TSTP Solution File: SWV197+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV197+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 20:30:27 EDT 2022
% Result : Theorem 17.15s 17.32s
% Output : CNFRefutation 17.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 106 ( 41 unt; 0 def)
% Number of atoms : 409 ( 219 equ)
% Maximal formula atoms : 51 ( 3 avg)
% Number of connectives : 427 ( 124 ~; 85 |; 194 &)
% ( 9 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 18 con; 0-3 aty)
% Number of variables : 97 ( 0 sgn 69 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(irreflexivity_gt,axiom,
! [X] : ~ gt(X,X) ).
fof(lt_gt,axiom,
! [X,Y] :
( lt(X,Y)
<=> gt(Y,X) ) ).
fof(leq_succ,axiom,
! [X,Y] :
( leq(X,Y)
=> leq(X,succ(Y)) ) ).
fof(leq_succ_gt_equiv,axiom,
! [X,Y] :
( leq(X,Y)
<=> gt(succ(Y),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_0008,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)
& ! [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(z_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(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)
& ! [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(z_defuse,E,F) = use ) ),
inference(strip,[],[quaternion_ds1_inuse_0008]) ).
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)
& ! [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(z_defuse,E,F) = use ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ lt(X,Y) ),
inference(canonicalize,[],[lt_gt]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ lt(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| lt(X,Y) )
& ( ~ lt(X,Y)
| gt(Y,X) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ lt(X,Y)
| gt(Y,X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ gt(Y,X)
| lt(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(canonicalize,[],[leq_succ_gt_equiv]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ gt(succ(Y),X)
<=> ~ leq(X,Y) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ( ~ gt(succ(Y),X)
| leq(X,Y) )
& ( ~ leq(X,Y)
| gt(succ(Y),X) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ leq(X,Y)
| gt(succ(Y),X) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,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
& leq(n0,pv5)
& leq(pv5,n0)
& leq(pv5,n998)
& ? [E,F] :
( a_select3(z_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_10,plain,
? [E,F] :
( a_select3(z_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 ) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( a_select3(z_defuse,skolemFOFtoCNF_E,skolemFOFtoCNF_F) != use
& leq(n0,skolemFOFtoCNF_E)
& leq(n0,skolemFOFtoCNF_F)
& leq(skolemFOFtoCNF_E,n2)
& leq(skolemFOFtoCNF_F,pred(pv5))
& ( n0 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F )
& ( n1 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F )
& ( n2 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F ) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
leq(skolemFOFtoCNF_F,pred(pv5)),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(canonicalize,[],[leq_succ_succ]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ( ~ leq(X,Y)
| leq(succ(X),succ(Y)) )
& ( ~ leq(succ(X),succ(Y))
| leq(X,Y) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ leq(X,Y)
| leq(succ(X),succ(Y)) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X] : succ(pred(X)) = X,
inference(canonicalize,[],[succ_pred]) ).
fof(normalize_0_18,plain,
! [X] : succ(pred(X)) = X,
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
succ(n0) = n1,
inference(canonicalize,[],[successor_1]) ).
fof(normalize_0_20,plain,
leq(pv5,n0),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_21,plain,
! [X] :
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(canonicalize,[],[finite_domain_0]) ).
fof(normalize_0_22,plain,
! [X] :
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
leq(n0,pv5),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_24,plain,
! [X,Y] :
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(canonicalize,[],[leq_succ]) ).
fof(normalize_0_25,plain,
! [X,Y] :
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
leq(n0,skolemFOFtoCNF_F),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_27,plain,
! [X] : ~ gt(X,X),
inference(canonicalize,[],[irreflexivity_gt]) ).
fof(normalize_0_28,plain,
! [X] : ~ gt(X,X),
inference(specialize,[],[normalize_0_27]) ).
cnf(refute_0_0,plain,
( ~ lt(X,Y)
| gt(Y,X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ lt(n1,n1)
| gt(n1,n1) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(n1)),bind(Y,$fot(n1))]]) ).
cnf(refute_0_2,plain,
( ~ gt(Y,X)
| lt(X,Y) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ gt(succ(pv5),succ(skolemFOFtoCNF_F))
| lt(succ(skolemFOFtoCNF_F),succ(pv5)) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(succ(skolemFOFtoCNF_F))),bind(Y,$fot(succ(pv5)))]]) ).
cnf(refute_0_4,plain,
( ~ leq(X,Y)
| gt(succ(Y),X) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ leq(succ(skolemFOFtoCNF_F),pv5)
| gt(succ(pv5),succ(skolemFOFtoCNF_F)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(succ(skolemFOFtoCNF_F))),bind(Y,$fot(pv5))]]) ).
cnf(refute_0_6,plain,
leq(skolemFOFtoCNF_F,pred(pv5)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( ~ leq(X,Y)
| leq(succ(X),succ(Y)) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_8,plain,
( ~ leq(skolemFOFtoCNF_F,pred(pv5))
| leq(succ(skolemFOFtoCNF_F),succ(pred(pv5))) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_F)),bind(Y,$fot(pred(pv5)))]]) ).
cnf(refute_0_9,plain,
leq(succ(skolemFOFtoCNF_F),succ(pred(pv5))),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,pred(pv5)) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
succ(pred(X)) = X,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_11,plain,
succ(pred(pv5)) = pv5,
inference(subst,[],[refute_0_10:[bind(X,$fot(pv5))]]) ).
cnf(refute_0_12,plain,
( succ(pred(pv5)) != pv5
| ~ leq(succ(skolemFOFtoCNF_F),succ(pred(pv5)))
| leq(succ(skolemFOFtoCNF_F),pv5) ),
introduced(tautology,[equality,[$cnf( leq(succ(skolemFOFtoCNF_F),succ(pred(pv5))) ),[1],$fot(pv5)]]) ).
cnf(refute_0_13,plain,
( ~ leq(succ(skolemFOFtoCNF_F),succ(pred(pv5)))
| leq(succ(skolemFOFtoCNF_F),pv5) ),
inference(resolve,[$cnf( $equal(succ(pred(pv5)),pv5) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
leq(succ(skolemFOFtoCNF_F),pv5),
inference(resolve,[$cnf( leq(succ(skolemFOFtoCNF_F),succ(pred(pv5))) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
gt(succ(pv5),succ(skolemFOFtoCNF_F)),
inference(resolve,[$cnf( leq(succ(skolemFOFtoCNF_F),pv5) )],[refute_0_14,refute_0_5]) ).
cnf(refute_0_16,plain,
lt(succ(skolemFOFtoCNF_F),succ(pv5)),
inference(resolve,[$cnf( gt(succ(pv5),succ(skolemFOFtoCNF_F)) )],[refute_0_15,refute_0_3]) ).
cnf(refute_0_17,plain,
succ(n0) = n1,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_18,plain,
leq(pv5,n0),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_19,plain,
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_20,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,n0)
| pv5 = n0 ),
inference(subst,[],[refute_0_19:[bind(X,$fot(pv5))]]) ).
cnf(refute_0_21,plain,
( ~ leq(n0,pv5)
| pv5 = n0 ),
inference(resolve,[$cnf( leq(pv5,n0) )],[refute_0_18,refute_0_20]) ).
cnf(refute_0_22,plain,
leq(n0,pv5),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_23,plain,
pv5 = n0,
inference(resolve,[$cnf( leq(n0,pv5) )],[refute_0_22,refute_0_21]) ).
cnf(refute_0_24,plain,
succ(pv5) = succ(pv5),
introduced(tautology,[refl,[$fot(succ(pv5))]]) ).
cnf(refute_0_25,plain,
( pv5 != n0
| succ(pv5) != succ(pv5)
| succ(pv5) = succ(n0) ),
introduced(tautology,[equality,[$cnf( $equal(succ(pv5),succ(pv5)) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_26,plain,
( pv5 != n0
| succ(pv5) = succ(n0) ),
inference(resolve,[$cnf( $equal(succ(pv5),succ(pv5)) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
succ(pv5) = succ(n0),
inference(resolve,[$cnf( $equal(pv5,n0) )],[refute_0_23,refute_0_26]) ).
cnf(refute_0_28,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_29,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_30,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_32,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( succ(n0) != n1
| succ(pv5) != succ(n0)
| succ(pv5) = n1 ),
inference(subst,[],[refute_0_32:[bind(X0,$fot(succ(pv5))),bind(Y0,$fot(succ(n0))),bind(Z,$fot(n1))]]) ).
cnf(refute_0_34,plain,
( succ(n0) != n1
| succ(pv5) = n1 ),
inference(resolve,[$cnf( $equal(succ(pv5),succ(n0)) )],[refute_0_27,refute_0_33]) ).
cnf(refute_0_35,plain,
succ(pv5) = n1,
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_17,refute_0_34]) ).
cnf(refute_0_36,plain,
( succ(pv5) != n1
| ~ lt(succ(skolemFOFtoCNF_F),succ(pv5))
| lt(succ(skolemFOFtoCNF_F),n1) ),
introduced(tautology,[equality,[$cnf( lt(succ(skolemFOFtoCNF_F),succ(pv5)) ),[1],$fot(n1)]]) ).
cnf(refute_0_37,plain,
( ~ lt(succ(skolemFOFtoCNF_F),succ(pv5))
| lt(succ(skolemFOFtoCNF_F),n1) ),
inference(resolve,[$cnf( $equal(succ(pv5),n1) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
lt(succ(skolemFOFtoCNF_F),n1),
inference(resolve,[$cnf( lt(succ(skolemFOFtoCNF_F),succ(pv5)) )],[refute_0_16,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ leq(n0,skolemFOFtoCNF_F)
| ~ leq(skolemFOFtoCNF_F,n0)
| skolemFOFtoCNF_F = n0 ),
inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_40,plain,
( ~ leq(X,Y)
| leq(X,succ(Y)) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_41,plain,
( ~ leq(skolemFOFtoCNF_F,pred(pv5))
| leq(skolemFOFtoCNF_F,succ(pred(pv5))) ),
inference(subst,[],[refute_0_40:[bind(X,$fot(skolemFOFtoCNF_F)),bind(Y,$fot(pred(pv5)))]]) ).
cnf(refute_0_42,plain,
leq(skolemFOFtoCNF_F,succ(pred(pv5))),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,pred(pv5)) )],[refute_0_6,refute_0_41]) ).
cnf(refute_0_43,plain,
( succ(pred(pv5)) != pv5
| ~ leq(skolemFOFtoCNF_F,succ(pred(pv5)))
| leq(skolemFOFtoCNF_F,pv5) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_F,succ(pred(pv5))) ),[1],$fot(pv5)]]) ).
cnf(refute_0_44,plain,
( ~ leq(skolemFOFtoCNF_F,succ(pred(pv5)))
| leq(skolemFOFtoCNF_F,pv5) ),
inference(resolve,[$cnf( $equal(succ(pred(pv5)),pv5) )],[refute_0_11,refute_0_43]) ).
cnf(refute_0_45,plain,
leq(skolemFOFtoCNF_F,pv5),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,succ(pred(pv5))) )],[refute_0_42,refute_0_44]) ).
cnf(refute_0_46,plain,
( pv5 != n0
| ~ leq(skolemFOFtoCNF_F,pv5)
| leq(skolemFOFtoCNF_F,n0) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_F,pv5) ),[1],$fot(n0)]]) ).
cnf(refute_0_47,plain,
( ~ leq(skolemFOFtoCNF_F,pv5)
| leq(skolemFOFtoCNF_F,n0) ),
inference(resolve,[$cnf( $equal(pv5,n0) )],[refute_0_23,refute_0_46]) ).
cnf(refute_0_48,plain,
leq(skolemFOFtoCNF_F,n0),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,pv5) )],[refute_0_45,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ leq(n0,skolemFOFtoCNF_F)
| skolemFOFtoCNF_F = n0 ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,n0) )],[refute_0_48,refute_0_39]) ).
cnf(refute_0_50,plain,
leq(n0,skolemFOFtoCNF_F),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_51,plain,
skolemFOFtoCNF_F = n0,
inference(resolve,[$cnf( leq(n0,skolemFOFtoCNF_F) )],[refute_0_50,refute_0_49]) ).
cnf(refute_0_52,plain,
succ(skolemFOFtoCNF_F) = succ(skolemFOFtoCNF_F),
introduced(tautology,[refl,[$fot(succ(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_F != n0
| succ(skolemFOFtoCNF_F) != succ(skolemFOFtoCNF_F)
| succ(skolemFOFtoCNF_F) = succ(n0) ),
introduced(tautology,[equality,[$cnf( $equal(succ(skolemFOFtoCNF_F),succ(skolemFOFtoCNF_F)) ),[1,0],$fot(n0)]]) ).
cnf(refute_0_54,plain,
( skolemFOFtoCNF_F != n0
| succ(skolemFOFtoCNF_F) = succ(n0) ),
inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_F),succ(skolemFOFtoCNF_F)) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
succ(skolemFOFtoCNF_F) = succ(n0),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_F,n0) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( succ(n0) != n1
| succ(skolemFOFtoCNF_F) != succ(n0)
| succ(skolemFOFtoCNF_F) = n1 ),
inference(subst,[],[refute_0_32:[bind(X0,$fot(succ(skolemFOFtoCNF_F))),bind(Y0,$fot(succ(n0))),bind(Z,$fot(n1))]]) ).
cnf(refute_0_57,plain,
( succ(n0) != n1
| succ(skolemFOFtoCNF_F) = n1 ),
inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_F),succ(n0)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
succ(skolemFOFtoCNF_F) = n1,
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_17,refute_0_57]) ).
cnf(refute_0_59,plain,
( succ(skolemFOFtoCNF_F) != n1
| ~ lt(succ(skolemFOFtoCNF_F),n1)
| lt(n1,n1) ),
introduced(tautology,[equality,[$cnf( lt(succ(skolemFOFtoCNF_F),n1) ),[0],$fot(n1)]]) ).
cnf(refute_0_60,plain,
( ~ lt(succ(skolemFOFtoCNF_F),n1)
| lt(n1,n1) ),
inference(resolve,[$cnf( $equal(succ(skolemFOFtoCNF_F),n1) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
lt(n1,n1),
inference(resolve,[$cnf( lt(succ(skolemFOFtoCNF_F),n1) )],[refute_0_38,refute_0_60]) ).
cnf(refute_0_62,plain,
gt(n1,n1),
inference(resolve,[$cnf( lt(n1,n1) )],[refute_0_61,refute_0_1]) ).
cnf(refute_0_63,plain,
~ gt(X,X),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_64,plain,
~ gt(n1,n1),
inference(subst,[],[refute_0_63:[bind(X,$fot(n1))]]) ).
cnf(refute_0_65,plain,
$false,
inference(resolve,[$cnf( gt(n1,n1) )],[refute_0_62,refute_0_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV197+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.10/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 16 01:38:33 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 17.15/17.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.15/17.32
% 17.15/17.32 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 17.15/17.32
%------------------------------------------------------------------------------