TSTP Solution File: SWV199+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV199+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 20:30:28 EDT 2022
% Result : Theorem 108.23s 108.42s
% Output : CNFRefutation 108.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 24
% Syntax : Number of formulae : 131 ( 51 unt; 0 def)
% Number of atoms : 454 ( 277 equ)
% Maximal formula atoms : 51 ( 3 avg)
% Number of connectives : 471 ( 148 ~; 108 |; 194 &)
% ( 6 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 18 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 57 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(leq_gt2,axiom,
! [X,Y] :
( ( leq(X,Y)
& X != Y )
=> gt(Y,X) ) ).
fof(leq_gt_pred,axiom,
! [X,Y] :
( leq(X,pred(Y))
<=> gt(Y,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_0010,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,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(successor_2,axiom,
succ(succ(n0)) = n2 ).
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,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_0010]) ).
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,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] : succ(pred(X)) = X,
inference(canonicalize,[],[succ_pred]) ).
fof(normalize_0_1,plain,
! [X] : succ(pred(X)) = X,
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X] :
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(canonicalize,[],[finite_domain_0]) ).
fof(normalize_0_3,plain,
! [X] :
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(canonicalize,[],[leq_succ_succ]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ leq(X,Y)
<=> ~ leq(succ(X),succ(Y)) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ( ~ leq(X,Y)
| leq(succ(X),succ(Y)) )
& ( ~ leq(succ(X),succ(Y))
| leq(X,Y) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
succ(n0) = n1,
inference(canonicalize,[],[successor_1]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(canonicalize,[],[leq_gt_pred]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ gt(Y,X)
<=> ~ leq(X,pred(Y)) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ( ~ gt(Y,X)
| leq(X,pred(Y)) )
& ( ~ leq(X,pred(Y))
| gt(Y,X) ) ),
inference(clausify,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ~ gt(Y,X)
| leq(X,pred(Y)) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,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,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_14,plain,
? [E,F] :
( a_select3(z_defuse,E,F) != use
& leq(E,n2)
& leq(F,pv5)
& leq(n0,E)
& leq(n0,F)
& ( n0 != E
| pv5 != F )
& ( n1 != E
| pv5 != F )
& ( n2 != E
| pv5 != F ) ),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_15,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,pv5)
& ( n0 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F )
& ( n1 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F )
& ( n2 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F ) ),
inference(skolemize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
leq(skolemFOFtoCNF_E,n2),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| gt(Y,X) ),
inference(canonicalize,[],[leq_gt2]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ leq(X,Y)
| X = Y
| gt(Y,X) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
( n2 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_20,plain,
leq(pv5,n0),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_21,plain,
leq(n0,pv5),
inference(conjunct,[],[normalize_0_13]) ).
fof(normalize_0_22,plain,
leq(skolemFOFtoCNF_F,pv5),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_23,plain,
leq(n0,skolemFOFtoCNF_F),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_24,plain,
! [X] : pred(succ(X)) = X,
inference(canonicalize,[],[pred_succ]) ).
fof(normalize_0_25,plain,
! [X] : pred(succ(X)) = X,
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[successor_2]) ).
fof(normalize_0_27,plain,
leq(n0,skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_28,plain,
( n0 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_29,plain,
( n1 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F ),
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
succ(pred(X)) = X,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
succ(pred(skolemFOFtoCNF_E)) = skolemFOFtoCNF_E,
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_2,plain,
( ~ leq(X,n0)
| ~ leq(n0,X)
| X = n0 ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ leq(n0,pred(skolemFOFtoCNF_E))
| ~ leq(pred(skolemFOFtoCNF_E),n0)
| pred(skolemFOFtoCNF_E) = n0 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(pred(skolemFOFtoCNF_E)))]]) ).
cnf(refute_0_4,plain,
( ~ leq(succ(X),succ(Y))
| leq(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ leq(succ(X_7564),succ(n0))
| leq(X_7564,n0) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_7564)),bind(Y,$fot(n0))]]) ).
cnf(refute_0_6,plain,
succ(n0) = n1,
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( succ(n0) != n1
| ~ leq(succ(X_7564),n1)
| leq(succ(X_7564),succ(n0)) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(X_7564),succ(n0)) ),[1],$fot(n1)]]) ).
cnf(refute_0_8,plain,
( ~ leq(succ(X_7564),n1)
| leq(succ(X_7564),succ(n0)) ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ leq(succ(X_7564),n1)
| leq(X_7564,n0) ),
inference(resolve,[$cnf( leq(succ(X_7564),succ(n0)) )],[refute_0_8,refute_0_5]) ).
cnf(refute_0_10,plain,
( ~ leq(succ(pred(X)),n1)
| leq(pred(X),n0) ),
inference(subst,[],[refute_0_9:[bind(X_7564,$fot(pred(X)))]]) ).
cnf(refute_0_11,plain,
( succ(pred(X)) != X
| ~ leq(X,n1)
| leq(succ(pred(X)),n1) ),
introduced(tautology,[equality,[$cnf( ~ leq(succ(pred(X)),n1) ),[0],$fot(X)]]) ).
cnf(refute_0_12,plain,
( ~ leq(X,n1)
| leq(succ(pred(X)),n1) ),
inference(resolve,[$cnf( $equal(succ(pred(X)),X) )],[refute_0_0,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ leq(X,n1)
| leq(pred(X),n0) ),
inference(resolve,[$cnf( leq(succ(pred(X)),n1) )],[refute_0_12,refute_0_10]) ).
cnf(refute_0_14,plain,
( ~ leq(skolemFOFtoCNF_E,n1)
| leq(pred(skolemFOFtoCNF_E),n0) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_15,plain,
( ~ gt(Y,X)
| leq(X,pred(Y)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_16,plain,
( ~ gt(n2,skolemFOFtoCNF_E)
| leq(skolemFOFtoCNF_E,pred(n2)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_E)),bind(Y,$fot(n2))]]) ).
cnf(refute_0_17,plain,
leq(skolemFOFtoCNF_E,n2),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_18,plain,
( ~ leq(X,Y)
| X = Y
| gt(Y,X) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_19,plain,
( ~ leq(skolemFOFtoCNF_E,n2)
| skolemFOFtoCNF_E = n2
| gt(n2,skolemFOFtoCNF_E) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_E)),bind(Y,$fot(n2))]]) ).
cnf(refute_0_20,plain,
( skolemFOFtoCNF_E = n2
| gt(n2,skolemFOFtoCNF_E) ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_E,n2) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( n2 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_22,plain,
leq(pv5,n0),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_23,plain,
( ~ leq(n0,pv5)
| ~ leq(pv5,n0)
| pv5 = n0 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(pv5))]]) ).
cnf(refute_0_24,plain,
( ~ leq(n0,pv5)
| pv5 = n0 ),
inference(resolve,[$cnf( leq(pv5,n0) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
leq(n0,pv5),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_26,plain,
pv5 = n0,
inference(resolve,[$cnf( leq(n0,pv5) )],[refute_0_25,refute_0_24]) ).
cnf(refute_0_27,plain,
( n0 != skolemFOFtoCNF_F
| pv5 != n0
| pv5 = skolemFOFtoCNF_F ),
introduced(tautology,[equality,[$cnf( $equal(pv5,n0) ),[1],$fot(skolemFOFtoCNF_F)]]) ).
cnf(refute_0_28,plain,
( n0 != skolemFOFtoCNF_F
| pv5 = skolemFOFtoCNF_F ),
inference(resolve,[$cnf( $equal(pv5,n0) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( n0 != skolemFOFtoCNF_F
| n2 != skolemFOFtoCNF_E ),
inference(resolve,[$cnf( $equal(pv5,skolemFOFtoCNF_F) )],[refute_0_28,refute_0_21]) ).
cnf(refute_0_30,plain,
( ~ leq(n0,skolemFOFtoCNF_F)
| ~ leq(skolemFOFtoCNF_F,n0)
| skolemFOFtoCNF_F = n0 ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_F))]]) ).
cnf(refute_0_31,plain,
leq(skolemFOFtoCNF_F,pv5),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_32,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_33,plain,
( ~ leq(skolemFOFtoCNF_F,pv5)
| leq(skolemFOFtoCNF_F,n0) ),
inference(resolve,[$cnf( $equal(pv5,n0) )],[refute_0_26,refute_0_32]) ).
cnf(refute_0_34,plain,
leq(skolemFOFtoCNF_F,n0),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,pv5) )],[refute_0_31,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ leq(n0,skolemFOFtoCNF_F)
| skolemFOFtoCNF_F = n0 ),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_F,n0) )],[refute_0_34,refute_0_30]) ).
cnf(refute_0_36,plain,
leq(n0,skolemFOFtoCNF_F),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_37,plain,
skolemFOFtoCNF_F = n0,
inference(resolve,[$cnf( leq(n0,skolemFOFtoCNF_F) )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
( n0 != n0
| skolemFOFtoCNF_F != n0
| n0 = skolemFOFtoCNF_F ),
introduced(tautology,[equality,[$cnf( ~ $equal(n0,skolemFOFtoCNF_F) ),[1],$fot(n0)]]) ).
cnf(refute_0_39,plain,
( n0 != n0
| n0 = skolemFOFtoCNF_F ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_F,n0) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( n0 != n0
| n2 != skolemFOFtoCNF_E ),
inference(resolve,[$cnf( $equal(n0,skolemFOFtoCNF_F) )],[refute_0_39,refute_0_29]) ).
cnf(refute_0_41,plain,
n0 = n0,
introduced(tautology,[refl,[$fot(n0)]]) ).
cnf(refute_0_42,plain,
n2 != skolemFOFtoCNF_E,
inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_41,refute_0_40]) ).
cnf(refute_0_43,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_44,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_45,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
( skolemFOFtoCNF_E != n2
| n2 = skolemFOFtoCNF_E ),
inference(subst,[],[refute_0_45:[bind(X0,$fot(skolemFOFtoCNF_E)),bind(Y0,$fot(n2))]]) ).
cnf(refute_0_47,plain,
skolemFOFtoCNF_E != n2,
inference(resolve,[$cnf( $equal(n2,skolemFOFtoCNF_E) )],[refute_0_46,refute_0_42]) ).
cnf(refute_0_48,plain,
gt(n2,skolemFOFtoCNF_E),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_E,n2) )],[refute_0_20,refute_0_47]) ).
cnf(refute_0_49,plain,
leq(skolemFOFtoCNF_E,pred(n2)),
inference(resolve,[$cnf( gt(n2,skolemFOFtoCNF_E) )],[refute_0_48,refute_0_16]) ).
cnf(refute_0_50,plain,
pred(succ(X)) = X,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_51,plain,
pred(succ(n1)) = n1,
inference(subst,[],[refute_0_50:[bind(X,$fot(n1))]]) ).
cnf(refute_0_52,plain,
succ(succ(n0)) = n2,
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_53,plain,
succ(succ(n0)) = succ(succ(n0)),
introduced(tautology,[refl,[$fot(succ(succ(n0)))]]) ).
cnf(refute_0_54,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_55,plain,
( succ(n0) != n1
| succ(succ(n0)) = succ(n1) ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(succ(n0))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
succ(succ(n0)) = succ(n1),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_6,refute_0_55]) ).
cnf(refute_0_57,plain,
( succ(succ(n0)) != n2
| succ(succ(n0)) != succ(n1)
| succ(n1) = n2 ),
introduced(tautology,[equality,[$cnf( $equal(succ(succ(n0)),n2) ),[0],$fot(succ(n1))]]) ).
cnf(refute_0_58,plain,
( succ(succ(n0)) != n2
| succ(n1) = n2 ),
inference(resolve,[$cnf( $equal(succ(succ(n0)),succ(n1)) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
succ(n1) = n2,
inference(resolve,[$cnf( $equal(succ(succ(n0)),n2) )],[refute_0_52,refute_0_58]) ).
cnf(refute_0_60,plain,
( pred(succ(n1)) != n1
| succ(n1) != n2
| pred(n2) = n1 ),
introduced(tautology,[equality,[$cnf( $equal(pred(succ(n1)),n1) ),[0,0],$fot(n2)]]) ).
cnf(refute_0_61,plain,
( pred(succ(n1)) != n1
| pred(n2) = n1 ),
inference(resolve,[$cnf( $equal(succ(n1),n2) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
pred(n2) = n1,
inference(resolve,[$cnf( $equal(pred(succ(n1)),n1) )],[refute_0_51,refute_0_61]) ).
cnf(refute_0_63,plain,
( pred(n2) != n1
| ~ leq(skolemFOFtoCNF_E,pred(n2))
| leq(skolemFOFtoCNF_E,n1) ),
introduced(tautology,[equality,[$cnf( leq(skolemFOFtoCNF_E,pred(n2)) ),[1],$fot(n1)]]) ).
cnf(refute_0_64,plain,
( ~ leq(skolemFOFtoCNF_E,pred(n2))
| leq(skolemFOFtoCNF_E,n1) ),
inference(resolve,[$cnf( $equal(pred(n2),n1) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
leq(skolemFOFtoCNF_E,n1),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_E,pred(n2)) )],[refute_0_49,refute_0_64]) ).
cnf(refute_0_66,plain,
leq(pred(skolemFOFtoCNF_E),n0),
inference(resolve,[$cnf( leq(skolemFOFtoCNF_E,n1) )],[refute_0_65,refute_0_14]) ).
cnf(refute_0_67,plain,
( ~ leq(n0,pred(skolemFOFtoCNF_E))
| pred(skolemFOFtoCNF_E) = n0 ),
inference(resolve,[$cnf( leq(pred(skolemFOFtoCNF_E),n0) )],[refute_0_66,refute_0_3]) ).
cnf(refute_0_68,plain,
( ~ gt(skolemFOFtoCNF_E,n0)
| leq(n0,pred(skolemFOFtoCNF_E)) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(n0)),bind(Y,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_69,plain,
leq(n0,skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_70,plain,
( ~ leq(n0,skolemFOFtoCNF_E)
| n0 = skolemFOFtoCNF_E
| gt(skolemFOFtoCNF_E,n0) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(n0)),bind(Y,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_71,plain,
( n0 = skolemFOFtoCNF_E
| gt(skolemFOFtoCNF_E,n0) ),
inference(resolve,[$cnf( leq(n0,skolemFOFtoCNF_E) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( n0 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_73,plain,
( n0 != skolemFOFtoCNF_E
| n0 != skolemFOFtoCNF_F ),
inference(resolve,[$cnf( $equal(pv5,skolemFOFtoCNF_F) )],[refute_0_28,refute_0_72]) ).
cnf(refute_0_74,plain,
( n0 != n0
| n0 != skolemFOFtoCNF_E ),
inference(resolve,[$cnf( $equal(n0,skolemFOFtoCNF_F) )],[refute_0_39,refute_0_73]) ).
cnf(refute_0_75,plain,
n0 != skolemFOFtoCNF_E,
inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_41,refute_0_74]) ).
cnf(refute_0_76,plain,
gt(skolemFOFtoCNF_E,n0),
inference(resolve,[$cnf( $equal(n0,skolemFOFtoCNF_E) )],[refute_0_71,refute_0_75]) ).
cnf(refute_0_77,plain,
leq(n0,pred(skolemFOFtoCNF_E)),
inference(resolve,[$cnf( gt(skolemFOFtoCNF_E,n0) )],[refute_0_76,refute_0_68]) ).
cnf(refute_0_78,plain,
pred(skolemFOFtoCNF_E) = n0,
inference(resolve,[$cnf( leq(n0,pred(skolemFOFtoCNF_E)) )],[refute_0_77,refute_0_67]) ).
cnf(refute_0_79,plain,
( pred(skolemFOFtoCNF_E) != n0
| succ(pred(skolemFOFtoCNF_E)) != skolemFOFtoCNF_E
| succ(n0) = skolemFOFtoCNF_E ),
introduced(tautology,[equality,[$cnf( $equal(succ(pred(skolemFOFtoCNF_E)),skolemFOFtoCNF_E) ),[0,0],$fot(n0)]]) ).
cnf(refute_0_80,plain,
( succ(pred(skolemFOFtoCNF_E)) != skolemFOFtoCNF_E
| succ(n0) = skolemFOFtoCNF_E ),
inference(resolve,[$cnf( $equal(pred(skolemFOFtoCNF_E),n0) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
succ(n0) = skolemFOFtoCNF_E,
inference(resolve,[$cnf( $equal(succ(pred(skolemFOFtoCNF_E)),skolemFOFtoCNF_E) )],[refute_0_1,refute_0_80]) ).
cnf(refute_0_82,plain,
( succ(n0) != n1
| succ(n0) != skolemFOFtoCNF_E
| n1 = skolemFOFtoCNF_E ),
introduced(tautology,[equality,[$cnf( $equal(succ(n0),skolemFOFtoCNF_E) ),[0],$fot(n1)]]) ).
cnf(refute_0_83,plain,
( succ(n0) != skolemFOFtoCNF_E
| n1 = skolemFOFtoCNF_E ),
inference(resolve,[$cnf( $equal(succ(n0),n1) )],[refute_0_6,refute_0_82]) ).
cnf(refute_0_84,plain,
n1 = skolemFOFtoCNF_E,
inference(resolve,[$cnf( $equal(succ(n0),skolemFOFtoCNF_E) )],[refute_0_81,refute_0_83]) ).
cnf(refute_0_85,plain,
( n1 != skolemFOFtoCNF_E
| pv5 != skolemFOFtoCNF_F ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_86,plain,
( n0 != skolemFOFtoCNF_F
| n1 != skolemFOFtoCNF_E ),
inference(resolve,[$cnf( $equal(pv5,skolemFOFtoCNF_F) )],[refute_0_28,refute_0_85]) ).
cnf(refute_0_87,plain,
( n0 != n0
| n1 != skolemFOFtoCNF_E ),
inference(resolve,[$cnf( $equal(n0,skolemFOFtoCNF_F) )],[refute_0_39,refute_0_86]) ).
cnf(refute_0_88,plain,
n1 != skolemFOFtoCNF_E,
inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_41,refute_0_87]) ).
cnf(refute_0_89,plain,
$false,
inference(resolve,[$cnf( $equal(n1,skolemFOFtoCNF_E) )],[refute_0_84,refute_0_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SWV199+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.36 % Computer : n029.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Wed Jun 15 16:25:26 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 108.23/108.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 108.23/108.42
% 108.23/108.42 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 108.23/108.43
%------------------------------------------------------------------------------