TSTP Solution File: SWV192+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV192+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 20:30:26 EDT 2022
% Result : Theorem 39.66s 39.85s
% Output : CNFRefutation 39.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 53
% Syntax : Number of formulae : 222 ( 108 unt; 0 def)
% Number of atoms : 583 ( 419 equ)
% Maximal formula atoms : 52 ( 2 avg)
% Number of connectives : 544 ( 183 ~; 157 |; 183 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 44 ( 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 : 171 ( 0 sgn 72 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ).
fof(gt_succ,axiom,
! [X] : gt(succ(X),X) ).
fof(leq_succ,axiom,
! [X,Y] :
( leq(X,Y)
=> leq(X,succ(Y)) ) ).
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(quaternion_ds1_inuse_0003,conjecture,
( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& gt(pv5,n0)
& ! [A,B] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n2)
& leq(B,pred(pv5)) )
=> a_select3(u_defuse,A,B) = use )
& ! [C,D] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,pred(pv5)) )
=> a_select3(z_defuse,C,D) = use ) )
=> ! [E,F] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n2)
& leq(F,pred(pv5)) )
=> ( ( ~ ( n0 = E
& pv5 = F )
& ~ ( n1 = E
& pv5 = F )
& ~ ( n2 = E
& pv5 = F ) )
=> a_select3(u_defuse,E,F) = use ) ) ) ).
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,
( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& gt(pv5,n0)
& ! [A,B] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n2)
& leq(B,pred(pv5)) )
=> a_select3(u_defuse,A,B) = use )
& ! [C,D] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,pred(pv5)) )
=> a_select3(z_defuse,C,D) = use ) )
=> ! [E,F] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n2)
& leq(F,pred(pv5))
& ~ ( n0 = E
& pv5 = F )
& ~ ( n1 = E
& pv5 = F )
& ~ ( n2 = E
& pv5 = F ) )
=> a_select3(u_defuse,E,F) = use ) ),
inference(strip,[],[quaternion_ds1_inuse_0003]) ).
fof(negate_0_0,plain,
~ ( ( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& gt(pv5,n0)
& ! [A,B] :
( ( leq(n0,A)
& leq(n0,B)
& leq(A,n2)
& leq(B,pred(pv5)) )
=> a_select3(u_defuse,A,B) = use )
& ! [C,D] :
( ( leq(n0,C)
& leq(n0,D)
& leq(C,n2)
& leq(D,pred(pv5)) )
=> a_select3(z_defuse,C,D) = use ) )
=> ! [E,F] :
( ( leq(n0,E)
& leq(n0,F)
& leq(E,n2)
& leq(F,pred(pv5))
& ~ ( n0 = E
& pv5 = F )
& ~ ( n1 = E
& pv5 = F )
& ~ ( n2 = E
& pv5 = F ) )
=> a_select3(u_defuse,E,F) = use ) ),
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,
succ(n0) = n1,
inference(canonicalize,[],[successor_1]) ).
fof(normalize_0_10,plain,
( a_select2(rho_defuse,n0) = use
& a_select2(rho_defuse,n1) = use
& a_select2(rho_defuse,n2) = use
& a_select2(sigma_defuse,n0) = use
& a_select2(sigma_defuse,n1) = use
& a_select2(sigma_defuse,n2) = use
& a_select2(sigma_defuse,n3) = use
& a_select2(sigma_defuse,n4) = use
& a_select2(sigma_defuse,n5) = use
& a_select2(xinit_defuse,n3) = use
& a_select2(xinit_defuse,n4) = use
& a_select2(xinit_defuse,n5) = use
& a_select2(xinit_mean_defuse,n0) = use
& a_select2(xinit_mean_defuse,n1) = use
& a_select2(xinit_mean_defuse,n2) = use
& a_select2(xinit_mean_defuse,n3) = use
& a_select2(xinit_mean_defuse,n4) = use
& a_select2(xinit_mean_defuse,n5) = use
& a_select2(xinit_noise_defuse,n0) = use
& a_select2(xinit_noise_defuse,n1) = use
& a_select2(xinit_noise_defuse,n2) = use
& a_select2(xinit_noise_defuse,n3) = use
& a_select2(xinit_noise_defuse,n4) = use
& a_select2(xinit_noise_defuse,n5) = use
& a_select3(u_defuse,n0,n0) = use
& a_select3(u_defuse,n1,n0) = use
& a_select3(u_defuse,n2,n0) = use
& gt(pv5,n0)
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ? [E,F] :
( a_select3(u_defuse,E,F) != use
& leq(E,n2)
& leq(F,pred(pv5))
& leq(n0,E)
& leq(n0,F)
& ( n0 != E
| pv5 != F )
& ( n1 != E
| pv5 != F )
& ( n2 != E
| pv5 != F ) )
& ! [A,B] :
( ~ leq(A,n2)
| ~ leq(B,pred(pv5))
| ~ leq(n0,A)
| ~ leq(n0,B)
| a_select3(u_defuse,A,B) = use )
& ! [C,D] :
( ~ leq(C,n2)
| ~ leq(D,pred(pv5))
| ~ leq(n0,C)
| ~ leq(n0,D)
| a_select3(z_defuse,C,D) = use ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
leq(pv5,n0),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(canonicalize,[],[leq_succ]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(canonicalize,[],[leq_succ_succ]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ( ~ leq(X,Y)
| leq(succ(X),succ(Y)) )
& ( ~ leq(succ(X),succ(Y))
| leq(X,Y) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [X] : succ(pred(X)) = X,
inference(canonicalize,[],[succ_pred]) ).
fof(normalize_0_19,plain,
! [X] : succ(pred(X)) = X,
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X] :
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(canonicalize,[],[finite_domain_0]) ).
fof(normalize_0_21,plain,
! [X] :
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
gt(pv5,n0),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(canonicalize,[],[leq_gt_pred]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( ~ leq(X,pred(Y))
| gt(Y,X) ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
leq(n0,pv5),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_28,plain,
succ(succ(succ(n0))) = n3,
inference(canonicalize,[],[successor_3]) ).
fof(normalize_0_29,plain,
! [X] : plus(X,n2) = succ(succ(X)),
inference(canonicalize,[],[succ_plus_2_r]) ).
fof(normalize_0_30,plain,
! [X] : plus(X,n2) = succ(succ(X)),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[successor_2]) ).
fof(normalize_0_32,plain,
! [X] : ~ gt(X,X),
inference(canonicalize,[],[irreflexivity_gt]) ).
fof(normalize_0_33,plain,
! [X] : ~ gt(X,X),
inference(specialize,[],[normalize_0_32]) ).
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_11)))) = succ(succ(X_11)),
inference(subst,[],[refute_0_1:[bind(X,$fot(succ(succ(X_11))))]]) ).
cnf(refute_0_3,plain,
plus(X,n3) = succ(succ(succ(X))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
plus(X_11,n3) = succ(succ(succ(X_11))),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_11))]]) ).
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( $equal(X0,X0) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( plus(X_11,n3) != succ(succ(succ(X_11)))
| succ(succ(succ(X_11))) = plus(X_11,n3) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(plus(X_11,n3))),bind(Y0,$fot(succ(succ(succ(X_11)))))]]) ).
cnf(refute_0_9,plain,
succ(succ(succ(X_11))) = plus(X_11,n3),
inference(resolve,[$cnf( $equal(plus(X_11,n3),succ(succ(succ(X_11)))) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( pred(succ(succ(succ(X_11)))) != succ(succ(X_11))
| succ(succ(succ(X_11))) != plus(X_11,n3)
| pred(plus(X_11,n3)) = succ(succ(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(pred(succ(succ(succ(X_11)))),succ(succ(X_11))) ),[0,0],$fot(plus(X_11,n3))]]) ).
cnf(refute_0_11,plain,
( pred(succ(succ(succ(X_11)))) != succ(succ(X_11))
| pred(plus(X_11,n3)) = succ(succ(X_11)) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(X_11))),plus(X_11,n3)) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
pred(plus(X_11,n3)) = succ(succ(X_11)),
inference(resolve,[$cnf( $equal(pred(succ(succ(succ(X_11)))),succ(succ(X_11))) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
pred(succ(X_11)) = X_11,
inference(subst,[],[refute_0_1:[bind(X,$fot(X_11))]]) ).
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,
succ(n0) = n1,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_17,plain,
leq(pv5,n0),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_19,plain,
( ~ leq(pv5,n0)
| leq(pv5,succ(n0)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(pv5)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_20,plain,
leq(pv5,succ(n0)),
inference(resolve,[$cnf( leq(pv5,n0) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( succ(n0) != n1
| ~ leq(pv5,succ(n0))
| leq(pv5,n1) ),
introduced(tautology,[equality,[$cnf( leq(pv5,succ(n0)) ),[1],$fot(n1)]]) ).
cnf(refute_0_22,plain,
( ~ leq(pv5,succ(n0))
| leq(pv5,n1) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_16,refute_0_21]) ).
cnf(refute_0_23,plain,
leq(pv5,n1),
inference(resolve,[$cnf( leq(pv5,succ(n0)) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_25,plain,
( ~ leq(succ(X_1610),succ(n0))
| leq(X_1610,n0) ),
inference(subst,[],[refute_0_24:[bind(X,$fot(X_1610)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_26,plain,
( succ(n0) != n1
| ~ leq(succ(X_1610),n1)
| leq(succ(X_1610),succ(n0)) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(X_1610),succ(n0)) ),[1],$fot(n1)]]) ).
cnf(refute_0_27,plain,
( ~ leq(succ(X_1610),n1)
| leq(succ(X_1610),succ(n0)) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_16,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ leq(succ(X_1610),n1)
| leq(X_1610,n0) ),
inference(resolve,[$cnf( leq(succ(X_1610),succ(n0)) )],[refute_0_27,refute_0_25]) ).
cnf(refute_0_29,plain,
( ~ leq(succ(pred(X)),n1)
| leq(pred(X),n0) ),
inference(subst,[],[refute_0_28:[bind(X_1610,$fot(pred(X)))]]) ).
cnf(refute_0_30,plain,
succ(pred(X)) = X,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_31,plain,
( succ(pred(X)) != X
| ~ leq(X,n1)
| leq(succ(pred(X)),n1) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(pred(X)),n1) ),[0],$fot(X)]]) ).
cnf(refute_0_32,plain,
( ~ leq(X,n1)
| leq(succ(pred(X)),n1) ),
inference(resolve,[$cnf( $equal(succ(pred(X)),X) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ leq(X,n1)
| leq(pred(X),n0) ),
inference(resolve,[$cnf( leq(succ(pred(X)),n1) )],[refute_0_32,refute_0_29]) ).
cnf(refute_0_34,plain,
( ~ leq(pv5,n1)
| leq(pred(pv5),n0) ),
inference(subst,[],[refute_0_33:[bind(X,$fot(pv5))]]) ).
cnf(refute_0_35,plain,
leq(pred(pv5),n0),
inference(resolve,[$cnf( leq(pv5,n1) )],[refute_0_23,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_37,plain,
( ~ leq(n0,pred(pv5))
| ~ leq(pred(pv5),n0)
| pred(pv5) = n0 ),
inference(subst,[],[refute_0_36:[bind(X,$fot(pred(pv5)))]]) ).
cnf(refute_0_38,plain,
( ~ leq(n0,pred(pv5))
| pred(pv5) = n0 ),
inference(resolve,[$cnf( leq(pred(pv5),n0) )],[refute_0_35,refute_0_37]) ).
cnf(refute_0_39,plain,
gt(pv5,n0),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_40,plain,
( ~ gt(Y,X)
| leq(X,pred(Y)) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_41,plain,
( ~ gt(pv5,n0)
| leq(n0,pred(pv5)) ),
inference(subst,[],[refute_0_40:[bind(X,$fot(n0)),bind(Y,$fot(pv5))]]) ).
cnf(refute_0_42,plain,
leq(n0,pred(pv5)),
inference(resolve,[$cnf( gt(pv5,n0) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
pred(pv5) = n0,
inference(resolve,[$cnf( leq(n0,pred(pv5)) )],[refute_0_42,refute_0_38]) ).
cnf(refute_0_44,plain,
pred(succ(tptp_minus_1)) = tptp_minus_1,
inference(subst,[],[refute_0_1:[bind(X,$fot(tptp_minus_1))]]) ).
cnf(refute_0_45,plain,
( pred(succ(tptp_minus_1)) != tptp_minus_1
| succ(tptp_minus_1) != n0
| pred(n0) = tptp_minus_1 ),
introduced(tautology,[equality,[$cnf( $equal(pred(succ(tptp_minus_1)),tptp_minus_1) ),[0,0],$fot(n0)]]) ).
cnf(refute_0_46,plain,
( pred(succ(tptp_minus_1)) != tptp_minus_1
| pred(n0) = tptp_minus_1 ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n0) )],[refute_0_15,refute_0_45]) ).
cnf(refute_0_47,plain,
pred(n0) = tptp_minus_1,
inference(resolve,[$cnf( $equal(pred(succ(tptp_minus_1)),tptp_minus_1) )],[refute_0_44,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,n0)
| pv5 = n0 ),
inference(subst,[],[refute_0_36:[bind(X,$fot(pv5))]]) ).
cnf(refute_0_49,plain,
( ~ leq(n0,pv5)
| pv5 = n0 ),
inference(resolve,[$cnf( leq(pv5,n0) )],[refute_0_17,refute_0_48]) ).
cnf(refute_0_50,plain,
leq(n0,pv5),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_51,plain,
pv5 = n0,
inference(resolve,[$cnf( leq(n0,pv5) )],[refute_0_50,refute_0_49]) ).
cnf(refute_0_52,plain,
pred(pv5) = pred(pv5),
introduced(tautology,[refl,[$fot(pred(pv5))]]) ).
cnf(refute_0_53,plain,
( pred(pv5) != pred(pv5)
| pv5 != n0
| pred(pv5) = pred(n0) ),
introduced(tautology,[equality,[$cnf( $equal(pred(pv5),pred(pv5)) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_54,plain,
( pv5 != n0
| pred(pv5) = pred(n0) ),
inference(resolve,[$cnf( $equal(pred(pv5),pred(pv5)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
pred(pv5) = pred(n0),
inference(resolve,[$cnf( $equal(pv5,n0) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_57,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_7,refute_0_56]) ).
cnf(refute_0_58,plain,
( pred(n0) != tptp_minus_1
| pred(pv5) != pred(n0)
| pred(pv5) = tptp_minus_1 ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(pred(pv5))),bind(Y0,$fot(pred(n0))),bind(Z,$fot(tptp_minus_1))]]) ).
cnf(refute_0_59,plain,
( pred(n0) != tptp_minus_1
| pred(pv5) = tptp_minus_1 ),
inference(resolve,[$cnf( $equal(pred(pv5),pred(n0)) )],[refute_0_55,refute_0_58]) ).
cnf(refute_0_60,plain,
pred(pv5) = tptp_minus_1,
inference(resolve,[$cnf( $equal(pred(n0),tptp_minus_1) )],[refute_0_47,refute_0_59]) ).
cnf(refute_0_61,plain,
( pred(pv5) != n0
| pred(pv5) != tptp_minus_1
| tptp_minus_1 = n0 ),
introduced(tautology,[equality,[$cnf( $equal(pred(pv5),n0) ),[0],$fot(tptp_minus_1)]]) ).
cnf(refute_0_62,plain,
( pred(pv5) != n0
| tptp_minus_1 = n0 ),
inference(resolve,[$cnf( $equal(pred(pv5),tptp_minus_1) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
tptp_minus_1 = n0,
inference(resolve,[$cnf( $equal(pred(pv5),n0) )],[refute_0_43,refute_0_62]) ).
cnf(refute_0_64,plain,
succ(tptp_minus_1) = succ(tptp_minus_1),
introduced(tautology,[refl,[$fot(succ(tptp_minus_1))]]) ).
cnf(refute_0_65,plain,
( succ(tptp_minus_1) != succ(tptp_minus_1)
| tptp_minus_1 != n0
| succ(tptp_minus_1) = succ(n0) ),
introduced(tautology,[equality,[$cnf( $equal(succ(tptp_minus_1),succ(tptp_minus_1)) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_66,plain,
( tptp_minus_1 != n0
| succ(tptp_minus_1) = succ(n0) ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),succ(tptp_minus_1)) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
succ(tptp_minus_1) = succ(n0),
inference(resolve,[$cnf( $equal(tptp_minus_1,n0) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
( succ(n0) != n1
| succ(tptp_minus_1) != succ(n0)
| succ(tptp_minus_1) = n1 ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(succ(tptp_minus_1))),bind(Y0,$fot(succ(n0))),bind(Z,$fot(n1))]]) ).
cnf(refute_0_69,plain,
( succ(n0) != n1
| succ(tptp_minus_1) = n1 ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),succ(n0)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
succ(tptp_minus_1) = n1,
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_16,refute_0_69]) ).
cnf(refute_0_71,plain,
( succ(tptp_minus_1) != n0
| succ(tptp_minus_1) != n1
| n1 = n0 ),
introduced(tautology,[equality,[$cnf( $equal(succ(tptp_minus_1),n0) ),[0],$fot(n1)]]) ).
cnf(refute_0_72,plain,
( succ(tptp_minus_1) != n0
| n1 = n0 ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n1) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
n1 = n0,
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n0) )],[refute_0_15,refute_0_72]) ).
cnf(refute_0_74,plain,
plus(X,n1) = plus(X,n1),
introduced(tautology,[refl,[$fot(plus(X,n1))]]) ).
cnf(refute_0_75,plain,
( n1 != n0
| plus(X,n1) != plus(X,n1)
| plus(X,n1) = plus(X,n0) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X,n1),plus(X,n1)) ),[1,1],$fot(n0)]]) ).
cnf(refute_0_76,plain,
( n1 != n0
| plus(X,n1) = plus(X,n0) ),
inference(resolve,[$cnf( $equal(plus(X,n1),plus(X,n1)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
plus(X,n1) = plus(X,n0),
inference(resolve,[$cnf( $equal(n1,n0) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
( plus(X,n1) != plus(X,n0)
| plus(X,n1) != succ(X)
| plus(X,n0) = succ(X) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X,n1),succ(X)) ),[0],$fot(plus(X,n0))]]) ).
cnf(refute_0_79,plain,
( plus(X,n1) != succ(X)
| plus(X,n0) = succ(X) ),
inference(resolve,[$cnf( $equal(plus(X,n1),plus(X,n0)) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
plus(X,n0) = succ(X),
inference(resolve,[$cnf( $equal(plus(X,n1),succ(X)) )],[refute_0_14,refute_0_79]) ).
cnf(refute_0_81,plain,
plus(X_11,n0) = succ(X_11),
inference(subst,[],[refute_0_80:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_82,plain,
succ(succ(succ(n0))) = n3,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_83,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_84,plain,
succ(succ(succ(X))) = plus(X,n3),
inference(resolve,[$cnf( $equal(plus(X,n3),succ(succ(succ(X)))) )],[refute_0_3,refute_0_83]) ).
cnf(refute_0_85,plain,
succ(succ(succ(n0))) = plus(n0,n3),
inference(subst,[],[refute_0_84:[bind(X,$fot(n0))]]) ).
cnf(refute_0_86,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_87,plain,
( succ(succ(succ(n0))) != n3
| plus(n0,n3) = n3 ),
inference(resolve,[$cnf( $equal(succ(succ(succ(n0))),plus(n0,n3)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
plus(n0,n3) = n3,
inference(resolve,[$cnf( $equal(succ(succ(succ(n0))),n3) )],[refute_0_82,refute_0_87]) ).
cnf(refute_0_89,plain,
( n1 != n0
| succ(n0) != n1
| succ(n0) = n0 ),
introduced(tautology,[equality,[$cnf( $equal(succ(n0),n1) ),[1],$fot(n0)]]) ).
cnf(refute_0_90,plain,
( succ(n0) != n1
| succ(n0) = n0 ),
inference(resolve,[$cnf( $equal(n1,n0) )],[refute_0_73,refute_0_89]) ).
cnf(refute_0_91,plain,
succ(n0) = n0,
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_16,refute_0_90]) ).
cnf(refute_0_92,plain,
plus(X,n2) = succ(succ(X)),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_93,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_94,plain,
succ(succ(n0)) = succ(succ(n0)),
introduced(tautology,[refl,[$fot(succ(succ(n0)))]]) ).
cnf(refute_0_95,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_96,plain,
( succ(n0) != n1
| succ(succ(n0)) = succ(n1) ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
succ(succ(n0)) = succ(n1),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_16,refute_0_96]) ).
cnf(refute_0_98,plain,
( succ(succ(n0)) != n2
| succ(succ(n0)) != succ(n1)
| succ(n1) = n2 ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),n2) ),[0],$fot(succ(n1))]]) ).
cnf(refute_0_99,plain,
( succ(succ(n0)) != n2
| succ(n1) = n2 ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(n1)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
succ(n1) = n2,
inference(resolve,[$cnf( $equal(succ(succ(n0)),n2) )],[refute_0_93,refute_0_99]) ).
cnf(refute_0_101,plain,
succ(n1) = succ(n1),
introduced(tautology,[refl,[$fot(succ(n1))]]) ).
cnf(refute_0_102,plain,
( n1 != n0
| succ(n1) != succ(n1)
| succ(n1) = succ(n0) ),
introduced(tautology,[equality,[$cnf( $equal(succ(n1),succ(n1)) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_103,plain,
( n1 != n0
| succ(n1) = succ(n0) ),
inference(resolve,[$cnf( $equal(succ(n1),succ(n1)) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
succ(n1) = succ(n0),
inference(resolve,[$cnf( $equal(n1,n0) )],[refute_0_73,refute_0_103]) ).
cnf(refute_0_105,plain,
( succ(n0) != n0
| succ(n1) != succ(n0)
| succ(n1) = n0 ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(succ(n1))),bind(Y0,$fot(succ(n0))),bind(Z,$fot(n0))]]) ).
cnf(refute_0_106,plain,
( succ(n0) != n0
| succ(n1) = n0 ),
inference(resolve,[$cnf( $equal(succ(n1),succ(n0)) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
succ(n1) = n0,
inference(resolve,[$cnf( $equal(succ(n0),n0) )],[refute_0_91,refute_0_106]) ).
cnf(refute_0_108,plain,
( succ(n1) != n0
| succ(n1) != n2
| n0 = n2 ),
introduced(tautology,[equality,[$cnf( $equal(succ(n1),n2) ),[0],$fot(n0)]]) ).
cnf(refute_0_109,plain,
( succ(n1) != n2
| n0 = n2 ),
inference(resolve,[$cnf( $equal(succ(n1),n0) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
n0 = n2,
inference(resolve,[$cnf( $equal(succ(n1),n2) )],[refute_0_100,refute_0_109]) ).
cnf(refute_0_111,plain,
( n0 != n2
| n2 = n0 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(n0)),bind(Y0,$fot(n2))]]) ).
cnf(refute_0_112,plain,
n2 = n0,
inference(resolve,[$cnf( $equal(n0,n2) )],[refute_0_110,refute_0_111]) ).
cnf(refute_0_113,plain,
plus(X,n2) = plus(X,n2),
introduced(tautology,[refl,[$fot(plus(X,n2))]]) ).
cnf(refute_0_114,plain,
( n2 != n0
| plus(X,n2) != plus(X,n2)
| plus(X,n2) = plus(X,n0) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X,n2),plus(X,n2)) ),[1,1],$fot(n0)]]) ).
cnf(refute_0_115,plain,
( n2 != n0
| plus(X,n2) = plus(X,n0) ),
inference(resolve,[$cnf( $equal(plus(X,n2),plus(X,n2)) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
plus(X,n2) = plus(X,n0),
inference(resolve,[$cnf( $equal(n2,n0) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
( plus(X,n0) != succ(X)
| plus(X,n2) != plus(X,n0)
| plus(X,n2) = succ(X) ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(plus(X,n2))),bind(Y0,$fot(plus(X,n0))),bind(Z,$fot(succ(X)))]]) ).
cnf(refute_0_118,plain,
( plus(X,n0) != succ(X)
| plus(X,n2) = succ(X) ),
inference(resolve,[$cnf( $equal(plus(X,n2),plus(X,n0)) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
plus(X,n2) = succ(X),
inference(resolve,[$cnf( $equal(plus(X,n0),succ(X)) )],[refute_0_80,refute_0_118]) ).
cnf(refute_0_120,plain,
( plus(X,n2) != succ(X)
| plus(X,n2) != succ(succ(X))
| succ(X) = succ(succ(X)) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X,n2),succ(succ(X))) ),[0],$fot(succ(X))]]) ).
cnf(refute_0_121,plain,
( plus(X,n2) != succ(succ(X))
| succ(X) = succ(succ(X)) ),
inference(resolve,[$cnf( $equal(plus(X,n2),succ(X)) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
succ(X) = succ(succ(X)),
inference(resolve,[$cnf( $equal(plus(X,n2),succ(succ(X))) )],[refute_0_92,refute_0_121]) ).
cnf(refute_0_123,plain,
( succ(X) != succ(succ(X))
| succ(succ(X)) = succ(X) ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(succ(X))),bind(Y0,$fot(succ(succ(X))))]]) ).
cnf(refute_0_124,plain,
succ(succ(X)) = succ(X),
inference(resolve,[$cnf( $equal(succ(X),succ(succ(X))) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
succ(succ(succ(X))) = succ(succ(X)),
inference(subst,[],[refute_0_124:[bind(X,$fot(succ(X)))]]) ).
cnf(refute_0_126,plain,
( succ(succ(X)) != succ(X)
| succ(succ(succ(X))) != succ(succ(X))
| succ(succ(succ(X))) = succ(X) ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(succ(succ(succ(X))))),bind(Y0,$fot(succ(succ(X)))),bind(Z,$fot(succ(X)))]]) ).
cnf(refute_0_127,plain,
( succ(succ(X)) != succ(X)
| succ(succ(succ(X))) = succ(X) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(X))),succ(succ(X))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
succ(succ(succ(X))) = succ(X),
inference(resolve,[$cnf( $equal(succ(succ(X)),succ(X)) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
( plus(X,n3) != succ(succ(succ(X)))
| succ(succ(succ(X))) != succ(X)
| plus(X,n3) = succ(X) ),
introduced(tautology,[equality,[$cnf( ~ $equal(plus(X,n3),succ(X)) ),[0],$fot(succ(succ(succ(X))))]]) ).
cnf(refute_0_130,plain,
( plus(X,n3) != succ(succ(succ(X)))
| plus(X,n3) = succ(X) ),
inference(resolve,[$cnf( $equal(succ(succ(succ(X))),succ(X)) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
plus(X,n3) = succ(X),
inference(resolve,[$cnf( $equal(plus(X,n3),succ(succ(succ(X)))) )],[refute_0_3,refute_0_130]) ).
cnf(refute_0_132,plain,
plus(n0,n3) = succ(n0),
inference(subst,[],[refute_0_131:[bind(X,$fot(n0))]]) ).
cnf(refute_0_133,plain,
( plus(n0,n3) != succ(n0)
| succ(n0) != n0
| plus(n0,n3) = n0 ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(plus(n0,n3))),bind(Y0,$fot(succ(n0))),bind(Z,$fot(n0))]]) ).
cnf(refute_0_134,plain,
( succ(n0) != n0
| plus(n0,n3) = n0 ),
inference(resolve,[$cnf( $equal(plus(n0,n3),succ(n0)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
plus(n0,n3) = n0,
inference(resolve,[$cnf( $equal(succ(n0),n0) )],[refute_0_91,refute_0_134]) ).
cnf(refute_0_136,plain,
( plus(n0,n3) != n0
| plus(n0,n3) != n3
| n0 = n3 ),
introduced(tautology,[equality,[$cnf( $equal(plus(n0,n3),n3) ),[0],$fot(n0)]]) ).
cnf(refute_0_137,plain,
( plus(n0,n3) != n3
| n0 = n3 ),
inference(resolve,[$cnf( $equal(plus(n0,n3),n0) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
n0 = n3,
inference(resolve,[$cnf( $equal(plus(n0,n3),n3) )],[refute_0_88,refute_0_137]) ).
cnf(refute_0_139,plain,
( n0 != n3
| n3 = n0 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(n0)),bind(Y0,$fot(n3))]]) ).
cnf(refute_0_140,plain,
n3 = n0,
inference(resolve,[$cnf( $equal(n0,n3) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
plus(X_11,n3) = plus(X_11,n3),
introduced(tautology,[refl,[$fot(plus(X_11,n3))]]) ).
cnf(refute_0_142,plain,
( n3 != n0
| plus(X_11,n3) != plus(X_11,n3)
| plus(X_11,n3) = plus(X_11,n0) ),
introduced(tautology,[equality,[$cnf( $equal(plus(X_11,n3),plus(X_11,n3)) ),[1,1],$fot(n0)]]) ).
cnf(refute_0_143,plain,
( n3 != n0
| plus(X_11,n3) = plus(X_11,n0) ),
inference(resolve,[$cnf( $equal(plus(X_11,n3),plus(X_11,n3)) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
plus(X_11,n3) = plus(X_11,n0),
inference(resolve,[$cnf( $equal(n3,n0) )],[refute_0_140,refute_0_143]) ).
cnf(refute_0_145,plain,
( plus(X_11,n0) != succ(X_11)
| plus(X_11,n3) != plus(X_11,n0)
| plus(X_11,n3) = succ(X_11) ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(plus(X_11,n3))),bind(Y0,$fot(plus(X_11,n0))),bind(Z,$fot(succ(X_11)))]]) ).
cnf(refute_0_146,plain,
( plus(X_11,n0) != succ(X_11)
| plus(X_11,n3) = succ(X_11) ),
inference(resolve,[$cnf( $equal(plus(X_11,n3),plus(X_11,n0)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
plus(X_11,n3) = succ(X_11),
inference(resolve,[$cnf( $equal(plus(X_11,n0),succ(X_11)) )],[refute_0_81,refute_0_146]) ).
cnf(refute_0_148,plain,
pred(plus(X_11,n3)) = pred(plus(X_11,n3)),
introduced(tautology,[refl,[$fot(pred(plus(X_11,n3)))]]) ).
cnf(refute_0_149,plain,
( plus(X_11,n3) != succ(X_11)
| pred(plus(X_11,n3)) != pred(plus(X_11,n3))
| pred(plus(X_11,n3)) = pred(succ(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(pred(plus(X_11,n3)),pred(plus(X_11,n3))) ),[1,0],$fot(succ(X_11))]]) ).
cnf(refute_0_150,plain,
( plus(X_11,n3) != succ(X_11)
| pred(plus(X_11,n3)) = pred(succ(X_11)) ),
inference(resolve,[$cnf( $equal(pred(plus(X_11,n3)),pred(plus(X_11,n3))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
pred(plus(X_11,n3)) = pred(succ(X_11)),
inference(resolve,[$cnf( $equal(plus(X_11,n3),succ(X_11)) )],[refute_0_147,refute_0_150]) ).
cnf(refute_0_152,plain,
( pred(plus(X_11,n3)) != pred(succ(X_11))
| pred(succ(X_11)) != X_11
| pred(plus(X_11,n3)) = X_11 ),
inference(subst,[],[refute_0_57:[bind(X0,$fot(pred(plus(X_11,n3)))),bind(Y0,$fot(pred(succ(X_11)))),bind(Z,$fot(X_11))]]) ).
cnf(refute_0_153,plain,
( pred(succ(X_11)) != X_11
| pred(plus(X_11,n3)) = X_11 ),
inference(resolve,[$cnf( $equal(pred(plus(X_11,n3)),pred(succ(X_11))) )],[refute_0_151,refute_0_152]) ).
cnf(refute_0_154,plain,
pred(plus(X_11,n3)) = X_11,
inference(resolve,[$cnf( $equal(pred(succ(X_11)),X_11) )],[refute_0_13,refute_0_153]) ).
cnf(refute_0_155,plain,
( pred(plus(X_11,n3)) != X_11
| pred(plus(X_11,n3)) != succ(succ(X_11))
| X_11 = succ(succ(X_11)) ),
introduced(tautology,[equality,[$cnf( $equal(pred(plus(X_11,n3)),succ(succ(X_11))) ),[0],$fot(X_11)]]) ).
cnf(refute_0_156,plain,
( pred(plus(X_11,n3)) != succ(succ(X_11))
| X_11 = succ(succ(X_11)) ),
inference(resolve,[$cnf( $equal(pred(plus(X_11,n3)),X_11) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
succ(succ(X_11)) = succ(X_11),
inference(subst,[],[refute_0_124:[bind(X,$fot(X_11))]]) ).
cnf(refute_0_158,plain,
( X_11 != succ(succ(X_11))
| succ(succ(X_11)) != succ(X_11)
| X_11 = succ(X_11) ),
introduced(tautology,[equality,[$cnf( ~ $equal(X_11,succ(X_11)) ),[0],$fot(succ(succ(X_11)))]]) ).
cnf(refute_0_159,plain,
( X_11 != succ(succ(X_11))
| X_11 = succ(X_11) ),
inference(resolve,[$cnf( $equal(succ(succ(X_11)),succ(X_11)) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
( pred(plus(X_11,n3)) != succ(succ(X_11))
| X_11 = succ(X_11) ),
inference(resolve,[$cnf( $equal(X_11,succ(succ(X_11))) )],[refute_0_156,refute_0_159]) ).
cnf(refute_0_161,plain,
X_11 = succ(X_11),
inference(resolve,[$cnf( $equal(pred(plus(X_11,n3)),succ(succ(X_11))) )],[refute_0_12,refute_0_160]) ).
cnf(refute_0_162,plain,
( X_11 != succ(X_11)
| succ(X_11) = X_11 ),
inference(subst,[],[refute_0_7:[bind(X0,$fot(X_11)),bind(Y0,$fot(succ(X_11)))]]) ).
cnf(refute_0_163,plain,
succ(X_11) = X_11,
inference(resolve,[$cnf( $equal(X_11,succ(X_11)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
succ(X) = X,
inference(subst,[],[refute_0_163:[bind(X_11,$fot(X))]]) ).
cnf(refute_0_165,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_166,plain,
( ~ gt(succ(X),X)
| gt(X,X) ),
inference(resolve,[$cnf( $equal(succ(X),X) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
gt(X,X),
inference(resolve,[$cnf( gt(succ(X),X) )],[refute_0_0,refute_0_166]) ).
cnf(refute_0_168,plain,
~ gt(X,X),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_169,plain,
$false,
inference(resolve,[$cnf( gt(X,X) )],[refute_0_167,refute_0_168]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV192+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Wed Jun 15 19:49:57 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 39.66/39.85 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 39.66/39.85
% 39.66/39.85 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 39.66/39.86
%------------------------------------------------------------------------------