounter,
inference(resolve,[$cnf( $equal(loopcounter,tptp_minus_1) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
succ(tptp_minus_1) = succ(tptp_minus_1),
introduced(tautology,[refl,[$fot(succ(tptp_minus_1))]]) ).
cnf(refute_0_97,plain,
( succ(tptp_minus_1) != succ(tptp_minus_1)
| tptp_minus_1 != loopcounter
| succ(tptp_minus_1) = succ(loopcounter) ),
introduced(tautology,[equality,[$cnf( $equal(succ(tptp_minus_1),succ(tptp_minus_1)) ),[1,0],$fot(loopcounter)]]) ).
cnf(refute_0_98,plain,
( tptp_minus_1 != loopcounter
| succ(tptp_minus_1) = succ(loopcounter) ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),succ(tptp_minus_1)) )],[refute_0_96,refute_0_97]) ).
cnf(refute_0_99,plain,
succ(tptp_minus_1) = succ(loopcounter),
inference(resolve,[$cnf( $equal(tptp_minus_1,loopcounter) )],[refute_0_95,refute_0_98]) ).
cnf(refute_0_100,plain,
( succ(loopcounter) != n1
| succ(tptp_minus_1) != succ(loopcounter)
| succ(tptp_minus_1) = n1 ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(succ(tptp_minus_1))),bind(Y0,$fot(succ(loopcounter))),bind(Z,$fot(n1))]]) ).
cnf(refute_0_101,plain,
( succ(loopcounter) != n1
| succ(tptp_minus_1) = n1 ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),succ(loopcounter)) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
succ(tptp_minus_1) = n1,
inference(resolve,[$cnf( $equal(succ(loopcounter),n1) )],[refute_0_51,refute_0_101]) ).
cnf(refute_0_103,plain,
( succ(tptp_minus_1) != loopcounter
| succ(tptp_minus_1) != n1
| n1 = loopcounter ),
introduced(tautology,[equality,[$cnf( $equal(succ(tptp_minus_1),loopcounter) ),[0],$fot(n1)]]) ).
cnf(refute_0_104,plain,
( succ(tptp_minus_1) != loopcounter
| n1 = loopcounter ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n1) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
n1 = loopcounter,
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),loopcounter) )],[refute_0_44,refute_0_104]) ).
cnf(refute_0_106,plain,
plus(X,n1) = plus(X,n1),
introduced(tautology,[refl,[$fot(plus(X,n1))]]) ).
cnf(refute_0_107,plain,
( n1 != loopcounter
| plus(X,n1) != plus(X,n1)
| plus(X,n1) = plus(X,loopcounter) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X,n1),plus(X,n1)) ),[1,1],$fot(loopcounter)]]) ).
cnf(refute_0_108,plain,
( n1 != loopcounter
| plus(X,n1) = plus(X,loopcounter) ),
inference(resolve,[$cnf( $equal(plus(X,n1),plus(X,n1)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
plus(X,n1) = plus(X,loopcounter),
inference(resolve,[$cnf( $equal(n1,loopcounter) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
( plus(X,n1) != plus(X,loopcounter)
| plus(X,n1) != succ(X)
| plus(X,loopcounter) = succ(X) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X,n1),succ(X)) ),[0],$fot(plus(X,loopcounter))]]) ).
cnf(refute_0_111,plain,
( plus(X,n1) != succ(X)
| plus(X,loopcounter) = succ(X) ),
inference(resolve,[$cnf( $equal(plus(X,n1),plus(X,loopcounter)) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
plus(X,loopcounter) = succ(X),
inference(resolve,[$cnf( $equal(plus(X,n1),succ(X)) )],[refute_0_14,refute_0_111]) ).
cnf(refute_0_113,plain,
plus(X_12,loopcounter) = succ(X_12),
inference(subst,[],[refute_0_112:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_114,plain,
succ(succ(succ(n0))) = n3,
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_115,plain,
( plus(X,n3) != succ(succ(succ(X)))
| succ(succ(succ(X))) = plus(X,n3) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(X,n3))),bind(Y0,$fot(succ(succ(succ(X)))))]]) ).
cnf(refute_0_116,plain,
succ(succ(succ(X))) = plus(X,n3),
inference(resolve,[$cnf( $equal(plus(X,n3),succ(succ(succ(X)))) )],[refute_0_3,refute_0_115]) ).
cnf(refute_0_117,plain,
succ(succ(succ(n0))) = plus(n0,n3),
inference(subst,[],[refute_0_116:[bind(X,$fot(n0))]]) ).
cnf(refute_0_118,plain,
( succ(succ(succ(n0))) != n3
| succ(succ(succ(n0))) != plus(n0,n3)
| plus(n0,n3) = n3 ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(succ(n0))),n3) ),[0],$fot(plus(n0,n3))]]) ).
cnf(refute_0_119,plain,
( succ(succ(succ(n0))) != n3
| plus(n0,n3) = n3 ),
inference(resolve,[$cnf( $equal(succ(succ(succ(n0))),plus(n0,n3)) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
plus(n0,n3) = n3,
inference(resolve,[$cnf( $equal(succ(succ(succ(n0))),n3) )],[refute_0_114,refute_0_119]) ).
cnf(refute_0_121,plain,
plus(n0,n3) = plus(n0,n3),
introduced(tautology,[refl,[$fot(plus(n0,n3))]]) ).
cnf(refute_0_122,plain,
( n0 != loopcounter
| plus(n0,n3) != plus(n0,n3)
| plus(n0,n3) = plus(loopcounter,n3) ),
introduced(tautology,[equality,[$cnf( $equal(plus(n0,n3),plus(n0,n3)) ),[1,0],$fot(loopcounter)]]) ).
cnf(refute_0_123,plain,
( n0 != loopcounter
| plus(n0,n3) = plus(loopcounter,n3) ),
inference(resolve,[$cnf( $equal(plus(n0,n3),plus(n0,n3)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
plus(n0,n3) = plus(loopcounter,n3),
inference(resolve,[$cnf( $equal(n0,loopcounter) )],[refute_0_41,refute_0_123]) ).
cnf(refute_0_125,plain,
( plus(n0,n3) != n3
| plus(n0,n3) != plus(loopcounter,n3)
| plus(loopcounter,n3) = n3 ),
introduced(tautology,[equality,[$cnf( $equal(plus(n0,n3),n3) ),[0],$fot(plus(loopcounter,n3))]]) ).
cnf(refute_0_126,plain,
( plus(n0,n3) != n3
| plus(loopcounter,n3) = n3 ),
inference(resolve,[$cnf( $equal(plus(n0,n3),plus(loopcounter,n3)) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
plus(loopcounter,n3) = n3,
inference(resolve,[$cnf( $equal(plus(n0,n3),n3) )],[refute_0_120,refute_0_126]) ).
cnf(refute_0_128,plain,
( n1 != loopcounter
| succ(loopcounter) != n1
| succ(loopcounter) = loopcounter ),
introduced(tautology,[equality,[$cnf( $equal(succ(loopcounter),n1) ),[1],$fot(loopcounter)]]) ).
cnf(refute_0_129,plain,
( succ(loopcounter) != n1
| succ(loopcounter) = loopcounter ),
inference(resolve,[$cnf( $equal(n1,loopcounter) )],[refute_0_105,refute_0_128]) ).
cnf(refute_0_130,plain,
succ(loopcounter) = loopcounter,
inference(resolve,[$cnf( $equal(succ(loopcounter),n1) )],[refute_0_51,refute_0_129]) ).
cnf(refute_0_131,plain,
plus(X,n2) = succ(succ(X)),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_132,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_133,plain,
succ(succ(n0)) = succ(succ(n0)),
introduced(tautology,[refl,[$fot(succ(succ(n0)))]]) ).
cnf(refute_0_134,plain,
( succ(n0) != n1
| succ(succ(n0)) != succ(succ(n0))
| succ(succ(n0)) = succ(n1) ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) ),[1,0],$fot(n1)]]) ).
cnf(refute_0_135,plain,
( succ(n0) != n1
| succ(succ(n0)) = succ(n1) ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
succ(succ(n0)) = succ(n1),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_21,refute_0_135]) ).
cnf(refute_0_137,plain,
( succ(succ(n0)) != n2
| succ(succ(n0)) != succ(n1)
| succ(n1) = n2 ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),n2) ),[0],$fot(succ(n1))]]) ).
cnf(refute_0_138,plain,
( succ(succ(n0)) != n2
| succ(n1) = n2 ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(n1)) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
succ(n1) = n2,
inference(resolve,[$cnf( $equal(succ(succ(n0)),n2) )],[refute_0_132,refute_0_138]) ).
cnf(refute_0_140,plain,
succ(n1) = succ(n1),
introduced(tautology,[refl,[$fot(succ(n1))]]) ).
cnf(refute_0_141,plain,
( n1 != loopcounter
| succ(n1) != succ(n1)
| succ(n1) = succ(loopcounter) ),
introduced(tautology,[equality,[$cnf( $equal(succ(n1),succ(n1)) ),[1,0],$fot(loopcounter)]]) ).
cnf(refute_0_142,plain,
( n1 != loopcounter
| succ(n1) = succ(loopcounter) ),
inference(resolve,[$cnf( $equal(succ(n1),succ(n1)) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
succ(n1) = succ(loopcounter),
inference(resolve,[$cnf( $equal(n1,loopcounter) )],[refute_0_105,refute_0_142]) ).
cnf(refute_0_144,plain,
( succ(loopcounter) != loopcounter
| succ(n1) != succ(loopcounter)
| succ(n1) = loopcounter ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(succ(n1))),bind(Y0,$fot(succ(loopcounter))),bind(Z,$fot(loopcounter))]]) ).
cnf(refute_0_145,plain,
( succ(loopcounter) != loopcounter
| succ(n1) = loopcounter ),
inference(resolve,[$cnf( $equal(succ(n1),succ(loopcounter)) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
succ(n1) = loopcounter,
inference(resolve,[$cnf( $equal(succ(loopcounter),loopcounter) )],[refute_0_130,refute_0_145]) ).
cnf(refute_0_147,plain,
( succ(n1) != loopcounter
| succ(n1) != n2
| loopcounter = n2 ),
introduced(tautology,[equality,[$cnf( $equal(succ(n1),n2) ),[0],$fot(loopcounter)]]) ).
cnf(refute_0_148,plain,
( succ(n1) != n2
| loopcounter = n2 ),
inference(resolve,[$cnf( $equal(succ(n1),loopcounter) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
loopcounter = n2,
inference(resolve,[$cnf( $equal(succ(n1),n2) )],[refute_0_139,refute_0_148]) ).
cnf(refute_0_150,plain,
( loopcounter != n2
| n2 = loopcounter ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(loopcounter)),bind(Y0,$fot(n2))]]) ).
cnf(refute_0_151,plain,
n2 = loopcounter,
inference(resolve,[$cnf( $equal(loopcounter,n2) )],[refute_0_149,refute_0_150]) ).
cnf(refute_0_152,plain,
plus(X,n2) = plus(X,n2),
introduced(tautology,[refl,[$fot(plus(X,n2))]]) ).
cnf(refute_0_153,plain,
( n2 != loopcounter
| plus(X,n2) != plus(X,n2)
| plus(X,n2) = plus(X,loopcounter) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X,n2),plus(X,n2)) ),[1,1],$fot(loopcounter)]]) ).
cnf(refute_0_154,plain,
( n2 != loopcounter
| plus(X,n2) = plus(X,loopcounter) ),
inference(resolve,[$cnf( $equal(plus(X,n2),plus(X,n2)) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
plus(X,n2) = plus(X,loopcounter),
inference(resolve,[$cnf( $equal(n2,loopcounter) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
( plus(X,loopcounter) != succ(X)
| plus(X,n2) != plus(X,loopcounter)
| plus(X,n2) = succ(X) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(plus(X,n2))),bind(Y0,$fot(plus(X,loopcounter))),bind(Z,$fot(succ(X)))]]) ).
cnf(refute_0_157,plain,
( plus(X,loopcounter) != succ(X)
| plus(X,n2) = succ(X) ),
inference(resolve,[$cnf( $equal(plus(X,n2),plus(X,loopcounter)) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
plus(X,n2) = succ(X),
inference(resolve,[$cnf( $equal(plus(X,loopcounter),succ(X)) )],[refute_0_112,refute_0_157]) ).
cnf(refute_0_159,plain,
( plus(X,n2) != succ(X)
| plus(X,n2) != succ(succ(X))
| succ(X) = succ(succ(X)) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X,n2),succ(succ(X))) ),[0],$fot(succ(X))]]) ).
cnf(refute_0_160,plain,
( plus(X,n2) != succ(succ(X))
| succ(X) = succ(succ(X)) ),
inference(resolve,[$cnf( $equal(plus(X,n2),succ(X)) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
succ(X) = succ(succ(X)),
inference(resolve,[$cnf( $equal(plus(X,n2),succ(succ(X))) )],[refute_0_131,refute_0_160]) ).
cnf(refute_0_162,plain,
( succ(X) != succ(succ(X))
| succ(succ(X)) = succ(X) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(succ(X))),bind(Y0,$fot(succ(succ(X))))]]) ).
cnf(refute_0_163,plain,
succ(succ(X)) = succ(X),
inference(resolve,[$cnf( $equal(succ(X),succ(succ(X))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
succ(succ(succ(X))) = succ(succ(X)),
inference(subst,[],[refute_0_163:[bind(X,$fot(succ(X)))]]) ).
cnf(refute_0_165,plain,
( succ(succ(X)) != succ(X)
| succ(succ(succ(X))) != succ(succ(X))
| succ(succ(succ(X))) = succ(X) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(succ(succ(succ(X))))),bind(Y0,$fot(succ(succ(X)))),bind(Z,$fot(succ(X)))]]) ).
cnf(refute_0_166,plain,
( succ(succ(X)) != succ(X)
| succ(succ(succ(X))) = succ(X) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(X))),succ(succ(X))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
succ(succ(succ(X))) = succ(X),
inference(resolve,[$cnf( $equal(succ(succ(X)),succ(X)) )],[refute_0_163,refute_0_166]) ).
cnf(refute_0_168,plain,
( plus(X,n3) != succ(succ(succ(X)))
| succ(succ(succ(X))) != succ(X)
| plus(X,n3) = succ(X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(X,n3),succ(X)) ),[0],$fot(succ(succ(succ(X))))]]) ).
cnf(refute_0_169,plain,
( plus(X,n3) != succ(succ(succ(X)))
| plus(X,n3) = succ(X) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(X))),succ(X)) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
plus(X,n3) = succ(X),
inference(resolve,[$cnf( $equal(plus(X,n3),succ(succ(succ(X)))) )],[refute_0_3,refute_0_169]) ).
cnf(refute_0_171,plain,
plus(loopcounter,n3) = succ(loopcounter),
inference(subst,[],[refute_0_170:[bind(X,$fot(loopcounter))]]) ).
cnf(refute_0_172,plain,
( plus(loopcounter,n3) != succ(loopcounter)
| succ(loopcounter) != loopcounter
| plus(loopcounter,n3) = loopcounter ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(plus(loopcounter,n3))),bind(Y0,$fot(succ(loopcounter))),bind(Z,$fot(loopcounter))]]) ).
cnf(refute_0_173,plain,
( succ(loopcounter) != loopcounter
| plus(loopcounter,n3) = loopcounter ),
inference(resolve,[$cnf( $equal(plus(loopcounter,n3),succ(loopcounter)) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
plus(loopcounter,n3) = loopcounter,
inference(resolve,[$cnf( $equal(succ(loopcounter),loopcounter) )],[refute_0_130,refute_0_173]) ).
cnf(refute_0_175,plain,
( plus(loopcounter,n3) != loopcounter
| plus(loopcounter,n3) != n3
| loopcounter = n3 ),
introduced(tautology,[equality,[$cnf( $equal(plus(loopcounter,n3),n3) ),[0],$fot(loopcounter)]]) ).
cnf(refute_0_176,plain,
( plus(loopcounter,n3) != n3
| loopcounter = n3 ),
inference(resolve,[$cnf( $equal(plus(loopcounter,n3),loopcounter) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
loopcounter = n3,
inference(resolve,[$cnf( $equal(plus(loopcounter,n3),n3) )],[refute_0_127,refute_0_176]) ).
cnf(refute_0_178,plain,
( loopcounter != n3
| n3 = loopcounter ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(loopcounter)),bind(Y0,$fot(n3))]]) ).
cnf(refute_0_179,plain,
n3 = loopcounter,
inference(resolve,[$cnf( $equal(loopcounter,n3) )],[refute_0_177,refute_0_178]) ).
cnf(refute_0_180,plain,
plus(X_12,n3) = plus(X_12,n3),
introduced(tautology,[refl,[$fot(plus(X_12,n3))]]) ).
cnf(refute_0_181,plain,
( n3 != loopcounter
| plus(X_12,n3) != plus(X_12,n3)
| plus(X_12,n3) = plus(X_12,loopcounter) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X_12,n3),plus(X_12,n3)) ),[1,1],$fot(loopcounter)]]) ).
cnf(refute_0_182,plain,
( n3 != loopcounter
| plus(X_12,n3) = plus(X_12,loopcounter) ),
inference(resolve,[$cnf( $equal(plus(X_12,n3),plus(X_12,n3)) )],[refute_0_180,refute_0_181]) ).
cnf(refute_0_183,plain,
plus(X_12,n3) = plus(X_12,loopcounter),
inference(resolve,[$cnf( $equal(n3,loopcounter) )],[refute_0_179,refute_0_182]) ).
cnf(refute_0_184,plain,
( plus(X_12,loopcounter) != succ(X_12)
| plus(X_12,n3) != plus(X_12,loopcounter)
| plus(X_12,n3) = succ(X_12) ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(plus(X_12,n3))),bind(Y0,$fot(plus(X_12,loopcounter))),bind(Z,$fot(succ(X_12)))]]) ).
cnf(refute_0_185,plain,
( plus(X_12,loopcounter) != succ(X_12)
| plus(X_12,n3) = succ(X_12) ),
inference(resolve,[$cnf( $equal(plus(X_12,n3),plus(X_12,loopcounter)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
plus(X_12,n3) = succ(X_12),
inference(resolve,[$cnf( $equal(plus(X_12,loopcounter),succ(X_12)) )],[refute_0_113,refute_0_185]) ).
cnf(refute_0_187,plain,
pred(plus(X_12,n3)) = pred(plus(X_12,n3)),
introduced(tautology,[refl,[$fot(pred(plus(X_12,n3)))]]) ).
cnf(refute_0_188,plain,
( plus(X_12,n3) != succ(X_12)
| pred(plus(X_12,n3)) != pred(plus(X_12,n3))
| pred(plus(X_12,n3)) = pred(succ(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(pred(plus(X_12,n3)),pred(plus(X_12,n3))) ),[1,0],$fot(succ(X_12))]]) ).
cnf(refute_0_189,plain,
( plus(X_12,n3) != succ(X_12)
| pred(plus(X_12,n3)) = pred(succ(X_12)) ),
inference(resolve,[$cnf( $equal(pred(plus(X_12,n3)),pred(plus(X_12,n3))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
pred(plus(X_12,n3)) = pred(succ(X_12)),
inference(resolve,[$cnf( $equal(plus(X_12,n3),succ(X_12)) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
( pred(plus(X_12,n3)) != pred(succ(X_12))
| pred(succ(X_12)) != X_12
| pred(plus(X_12,n3)) = X_12 ),
inference(subst,[],[refute_0_87:[bind(X0,$fot(pred(plus(X_12,n3)))),bind(Y0,$fot(pred(succ(X_12)))),bind(Z,$fot(X_12))]]) ).
cnf(refute_0_192,plain,
( pred(succ(X_12)) != X_12
| pred(plus(X_12,n3)) = X_12 ),
inference(resolve,[$cnf( $equal(pred(plus(X_12,n3)),pred(succ(X_12))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
pred(plus(X_12,n3)) = X_12,
inference(resolve,[$cnf( $equal(pred(succ(X_12)),X_12) )],[refute_0_13,refute_0_192]) ).
cnf(refute_0_194,plain,
( pred(plus(X_12,n3)) != X_12
| pred(plus(X_12,n3)) != succ(succ(X_12))
| X_12 = succ(succ(X_12)) ),
introduced(tautology,[equality,[$cnf( $equal(pred(plus(X_12,n3)),succ(succ(X_12))) ),[0],$fot(X_12)]]) ).
cnf(refute_0_195,plain,
( pred(plus(X_12,n3)) != succ(succ(X_12))
| X_12 = succ(succ(X_12)) ),
inference(resolve,[$cnf( $equal(pred(plus(X_12,n3)),X_12) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
succ(succ(X_12)) = succ(X_12),
inference(subst,[],[refute_0_163:[bind(X,$fot(X_12))]]) ).
cnf(refute_0_197,plain,
( X_12 != succ(succ(X_12))
| succ(succ(X_12)) != succ(X_12)
| X_12 = succ(X_12) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_12,succ(X_12)) ),[0],$fot(succ(succ(X_12)))]]) ).
cnf(refute_0_198,plain,
( X_12 != succ(succ(X_12))
| X_12 = succ(X_12) ),
inference(resolve,[$cnf( $equal(succ(succ(X_12)),succ(X_12)) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
( pred(plus(X_12,n3)) != succ(succ(X_12))
| X_12 = succ(X_12) ),
inference(resolve,[$cnf( $equal(X_12,succ(succ(X_12))) )],[refute_0_195,refute_0_198]) ).
cnf(refute_0_200,plain,
X_12 = succ(X_12),
inference(resolve,[$cnf( $equal(pred(plus(X_12,n3)),succ(succ(X_12))) )],[refute_0_12,refute_0_199]) ).
cnf(refute_0_201,plain,
( X_12 != succ(X_12)
| succ(X_12) = X_12 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_12)),bind(Y0,$fot(succ(X_12)))]]) ).
cnf(refute_0_202,plain,
succ(X_12) = X_12,
inference(resolve,[$cnf( $equal(X_12,succ(X_12)) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
succ(X) = X,
inference(subst,[],[refute_0_202:[bind(X_12,$fot(X))]]) ).
cnf(refute_0_204,plain,
( succ(X) != X
| ~ gt(succ(X),X)
| gt(X,X) ),
introduced(tautology,[equality,[$cnf( gt(succ(X),X) ),[0],$fot(X)]]) ).
cnf(refute_0_205,plain,
( ~ gt(succ(X),X)
| gt(X,X) ),
inference(resolve,[$cnf( $equal(succ(X),X) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
gt(X,X),
inference(resolve,[$cnf( gt(succ(X),X) )],[refute_0_0,refute_0_205]) ).
cnf(refute_0_207,plain,
~ gt(X,X),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_208,plain,
$false,
inference(resolve,[$cnf( gt(X,X) )],[refute_0_206,refute_0_207]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWV181+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n010.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 07:54:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 32.87/33.07 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.87/33.07
% 32.87/33.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.87/33.08
%------------------------------------------------------------------------------