TSTP Solution File: SWV154+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV154+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 20:30:18 EDT 2022
% Result : Theorem 0.40s 0.61s
% Output : CNFRefutation 0.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 20
% Syntax : Number of formulae : 60 ( 28 unt; 0 def)
% Number of atoms : 161 ( 116 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 151 ( 50 ~; 43 |; 45 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 12 con; 0-3 aty)
% Number of variables : 24 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0004,conjecture,
( ( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv12)) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pv12) )
=> ( pv12 = C
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ) ) ).
fof(subgoal_0,plain,
( ( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv12)) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pv12)
& pv12 = C )
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
inference(strip,[],[cl5_nebula_norm_0004]) ).
fof(negate_0_0,plain,
~ ( ( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ! [A] :
( ( leq(n0,A)
& leq(A,pred(pv12)) )
=> a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [B] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) )
=> ! [C] :
( ( leq(n0,C)
& leq(C,pv12)
& pv12 = C )
=> divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
& leq(n0,pv10)
& leq(n0,pv12)
& leq(pv10,n135299)
& leq(pv12,n4)
& ? [C] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = C
& leq(C,pv12)
& leq(n0,C) )
& ! [A] :
( ~ leq(A,pred(pv12))
| ~ leq(n0,A)
| a_select3(q,pv10,A) = divide(sqrt(times(minus(a_select3(center,A,n0),a_select2(x,pv10)),minus(a_select3(center,A,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )
& ! [B] :
( ~ leq(B,pred(pv10))
| ~ leq(n0,B)
| sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
? [C] :
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,C,n0),a_select2(x,pv10)),minus(a_select3(center,C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = C
& leq(C,pv12)
& leq(n0,C) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
& pv12 = skolemFOFtoCNF_C
& leq(n0,skolemFOFtoCNF_C)
& leq(skolemFOFtoCNF_C,pv12) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_5,plain,
pv12 = skolemFOFtoCNF_C,
inference(conjunct,[],[normalize_0_2]) ).
cnf(refute_0_0,plain,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
pv70 = sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( pv70 != sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))
| sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(pv70)),bind(Y,$fot(sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))))]]) ).
cnf(refute_0_6,plain,
sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) = pv70,
inference(resolve,[$cnf( $equal(pv70,sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
introduced(tautology,[refl,[$fot(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))))]]) ).
cnf(refute_0_8,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) != pv70
| divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) ),
introduced(tautology,[equality,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) ),[1,1],$fot(pv70)]]) ).
cnf(refute_0_9,plain,
( sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))) != pv70
| divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) ),
inference(resolve,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),
inference(resolve,[$cnf( $equal(sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))),pv70) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
pv12 = skolemFOFtoCNF_C,
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_12,plain,
( pv12 != skolemFOFtoCNF_C
| skolemFOFtoCNF_C = pv12 ),
inference(subst,[],[refute_0_4:[bind(X,$fot(pv12)),bind(Y,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_13,plain,
skolemFOFtoCNF_C = pv12,
inference(resolve,[$cnf( $equal(pv12,skolemFOFtoCNF_C) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
a_select3(center,skolemFOFtoCNF_C,n0) = a_select3(center,skolemFOFtoCNF_C,n0),
introduced(tautology,[refl,[$fot(a_select3(center,skolemFOFtoCNF_C,n0))]]) ).
cnf(refute_0_15,plain,
( a_select3(center,skolemFOFtoCNF_C,n0) != a_select3(center,skolemFOFtoCNF_C,n0)
| skolemFOFtoCNF_C != pv12
| a_select3(center,skolemFOFtoCNF_C,n0) = a_select3(center,pv12,n0) ),
introduced(tautology,[equality,[$cnf( $equal(a_select3(center,skolemFOFtoCNF_C,n0),a_select3(center,skolemFOFtoCNF_C,n0)) ),[1,1],$fot(pv12)]]) ).
cnf(refute_0_16,plain,
( skolemFOFtoCNF_C != pv12
| a_select3(center,skolemFOFtoCNF_C,n0) = a_select3(center,pv12,n0) ),
inference(resolve,[$cnf( $equal(a_select3(center,skolemFOFtoCNF_C,n0),a_select3(center,skolemFOFtoCNF_C,n0)) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
a_select3(center,skolemFOFtoCNF_C,n0) = a_select3(center,pv12,n0),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C,pv12) )],[refute_0_13,refute_0_16]) ).
cnf(refute_0_18,plain,
minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) = minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),
introduced(tautology,[refl,[$fot(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))]]) ).
cnf(refute_0_19,plain,
( a_select3(center,skolemFOFtoCNF_C,n0) != a_select3(center,pv12,n0)
| minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) != minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))
| minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) = minus(a_select3(center,pv12,n0),a_select2(x,pv10)) ),
introduced(tautology,[equality,[$cnf( $equal(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) ),[1,0],$fot(a_select3(center,pv12,n0))]]) ).
cnf(refute_0_20,plain,
( a_select3(center,skolemFOFtoCNF_C,n0) != a_select3(center,pv12,n0)
| minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) = minus(a_select3(center,pv12,n0),a_select2(x,pv10)) ),
inference(resolve,[$cnf( $equal(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) = minus(a_select3(center,pv12,n0),a_select2(x,pv10)),
inference(resolve,[$cnf( $equal(a_select3(center,skolemFOFtoCNF_C,n0),a_select3(center,pv12,n0)) )],[refute_0_17,refute_0_20]) ).
cnf(refute_0_22,plain,
times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),
introduced(tautology,[refl,[$fot(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))))]]) ).
cnf(refute_0_23,plain,
( minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) != minus(a_select3(center,pv12,n0),a_select2(x,pv10))
| times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) != times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))
| times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))) ),
introduced(tautology,[equality,[$cnf( $equal(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) ),[1,1],$fot(minus(a_select3(center,pv12,n0),a_select2(x,pv10)))]]) ).
cnf(refute_0_24,plain,
( minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) != minus(a_select3(center,pv12,n0),a_select2(x,pv10))
| times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))) ),
inference(resolve,[$cnf( $equal(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))),
inference(resolve,[$cnf( $equal(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))) )],[refute_0_21,refute_0_24]) ).
cnf(refute_0_26,plain,
times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),
introduced(tautology,[refl,[$fot(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))))]]) ).
cnf(refute_0_27,plain,
( minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) != minus(a_select3(center,pv12,n0),a_select2(x,pv10))
| times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) != times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))
| times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) ),
introduced(tautology,[equality,[$cnf( $equal(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) ),[1,0],$fot(minus(a_select3(center,pv12,n0),a_select2(x,pv10)))]]) ).
cnf(refute_0_28,plain,
( minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)) != minus(a_select3(center,pv12,n0),a_select2(x,pv10))
| times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) ),
inference(resolve,[$cnf( $equal(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),
inference(resolve,[$cnf( $equal(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))) )],[refute_0_21,refute_0_28]) ).
cnf(refute_0_30,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_31,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_4,refute_0_30]) ).
cnf(refute_0_32,plain,
( times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) != times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))
| times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) != times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))
| times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))))),bind(Y,$fot(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))))),bind(Z,$fot(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))))]]) ).
cnf(refute_0_33,plain,
( times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) != times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))
| times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))) ),
inference(resolve,[$cnf( $equal(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) = times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))),
inference(resolve,[$cnf( $equal(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))) )],[refute_0_25,refute_0_33]) ).
cnf(refute_0_35,plain,
sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) = sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),
introduced(tautology,[refl,[$fot(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))))]]) ).
cnf(refute_0_36,plain,
( sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) != sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))))
| times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) != times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))
| sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) = sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))) ),
introduced(tautology,[equality,[$cnf( $equal(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))))) ),[1,0],$fot(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))))]]) ).
cnf(refute_0_37,plain,
( times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))) != times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))
| sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) = sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))) ),
inference(resolve,[$cnf( $equal(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) = sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),
inference(resolve,[$cnf( $equal(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10))),times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))) )],[refute_0_34,refute_0_37]) ).
cnf(refute_0_39,plain,
divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
introduced(tautology,[refl,[$fot(divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))))]]) ).
cnf(refute_0_40,plain,
( divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) != sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))))
| divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ),
introduced(tautology,[equality,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) ),[1,0],$fot(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))))]]) ).
cnf(refute_0_41,plain,
( sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))) != sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))))
| divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ),
inference(resolve,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),
inference(resolve,[$cnf( $equal(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10))))) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)
| divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))
| divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) ),
inference(subst,[],[refute_0_31:[bind(X,$fot(divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))))),bind(Y,$fot(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))))),bind(Z,$fot(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)))]]) ).
cnf(refute_0_44,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)
| divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) ),
inference(resolve,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),
inference(resolve,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)) )],[refute_0_10,refute_0_44]) ).
cnf(refute_0_46,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)
| divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)
| divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) ),[1],$fot(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70))]]) ).
cnf(refute_0_47,plain,
( divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)
| divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))) ),
inference(resolve,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)))))),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) != divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),
inference(resolve,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),divide(sqrt(times(minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)),minus(a_select3(center,skolemFOFtoCNF_C,n0),a_select2(x,pv10)))),sum(n0,n4,sqrt(times(minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10)),minus(a_select3(center,tptp_sum_index,n0),a_select2(x,pv10))))))) )],[refute_0_47,refute_0_0]) ).
cnf(refute_0_49,plain,
divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70) = divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),
introduced(tautology,[refl,[$fot(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70))]]) ).
cnf(refute_0_50,plain,
$false,
inference(resolve,[$cnf( $equal(divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70),divide(sqrt(times(minus(a_select3(center,pv12,n0),a_select2(x,pv10)),minus(a_select3(center,pv12,n0),a_select2(x,pv10)))),pv70)) )],[refute_0_49,refute_0_48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SWV154+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.03/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Wed Jun 15 12:19:45 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.40/0.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.40/0.61
% 0.40/0.61 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.40/0.63
%------------------------------------------------------------------------------