TSTP Solution File: SWV046+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV046+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 20:29:56 EDT 2022
% Result : Theorem 0.92s 1.15s
% Output : CNFRefutation 1.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 28
% Syntax : Number of formulae : 101 ( 58 unt; 0 def)
% Number of atoms : 244 ( 189 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 212 ( 69 ~; 47 |; 81 &)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 24 ( 24 usr; 15 con; 0-3 aty)
% Number of variables : 35 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sum_plus_base,axiom,
! [Body] : sum(n0,tptp_minus_1,Body) = n0 ).
fof(succ_tptp_minus_1,axiom,
succ(tptp_minus_1) = n0 ).
fof(pred_minus_1,axiom,
! [X] : minus(X,n1) = pred(X) ).
fof(pred_succ,axiom,
! [X] : pred(succ(X)) = X ).
fof(sel2_update_1,axiom,
! [X,U,VAL] : a_select2(tptp_update2(X,U,VAL),U) = VAL ).
fof(ttrue,axiom,
true ).
fof(cl5_nebula_norm_0010,conjecture,
( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1)) )
=> ( ( n0 != pv44
=> ( n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1)) ) )
& ( n0 = pv44
=> true ) ) ) ).
fof(subgoal_0,plain,
( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& n0 != pv44 )
=> n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
inference(strip,[],[cl5_nebula_norm_0010]) ).
fof(subgoal_1,plain,
( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& n0 != pv44
& n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )
=> pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) ),
inference(strip,[],[cl5_nebula_norm_0010]) ).
fof(subgoal_2,plain,
( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& n0 != pv44
& n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) )
=> leq(n0,pv35) ),
inference(strip,[],[cl5_nebula_norm_0010]) ).
fof(subgoal_3,plain,
( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& n0 != pv44
& n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& leq(n0,pv35) )
=> leq(pv35,minus(n5,n1)) ),
inference(strip,[],[cl5_nebula_norm_0010]) ).
fof(subgoal_4,plain,
( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& ( n0 != pv44
=> ( n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1)) ) )
& n0 = pv44 )
=> true ),
inference(strip,[],[cl5_nebula_norm_0010]) ).
fof(negate_0_0,plain,
~ ( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& n0 != pv44 )
=> n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( n0 != pv44
& n0 != sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
n0 != sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [U,VAL,X] : a_select2(tptp_update2(X,U,VAL),U) = VAL,
inference(canonicalize,[],[sel2_update_1]) ).
fof(normalize_0_3,plain,
! [U,VAL,X] : a_select2(tptp_update2(X,U,VAL),U) = VAL,
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : minus(X,n1) = pred(X),
inference(canonicalize,[],[pred_minus_1]) ).
fof(normalize_0_5,plain,
! [X] : minus(X,n1) = pred(X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
inference(canonicalize,[],[sum_plus_base]) ).
fof(normalize_0_7,plain,
! [Body] : sum(n0,tptp_minus_1,Body) = n0,
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] : pred(succ(X)) = X,
inference(canonicalize,[],[pred_succ]) ).
fof(normalize_0_9,plain,
! [X] : pred(succ(X)) = X,
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
succ(tptp_minus_1) = n0,
inference(canonicalize,[],[succ_tptp_minus_1]) ).
cnf(refute_0_0,plain,
n0 != sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
a_select2(tptp_update2(X,U,VAL),U) = VAL,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35) = divide(pv80,pv44),
inference(subst,[],[refute_0_1:[bind(U,$fot(pv35)),bind(VAL,$fot(divide(pv80,pv44))),bind(X,$fot(mu))]]) ).
cnf(refute_0_3,plain,
minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) = minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),
introduced(tautology,[refl,[$fot(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)))]]) ).
cnf(refute_0_4,plain,
( a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35) != divide(pv80,pv44)
| minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) != minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35))
| minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) = minus(a_select2(x,pv83),divide(pv80,pv44)) ),
introduced(tautology,[equality,[$cnf( $equal(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35))) ),[1,1],$fot(divide(pv80,pv44))]]) ).
cnf(refute_0_5,plain,
( a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35) != divide(pv80,pv44)
| minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) = minus(a_select2(x,pv83),divide(pv80,pv44)) ),
inference(resolve,[$cnf( $equal(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35))) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) = minus(a_select2(x,pv83),divide(pv80,pv44)),
inference(resolve,[$cnf( $equal(a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35),divide(pv80,pv44)) )],[refute_0_2,refute_0_5]) ).
cnf(refute_0_7,plain,
times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)) = times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)),
introduced(tautology,[refl,[$fot(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))]]) ).
cnf(refute_0_8,plain,
( minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) != minus(a_select2(x,pv83),divide(pv80,pv44))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)) != times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)) ),
introduced(tautology,[equality,[$cnf( $equal(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) ),[1,0],$fot(minus(a_select2(x,pv83),divide(pv80,pv44)))]]) ).
cnf(refute_0_9,plain,
( minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) != minus(a_select2(x,pv83),divide(pv80,pv44))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)) ),
inference(resolve,[$cnf( $equal(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)),
inference(resolve,[$cnf( $equal(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),minus(a_select2(x,pv83),divide(pv80,pv44))) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),
introduced(tautology,[refl,[$fot(times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))]]) ).
cnf(refute_0_12,plain,
( times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) != times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)) != times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))
| times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))) ),
introduced(tautology,[equality,[$cnf( $equal(times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),[1,1],$fot(times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))]]) ).
cnf(refute_0_13,plain,
( times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)) != times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))
| times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))) ),
inference(resolve,[$cnf( $equal(times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))),
inference(resolve,[$cnf( $equal(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),
introduced(tautology,[refl,[$fot(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))]]) ).
cnf(refute_0_16,plain,
( minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) != minus(a_select2(x,pv83),divide(pv80,pv44))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) != times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) ),
introduced(tautology,[equality,[$cnf( $equal(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),[1,0],$fot(minus(a_select2(x,pv83),divide(pv80,pv44)))]]) ).
cnf(refute_0_17,plain,
( minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)) != minus(a_select2(x,pv83),divide(pv80,pv44))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) ),
inference(resolve,[$cnf( $equal(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),
inference(resolve,[$cnf( $equal(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),minus(a_select2(x,pv83),divide(pv80,pv44))) )],[refute_0_6,refute_0_17]) ).
cnf(refute_0_19,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_20,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_21,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) != times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) != times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))),bind(Y,$fot(times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))),bind(Z,$fot(times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))))]]) ).
cnf(refute_0_25,plain,
( times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) != times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))) ),
inference(resolve,[$cnf( $equal(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )],[refute_0_18,refute_0_24]) ).
cnf(refute_0_26,plain,
times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) = times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))),
inference(resolve,[$cnf( $equal(times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) )],[refute_0_14,refute_0_25]) ).
cnf(refute_0_27,plain,
sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),
introduced(tautology,[refl,[$fot(sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))))]]) ).
cnf(refute_0_28,plain,
( sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
| times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) != times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
introduced(tautology,[equality,[$cnf( $equal(sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))) ),[1,2],$fot(times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))]]) ).
cnf(refute_0_29,plain,
( times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))) != times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
inference(resolve,[$cnf( $equal(sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),
inference(resolve,[$cnf( $equal(times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
minus(X,n1) = pred(X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_32,plain,
minus(n0,n1) = pred(n0),
inference(subst,[],[refute_0_31:[bind(X,$fot(n0))]]) ).
cnf(refute_0_33,plain,
sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),
introduced(tautology,[refl,[$fot(sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))))]]) ).
cnf(refute_0_34,plain,
( minus(n0,n1) != pred(n0)
| sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
| sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
introduced(tautology,[equality,[$cnf( $equal(sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))) ),[1,1],$fot(pred(n0))]]) ).
cnf(refute_0_35,plain,
( minus(n0,n1) != pred(n0)
| sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
inference(resolve,[$cnf( $equal(sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),
inference(resolve,[$cnf( $equal(minus(n0,n1),pred(n0)) )],[refute_0_32,refute_0_35]) ).
cnf(refute_0_37,plain,
( sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))
| sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))))),bind(Y,$fot(sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))))),bind(Z,$fot(sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))))]]) ).
cnf(refute_0_38,plain,
( sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))
| sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
inference(resolve,[$cnf( $equal(sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),
inference(resolve,[$cnf( $equal(sum(n0,pred(n0),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))) )],[refute_0_30,refute_0_38]) ).
cnf(refute_0_40,plain,
( n0 != sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))
| sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) != sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))
| n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(n0,sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))) ),[1],$fot(sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))))]]) ).
cnf(refute_0_41,plain,
( n0 != sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))
| n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) ),
inference(resolve,[$cnf( $equal(sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))),sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
n0 != sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),
inference(resolve,[$cnf( $equal(n0,sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))) )],[refute_0_41,refute_0_0]) ).
cnf(refute_0_43,plain,
sum(n0,tptp_minus_1,Body) = n0,
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_44,plain,
sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) = n0,
inference(subst,[],[refute_0_43:[bind(Body,$fot(times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))))]]) ).
cnf(refute_0_45,plain,
pred(succ(X)) = X,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_46,plain,
pred(succ(tptp_minus_1)) = tptp_minus_1,
inference(subst,[],[refute_0_45:[bind(X,$fot(tptp_minus_1))]]) ).
cnf(refute_0_47,plain,
succ(tptp_minus_1) = n0,
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_48,plain,
( pred(succ(tptp_minus_1)) != tptp_minus_1
| succ(tptp_minus_1) != n0
| pred(n0) = tptp_minus_1 ),
introduced(tautology,[equality,[$cnf( $equal(pred(succ(tptp_minus_1)),tptp_minus_1) ),[0,0],$fot(n0)]]) ).
cnf(refute_0_49,plain,
( pred(succ(tptp_minus_1)) != tptp_minus_1
| pred(n0) = tptp_minus_1 ),
inference(resolve,[$cnf( $equal(succ(tptp_minus_1),n0) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
pred(n0) = tptp_minus_1,
inference(resolve,[$cnf( $equal(pred(succ(tptp_minus_1)),tptp_minus_1) )],[refute_0_46,refute_0_49]) ).
cnf(refute_0_51,plain,
sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),
introduced(tautology,[refl,[$fot(sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))))]]) ).
cnf(refute_0_52,plain,
( pred(n0) != tptp_minus_1
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) = sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
introduced(tautology,[equality,[$cnf( $equal(sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))) ),[1,1],$fot(tptp_minus_1)]]) ).
cnf(refute_0_53,plain,
( pred(n0) != tptp_minus_1
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) = sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
inference(resolve,[$cnf( $equal(sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) = sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),
inference(resolve,[$cnf( $equal(pred(n0),tptp_minus_1) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))
| sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) = n0 ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))))),bind(Y,$fot(sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))))),bind(Z,$fot(n0))]]) ).
cnf(refute_0_56,plain,
( sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) = n0 ),
inference(resolve,[$cnf( $equal(sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) = n0,
inference(resolve,[$cnf( $equal(sum(n0,tptp_minus_1,times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),n0) )],[refute_0_44,refute_0_56]) ).
cnf(refute_0_58,plain,
( n0 != n0
| sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) != n0
| n0 = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(n0,sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))) ),[1],$fot(n0)]]) ).
cnf(refute_0_59,plain,
( n0 != n0
| n0 = sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))) ),
inference(resolve,[$cnf( $equal(sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35)))),n0) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
n0 != n0,
inference(resolve,[$cnf( $equal(n0,sum(n0,pred(n0),times(minus(a_select2(x,pv83),divide(pv80,pv44)),times(minus(a_select2(x,pv83),divide(pv80,pv44)),a_select3(q,pv83,pv35))))) )],[refute_0_59,refute_0_42]) ).
cnf(refute_0_61,plain,
n0 = n0,
introduced(tautology,[refl,[$fot(n0)]]) ).
cnf(refute_0_62,plain,
$false,
inference(resolve,[$cnf( $equal(n0,n0) )],[refute_0_61,refute_0_60]) ).
fof(negate_1_0,plain,
~ ( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& n0 != pv44
& n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35)))) )
=> pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
$false,
inference(canonicalize,[],[negate_1_0]) ).
cnf(refute_1_0,plain,
$false,
inference(canonicalize,[],[normalize_1_0]) ).
fof(negate_2_0,plain,
~ ( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& n0 != pv44
& n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35)) )
=> leq(n0,pv35) ),
inference(negate,[],[subgoal_2]) ).
fof(normalize_2_0,plain,
$false,
inference(canonicalize,[],[negate_2_0]) ).
cnf(refute_2_0,plain,
$false,
inference(canonicalize,[],[normalize_2_0]) ).
fof(negate_3_0,plain,
~ ( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& n0 != pv44
& n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& leq(n0,pv35) )
=> leq(pv35,minus(n5,n1)) ),
inference(negate,[],[subgoal_3]) ).
fof(normalize_3_0,plain,
$false,
inference(canonicalize,[],[negate_3_0]) ).
cnf(refute_3_0,plain,
$false,
inference(canonicalize,[],[normalize_3_0]) ).
fof(negate_4_0,plain,
~ ( ( pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& ( n0 != pv44
=> ( n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1)) ) )
& n0 = pv44 )
=> true ),
inference(negate,[],[subgoal_4]) ).
fof(normalize_4_0,plain,
( ~ true
& n0 = pv44
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& pv80 = sum(n0,minus(n135300,n1),times(a_select3(q,pv81,pv35),a_select2(x,pv81)))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1))
& ( n0 = pv44
| ( n0 = sum(n0,minus(n0,n1),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),times(minus(a_select2(x,pv83),a_select2(tptp_update2(mu,pv35,divide(pv80,pv44)),pv35)),a_select3(q,pv83,pv35))))
& pv78 = sum(n0,minus(n135300,n1),a_select3(q,pv79,pv35))
& leq(n0,pv35)
& leq(pv35,minus(n5,n1)) ) ) ),
inference(canonicalize,[],[negate_4_0]) ).
fof(normalize_4_1,plain,
true,
inference(canonicalize,[],[ttrue]) ).
fof(normalize_4_2,plain,
$false,
inference(simplify,[],[normalize_4_0,normalize_4_1]) ).
cnf(refute_4_0,plain,
$false,
inference(canonicalize,[],[normalize_4_2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV046+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Tue Jun 14 16:00:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.92/1.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.92/1.15
% 0.92/1.15 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.00/1.17
%------------------------------------------------------------------------------