## TPTP Problem File: MSC010+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : MSC010+1 : TPTP v7.5.0. Released v3.1.0.
% Domain   : Miscellaneous
% Problem  : Simple, but hard, obligation from proof verification
% Version  : Especial.
% English  : Verification of the negation of a conjecture, which is simply to
%            prove the double negated version of a formula from the formula.

% Refs     :
% Source   : [TPTP]
% Names    :

% Status   : Theorem
% Rating   : 0.22 v7.4.0, 0.23 v7.3.0, 0.21 v7.2.0, 0.17 v7.1.0, 0.22 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.25 v6.2.0, 0.32 v6.1.0, 0.33 v6.0.0, 0.22 v5.5.0, 0.33 v5.4.0, 0.39 v5.3.0, 0.52 v5.2.0, 0.35 v5.1.0, 0.38 v5.0.0, 0.42 v4.1.0, 0.48 v4.0.0, 0.50 v3.7.0, 0.45 v3.5.0, 0.47 v3.4.0, 0.58 v3.3.0, 0.57 v3.2.0, 0.82 v3.1.0
% Syntax   : Number of formulae    :    2 (   0 unit)
%            Number of atoms       :  136 (  30 equality)
%            Maximal formula depth :   26 (  25 average)
%            Number of connectives :  140 (   6   ~;   0   |; 102   &)
%                                         (   0 <=>;  32  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :    3 (   0 propositional; 2-2 arity)
%            Number of functors    :   18 (  16 constant; 0-3 arity)
%            Number of variables   :   44 (   0 sgn;  44   !;   0   ?)
%            Maximal term depth    :    2 (   1 average)
% SPC      : FOF_THM_RFO_SEQ

%------------------------------------------------------------------------------
fof(n1,axiom,
( ( pv63 != pv64
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1,X2] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> a_select3(h_ds1_filter_init,X1,X2) = init )
& ! [X3,X4] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> a_select3(phi_ds1_filter_init,X3,X4) = init )
& ! [X5,X6] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> a_select3(dv_ds1_filter_init,X5,X6) = init )
& ! [X7,X8] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> a_select3(q_ds1_filter_init,X7,X8) = init )
& ! [X9,X10] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> a_select3(r_ds1_filter_init,X9,X10) = init )
& ! [X11,X12] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
& ! [X13,X14] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> a_select3(pminus_ds1_filter_init,X13,X14) = init )
& ! [X15,X16] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( X15 = pv63
& gt(pv64,X16) )
=> a_select3(id_ds1_filter_init,X15,X16) = init ) )
& ! [X17,X18] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> a_select3(id_ds1_filter_init,X17,X18) = init ) )
& ! [X19] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
=> ! [X21,X22] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( pv64 != X22
& X21 = pv63
& leq(X22,pv64) )
=> a_select3(id_ds1_filter_init,X21,X22) = init ) ) )).

fof(n91,conjecture,
( ~ ~ ( ( pv63 != pv64
& leq(n0,pv5)
& leq(n0,pv63)
& leq(n0,pv64)
& leq(pv5,n998)
& leq(pv63,n5)
& leq(pv64,n5)
& ! [X1,X2] :
( ( leq(n0,X1)
& leq(n0,X2)
& leq(X1,n2)
& leq(X2,n5) )
=> a_select3(h_ds1_filter_init,X1,X2) = init )
& ! [X3,X4] :
( ( leq(n0,X3)
& leq(n0,X4)
& leq(X3,n5)
& leq(X4,n5) )
=> a_select3(phi_ds1_filter_init,X3,X4) = init )
& ! [X5,X6] :
( ( leq(n0,X5)
& leq(n0,X6)
& leq(X5,n5)
& leq(X6,n0) )
=> a_select3(dv_ds1_filter_init,X5,X6) = init )
& ! [X7,X8] :
( ( leq(n0,X7)
& leq(n0,X8)
& leq(X7,n5)
& leq(X8,n5) )
=> a_select3(q_ds1_filter_init,X7,X8) = init )
& ! [X9,X10] :
( ( leq(n0,X9)
& leq(n0,X10)
& leq(X9,n2)
& leq(X10,n2) )
=> a_select3(r_ds1_filter_init,X9,X10) = init )
& ! [X11,X12] :
( ( leq(n0,X11)
& leq(n0,X12)
& leq(X11,n5)
& leq(X12,n0) )
=> a_select3(xhatmin_ds1_filter_init,X11,X12) = init )
& ! [X13,X14] :
( ( leq(n0,X13)
& leq(n0,X14)
& leq(X13,n5)
& leq(X14,n5) )
=> a_select3(pminus_ds1_filter_init,X13,X14) = init )
& ! [X15,X16] :
( ( leq(n0,X15)
& leq(n0,X16)
& leq(X15,n5)
& leq(X16,n5) )
=> ( ( X15 = pv63
& gt(pv64,X16) )
=> a_select3(id_ds1_filter_init,X15,X16) = init ) )
& ! [X17,X18] :
( ( leq(n0,X17)
& leq(n0,X18)
& leq(X17,n5)
& leq(X18,n5) )
=> ( gt(pv63,X17)
=> a_select3(id_ds1_filter_init,X17,X18) = init ) )
& ! [X19] :
( ( leq(n0,X19)
& leq(X19,pred(pv63)) )
=> ! [X20] :
( ( leq(n0,X20)
& leq(X20,n5) )
=> a_select3(id_ds1_filter_init,X19,X20) = init ) ) )
=> ! [X21,X22] :
( ( leq(n0,X21)
& leq(n0,X22)
& leq(X21,n5)
& leq(X22,n5) )
=> ( ( pv64 != X22
& X21 = pv63
& leq(X22,pv64) )
=> a_select3(id_ds1_filter_init,X21,X22) = init ) ) ) )).

%------------------------------------------------------------------------------
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