%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SYN938+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 03:18:22 PM UTC 2026
% Result : Theorem 0.72s 0.62s
% Output : CNFRefutation 0.72s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats ran out of CPU time)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ( ( ? [Y] :
( q1(Y)
=> r1(Y) )
& ! [X] :
( p1(X)
=> q1(X) ) )
=> ? [Z] :
( p1(Z)
=> r1(Z) ) )
& ! [B] :
( ! [Y] :
( ( r1(B)
=> r1(Y) )
=> p(f(Y),Y) )
=> ? [X,Y] :
( ( q(f(B),B)
=> q(X,Y) )
& p(X,Y) ) )
& ! [A,B] :
? [X,Y] :
( ( s1(A)
& ( s1(A)
=> p(X,Y) )
& r1(B)
& r1(A)
& ( r1(Y)
=> p(B,Y) )
& q1(B)
& q1(A)
& ( q1(X)
=> p(X,A) ) )
=> p(A,B) )
& ( ( b0
& a0 )
=> ( a0
<=> b0 ) )
& ( b0
| a0
| ( a0
<=> b0 ) )
& ! [A] :
( ( ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
=> q1(A) )
& ( ! [X,Y] : p(X,Y)
=> ! [X] : p(X,X) )
& ( ? [X] : p1(X)
=> ? [Y] : p1(Y) )
& ( p1(z)
=> p1(z) )
& ( ? [X] :
! [Y] : p(X,Y)
=> ! [Y] :
? [X] : p(X,Y) )
& ? [Y] :
( ? [X] : p1(X)
=> p1(Y) )
& ! [A,B] :
? [X,Y] :
( ( p1(X)
=> r1(Y) )
=> ( p1(A)
=> r1(B) ) )
& ! [B] :
( ( r1(B)
& ! [X] :
( p1(X)
=> q1(X) ) )
=> ( ! [Y] :
( r1(Y)
=> p1(Y) )
=> q1(B) ) )
& ? [X] :
! [Y] :
( p1(X)
=> p1(Y) )
& ! [A,B] :
( ! [Y] :
( q1(Y)
=> p1(Y) )
=> ? [X] :
( ( q1(X)
=> p1(B) )
& ( p1(X)
=> p1(A) ) ) )
& ( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) )
& ? [Z] :
! [X] :
? [Y] :
( ( ( p(Y,Z)
& p(Z,Y) )
=> p(Y,X) )
& ( p(Y,X)
=> ? [W] : p(W,Y) ) )
& ( ? [X] : p1(X)
=> ? [Z] : p1(Z) )
& ( ? [X] : p1(X)
<=> ? [Y] : p1(Y) )
& ( ! [X] : p1(X)
=> ( ! [Y] : p1(Y)
& ! [X] : p1(X) ) )
& ! [A,B] :
( ! [X] : p1(X)
=> ( p1(B)
& p1(A) ) )
& ( ? [X,Y] : a(X,Y)
<=> ? [Y,X] : a(X,Y) )
& ( ? [X] : b(X)
=> ? [X] :
( b(X)
| a1(X) ) )
& ( ( ! [X] : b(X)
& ? [X] : a1(X) )
=> ? [X] :
( b(X)
& a1(X) ) )
& ~ ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
& ( ? [X] :
( a1(X)
=> b(X) )
=> ( ! [X] : a1(X)
=> ? [X] : b(X) ) )
& ( ! [X] :
( a1(X)
=> b(X) )
=> ( ? [X] : a1(X)
=> ? [X] : b(X) ) )
& ! [A,B] :
( ! [Z] :
( q1(Z)
=> p1(Z) )
=> ? [X] :
( ( q1(X)
=> p1(B) )
& ( p1(X)
=> p1(A) ) ) )
& ( ! [X] :
( p1(X)
=> q1(X) )
=> ( ! [X] : p1(X)
=> ! [X] : q1(X) ) )
& ( ! [X] : p1(X)
=> ? [Y] : p1(Y) )
& ( ? [X] : p1(X)
=> ( ( a0
=> ( ( q0
=> q0 )
& ( ~ b0
| b0 ) ) )
& ? [X] : p1(X) ) )
& ! [A,B] :
( ! [Y] :
( q1(Y)
=> p1(Y) )
=> ? [X] :
( ( q1(X)
=> p1(B) )
& ( p1(X)
=> p1(A) ) ) )
& ! [A,B,C] :
( ( ! [X,Y] :
( r(X,Y)
=> q(X,Y) )
& ! [X] :
( s1(X)
=> p1(X) )
& r(B,C)
& s1(B)
& s1(A) )
=> ? [X,Y] :
( q(X,Y)
& p1(X) ) )
& ( ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) )
=> ? [Z] : a(Z,Z) )
& ( ! [X] :
? [Y] :
( q1(Y)
& p1(X) )
=> ? [Z] :
! [Y] :
( r1(Z)
| p1(Y) ) )
& ( ( ? [Y] : q1(Y)
& ! [X] : p1(X) )
=> ? [Z] :
! [Y] :
( r1(Z)
| p1(Y) ) )
& ( ! [X] : p1(X)
=> ! [A,B] :
( p1(B)
& p1(A) ) )
& ! [A,B,C] :
( ( ! [X,Y] :
( r(X,Y)
=> q(X,Y) )
& ! [X] :
( s1(X)
=> p1(X) )
& r(B,C)
& s1(B)
& s1(A) )
=> ? [X,Y] :
( q(X,Y)
& p1(X) ) )
& ! [A] :
? [X,X2,X3,X4,Y] :
( ( ( s(A,Y)
=> p1(Y) )
& ( e(X2)
=> ( c(f(X2))
| g(X2) ) )
& ( e(X)
=> ( s(X,f(X))
| g(X) ) )
& e(A)
& p1(A) )
=> ( ( c(X4)
& p1(X4) )
| ( g(X3)
& p1(X3) ) ) )
& ( ( ~ ! [X] :
( a1(X)
=> b(X) )
& ! [X] :
( a1(X)
=> ( c(X)
| b(X) ) ) )
=> ? [X] :
( c(X)
& a1(X) ) )
& ! [B,C] :
( q1(f(B))
=> ? [X,Y] :
( q1(X)
& ( p1(f(Y))
=> ( ( r1(Y)
=> ( r1(C)
& r1(B) ) )
& p1(X) ) ) ) )
& ! [B,C] :
( ! [Z] : q1(f(Z))
=> ? [X,Y] :
( q1(X)
& ( p1(f(Y))
=> ( ( r1(Y)
=> ( r1(C)
& r1(B) ) )
& p1(X) ) ) ) )
& ! [C,B] :
( ! [Z] : q1(f(Z))
=> ? [X,Y] :
( q1(X)
& ( r1(Y)
=> ( r1(C)
& r1(B) ) )
& ( p1(f(Y))
=> p1(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ( ( ? [Y] :
( q1(Y)
=> r1(Y) )
& ! [X] :
( p1(X)
=> q1(X) ) )
=> ? [Z] :
( p1(Z)
=> r1(Z) ) )
& ! [B] :
( ! [Y] :
( ( r1(B)
=> r1(Y) )
=> p(f(Y),Y) )
=> ? [X,Y] :
( ( q(f(B),B)
=> q(X,Y) )
& p(X,Y) ) )
& ! [A,B] :
? [X,Y] :
( ( s1(A)
& ( s1(A)
=> p(X,Y) )
& r1(B)
& r1(A)
& ( r1(Y)
=> p(B,Y) )
& q1(B)
& q1(A)
& ( q1(X)
=> p(X,A) ) )
=> p(A,B) )
& ( ( b0
& a0 )
=> ( a0
<=> b0 ) )
& ( b0
| a0
| ( a0
<=> b0 ) )
& ! [A] :
( ( ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
=> q1(A) )
& ( ! [X,Y] : p(X,Y)
=> ! [X] : p(X,X) )
& ( ? [X] : p1(X)
=> ? [Y] : p1(Y) )
& ( p1(z)
=> p1(z) )
& ( ? [X] :
! [Y] : p(X,Y)
=> ! [Y] :
? [X] : p(X,Y) )
& ? [Y] :
( ? [X] : p1(X)
=> p1(Y) )
& ! [A,B] :
? [X,Y] :
( ( p1(X)
=> r1(Y) )
=> ( p1(A)
=> r1(B) ) )
& ! [B] :
( ( r1(B)
& ! [X] :
( p1(X)
=> q1(X) ) )
=> ( ! [Y] :
( r1(Y)
=> p1(Y) )
=> q1(B) ) )
& ? [X] :
! [Y] :
( p1(X)
=> p1(Y) )
& ! [A,B] :
( ! [Y] :
( q1(Y)
=> p1(Y) )
=> ? [X] :
( ( q1(X)
=> p1(B) )
& ( p1(X)
=> p1(A) ) ) )
& ( ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [A,B] :
( eq(A,B)
=> eq(B,A) ) )
& ? [Z] :
! [X] :
? [Y] :
( ( ( p(Y,Z)
& p(Z,Y) )
=> p(Y,X) )
& ( p(Y,X)
=> ? [W] : p(W,Y) ) )
& ( ? [X] : p1(X)
=> ? [Z] : p1(Z) )
& ( ? [X] : p1(X)
<=> ? [Y] : p1(Y) )
& ( ! [X] : p1(X)
=> ( ! [Y] : p1(Y)
& ! [X] : p1(X) ) )
& ! [A,B] :
( ! [X] : p1(X)
=> ( p1(B)
& p1(A) ) )
& ( ? [X,Y] : a(X,Y)
<=> ? [Y,X] : a(X,Y) )
& ( ? [X] : b(X)
=> ? [X] :
( b(X)
| a1(X) ) )
& ( ( ! [X] : b(X)
& ? [X] : a1(X) )
=> ? [X] :
( b(X)
& a1(X) ) )
& ~ ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
& ( ? [X] :
( a1(X)
=> b(X) )
=> ( ! [X] : a1(X)
=> ? [X] : b(X) ) )
& ( ! [X] :
( a1(X)
=> b(X) )
=> ( ? [X] : a1(X)
=> ? [X] : b(X) ) )
& ! [A,B] :
( ! [Z] :
( q1(Z)
=> p1(Z) )
=> ? [X] :
( ( q1(X)
=> p1(B) )
& ( p1(X)
=> p1(A) ) ) )
& ( ! [X] :
( p1(X)
=> q1(X) )
=> ( ! [X] : p1(X)
=> ! [X] : q1(X) ) )
& ( ! [X] : p1(X)
=> ? [Y] : p1(Y) )
& ( ? [X] : p1(X)
=> ( ( a0
=> ( ( q0
=> q0 )
& ( ~ b0
| b0 ) ) )
& ? [X] : p1(X) ) )
& ! [A,B] :
( ! [Y] :
( q1(Y)
=> p1(Y) )
=> ? [X] :
( ( q1(X)
=> p1(B) )
& ( p1(X)
=> p1(A) ) ) )
& ! [A,B,C] :
( ( ! [X,Y] :
( r(X,Y)
=> q(X,Y) )
& ! [X] :
( s1(X)
=> p1(X) )
& r(B,C)
& s1(B)
& s1(A) )
=> ? [X,Y] :
( q(X,Y)
& p1(X) ) )
& ( ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) )
=> ? [Z] : a(Z,Z) )
& ( ! [X] :
? [Y] :
( q1(Y)
& p1(X) )
=> ? [Z] :
! [Y] :
( r1(Z)
| p1(Y) ) )
& ( ( ? [Y] : q1(Y)
& ! [X] : p1(X) )
=> ? [Z] :
! [Y] :
( r1(Z)
| p1(Y) ) )
& ( ! [X] : p1(X)
=> ! [A,B] :
( p1(B)
& p1(A) ) )
& ! [A,B,C] :
( ( ! [X,Y] :
( r(X,Y)
=> q(X,Y) )
& ! [X] :
( s1(X)
=> p1(X) )
& r(B,C)
& s1(B)
& s1(A) )
=> ? [X,Y] :
( q(X,Y)
& p1(X) ) )
& ! [A] :
? [X,X2,X3,X4,Y] :
( ( ( s(A,Y)
=> p1(Y) )
& ( e(X2)
=> ( c(f(X2))
| g(X2) ) )
& ( e(X)
=> ( s(X,f(X))
| g(X) ) )
& e(A)
& p1(A) )
=> ( ( c(X4)
& p1(X4) )
| ( g(X3)
& p1(X3) ) ) )
& ( ( ~ ! [X] :
( a1(X)
=> b(X) )
& ! [X] :
( a1(X)
=> ( c(X)
| b(X) ) ) )
=> ? [X] :
( c(X)
& a1(X) ) )
& ! [B,C] :
( q1(f(B))
=> ? [X,Y] :
( q1(X)
& ( p1(f(Y))
=> ( ( r1(Y)
=> ( r1(C)
& r1(B) ) )
& p1(X) ) ) ) )
& ! [B,C] :
( ! [Z] : q1(f(Z))
=> ? [X,Y] :
( q1(X)
& ( p1(f(Y))
=> ( ( r1(Y)
=> ( r1(C)
& r1(B) ) )
& p1(X) ) ) ) )
& ! [C,B] :
( ! [Z] : q1(f(Z))
=> ? [X,Y] :
( q1(X)
& ( r1(Y)
=> ( r1(C)
& r1(B) ) )
& ( p1(f(Y))
=> p1(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ( ! [Z] :
( ~ r1(Z)
& p1(Z) )
& ? [Y] :
( r1(Y)
| ~ q1(Y) )
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ? [B] :
( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(B),B) )
| ~ p(X,Y) )
& ! [Y] :
( p(f(Y),Y)
| ( ~ r1(Y)
& r1(B) ) ) )
| ? [A,B] :
! [X,Y] :
( ~ p(A,B)
& s1(A)
& ( p(X,Y)
| ~ s1(A) )
& r1(B)
& r1(A)
& ( p(B,Y)
| ~ r1(Y) )
& q1(B)
& q1(A)
& ( p(X,A)
| ~ q1(X) ) )
| ( ( a0
<~> b0 )
& b0
& a0 )
| ( ~ b0
& ~ a0
& ( a0
<~> b0 ) )
| ? [A] :
( ~ q1(A)
& ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
| ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,definition,
( sP0_prd
<=> ( ? [B] :
( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(B),B) )
| ~ p(X,Y) )
& ! [Y] :
( p(f(Y),Y)
| ( ~ r1(Y)
& r1(B) ) ) )
| ? [A,B] :
! [X,Y] :
( ~ p(A,B)
& s1(A)
& ( p(X,Y)
| ~ s1(A) )
& r1(B)
& r1(A)
& ( p(B,Y)
| ~ r1(Y) )
& q1(B)
& q1(A)
& ( p(X,A)
| ~ q1(X) ) )
| ( ( a0
<~> b0 )
& b0
& a0 )
| ( ~ b0
& ~ a0
& ( a0
<~> b0 ) )
| ? [A] :
( ~ q1(A)
& ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
| ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f5,plain,
( ( ! [Z] :
( ~ r1(Z)
& p1(Z) )
& ? [Y] :
( r1(Y)
| ~ q1(Y) )
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| sP0_prd ),
inference(formula_renaming,[status(thm)],[f3,f4]) ).
fof(f6,plain,
( ( ! [Z] : ~ r1(Z)
& ! [Z] : p1(Z)
& ( ? [Y] : r1(Y)
| ? [Y] : ~ q1(Y) )
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| sP0_prd ),
inference(miniscoping,[status(thm)],[f5]) ).
fof(f7,plain,
( ( ! [Z] : ~ r1(Z)
& ! [Z] : p1(Z)
& ( r1(sK1_skl)
| ~ q1(sK0_skl) )
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| sP0_prd ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(Y,sK0_skl),skolemize(Y,sK1_skl)],[f6]) ).
fof(f8,plain,
! [X0] :
( q1(X0)
| ~ p1(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
( r1(sK1_skl)
| ~ q1(sK0_skl)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f10,plain,
! [X0] :
( p1(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f11,plain,
! [X0] :
( ~ r1(X0)
| sP0_prd ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f12,definition,
( sP1_prd
<=> ( ? [A,B] :
! [X,Y] :
( ~ p(A,B)
& s1(A)
& ( p(X,Y)
| ~ s1(A) )
& r1(B)
& r1(A)
& ( p(B,Y)
| ~ r1(Y) )
& q1(B)
& q1(A)
& ( p(X,A)
| ~ q1(X) ) )
| ( ( a0
<~> b0 )
& b0
& a0 )
| ( ~ b0
& ~ a0
& ( a0
<~> b0 ) )
| ? [A] :
( ~ q1(A)
& ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
| ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f13,plain,
( sP0_prd
<=> ( ? [B] :
( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(B),B) )
| ~ p(X,Y) )
& ! [Y] :
( p(f(Y),Y)
| ( ~ r1(Y)
& r1(B) ) ) )
| sP1_prd ) ),
inference(formula_renaming,[status(thm)],[f4,f12]) ).
fof(f14,plain,
( ( ( ! [B] :
( ? [X,Y] :
( ( q(X,Y)
| ~ q(f(B),B) )
& p(X,Y) )
| ? [Y] :
( ~ p(f(Y),Y)
& ( r1(Y)
| ~ r1(B) ) ) )
& ~ sP1_prd )
| sP0_prd )
& ( ? [B] :
( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(B),B) )
| ~ p(X,Y) )
& ! [Y] :
( p(f(Y),Y)
| ( ~ r1(Y)
& r1(B) ) ) )
| sP1_prd
| ~ sP0_prd ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ( ( ! [B] :
( ( ( q(sK4_skl(B),sK5_skl(B))
| ~ q(f(B),B) )
& p(sK4_skl(B),sK5_skl(B)) )
| ( ~ p(f(sK3_skl(B)),sK3_skl(B))
& ( r1(sK3_skl(B))
| ~ r1(B) ) ) )
& ~ sP1_prd )
| sP0_prd )
& ( ( ! [X,Y] :
( ( ~ q(X,Y)
& q(f(sK2_skl),sK2_skl) )
| ~ p(X,Y) )
& ! [Y] :
( p(f(Y),Y)
| ( ~ r1(Y)
& r1(sK2_skl) ) ) )
| sP1_prd
| ~ sP0_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl,sK5_skl]),skolemize(B,sK2_skl),skolemize(Y,sK3_skl(B)),skolemize(X,sK4_skl(B)),skolemize(Y,sK5_skl(B))],[f14]) ).
fof(f16,plain,
! [X0] :
( p(f(X0),X0)
| r1(sK2_skl)
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0] :
( p(f(X0),X0)
| ~ r1(X0)
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( q(f(sK2_skl),sK2_skl)
| ~ p(X0,X1)
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f19,plain,
! [X0,X1] :
( ~ q(X0,X1)
| ~ p(X0,X1)
| sP1_prd
| ~ sP0_prd ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f25,definition,
( sP2_prd
<=> ( ( ( a0
<~> b0 )
& b0
& a0 )
| ( ~ b0
& ~ a0
& ( a0
<~> b0 ) )
| ? [A] :
( ~ q1(A)
& ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
| ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP2_prd])],[]) ).
fof(f26,plain,
( sP1_prd
<=> ( ? [A,B] :
! [X,Y] :
( ~ p(A,B)
& s1(A)
& ( p(X,Y)
| ~ s1(A) )
& r1(B)
& r1(A)
& ( p(B,Y)
| ~ r1(Y) )
& q1(B)
& q1(A)
& ( p(X,A)
| ~ q1(X) ) )
| sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f12,f25]) ).
fof(f27,definition,
! [A,B,X,Y] :
( sP3_prd(Y,X,B,A)
<=> ( r1(B)
& r1(A)
& ( p(B,Y)
| ~ r1(Y) )
& q1(B)
& q1(A)
& ( p(X,A)
| ~ q1(X) ) ) ),
introduced(definition,[new_symbols(definition,[sP3_prd])],[]) ).
fof(f28,plain,
( sP1_prd
<=> ( ? [A,B] :
! [X,Y] :
( ~ p(A,B)
& s1(A)
& ( p(X,Y)
| ~ s1(A) )
& sP3_prd(Y,X,B,A) )
| sP2_prd ) ),
inference(formula_renaming,[status(thm)],[f26,f27]) ).
fof(f29,plain,
( ( ( ! [A,B] :
? [X,Y] :
( p(A,B)
| ~ s1(A)
| ( ~ p(X,Y)
& s1(A) )
| ~ sP3_prd(Y,X,B,A) )
& ~ sP2_prd )
| sP1_prd )
& ( ? [A,B] :
! [X,Y] :
( ~ p(A,B)
& s1(A)
& ( p(X,Y)
| ~ s1(A) )
& sP3_prd(Y,X,B,A) )
| sP2_prd
| ~ sP1_prd ) ),
inference(NNF_transformation,[status(thm)],[f28]) ).
fof(f30,plain,
( ( ( ! [A,B] :
( p(A,B)
| ~ s1(A)
| ( ? [X,Y] : ~ p(X,Y)
& s1(A) )
| ? [X,Y] : ~ sP3_prd(Y,X,B,A) )
& ~ sP2_prd )
| sP1_prd )
& ( ? [A,B] :
( ~ p(A,B)
& s1(A)
& ( ! [X,Y] : p(X,Y)
| ~ s1(A) )
& ! [X,Y] : sP3_prd(Y,X,B,A) )
| sP2_prd
| ~ sP1_prd ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
( ( ( ! [A,B] :
( p(A,B)
| ~ s1(A)
| ( ~ p(sK10_skl(B,A),sK11_skl(B,A))
& s1(A) )
| ~ sP3_prd(sK9_skl(B,A),sK8_skl(B,A),B,A) )
& ~ sP2_prd )
| sP1_prd )
& ( ( ~ p(sK6_skl,sK7_skl)
& s1(sK6_skl)
& ( ! [X,Y] : p(X,Y)
| ~ s1(sK6_skl) )
& ! [X,Y] : sP3_prd(Y,X,sK7_skl,sK6_skl) )
| sP2_prd
| ~ sP1_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl,sK7_skl,sK8_skl,sK9_skl,sK10_skl,sK11_skl]),skolemize(A,sK6_skl),skolemize(B,sK7_skl),skolemize(X,sK8_skl(B,A)),skolemize(Y,sK9_skl(B,A)),skolemize(X,sK10_skl(B,A)),skolemize(Y,sK11_skl(B,A))],[f30]) ).
fof(f33,plain,
! [X0,X1] :
( p(X0,X1)
| ~ s1(sK6_skl)
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
( s1(sK6_skl)
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,plain,
( ~ p(sK6_skl,sK7_skl)
| sP2_prd
| ~ sP1_prd ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f39,definition,
( sP4_prd
<=> ( ( ~ b0
& ~ a0
& ( a0
<~> b0 ) )
| ? [A] :
( ~ q1(A)
& ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
| ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP4_prd])],[]) ).
fof(f40,plain,
( sP2_prd
<=> ( ( ( a0
<~> b0 )
& b0
& a0 )
| sP4_prd ) ),
inference(formula_renaming,[status(thm)],[f25,f39]) ).
fof(f41,plain,
( ( ( ( ( ( ~ b0
| a0 )
& ( b0
| ~ a0 ) )
| ~ b0
| ~ a0 )
& ~ sP4_prd )
| sP2_prd )
& ( ( ( ~ b0
| ~ a0 )
& ( b0
| a0 )
& b0
& a0 )
| sP4_prd
| ~ sP2_prd ) ),
inference(NNF_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
( a0
| sP4_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
( b0
| sP4_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f45,plain,
( ~ b0
| ~ a0
| sP4_prd
| ~ sP2_prd ),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f59,definition,
( sP6_prd
<=> ( ? [A] :
( ~ q1(A)
& ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
| ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP6_prd])],[]) ).
fof(f60,plain,
( sP4_prd
<=> ( ( ~ b0
& ~ a0
& ( a0
<~> b0 ) )
| sP6_prd ) ),
inference(formula_renaming,[status(thm)],[f39,f59]) ).
fof(f61,plain,
( ( ( ( b0
| a0
| ( ( ~ b0
| a0 )
& ( b0
| ~ a0 ) ) )
& ~ sP6_prd )
| sP4_prd )
& ( ( ~ b0
& ~ a0
& ( ~ b0
| ~ a0 )
& ( b0
| a0 ) )
| sP6_prd
| ~ sP4_prd ) ),
inference(NNF_transformation,[status(thm)],[f60]) ).
fof(f62,plain,
( b0
| a0
| sP6_prd
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f64,plain,
( ~ a0
| sP6_prd
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f65,plain,
( ~ b0
| sP6_prd
| ~ sP4_prd ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f76,definition,
( sP7_prd
<=> ( ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP7_prd])],[]) ).
fof(f77,plain,
( sP6_prd
<=> ( ? [A] :
( ~ q1(A)
& ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
| sP7_prd ) ),
inference(formula_renaming,[status(thm)],[f59,f76]) ).
fof(f78,plain,
( ( ( ! [A] :
( q1(A)
| ? [X] :
( ~ q1(X)
| ~ p1(X) )
| ( ~ g0
& ~ f0 ) )
& ~ sP7_prd )
| sP6_prd )
& ( ? [A] :
( ~ q1(A)
& ! [X] :
( q1(X)
& p1(X) )
& ( g0
| f0 ) )
| sP7_prd
| ~ sP6_prd ) ),
inference(NNF_transformation,[status(thm)],[f77]) ).
fof(f79,plain,
( ( ( ( ! [A] : q1(A)
| ? [X] : ~ q1(X)
| ? [X] : ~ p1(X)
| ( ~ g0
& ~ f0 ) )
& ~ sP7_prd )
| sP6_prd )
& ( ( ? [A] : ~ q1(A)
& ! [X] : q1(X)
& ! [X] : p1(X)
& ( g0
| f0 ) )
| sP7_prd
| ~ sP6_prd ) ),
inference(miniscoping,[status(thm)],[f78]) ).
fof(f80,plain,
( ( ( ( ! [A] : q1(A)
| ~ q1(sK14_skl)
| ~ p1(sK13_skl)
| ( ~ g0
& ~ f0 ) )
& ~ sP7_prd )
| sP6_prd )
& ( ( ~ q1(sK12_skl)
& ! [X] : q1(X)
& ! [X] : p1(X)
& ( g0
| f0 ) )
| sP7_prd
| ~ sP6_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12_skl,sK13_skl,sK14_skl]),skolemize(A,sK12_skl),skolemize(X,sK13_skl),skolemize(X,sK14_skl)],[f79]) ).
fof(f83,plain,
! [X0] :
( q1(X0)
| sP7_prd
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f84,plain,
( ~ q1(sK12_skl)
| sP7_prd
| ~ sP6_prd ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f88,definition,
( sP8_prd
<=> ( ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP8_prd])],[]) ).
fof(f89,plain,
( sP7_prd
<=> ( ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| sP8_prd ) ),
inference(formula_renaming,[status(thm)],[f76,f88]) ).
fof(f90,plain,
( ( ( ( ! [X] : p(X,X)
| ? [X,Y] : ~ p(X,Y) )
& ~ sP8_prd )
| sP7_prd )
& ( ( ? [X] : ~ p(X,X)
& ! [X,Y] : p(X,Y) )
| sP8_prd
| ~ sP7_prd ) ),
inference(NNF_transformation,[status(thm)],[f89]) ).
fof(f91,plain,
( ( ( ( ! [X] : p(X,X)
| ~ p(sK16_skl,sK17_skl) )
& ~ sP8_prd )
| sP7_prd )
& ( ( ~ p(sK15_skl,sK15_skl)
& ! [X,Y] : p(X,Y) )
| sP8_prd
| ~ sP7_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15_skl,sK16_skl,sK17_skl]),skolemize(X,sK15_skl),skolemize(X,sK16_skl),skolemize(Y,sK17_skl)],[f90]) ).
fof(f92,plain,
! [X0,X1] :
( p(X0,X1)
| sP8_prd
| ~ sP7_prd ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f93,plain,
( ~ p(sK15_skl,sK15_skl)
| sP8_prd
| ~ sP7_prd ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f96,definition,
( sP9_prd
<=> ( ( ~ p1(z)
& p1(z) )
| ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP9_prd])],[]) ).
fof(f97,plain,
( sP8_prd
<=> ( ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| sP9_prd ) ),
inference(formula_renaming,[status(thm)],[f88,f96]) ).
fof(f98,plain,
( ( ( ( ? [Y] : p1(Y)
| ! [X] : ~ p1(X) )
& ~ sP9_prd )
| sP8_prd )
& ( ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| sP9_prd
| ~ sP8_prd ) ),
inference(NNF_transformation,[status(thm)],[f97]) ).
fof(f99,plain,
( ( ( ( p1(sK19_skl)
| ! [X] : ~ p1(X) )
& ~ sP9_prd )
| sP8_prd )
& ( ( ! [Y] : ~ p1(Y)
& p1(sK18_skl) )
| sP9_prd
| ~ sP8_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18_skl,sK19_skl]),skolemize(X,sK18_skl),skolemize(Y,sK19_skl)],[f98]) ).
fof(f100,plain,
( p1(sK18_skl)
| sP9_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f101,plain,
! [X0] :
( ~ p1(X0)
| sP9_prd
| ~ sP8_prd ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f104,definition,
( sP10_prd
<=> ( ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP10_prd])],[]) ).
fof(f105,plain,
( sP9_prd
<=> ( ( ~ p1(z)
& p1(z) )
| sP10_prd ) ),
inference(formula_renaming,[status(thm)],[f96,f104]) ).
fof(f106,plain,
( ( ( ( p1(z)
| ~ p1(z) )
& ~ sP10_prd )
| sP9_prd )
& ( ( ~ p1(z)
& p1(z) )
| sP10_prd
| ~ sP9_prd ) ),
inference(NNF_transformation,[status(thm)],[f105]) ).
fof(f107,plain,
( p1(z)
| sP10_prd
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
( ~ p1(z)
| sP10_prd
| ~ sP9_prd ),
inference(cnf_transformation,[status(thm)],[f106]) ).
fof(f111,definition,
( sP11_prd
<=> ( ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP11_prd])],[]) ).
fof(f112,plain,
( sP10_prd
<=> ( ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| sP11_prd ) ),
inference(formula_renaming,[status(thm)],[f104,f111]) ).
fof(f113,plain,
( ( ( ( ! [Y] :
? [X] : p(X,Y)
| ! [X] :
? [Y] : ~ p(X,Y) )
& ~ sP11_prd )
| sP10_prd )
& ( ( ? [Y] :
! [X] : ~ p(X,Y)
& ? [X] :
! [Y] : p(X,Y) )
| sP11_prd
| ~ sP10_prd ) ),
inference(NNF_transformation,[status(thm)],[f112]) ).
fof(f114,plain,
( ( ( ( ! [Y] : p(sK23_skl(Y),Y)
| ! [X] : ~ p(X,sK22_skl(X)) )
& ~ sP11_prd )
| sP10_prd )
& ( ( ! [X] : ~ p(X,sK21_skl)
& ! [Y] : p(sK20_skl,Y) )
| sP11_prd
| ~ sP10_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl,sK21_skl,sK22_skl,sK23_skl]),skolemize(X,sK20_skl),skolemize(Y,sK21_skl),skolemize(Y,sK22_skl(X)),skolemize(X,sK23_skl(Y))],[f113]) ).
fof(f115,plain,
! [X0] :
( p(sK20_skl,X0)
| sP11_prd
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0] :
( ~ p(X0,sK21_skl)
| sP11_prd
| ~ sP10_prd ),
inference(cnf_transformation,[status(thm)],[f114]) ).
fof(f119,definition,
( sP12_prd
<=> ( ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP12_prd])],[]) ).
fof(f120,plain,
( sP11_prd
<=> ( ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| sP12_prd ) ),
inference(formula_renaming,[status(thm)],[f111,f119]) ).
fof(f121,plain,
( ( ( ? [Y] :
( p1(Y)
| ! [X] : ~ p1(X) )
& ~ sP12_prd )
| sP11_prd )
& ( ! [Y] :
( ~ p1(Y)
& ? [X] : p1(X) )
| sP12_prd
| ~ sP11_prd ) ),
inference(NNF_transformation,[status(thm)],[f120]) ).
fof(f122,plain,
( ( ( ( ? [Y] : p1(Y)
| ! [X] : ~ p1(X) )
& ~ sP12_prd )
| sP11_prd )
& ( ( ! [Y] : ~ p1(Y)
& ? [X] : p1(X) )
| sP12_prd
| ~ sP11_prd ) ),
inference(miniscoping,[status(thm)],[f121]) ).
fof(f123,plain,
( ( ( ( p1(sK25_skl)
| ! [X] : ~ p1(X) )
& ~ sP12_prd )
| sP11_prd )
& ( ( ! [Y] : ~ p1(Y)
& p1(sK24_skl) )
| sP12_prd
| ~ sP11_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl]),skolemize(X,sK24_skl),skolemize(Y,sK25_skl)],[f122]) ).
fof(f124,plain,
( p1(sK24_skl)
| sP12_prd
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f125,plain,
! [X0] :
( ~ p1(X0)
| sP12_prd
| ~ sP11_prd ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f128,definition,
( sP13_prd
<=> ( ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP13_prd])],[]) ).
fof(f129,plain,
( sP12_prd
<=> ( ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| sP13_prd ) ),
inference(formula_renaming,[status(thm)],[f119,f128]) ).
fof(f130,plain,
( ( ( ! [A,B] :
? [X,Y] :
( r1(B)
| ~ p1(A)
| ( ~ r1(Y)
& p1(X) ) )
& ~ sP13_prd )
| sP12_prd )
& ( ? [A,B] :
! [X,Y] :
( ~ r1(B)
& p1(A)
& ( r1(Y)
| ~ p1(X) ) )
| sP13_prd
| ~ sP12_prd ) ),
inference(NNF_transformation,[status(thm)],[f129]) ).
fof(f131,plain,
( ( ( ( ! [B] : r1(B)
| ! [A] : ~ p1(A)
| ( ? [Y] : ~ r1(Y)
& ? [X] : p1(X) ) )
& ~ sP13_prd )
| sP12_prd )
& ( ( ? [B] : ~ r1(B)
& ? [A] : p1(A)
& ( ! [Y] : r1(Y)
| ! [X] : ~ p1(X) ) )
| sP13_prd
| ~ sP12_prd ) ),
inference(miniscoping,[status(thm)],[f130]) ).
fof(f132,plain,
( ( ( ( ! [B] : r1(B)
| ! [A] : ~ p1(A)
| ( ~ r1(sK29_skl)
& p1(sK28_skl) ) )
& ~ sP13_prd )
| sP12_prd )
& ( ( ~ r1(sK27_skl)
& p1(sK26_skl)
& ( ! [Y] : r1(Y)
| ! [X] : ~ p1(X) ) )
| sP13_prd
| ~ sP12_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl,sK28_skl,sK29_skl]),skolemize(A,sK26_skl),skolemize(B,sK27_skl),skolemize(X,sK28_skl),skolemize(Y,sK29_skl)],[f131]) ).
fof(f133,plain,
! [X0,X1] :
( r1(X1)
| ~ p1(X0)
| sP13_prd
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f134,plain,
( p1(sK26_skl)
| sP13_prd
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f135,plain,
( ~ r1(sK27_skl)
| sP13_prd
| ~ sP12_prd ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f139,definition,
( sP14_prd
<=> ( ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP14_prd])],[]) ).
fof(f140,plain,
( sP13_prd
<=> ( ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| sP14_prd ) ),
inference(formula_renaming,[status(thm)],[f128,f139]) ).
fof(f141,definition,
! [B] :
( sP15_prd(B)
<=> ( r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) ) ),
introduced(definition,[new_symbols(definition,[sP15_prd])],[]) ).
fof(f142,plain,
( sP13_prd
<=> ( ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& sP15_prd(B) )
| sP14_prd ) ),
inference(formula_renaming,[status(thm)],[f140,f141]) ).
fof(f143,plain,
( ( ( ! [B] :
( q1(B)
| ? [Y] :
( ~ p1(Y)
& r1(Y) )
| ~ sP15_prd(B) )
& ~ sP14_prd )
| sP13_prd )
& ( ? [B] :
( ~ q1(B)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& sP15_prd(B) )
| sP14_prd
| ~ sP13_prd ) ),
inference(NNF_transformation,[status(thm)],[f142]) ).
fof(f144,plain,
( ( ( ! [B] :
( q1(B)
| ( ~ p1(sK31_skl(B))
& r1(sK31_skl(B)) )
| ~ sP15_prd(B) )
& ~ sP14_prd )
| sP13_prd )
& ( ( ~ q1(sK30_skl)
& ! [Y] :
( p1(Y)
| ~ r1(Y) )
& sP15_prd(sK30_skl) )
| sP14_prd
| ~ sP13_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30_skl,sK31_skl]),skolemize(B,sK30_skl),skolemize(Y,sK31_skl(B))],[f143]) ).
fof(f145,plain,
( sP15_prd(sK30_skl)
| sP14_prd
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f146,plain,
! [X0] :
( p1(X0)
| ~ r1(X0)
| sP14_prd
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f147,plain,
( ~ q1(sK30_skl)
| sP14_prd
| ~ sP13_prd ),
inference(cnf_transformation,[status(thm)],[f144]) ).
fof(f151,definition,
( sP16_prd
<=> ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP16_prd])],[]) ).
fof(f152,plain,
( sP14_prd
<=> ( ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| sP16_prd ) ),
inference(formula_renaming,[status(thm)],[f139,f151]) ).
fof(f153,plain,
( ( ( ? [X] :
! [Y] :
( p1(Y)
| ~ p1(X) )
& ~ sP16_prd )
| sP14_prd )
& ( ! [X] :
? [Y] :
( ~ p1(Y)
& p1(X) )
| sP16_prd
| ~ sP14_prd ) ),
inference(NNF_transformation,[status(thm)],[f152]) ).
fof(f154,plain,
( ( ( ( ! [Y] : p1(Y)
| ? [X] : ~ p1(X) )
& ~ sP16_prd )
| sP14_prd )
& ( ( ? [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| sP16_prd
| ~ sP14_prd ) ),
inference(miniscoping,[status(thm)],[f153]) ).
fof(f155,plain,
( ( ( ( ! [Y] : p1(Y)
| ~ p1(sK33_skl) )
& ~ sP16_prd )
| sP14_prd )
& ( ( ~ p1(sK32_skl)
& ! [X] : p1(X) )
| sP16_prd
| ~ sP14_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32_skl,sK33_skl]),skolemize(Y,sK32_skl),skolemize(X,sK33_skl)],[f154]) ).
fof(f156,plain,
! [X0] :
( p1(X0)
| sP16_prd
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f157,plain,
( ~ p1(sK32_skl)
| sP16_prd
| ~ sP14_prd ),
inference(cnf_transformation,[status(thm)],[f155]) ).
fof(f160,plain,
! [B] :
( ( ~ r1(B)
| ? [X] :
( ~ q1(X)
& p1(X) )
| sP15_prd(B) )
& ( ( r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ~ sP15_prd(B) ) ),
inference(NNF_transformation,[status(thm)],[f141]) ).
fof(f161,plain,
( ! [B] :
( ~ r1(B)
| ? [X] :
( ~ q1(X)
& p1(X) )
| sP15_prd(B) )
& ! [B] :
( ( r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ~ sP15_prd(B) ) ),
inference(miniscoping,[status(thm)],[f160]) ).
fof(f162,plain,
( ! [B] :
( ~ r1(B)
| ( ~ q1(sK34_skl(B))
& p1(sK34_skl(B)) )
| sP15_prd(B) )
& ! [B] :
( ( r1(B)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ~ sP15_prd(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl]),skolemize(X,sK34_skl(B))],[f161]) ).
fof(f163,plain,
! [X0,X1] :
( q1(X1)
| ~ p1(X1)
| ~ sP15_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [X0] :
( r1(X0)
| ~ sP15_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f162]) ).
fof(f167,definition,
( sP17_prd
<=> ( ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP17_prd])],[]) ).
fof(f168,plain,
( sP16_prd
<=> ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| sP17_prd ) ),
inference(formula_renaming,[status(thm)],[f151,f167]) ).
fof(f169,plain,
( ( ( ! [A,B] :
( ? [X] :
( ( p1(B)
| ~ q1(X) )
& ( p1(A)
| ~ p1(X) ) )
| ? [Y] :
( ~ p1(Y)
& q1(Y) ) )
& ~ sP17_prd )
| sP16_prd )
& ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| sP17_prd
| ~ sP16_prd ) ),
inference(NNF_transformation,[status(thm)],[f168]) ).
fof(f170,plain,
( ( ( ( ! [A,B] :
? [X] :
( ( p1(B)
| ~ q1(X) )
& ( p1(A)
| ~ p1(X) ) )
| ? [Y] :
( ~ p1(Y)
& q1(Y) ) )
& ~ sP17_prd )
| sP16_prd )
& ( ( ? [A,B] :
! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| sP17_prd
| ~ sP16_prd ) ),
inference(miniscoping,[status(thm)],[f169]) ).
fof(f171,plain,
( ( ( ( ! [A,B] :
( ( p1(B)
| ~ q1(sK38_skl(B,A)) )
& ( p1(A)
| ~ p1(sK38_skl(B,A)) ) )
| ( ~ p1(sK37_skl)
& q1(sK37_skl) ) )
& ~ sP17_prd )
| sP16_prd )
& ( ( ! [X] :
( ( ~ p1(sK36_skl)
& q1(X) )
| ( ~ p1(sK35_skl)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| sP17_prd
| ~ sP16_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35_skl,sK36_skl,sK37_skl,sK38_skl]),skolemize(A,sK35_skl),skolemize(B,sK36_skl),skolemize(Y,sK37_skl),skolemize(X,sK38_skl(B,A))],[f170]) ).
fof(f172,plain,
! [X0] :
( p1(X0)
| ~ q1(X0)
| sP17_prd
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f173,plain,
! [X0] :
( q1(X0)
| p1(X0)
| sP17_prd
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f176,plain,
( ~ p1(sK36_skl)
| ~ p1(sK35_skl)
| sP17_prd
| ~ sP16_prd ),
inference(cnf_transformation,[status(thm)],[f171]) ).
fof(f182,definition,
( sP18_prd
<=> ( ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP18_prd])],[]) ).
fof(f183,plain,
( sP17_prd
<=> ( ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) )
| sP18_prd ) ),
inference(formula_renaming,[status(thm)],[f167,f182]) ).
fof(f184,definition,
! [X,Y,Z] :
( sP19_prd(Z,Y,X)
<=> ( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ),
introduced(definition,[new_symbols(definition,[sP19_prd])],[]) ).
fof(f185,plain,
( sP17_prd
<=> ( ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( eq(X,Y)
<=> ! [Z] : sP19_prd(Z,Y,X) ) )
| sP18_prd ) ),
inference(formula_renaming,[status(thm)],[f183,f184]) ).
fof(f186,plain,
( ( ( ( ! [A,B] :
( eq(B,A)
| ~ eq(A,B) )
| ? [X,Y] :
( ( ! [Z] : sP19_prd(Z,Y,X)
| eq(X,Y) )
& ( ? [Z] : ~ sP19_prd(Z,Y,X)
| ~ eq(X,Y) ) ) )
& ~ sP18_prd )
| sP17_prd )
& ( ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( ( ? [Z] : ~ sP19_prd(Z,Y,X)
| eq(X,Y) )
& ( ! [Z] : sP19_prd(Z,Y,X)
| ~ eq(X,Y) ) ) )
| sP18_prd
| ~ sP17_prd ) ),
inference(NNF_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
( ( ( ( ! [A,B] :
( eq(B,A)
| ~ eq(A,B) )
| ? [X,Y] :
( ( ! [Z] : sP19_prd(Z,Y,X)
| eq(X,Y) )
& ( ? [Z] : ~ sP19_prd(Z,Y,X)
| ~ eq(X,Y) ) ) )
& ~ sP18_prd )
| sP17_prd )
& ( ( ? [A,B] :
( ~ eq(B,A)
& eq(A,B) )
& ! [X,Y] :
( ? [Z] : ~ sP19_prd(Z,Y,X)
| eq(X,Y) )
& ! [X,Y] :
( ! [Z] : sP19_prd(Z,Y,X)
| ~ eq(X,Y) ) )
| sP18_prd
| ~ sP17_prd ) ),
inference(miniscoping,[status(thm)],[f186]) ).
fof(f188,plain,
( ( ( ( ! [A,B] :
( eq(B,A)
| ~ eq(A,B) )
| ( ( ! [Z] : sP19_prd(Z,sK43_skl,sK42_skl)
| eq(sK42_skl,sK43_skl) )
& ( ~ sP19_prd(sK44_skl,sK43_skl,sK42_skl)
| ~ eq(sK42_skl,sK43_skl) ) ) )
& ~ sP18_prd )
| sP17_prd )
& ( ( ~ eq(sK41_skl,sK40_skl)
& eq(sK40_skl,sK41_skl)
& ! [X,Y] :
( ~ sP19_prd(sK39_skl(Y,X),Y,X)
| eq(X,Y) )
& ! [X,Y] :
( ! [Z] : sP19_prd(Z,Y,X)
| ~ eq(X,Y) ) )
| sP18_prd
| ~ sP17_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl,sK42_skl,sK43_skl,sK44_skl]),skolemize(Z,sK39_skl(Y,X)),skolemize(A,sK40_skl),skolemize(B,sK41_skl),skolemize(X,sK42_skl),skolemize(Y,sK43_skl),skolemize(Z,sK44_skl)],[f187]) ).
fof(f189,plain,
! [X0,X1,X2] :
( sP19_prd(X2,X1,X0)
| ~ eq(X0,X1)
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f190,plain,
! [X0,X1] :
( ~ sP19_prd(sK39_skl(X1,X0),X1,X0)
| eq(X0,X1)
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f191,plain,
( eq(sK40_skl,sK41_skl)
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f192,plain,
( ~ eq(sK41_skl,sK40_skl)
| sP18_prd
| ~ sP17_prd ),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f196,definition,
( sP20_prd
<=> ( ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP20_prd])],[]) ).
fof(f197,plain,
( sP18_prd
<=> ( ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| ( ! [W] : ~ p(W,Y)
& p(Y,X) ) )
| sP20_prd ) ),
inference(formula_renaming,[status(thm)],[f182,f196]) ).
fof(f198,definition,
! [X,Y] :
( sP21_prd(Y,X)
<=> ( ! [W] : ~ p(W,Y)
& p(Y,X) ) ),
introduced(definition,[new_symbols(definition,[sP21_prd])],[]) ).
fof(f199,plain,
( sP18_prd
<=> ( ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| sP21_prd(Y,X) )
| sP20_prd ) ),
inference(formula_renaming,[status(thm)],[f197,f198]) ).
fof(f200,plain,
( ( ( ? [Z] :
! [X] :
? [Y] :
( ( p(Y,X)
| ~ p(Y,Z)
| ~ p(Z,Y) )
& ~ sP21_prd(Y,X) )
& ~ sP20_prd )
| sP18_prd )
& ( ! [Z] :
? [X] :
! [Y] :
( ( ~ p(Y,X)
& p(Y,Z)
& p(Z,Y) )
| sP21_prd(Y,X) )
| sP20_prd
| ~ sP18_prd ) ),
inference(NNF_transformation,[status(thm)],[f199]) ).
fof(f201,plain,
( ( ( ! [X] :
( ( p(sK47_skl(X),X)
| ~ p(sK47_skl(X),sK46_skl)
| ~ p(sK46_skl,sK47_skl(X)) )
& ~ sP21_prd(sK47_skl(X),X) )
& ~ sP20_prd )
| sP18_prd )
& ( ! [Z,Y] :
( ( ~ p(Y,sK45_skl(Z))
& p(Y,Z)
& p(Z,Y) )
| sP21_prd(Y,sK45_skl(Z)) )
| sP20_prd
| ~ sP18_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl,sK46_skl,sK47_skl]),skolemize(X,sK45_skl(Z)),skolemize(Z,sK46_skl),skolemize(Y,sK47_skl(X))],[f200]) ).
fof(f202,plain,
! [X0,X1] :
( p(X1,X0)
| sP21_prd(X0,sK45_skl(X1))
| sP20_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f203,plain,
! [X0,X1] :
( p(X0,X1)
| sP21_prd(X0,sK45_skl(X1))
| sP20_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f204,plain,
! [X0,X1] :
( ~ p(X0,sK45_skl(X1))
| sP21_prd(X0,sK45_skl(X1))
| sP20_prd
| ~ sP18_prd ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f208,plain,
! [X,Y,Z] :
( ( ( ( a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| sP19_prd(Z,Y,X) )
& ( ( ( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ sP19_prd(Z,Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f184]) ).
fof(f209,plain,
( ! [X,Y,Z] :
( ( ( a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| sP19_prd(Z,Y,X) )
& ! [X,Y,Z] :
( ( ( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ sP19_prd(Z,Y,X) ) ),
inference(miniscoping,[status(thm)],[f208]) ).
fof(f210,plain,
! [X0,X1,X2] :
( a_member_of(X0,X1)
| ~ a_member_of(X0,X2)
| ~ sP19_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f211,plain,
! [X0,X1,X2] :
( ~ a_member_of(X0,X1)
| a_member_of(X0,X2)
| ~ sP19_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f212,plain,
! [X0,X1,X2] :
( ~ a_member_of(X0,X1)
| ~ a_member_of(X0,X2)
| sP19_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f213,plain,
! [X0,X1,X2] :
( a_member_of(X0,X1)
| a_member_of(X0,X2)
| sP19_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f214,definition,
( sP22_prd
<=> ( ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP22_prd])],[]) ).
fof(f215,plain,
( sP20_prd
<=> ( ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| sP22_prd ) ),
inference(formula_renaming,[status(thm)],[f196,f214]) ).
fof(f216,plain,
( ( ( ( ? [Z] : p1(Z)
| ! [X] : ~ p1(X) )
& ~ sP22_prd )
| sP20_prd )
& ( ( ! [Z] : ~ p1(Z)
& ? [X] : p1(X) )
| sP22_prd
| ~ sP20_prd ) ),
inference(NNF_transformation,[status(thm)],[f215]) ).
fof(f217,plain,
( ( ( ( p1(sK49_skl)
| ! [X] : ~ p1(X) )
& ~ sP22_prd )
| sP20_prd )
& ( ( ! [Z] : ~ p1(Z)
& p1(sK48_skl) )
| sP22_prd
| ~ sP20_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48_skl,sK49_skl]),skolemize(X,sK48_skl),skolemize(Z,sK49_skl)],[f216]) ).
fof(f218,plain,
( p1(sK48_skl)
| sP22_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0] :
( ~ p1(X0)
| sP22_prd
| ~ sP20_prd ),
inference(cnf_transformation,[status(thm)],[f217]) ).
fof(f222,plain,
! [X,Y] :
( ( ? [W] : p(W,Y)
| ~ p(Y,X)
| sP21_prd(Y,X) )
& ( ( ! [W] : ~ p(W,Y)
& p(Y,X) )
| ~ sP21_prd(Y,X) ) ),
inference(NNF_transformation,[status(thm)],[f198]) ).
fof(f223,plain,
( ! [X,Y] :
( ? [W] : p(W,Y)
| ~ p(Y,X)
| sP21_prd(Y,X) )
& ! [X,Y] :
( ( ! [W] : ~ p(W,Y)
& p(Y,X) )
| ~ sP21_prd(Y,X) ) ),
inference(miniscoping,[status(thm)],[f222]) ).
fof(f224,plain,
( ! [X,Y] :
( p(sK50_skl(Y,X),Y)
| ~ p(Y,X)
| sP21_prd(Y,X) )
& ! [X,Y] :
( ( ! [W] : ~ p(W,Y)
& p(Y,X) )
| ~ sP21_prd(Y,X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50_skl]),skolemize(W,sK50_skl(Y,X))],[f223]) ).
fof(f225,plain,
! [X0,X1] :
( p(X0,X1)
| ~ sP21_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
! [X0,X1,X2] :
( ~ p(X2,X0)
| ~ sP21_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f228,definition,
( sP23_prd
<=> ( ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP23_prd])],[]) ).
fof(f229,plain,
( sP22_prd
<=> ( ( ? [X] : p1(X)
<~> ? [Y] : p1(Y) )
| sP23_prd ) ),
inference(formula_renaming,[status(thm)],[f214,f228]) ).
fof(f230,plain,
( ( ( ( ! [Y] : ~ p1(Y)
| ? [X] : p1(X) )
& ( ? [Y] : p1(Y)
| ! [X] : ~ p1(X) )
& ~ sP23_prd )
| sP22_prd )
& ( ( ( ! [Y] : ~ p1(Y)
| ! [X] : ~ p1(X) )
& ( ? [Y] : p1(Y)
| ? [X] : p1(X) ) )
| sP23_prd
| ~ sP22_prd ) ),
inference(NNF_transformation,[status(thm)],[f229]) ).
fof(f231,plain,
( ( ( ( ! [Y] : ~ p1(Y)
| p1(sK54_skl) )
& ( p1(sK53_skl)
| ! [X] : ~ p1(X) )
& ~ sP23_prd )
| sP22_prd )
& ( ( ( ! [Y] : ~ p1(Y)
| ! [X] : ~ p1(X) )
& ( p1(sK52_skl)
| p1(sK51_skl) ) )
| sP23_prd
| ~ sP22_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl,sK53_skl,sK54_skl]),skolemize(X,sK51_skl),skolemize(Y,sK52_skl),skolemize(Y,sK53_skl),skolemize(X,sK54_skl)],[f230]) ).
fof(f232,plain,
( p1(sK52_skl)
| p1(sK51_skl)
| sP23_prd
| ~ sP22_prd ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f233,plain,
! [X0,X1] :
( ~ p1(X1)
| ~ p1(X0)
| sP23_prd
| ~ sP22_prd ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f237,definition,
( sP24_prd
<=> ( ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP24_prd])],[]) ).
fof(f238,plain,
( sP23_prd
<=> ( ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| sP24_prd ) ),
inference(formula_renaming,[status(thm)],[f228,f237]) ).
fof(f239,plain,
( ( ( ( ( ! [Y] : p1(Y)
& ! [X] : p1(X) )
| ? [X] : ~ p1(X) )
& ~ sP24_prd )
| sP23_prd )
& ( ( ( ? [Y] : ~ p1(Y)
| ? [X] : ~ p1(X) )
& ! [X] : p1(X) )
| sP24_prd
| ~ sP23_prd ) ),
inference(NNF_transformation,[status(thm)],[f238]) ).
fof(f240,plain,
( ( ( ( ( ! [Y] : p1(Y)
& ! [X] : p1(X) )
| ~ p1(sK57_skl) )
& ~ sP24_prd )
| sP23_prd )
& ( ( ( ~ p1(sK56_skl)
| ~ p1(sK55_skl) )
& ! [X] : p1(X) )
| sP24_prd
| ~ sP23_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl,sK56_skl,sK57_skl]),skolemize(X,sK55_skl),skolemize(Y,sK56_skl),skolemize(X,sK57_skl)],[f239]) ).
fof(f241,plain,
! [X0] :
( p1(X0)
| sP24_prd
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f242,plain,
( ~ p1(sK56_skl)
| ~ p1(sK55_skl)
| sP24_prd
| ~ sP23_prd ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f246,definition,
( sP25_prd
<=> ( ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP25_prd])],[]) ).
fof(f247,plain,
( sP24_prd
<=> ( ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| sP25_prd ) ),
inference(formula_renaming,[status(thm)],[f237,f246]) ).
fof(f248,plain,
( ( ( ! [A,B] :
( ( p1(B)
& p1(A) )
| ? [X] : ~ p1(X) )
& ~ sP25_prd )
| sP24_prd )
& ( ? [A,B] :
( ( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| sP25_prd
| ~ sP24_prd ) ),
inference(NNF_transformation,[status(thm)],[f247]) ).
fof(f249,plain,
( ( ( ( ( ! [B] : p1(B)
& ! [A] : p1(A) )
| ? [X] : ~ p1(X) )
& ~ sP25_prd )
| sP24_prd )
& ( ( ( ? [B] : ~ p1(B)
| ? [A] : ~ p1(A) )
& ! [X] : p1(X) )
| sP25_prd
| ~ sP24_prd ) ),
inference(miniscoping,[status(thm)],[f248]) ).
fof(f250,plain,
( ( ( ( ( ! [B] : p1(B)
& ! [A] : p1(A) )
| ~ p1(sK60_skl) )
& ~ sP25_prd )
| sP24_prd )
& ( ( ( ~ p1(sK59_skl)
| ~ p1(sK58_skl) )
& ! [X] : p1(X) )
| sP25_prd
| ~ sP24_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK58_skl,sK59_skl,sK60_skl]),skolemize(A,sK58_skl),skolemize(B,sK59_skl),skolemize(X,sK60_skl)],[f249]) ).
fof(f251,plain,
! [X0] :
( p1(X0)
| sP25_prd
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f252,plain,
( ~ p1(sK59_skl)
| ~ p1(sK58_skl)
| sP25_prd
| ~ sP24_prd ),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f256,definition,
( sP26_prd
<=> ( ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP26_prd])],[]) ).
fof(f257,plain,
( sP25_prd
<=> ( ( ? [X,Y] : a(X,Y)
<~> ? [Y,X] : a(X,Y) )
| sP26_prd ) ),
inference(formula_renaming,[status(thm)],[f246,f256]) ).
fof(f258,plain,
( ( ( ( ! [Y,X] : ~ a(X,Y)
| ? [X,Y] : a(X,Y) )
& ( ? [Y,X] : a(X,Y)
| ! [X,Y] : ~ a(X,Y) )
& ~ sP26_prd )
| sP25_prd )
& ( ( ( ! [Y,X] : ~ a(X,Y)
| ! [X,Y] : ~ a(X,Y) )
& ( ? [Y,X] : a(X,Y)
| ? [X,Y] : a(X,Y) ) )
| sP26_prd
| ~ sP25_prd ) ),
inference(NNF_transformation,[status(thm)],[f257]) ).
fof(f259,plain,
( ( ( ( ! [Y,X] : ~ a(X,Y)
| a(sK67_skl,sK68_skl) )
& ( a(sK66_skl,sK65_skl)
| ! [X,Y] : ~ a(X,Y) )
& ~ sP26_prd )
| sP25_prd )
& ( ( ( ! [Y,X] : ~ a(X,Y)
| ! [X,Y] : ~ a(X,Y) )
& ( a(sK64_skl,sK63_skl)
| a(sK61_skl,sK62_skl) ) )
| sP26_prd
| ~ sP25_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK61_skl,sK62_skl,sK63_skl,sK64_skl,sK65_skl,sK66_skl,sK67_skl,sK68_skl]),skolemize(X,sK61_skl),skolemize(Y,sK62_skl),skolemize(Y,sK63_skl),skolemize(X,sK64_skl),skolemize(Y,sK65_skl),skolemize(X,sK66_skl),skolemize(X,sK67_skl),skolemize(Y,sK68_skl)],[f258]) ).
fof(f260,plain,
( a(sK64_skl,sK63_skl)
| a(sK61_skl,sK62_skl)
| sP26_prd
| ~ sP25_prd ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f261,plain,
! [X0,X1,X2,X3] :
( ~ a(X2,X3)
| ~ a(X0,X1)
| sP26_prd
| ~ sP25_prd ),
inference(cnf_transformation,[status(thm)],[f259]) ).
fof(f265,definition,
( sP27_prd
<=> ( ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP27_prd])],[]) ).
fof(f266,plain,
( sP26_prd
<=> ( ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| sP27_prd ) ),
inference(formula_renaming,[status(thm)],[f256,f265]) ).
fof(f267,plain,
( ( ( ( ? [X] :
( b(X)
| a1(X) )
| ! [X] : ~ b(X) )
& ~ sP27_prd )
| sP26_prd )
& ( ( ! [X] :
( ~ b(X)
& ~ a1(X) )
& ? [X] : b(X) )
| sP27_prd
| ~ sP26_prd ) ),
inference(NNF_transformation,[status(thm)],[f266]) ).
fof(f268,plain,
( ( ( ( ? [X] : b(X)
| ? [X] : a1(X)
| ! [X] : ~ b(X) )
& ~ sP27_prd )
| sP26_prd )
& ( ( ! [X] : ~ b(X)
& ! [X] : ~ a1(X)
& ? [X] : b(X) )
| sP27_prd
| ~ sP26_prd ) ),
inference(miniscoping,[status(thm)],[f267]) ).
fof(f269,plain,
( ( ( ( b(sK71_skl)
| a1(sK70_skl)
| ! [X] : ~ b(X) )
& ~ sP27_prd )
| sP26_prd )
& ( ( ! [X] : ~ b(X)
& ! [X] : ~ a1(X)
& b(sK69_skl) )
| sP27_prd
| ~ sP26_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK69_skl,sK70_skl,sK71_skl]),skolemize(X,sK69_skl),skolemize(X,sK70_skl),skolemize(X,sK71_skl)],[f268]) ).
fof(f270,plain,
( b(sK69_skl)
| sP27_prd
| ~ sP26_prd ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0] :
( ~ b(X0)
| sP27_prd
| ~ sP26_prd ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f275,definition,
( sP28_prd
<=> ( ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP28_prd])],[]) ).
fof(f276,plain,
( sP27_prd
<=> ( ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| sP28_prd ) ),
inference(formula_renaming,[status(thm)],[f265,f275]) ).
fof(f277,plain,
( ( ( ( ? [X] :
( b(X)
& a1(X) )
| ? [X] : ~ b(X)
| ! [X] : ~ a1(X) )
& ~ sP28_prd )
| sP27_prd )
& ( ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& ? [X] : a1(X) )
| sP28_prd
| ~ sP27_prd ) ),
inference(NNF_transformation,[status(thm)],[f276]) ).
fof(f278,plain,
( ( ( ( ( b(sK74_skl)
& a1(sK74_skl) )
| ~ b(sK73_skl)
| ! [X] : ~ a1(X) )
& ~ sP28_prd )
| sP27_prd )
& ( ( ! [X] :
( ~ b(X)
| ~ a1(X) )
& ! [X] : b(X)
& a1(sK72_skl) )
| sP28_prd
| ~ sP27_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK72_skl,sK73_skl,sK74_skl]),skolemize(X,sK72_skl),skolemize(X,sK73_skl),skolemize(X,sK74_skl)],[f277]) ).
fof(f279,plain,
( a1(sK72_skl)
| sP28_prd
| ~ sP27_prd ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f280,plain,
! [X0] :
( b(X0)
| sP28_prd
| ~ sP27_prd ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f281,plain,
! [X0] :
( ~ b(X0)
| ~ a1(X0)
| sP28_prd
| ~ sP27_prd ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f285,definition,
( sP29_prd
<=> ( ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP29_prd])],[]) ).
fof(f286,plain,
( sP28_prd
<=> ( ? [Y] :
! [X] :
( a(X,Y)
<=> ~ a(X,X) )
| sP29_prd ) ),
inference(formula_renaming,[status(thm)],[f275,f285]) ).
fof(f287,plain,
( ( ( ! [Y] :
? [X] :
( ( ~ a(X,X)
| a(X,Y) )
& ( a(X,X)
| ~ a(X,Y) ) )
& ~ sP29_prd )
| sP28_prd )
& ( ? [Y] :
! [X] :
( ( a(X,X)
| a(X,Y) )
& ( ~ a(X,X)
| ~ a(X,Y) ) )
| sP29_prd
| ~ sP28_prd ) ),
inference(NNF_transformation,[status(thm)],[f286]) ).
fof(f288,plain,
( ( ( ! [Y] :
? [X] :
( ( ~ a(X,X)
| a(X,Y) )
& ( a(X,X)
| ~ a(X,Y) ) )
& ~ sP29_prd )
| sP28_prd )
& ( ? [Y] :
( ! [X] :
( a(X,X)
| a(X,Y) )
& ! [X] :
( ~ a(X,X)
| ~ a(X,Y) ) )
| sP29_prd
| ~ sP28_prd ) ),
inference(miniscoping,[status(thm)],[f287]) ).
fof(f289,plain,
( ( ( ! [Y] :
( ( ~ a(sK76_skl(Y),sK76_skl(Y))
| a(sK76_skl(Y),Y) )
& ( a(sK76_skl(Y),sK76_skl(Y))
| ~ a(sK76_skl(Y),Y) ) )
& ~ sP29_prd )
| sP28_prd )
& ( ( ! [X] :
( a(X,X)
| a(X,sK75_skl) )
& ! [X] :
( ~ a(X,X)
| ~ a(X,sK75_skl) ) )
| sP29_prd
| ~ sP28_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK75_skl,sK76_skl]),skolemize(Y,sK75_skl),skolemize(X,sK76_skl(Y))],[f288]) ).
fof(f290,plain,
! [X0] :
( ~ a(X0,X0)
| ~ a(X0,sK75_skl)
| sP29_prd
| ~ sP28_prd ),
inference(cnf_transformation,[status(thm)],[f289]) ).
fof(f291,plain,
! [X0] :
( a(X0,X0)
| a(X0,sK75_skl)
| sP29_prd
| ~ sP28_prd ),
inference(cnf_transformation,[status(thm)],[f289]) ).
fof(f295,definition,
( sP30_prd
<=> ( ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP30_prd])],[]) ).
fof(f296,plain,
( sP29_prd
<=> ( ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| sP30_prd ) ),
inference(formula_renaming,[status(thm)],[f285,f295]) ).
fof(f297,plain,
( ( ( ( ? [X] : b(X)
| ? [X] : ~ a1(X)
| ! [X] :
( ~ b(X)
& a1(X) ) )
& ~ sP30_prd )
| sP29_prd )
& ( ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ? [X] :
( b(X)
| ~ a1(X) ) )
| sP30_prd
| ~ sP29_prd ) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
( ( ( ( ? [X] : b(X)
| ? [X] : ~ a1(X)
| ( ! [X] : ~ b(X)
& ! [X] : a1(X) ) )
& ~ sP30_prd )
| sP29_prd )
& ( ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ( ? [X] : b(X)
| ? [X] : ~ a1(X) ) )
| sP30_prd
| ~ sP29_prd ) ),
inference(miniscoping,[status(thm)],[f297]) ).
fof(f299,plain,
( ( ( ( b(sK80_skl)
| ~ a1(sK79_skl)
| ( ! [X] : ~ b(X)
& ! [X] : a1(X) ) )
& ~ sP30_prd )
| sP29_prd )
& ( ( ! [X] : ~ b(X)
& ! [X] : a1(X)
& ( b(sK78_skl)
| ~ a1(sK77_skl) ) )
| sP30_prd
| ~ sP29_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77_skl,sK78_skl,sK79_skl,sK80_skl]),skolemize(X,sK77_skl),skolemize(X,sK78_skl),skolemize(X,sK79_skl),skolemize(X,sK80_skl)],[f298]) ).
fof(f300,plain,
( b(sK78_skl)
| ~ a1(sK77_skl)
| sP30_prd
| ~ sP29_prd ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f301,plain,
! [X0] :
( a1(X0)
| sP30_prd
| ~ sP29_prd ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f302,plain,
! [X0] :
( ~ b(X0)
| sP30_prd
| ~ sP29_prd ),
inference(cnf_transformation,[status(thm)],[f299]) ).
fof(f306,definition,
( sP31_prd
<=> ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP31_prd])],[]) ).
fof(f307,plain,
( sP30_prd
<=> ( ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| sP31_prd ) ),
inference(formula_renaming,[status(thm)],[f295,f306]) ).
fof(f308,plain,
( ( ( ( ? [X] : b(X)
| ! [X] : ~ a1(X)
| ? [X] :
( ~ b(X)
& a1(X) ) )
& ~ sP31_prd )
| sP30_prd )
& ( ( ! [X] : ~ b(X)
& ? [X] : a1(X)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| sP31_prd
| ~ sP30_prd ) ),
inference(NNF_transformation,[status(thm)],[f307]) ).
fof(f309,plain,
( ( ( ( b(sK83_skl)
| ! [X] : ~ a1(X)
| ( ~ b(sK82_skl)
& a1(sK82_skl) ) )
& ~ sP31_prd )
| sP30_prd )
& ( ( ! [X] : ~ b(X)
& a1(sK81_skl)
& ! [X] :
( b(X)
| ~ a1(X) ) )
| sP31_prd
| ~ sP30_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK81_skl,sK82_skl,sK83_skl]),skolemize(X,sK81_skl),skolemize(X,sK82_skl),skolemize(X,sK83_skl)],[f308]) ).
fof(f310,plain,
! [X0] :
( b(X0)
| ~ a1(X0)
| sP31_prd
| ~ sP30_prd ),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f311,plain,
( a1(sK81_skl)
| sP31_prd
| ~ sP30_prd ),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f312,plain,
! [X0] :
( ~ b(X0)
| sP31_prd
| ~ sP30_prd ),
inference(cnf_transformation,[status(thm)],[f309]) ).
fof(f316,definition,
( sP32_prd
<=> ( ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP32_prd])],[]) ).
fof(f317,plain,
( sP31_prd
<=> ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| sP32_prd ) ),
inference(formula_renaming,[status(thm)],[f306,f316]) ).
fof(f318,plain,
( ( ( ! [A,B] :
( ? [X] :
( ( p1(B)
| ~ q1(X) )
& ( p1(A)
| ~ p1(X) ) )
| ? [Z] :
( ~ p1(Z)
& q1(Z) ) )
& ~ sP32_prd )
| sP31_prd )
& ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| sP32_prd
| ~ sP31_prd ) ),
inference(NNF_transformation,[status(thm)],[f317]) ).
fof(f319,plain,
( ( ( ( ! [A,B] :
? [X] :
( ( p1(B)
| ~ q1(X) )
& ( p1(A)
| ~ p1(X) ) )
| ? [Z] :
( ~ p1(Z)
& q1(Z) ) )
& ~ sP32_prd )
| sP31_prd )
& ( ( ? [A,B] :
! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| sP32_prd
| ~ sP31_prd ) ),
inference(miniscoping,[status(thm)],[f318]) ).
fof(f320,plain,
( ( ( ( ! [A,B] :
( ( p1(B)
| ~ q1(sK87_skl(B,A)) )
& ( p1(A)
| ~ p1(sK87_skl(B,A)) ) )
| ( ~ p1(sK86_skl)
& q1(sK86_skl) ) )
& ~ sP32_prd )
| sP31_prd )
& ( ( ! [X] :
( ( ~ p1(sK85_skl)
& q1(X) )
| ( ~ p1(sK84_skl)
& p1(X) ) )
& ! [Z] :
( p1(Z)
| ~ q1(Z) ) )
| sP32_prd
| ~ sP31_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK84_skl,sK85_skl,sK86_skl,sK87_skl]),skolemize(A,sK84_skl),skolemize(B,sK85_skl),skolemize(Z,sK86_skl),skolemize(X,sK87_skl(B,A))],[f319]) ).
fof(f321,plain,
! [X0] :
( p1(X0)
| ~ q1(X0)
| sP32_prd
| ~ sP31_prd ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [X0] :
( q1(X0)
| p1(X0)
| sP32_prd
| ~ sP31_prd ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f325,plain,
( ~ p1(sK85_skl)
| ~ p1(sK84_skl)
| sP32_prd
| ~ sP31_prd ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f331,definition,
( sP33_prd
<=> ( ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP33_prd])],[]) ).
fof(f332,plain,
( sP32_prd
<=> ( ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| sP33_prd ) ),
inference(formula_renaming,[status(thm)],[f316,f331]) ).
fof(f333,plain,
( ( ( ( ! [X] : q1(X)
| ? [X] : ~ p1(X)
| ? [X] :
( ~ q1(X)
& p1(X) ) )
& ~ sP33_prd )
| sP32_prd )
& ( ( ? [X] : ~ q1(X)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| sP33_prd
| ~ sP32_prd ) ),
inference(NNF_transformation,[status(thm)],[f332]) ).
fof(f334,plain,
( ( ( ( ! [X] : q1(X)
| ~ p1(sK90_skl)
| ( ~ q1(sK89_skl)
& p1(sK89_skl) ) )
& ~ sP33_prd )
| sP32_prd )
& ( ( ~ q1(sK88_skl)
& ! [X] : p1(X)
& ! [X] :
( q1(X)
| ~ p1(X) ) )
| sP33_prd
| ~ sP32_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK88_skl,sK89_skl,sK90_skl]),skolemize(X,sK88_skl),skolemize(X,sK89_skl),skolemize(X,sK90_skl)],[f333]) ).
fof(f335,plain,
! [X0] :
( q1(X0)
| ~ p1(X0)
| sP33_prd
| ~ sP32_prd ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f336,plain,
! [X0] :
( p1(X0)
| sP33_prd
| ~ sP32_prd ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f337,plain,
( ~ q1(sK88_skl)
| sP33_prd
| ~ sP32_prd ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f341,definition,
( sP34_prd
<=> ( ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP34_prd])],[]) ).
fof(f342,plain,
( sP33_prd
<=> ( ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| sP34_prd ) ),
inference(formula_renaming,[status(thm)],[f331,f341]) ).
fof(f343,plain,
( ( ( ( ? [Y] : p1(Y)
| ? [X] : ~ p1(X) )
& ~ sP34_prd )
| sP33_prd )
& ( ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| sP34_prd
| ~ sP33_prd ) ),
inference(NNF_transformation,[status(thm)],[f342]) ).
fof(f344,plain,
( ( ( ( p1(sK92_skl)
| ~ p1(sK91_skl) )
& ~ sP34_prd )
| sP33_prd )
& ( ( ! [Y] : ~ p1(Y)
& ! [X] : p1(X) )
| sP34_prd
| ~ sP33_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK91_skl,sK92_skl]),skolemize(X,sK91_skl),skolemize(Y,sK92_skl)],[f343]) ).
fof(f345,plain,
! [X0] :
( p1(X0)
| sP34_prd
| ~ sP33_prd ),
inference(cnf_transformation,[status(thm)],[f344]) ).
fof(f346,plain,
! [X0] :
( ~ p1(X0)
| sP34_prd
| ~ sP33_prd ),
inference(cnf_transformation,[status(thm)],[f344]) ).
fof(f349,definition,
( sP35_prd
<=> ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP35_prd])],[]) ).
fof(f350,plain,
( sP34_prd
<=> ( ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| sP35_prd ) ),
inference(formula_renaming,[status(thm)],[f341,f349]) ).
fof(f351,plain,
( ( ( ( ( ( ( ( q0
| ~ q0 )
& ( ~ b0
| b0 ) )
| ~ a0 )
& ? [X] : p1(X) )
| ! [X] : ~ p1(X) )
& ~ sP35_prd )
| sP34_prd )
& ( ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& ? [X] : p1(X) )
| sP35_prd
| ~ sP34_prd ) ),
inference(NNF_transformation,[status(thm)],[f350]) ).
fof(f352,plain,
( ( ( ( ( ( ( ( q0
| ~ q0 )
& ( ~ b0
| b0 ) )
| ~ a0 )
& p1(sK94_skl) )
| ! [X] : ~ p1(X) )
& ~ sP35_prd )
| sP34_prd )
& ( ( ( ( ( ( ~ q0
& q0 )
| ( b0
& ~ b0 ) )
& a0 )
| ! [X] : ~ p1(X) )
& p1(sK93_skl) )
| sP35_prd
| ~ sP34_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK93_skl,sK94_skl]),skolemize(X,sK93_skl),skolemize(X,sK94_skl)],[f351]) ).
fof(f353,plain,
( p1(sK93_skl)
| sP35_prd
| ~ sP34_prd ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f355,plain,
! [X0] :
( q0
| ~ b0
| ~ p1(X0)
| sP35_prd
| ~ sP34_prd ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f356,plain,
! [X0] :
( ~ q0
| ~ b0
| ~ p1(X0)
| sP35_prd
| ~ sP34_prd ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f357,plain,
! [X0] :
( q0
| b0
| ~ p1(X0)
| sP35_prd
| ~ sP34_prd ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f358,plain,
! [X0] :
( ~ q0
| b0
| ~ p1(X0)
| sP35_prd
| ~ sP34_prd ),
inference(cnf_transformation,[status(thm)],[f352]) ).
fof(f363,definition,
( sP36_prd
<=> ( ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP36_prd])],[]) ).
fof(f364,plain,
( sP35_prd
<=> ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| sP36_prd ) ),
inference(formula_renaming,[status(thm)],[f349,f363]) ).
fof(f365,plain,
( ( ( ! [A,B] :
( ? [X] :
( ( p1(B)
| ~ q1(X) )
& ( p1(A)
| ~ p1(X) ) )
| ? [Y] :
( ~ p1(Y)
& q1(Y) ) )
& ~ sP36_prd )
| sP35_prd )
& ( ? [A,B] :
( ! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| sP36_prd
| ~ sP35_prd ) ),
inference(NNF_transformation,[status(thm)],[f364]) ).
fof(f366,plain,
( ( ( ( ! [A,B] :
? [X] :
( ( p1(B)
| ~ q1(X) )
& ( p1(A)
| ~ p1(X) ) )
| ? [Y] :
( ~ p1(Y)
& q1(Y) ) )
& ~ sP36_prd )
| sP35_prd )
& ( ( ? [A,B] :
! [X] :
( ( ~ p1(B)
& q1(X) )
| ( ~ p1(A)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| sP36_prd
| ~ sP35_prd ) ),
inference(miniscoping,[status(thm)],[f365]) ).
fof(f367,plain,
( ( ( ( ! [A,B] :
( ( p1(B)
| ~ q1(sK98_skl(B,A)) )
& ( p1(A)
| ~ p1(sK98_skl(B,A)) ) )
| ( ~ p1(sK97_skl)
& q1(sK97_skl) ) )
& ~ sP36_prd )
| sP35_prd )
& ( ( ! [X] :
( ( ~ p1(sK96_skl)
& q1(X) )
| ( ~ p1(sK95_skl)
& p1(X) ) )
& ! [Y] :
( p1(Y)
| ~ q1(Y) ) )
| sP36_prd
| ~ sP35_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95_skl,sK96_skl,sK97_skl,sK98_skl]),skolemize(A,sK95_skl),skolemize(B,sK96_skl),skolemize(Y,sK97_skl),skolemize(X,sK98_skl(B,A))],[f366]) ).
fof(f368,plain,
! [X0] :
( p1(X0)
| ~ q1(X0)
| sP36_prd
| ~ sP35_prd ),
inference(cnf_transformation,[status(thm)],[f367]) ).
fof(f369,plain,
! [X0] :
( q1(X0)
| p1(X0)
| sP36_prd
| ~ sP35_prd ),
inference(cnf_transformation,[status(thm)],[f367]) ).
fof(f372,plain,
( ~ p1(sK96_skl)
| ~ p1(sK95_skl)
| sP36_prd
| ~ sP35_prd ),
inference(cnf_transformation,[status(thm)],[f367]) ).
fof(f378,definition,
( sP37_prd
<=> ( ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP37_prd])],[]) ).
fof(f379,plain,
( sP36_prd
<=> ( ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| sP37_prd ) ),
inference(formula_renaming,[status(thm)],[f363,f378]) ).
fof(f380,definition,
! [X] :
( sP38_prd(X)
<=> ( p1(X)
| ~ s1(X) ) ),
introduced(definition,[new_symbols(definition,[sP38_prd])],[]) ).
fof(f381,plain,
( sP36_prd
<=> ( ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] : sP38_prd(X)
& r(B,C)
& s1(B)
& s1(A) )
| sP37_prd ) ),
inference(formula_renaming,[status(thm)],[f379,f380]) ).
fof(f382,plain,
( ( ( ! [A,B,C] :
( ? [X,Y] :
( q(X,Y)
& p1(X) )
| ? [X,Y] :
( ~ q(X,Y)
& r(X,Y) )
| ? [X] : ~ sP38_prd(X)
| ~ r(B,C)
| ~ s1(B)
| ~ s1(A) )
& ~ sP37_prd )
| sP36_prd )
& ( ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] : sP38_prd(X)
& r(B,C)
& s1(B)
& s1(A) )
| sP37_prd
| ~ sP36_prd ) ),
inference(NNF_transformation,[status(thm)],[f381]) ).
fof(f383,plain,
( ( ( ( ? [X] :
( ? [Y] : q(X,Y)
& p1(X) )
| ? [X,Y] :
( ~ q(X,Y)
& r(X,Y) )
| ? [X] : ~ sP38_prd(X)
| ! [B] :
( ! [C] : ~ r(B,C)
| ~ s1(B)
| ! [A] : ~ s1(A) ) )
& ~ sP37_prd )
| sP36_prd )
& ( ( ! [X] :
( ! [Y] : ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] : sP38_prd(X)
& ? [B] :
( ? [C] : r(B,C)
& s1(B)
& ? [A] : s1(A) ) )
| sP37_prd
| ~ sP36_prd ) ),
inference(miniscoping,[status(thm)],[f382]) ).
fof(f384,plain,
( ( ( ( ( q(sK105_skl,sK106_skl)
& p1(sK105_skl) )
| ( ~ q(sK103_skl,sK104_skl)
& r(sK103_skl,sK104_skl) )
| ~ sP38_prd(sK102_skl)
| ! [B] :
( ! [C] : ~ r(B,C)
| ~ s1(B)
| ! [A] : ~ s1(A) ) )
& ~ sP37_prd )
| sP36_prd )
& ( ( ! [X] :
( ! [Y] : ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] : sP38_prd(X)
& r(sK99_skl,sK101_skl)
& s1(sK99_skl)
& s1(sK100_skl) )
| sP37_prd
| ~ sP36_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK99_skl,sK100_skl,sK101_skl,sK102_skl,sK103_skl,sK104_skl,sK105_skl,sK106_skl]),skolemize(B,sK99_skl),skolemize(A,sK100_skl),skolemize(C,sK101_skl),skolemize(X,sK102_skl),skolemize(X,sK103_skl),skolemize(Y,sK104_skl),skolemize(X,sK105_skl),skolemize(Y,sK106_skl)],[f383]) ).
fof(f386,plain,
( s1(sK99_skl)
| sP37_prd
| ~ sP36_prd ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f387,plain,
( r(sK99_skl,sK101_skl)
| sP37_prd
| ~ sP36_prd ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [X0] :
( sP38_prd(X0)
| sP37_prd
| ~ sP36_prd ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f389,plain,
! [X0,X1] :
( q(X0,X1)
| ~ r(X0,X1)
| sP37_prd
| ~ sP36_prd ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f390,plain,
! [X0,X1] :
( ~ q(X0,X1)
| ~ p1(X0)
| sP37_prd
| ~ sP36_prd ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f396,definition,
( sP39_prd
<=> ( ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP39_prd])],[]) ).
fof(f397,plain,
( sP37_prd
<=> ( ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| sP39_prd ) ),
inference(formula_renaming,[status(thm)],[f378,f396]) ).
fof(f398,plain,
( ( ( ( ? [Z] : a(Z,Z)
| ? [X] :
! [Y] :
( ~ a(Y,Y)
| ~ a(X,Y) ) )
& ~ sP39_prd )
| sP37_prd )
& ( ( ! [Z] : ~ a(Z,Z)
& ! [X] :
? [Y] :
( a(Y,Y)
& a(X,Y) ) )
| sP39_prd
| ~ sP37_prd ) ),
inference(NNF_transformation,[status(thm)],[f397]) ).
fof(f399,plain,
( ( ( ( a(sK109_skl,sK109_skl)
| ! [Y] :
( ~ a(Y,Y)
| ~ a(sK108_skl,Y) ) )
& ~ sP39_prd )
| sP37_prd )
& ( ( ! [Z] : ~ a(Z,Z)
& ! [X] :
( a(sK107_skl(X),sK107_skl(X))
& a(X,sK107_skl(X)) ) )
| sP39_prd
| ~ sP37_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK107_skl,sK108_skl,sK109_skl]),skolemize(Y,sK107_skl(X)),skolemize(X,sK108_skl),skolemize(Z,sK109_skl)],[f398]) ).
fof(f401,plain,
! [X0] :
( a(sK107_skl(X0),sK107_skl(X0))
| sP39_prd
| ~ sP37_prd ),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f402,plain,
! [X0] :
( ~ a(X0,X0)
| sP39_prd
| ~ sP37_prd ),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f405,plain,
! [X] :
( ( ( ~ p1(X)
& s1(X) )
| sP38_prd(X) )
& ( p1(X)
| ~ s1(X)
| ~ sP38_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f380]) ).
fof(f406,plain,
( ! [X] :
( ( ~ p1(X)
& s1(X) )
| sP38_prd(X) )
& ! [X] :
( p1(X)
| ~ s1(X)
| ~ sP38_prd(X) ) ),
inference(miniscoping,[status(thm)],[f405]) ).
fof(f407,plain,
! [X0] :
( p1(X0)
| ~ s1(X0)
| ~ sP38_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f406]) ).
fof(f409,plain,
! [X0] :
( ~ p1(X0)
| sP38_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f406]) ).
fof(f410,definition,
( sP40_prd
<=> ( ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP40_prd])],[]) ).
fof(f411,plain,
( sP39_prd
<=> ( ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| sP40_prd ) ),
inference(formula_renaming,[status(thm)],[f396,f410]) ).
fof(f412,plain,
( ( ( ( ? [Z] :
! [Y] :
( r1(Z)
| p1(Y) )
| ? [X] :
! [Y] :
( ~ q1(Y)
| ~ p1(X) ) )
& ~ sP40_prd )
| sP39_prd )
& ( ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ! [X] :
? [Y] :
( q1(Y)
& p1(X) ) )
| sP40_prd
| ~ sP39_prd ) ),
inference(NNF_transformation,[status(thm)],[f411]) ).
fof(f413,plain,
( ( ( ( ? [Z] : r1(Z)
| ! [Y] : p1(Y)
| ! [Y] : ~ q1(Y)
| ? [X] : ~ p1(X) )
& ~ sP40_prd )
| sP39_prd )
& ( ( ! [Z] : ~ r1(Z)
& ? [Y] : ~ p1(Y)
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| sP40_prd
| ~ sP39_prd ) ),
inference(miniscoping,[status(thm)],[f412]) ).
fof(f414,plain,
( ( ( ( r1(sK113_skl)
| ! [Y] : p1(Y)
| ! [Y] : ~ q1(Y)
| ~ p1(sK112_skl) )
& ~ sP40_prd )
| sP39_prd )
& ( ( ! [Z] : ~ r1(Z)
& ~ p1(sK111_skl)
& q1(sK110_skl)
& ! [X] : p1(X) )
| sP40_prd
| ~ sP39_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK110_skl,sK111_skl,sK112_skl,sK113_skl]),skolemize(Y,sK110_skl),skolemize(Y,sK111_skl),skolemize(X,sK112_skl),skolemize(Z,sK113_skl)],[f413]) ).
fof(f415,plain,
! [X0] :
( p1(X0)
| sP40_prd
| ~ sP39_prd ),
inference(cnf_transformation,[status(thm)],[f414]) ).
fof(f417,plain,
( ~ p1(sK111_skl)
| sP40_prd
| ~ sP39_prd ),
inference(cnf_transformation,[status(thm)],[f414]) ).
fof(f421,definition,
( sP41_prd
<=> ( ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP41_prd])],[]) ).
fof(f422,plain,
( sP40_prd
<=> ( ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| sP41_prd ) ),
inference(formula_renaming,[status(thm)],[f410,f421]) ).
fof(f423,plain,
( ( ( ( ? [Z] :
! [Y] :
( r1(Z)
| p1(Y) )
| ! [Y] : ~ q1(Y)
| ? [X] : ~ p1(X) )
& ~ sP41_prd )
| sP40_prd )
& ( ( ! [Z] :
? [Y] :
( ~ r1(Z)
& ~ p1(Y) )
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| sP41_prd
| ~ sP40_prd ) ),
inference(NNF_transformation,[status(thm)],[f422]) ).
fof(f424,plain,
( ( ( ( ? [Z] : r1(Z)
| ! [Y] : p1(Y)
| ! [Y] : ~ q1(Y)
| ? [X] : ~ p1(X) )
& ~ sP41_prd )
| sP40_prd )
& ( ( ! [Z] : ~ r1(Z)
& ? [Y] : ~ p1(Y)
& ? [Y] : q1(Y)
& ! [X] : p1(X) )
| sP41_prd
| ~ sP40_prd ) ),
inference(miniscoping,[status(thm)],[f423]) ).
fof(f425,plain,
( ( ( ( r1(sK117_skl)
| ! [Y] : p1(Y)
| ! [Y] : ~ q1(Y)
| ~ p1(sK116_skl) )
& ~ sP41_prd )
| sP40_prd )
& ( ( ! [Z] : ~ r1(Z)
& ~ p1(sK115_skl)
& q1(sK114_skl)
& ! [X] : p1(X) )
| sP41_prd
| ~ sP40_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK114_skl,sK115_skl,sK116_skl,sK117_skl]),skolemize(Y,sK114_skl),skolemize(Y,sK115_skl),skolemize(X,sK116_skl),skolemize(Z,sK117_skl)],[f424]) ).
fof(f426,plain,
! [X0] :
( p1(X0)
| sP41_prd
| ~ sP40_prd ),
inference(cnf_transformation,[status(thm)],[f425]) ).
fof(f428,plain,
( ~ p1(sK115_skl)
| sP41_prd
| ~ sP40_prd ),
inference(cnf_transformation,[status(thm)],[f425]) ).
fof(f432,definition,
( sP42_prd
<=> ( ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP42_prd])],[]) ).
fof(f433,plain,
( sP41_prd
<=> ( ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| sP42_prd ) ),
inference(formula_renaming,[status(thm)],[f421,f432]) ).
fof(f434,plain,
( ( ( ( ! [A,B] :
( p1(B)
& p1(A) )
| ? [X] : ~ p1(X) )
& ~ sP42_prd )
| sP41_prd )
& ( ( ? [A,B] :
( ~ p1(B)
| ~ p1(A) )
& ! [X] : p1(X) )
| sP42_prd
| ~ sP41_prd ) ),
inference(NNF_transformation,[status(thm)],[f433]) ).
fof(f435,plain,
( ( ( ( ( ! [B] : p1(B)
& ! [A] : p1(A) )
| ? [X] : ~ p1(X) )
& ~ sP42_prd )
| sP41_prd )
& ( ( ( ? [B] : ~ p1(B)
| ? [A] : ~ p1(A) )
& ! [X] : p1(X) )
| sP42_prd
| ~ sP41_prd ) ),
inference(miniscoping,[status(thm)],[f434]) ).
fof(f436,plain,
( ( ( ( ( ! [B] : p1(B)
& ! [A] : p1(A) )
| ~ p1(sK120_skl) )
& ~ sP42_prd )
| sP41_prd )
& ( ( ( ~ p1(sK119_skl)
| ~ p1(sK118_skl) )
& ! [X] : p1(X) )
| sP42_prd
| ~ sP41_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK118_skl,sK119_skl,sK120_skl]),skolemize(A,sK118_skl),skolemize(B,sK119_skl),skolemize(X,sK120_skl)],[f435]) ).
fof(f437,plain,
! [X0] :
( p1(X0)
| sP42_prd
| ~ sP41_prd ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f438,plain,
( ~ p1(sK119_skl)
| ~ p1(sK118_skl)
| sP42_prd
| ~ sP41_prd ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f442,definition,
( sP43_prd
<=> ( ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP43_prd])],[]) ).
fof(f443,plain,
( sP42_prd
<=> ( ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] :
( p1(X)
| ~ s1(X) )
& r(B,C)
& s1(B)
& s1(A) )
| sP43_prd ) ),
inference(formula_renaming,[status(thm)],[f432,f442]) ).
fof(f444,definition,
! [X] :
( sP44_prd(X)
<=> ( p1(X)
| ~ s1(X) ) ),
introduced(definition,[new_symbols(definition,[sP44_prd])],[]) ).
fof(f445,plain,
( sP42_prd
<=> ( ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] : sP44_prd(X)
& r(B,C)
& s1(B)
& s1(A) )
| sP43_prd ) ),
inference(formula_renaming,[status(thm)],[f443,f444]) ).
fof(f446,plain,
( ( ( ! [A,B,C] :
( ? [X,Y] :
( q(X,Y)
& p1(X) )
| ? [X,Y] :
( ~ q(X,Y)
& r(X,Y) )
| ? [X] : ~ sP44_prd(X)
| ~ r(B,C)
| ~ s1(B)
| ~ s1(A) )
& ~ sP43_prd )
| sP42_prd )
& ( ? [A,B,C] :
( ! [X,Y] :
( ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] : sP44_prd(X)
& r(B,C)
& s1(B)
& s1(A) )
| sP43_prd
| ~ sP42_prd ) ),
inference(NNF_transformation,[status(thm)],[f445]) ).
fof(f447,plain,
( ( ( ( ? [X] :
( ? [Y] : q(X,Y)
& p1(X) )
| ? [X,Y] :
( ~ q(X,Y)
& r(X,Y) )
| ? [X] : ~ sP44_prd(X)
| ! [B] :
( ! [C] : ~ r(B,C)
| ~ s1(B)
| ! [A] : ~ s1(A) ) )
& ~ sP43_prd )
| sP42_prd )
& ( ( ! [X] :
( ! [Y] : ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] : sP44_prd(X)
& ? [B] :
( ? [C] : r(B,C)
& s1(B)
& ? [A] : s1(A) ) )
| sP43_prd
| ~ sP42_prd ) ),
inference(miniscoping,[status(thm)],[f446]) ).
fof(f448,plain,
( ( ( ( ( q(sK127_skl,sK128_skl)
& p1(sK127_skl) )
| ( ~ q(sK125_skl,sK126_skl)
& r(sK125_skl,sK126_skl) )
| ~ sP44_prd(sK124_skl)
| ! [B] :
( ! [C] : ~ r(B,C)
| ~ s1(B)
| ! [A] : ~ s1(A) ) )
& ~ sP43_prd )
| sP42_prd )
& ( ( ! [X] :
( ! [Y] : ~ q(X,Y)
| ~ p1(X) )
& ! [X,Y] :
( q(X,Y)
| ~ r(X,Y) )
& ! [X] : sP44_prd(X)
& r(sK121_skl,sK123_skl)
& s1(sK121_skl)
& s1(sK122_skl) )
| sP43_prd
| ~ sP42_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK121_skl,sK122_skl,sK123_skl,sK124_skl,sK125_skl,sK126_skl,sK127_skl,sK128_skl]),skolemize(B,sK121_skl),skolemize(A,sK122_skl),skolemize(C,sK123_skl),skolemize(X,sK124_skl),skolemize(X,sK125_skl),skolemize(Y,sK126_skl),skolemize(X,sK127_skl),skolemize(Y,sK128_skl)],[f447]) ).
fof(f450,plain,
( s1(sK121_skl)
| sP43_prd
| ~ sP42_prd ),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f451,plain,
( r(sK121_skl,sK123_skl)
| sP43_prd
| ~ sP42_prd ),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f452,plain,
! [X0] :
( sP44_prd(X0)
| sP43_prd
| ~ sP42_prd ),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f453,plain,
! [X0,X1] :
( q(X0,X1)
| ~ r(X0,X1)
| sP43_prd
| ~ sP42_prd ),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f454,plain,
! [X0,X1] :
( ~ q(X0,X1)
| ~ p1(X0)
| sP43_prd
| ~ sP42_prd ),
inference(cnf_transformation,[status(thm)],[f448]) ).
fof(f460,definition,
( sP45_prd
<=> ( ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP45_prd])],[]) ).
fof(f461,plain,
( sP43_prd
<=> ( ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& ( p1(Y)
| ~ s(A,Y) )
& ( c(f(X2))
| g(X2)
| ~ e(X2) )
& ( s(X,f(X))
| g(X)
| ~ e(X) )
& e(A)
& p1(A) )
| sP45_prd ) ),
inference(formula_renaming,[status(thm)],[f442,f460]) ).
fof(f462,definition,
! [X] :
( sP46_prd(X)
<=> ( s(X,f(X))
| g(X)
| ~ e(X) ) ),
introduced(definition,[new_symbols(definition,[sP46_prd])],[]) ).
fof(f463,definition,
! [X2] :
( sP47_prd(X2)
<=> ( c(f(X2))
| g(X2)
| ~ e(X2) ) ),
introduced(definition,[new_symbols(definition,[sP47_prd])],[]) ).
fof(f464,definition,
! [A,Y] :
( sP48_prd(Y,A)
<=> ( p1(Y)
| ~ s(A,Y) ) ),
introduced(definition,[new_symbols(definition,[sP48_prd])],[]) ).
fof(f465,plain,
( sP43_prd
<=> ( ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& sP48_prd(Y,A)
& sP47_prd(X2)
& sP46_prd(X)
& e(A)
& p1(A) )
| sP45_prd ) ),
inference(formula_renaming,[status(thm)],[f461,f464,f463,f462]) ).
fof(f466,plain,
( ( ( ! [A] :
? [X,X2,X3,X4,Y] :
( ( c(X4)
& p1(X4) )
| ( g(X3)
& p1(X3) )
| ~ sP48_prd(Y,A)
| ~ sP47_prd(X2)
| ~ sP46_prd(X)
| ~ e(A)
| ~ p1(A) )
& ~ sP45_prd )
| sP43_prd )
& ( ? [A] :
! [X,X2,X3,X4,Y] :
( ( ~ c(X4)
| ~ p1(X4) )
& ( ~ g(X3)
| ~ p1(X3) )
& sP48_prd(Y,A)
& sP47_prd(X2)
& sP46_prd(X)
& e(A)
& p1(A) )
| sP45_prd
| ~ sP43_prd ) ),
inference(NNF_transformation,[status(thm)],[f465]) ).
fof(f467,plain,
( ( ( ( ? [X4] :
( c(X4)
& p1(X4) )
| ? [X3] :
( g(X3)
& p1(X3) )
| ! [A] :
( ? [Y] : ~ sP48_prd(Y,A)
| ? [X2] : ~ sP47_prd(X2)
| ? [X] : ~ sP46_prd(X)
| ~ e(A)
| ~ p1(A) ) )
& ~ sP45_prd )
| sP43_prd )
& ( ( ! [X4] :
( ~ c(X4)
| ~ p1(X4) )
& ! [X3] :
( ~ g(X3)
| ~ p1(X3) )
& ? [A] :
( ! [Y] : sP48_prd(Y,A)
& ! [X2] : sP47_prd(X2)
& ! [X] : sP46_prd(X)
& e(A)
& p1(A) ) )
| sP45_prd
| ~ sP43_prd ) ),
inference(miniscoping,[status(thm)],[f466]) ).
fof(f468,plain,
( ( ( ( ( c(sK134_skl)
& p1(sK134_skl) )
| ( g(sK133_skl)
& p1(sK133_skl) )
| ! [A] :
( ~ sP48_prd(sK132_skl(A),A)
| ~ sP47_prd(sK131_skl(A))
| ~ sP46_prd(sK130_skl(A))
| ~ e(A)
| ~ p1(A) ) )
& ~ sP45_prd )
| sP43_prd )
& ( ( ! [X4] :
( ~ c(X4)
| ~ p1(X4) )
& ! [X3] :
( ~ g(X3)
| ~ p1(X3) )
& ! [Y] : sP48_prd(Y,sK129_skl)
& ! [X2] : sP47_prd(X2)
& ! [X] : sP46_prd(X)
& e(sK129_skl)
& p1(sK129_skl) )
| sP45_prd
| ~ sP43_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK129_skl,sK130_skl,sK131_skl,sK132_skl,sK133_skl,sK134_skl]),skolemize(A,sK129_skl),skolemize(X,sK130_skl(A)),skolemize(X2,sK131_skl(A)),skolemize(Y,sK132_skl(A)),skolemize(X3,sK133_skl),skolemize(X4,sK134_skl)],[f467]) ).
fof(f469,plain,
( p1(sK129_skl)
| sP45_prd
| ~ sP43_prd ),
inference(cnf_transformation,[status(thm)],[f468]) ).
fof(f470,plain,
( e(sK129_skl)
| sP45_prd
| ~ sP43_prd ),
inference(cnf_transformation,[status(thm)],[f468]) ).
fof(f471,plain,
! [X0] :
( sP46_prd(X0)
| sP45_prd
| ~ sP43_prd ),
inference(cnf_transformation,[status(thm)],[f468]) ).
fof(f472,plain,
! [X0] :
( sP47_prd(X0)
| sP45_prd
| ~ sP43_prd ),
inference(cnf_transformation,[status(thm)],[f468]) ).
fof(f473,plain,
! [X0] :
( sP48_prd(X0,sK129_skl)
| sP45_prd
| ~ sP43_prd ),
inference(cnf_transformation,[status(thm)],[f468]) ).
fof(f474,plain,
! [X0] :
( ~ g(X0)
| ~ p1(X0)
| sP45_prd
| ~ sP43_prd ),
inference(cnf_transformation,[status(thm)],[f468]) ).
fof(f475,plain,
! [X0] :
( ~ c(X0)
| ~ p1(X0)
| sP45_prd
| ~ sP43_prd ),
inference(cnf_transformation,[status(thm)],[f468]) ).
fof(f481,plain,
! [X] :
( ( ( ~ p1(X)
& s1(X) )
| sP44_prd(X) )
& ( p1(X)
| ~ s1(X)
| ~ sP44_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f444]) ).
fof(f482,plain,
( ! [X] :
( ( ~ p1(X)
& s1(X) )
| sP44_prd(X) )
& ! [X] :
( p1(X)
| ~ s1(X)
| ~ sP44_prd(X) ) ),
inference(miniscoping,[status(thm)],[f481]) ).
fof(f483,plain,
! [X0] :
( p1(X0)
| ~ s1(X0)
| ~ sP44_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f482]) ).
fof(f484,plain,
! [X0] :
( s1(X0)
| sP44_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f482]) ).
fof(f485,plain,
! [X0] :
( ~ p1(X0)
| sP44_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f482]) ).
fof(f486,definition,
( sP49_prd
<=> ( ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP49_prd])],[]) ).
fof(f487,plain,
( sP45_prd
<=> ( ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| sP49_prd ) ),
inference(formula_renaming,[status(thm)],[f460,f486]) ).
fof(f488,definition,
( sP50_prd
<=> ( ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) ) ),
introduced(definition,[new_symbols(definition,[sP50_prd])],[]) ).
fof(f489,plain,
( sP45_prd
<=> ( ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& sP50_prd )
| sP49_prd ) ),
inference(formula_renaming,[status(thm)],[f487,f488]) ).
fof(f490,plain,
( ( ( ( ? [X] :
( c(X)
& a1(X) )
| ~ sP50_prd )
& ~ sP49_prd )
| sP45_prd )
& ( ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& sP50_prd )
| sP49_prd
| ~ sP45_prd ) ),
inference(NNF_transformation,[status(thm)],[f489]) ).
fof(f491,plain,
( ( ( ( ( c(sK135_skl)
& a1(sK135_skl) )
| ~ sP50_prd )
& ~ sP49_prd )
| sP45_prd )
& ( ( ! [X] :
( ~ c(X)
| ~ a1(X) )
& sP50_prd )
| sP49_prd
| ~ sP45_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135_skl]),skolemize(X,sK135_skl)],[f490]) ).
fof(f492,plain,
( sP50_prd
| sP49_prd
| ~ sP45_prd ),
inference(cnf_transformation,[status(thm)],[f491]) ).
fof(f493,plain,
! [X0] :
( ~ c(X0)
| ~ a1(X0)
| sP49_prd
| ~ sP45_prd ),
inference(cnf_transformation,[status(thm)],[f491]) ).
fof(f497,plain,
! [X] :
( ( ( ~ s(X,f(X))
& ~ g(X)
& e(X) )
| sP46_prd(X) )
& ( s(X,f(X))
| g(X)
| ~ e(X)
| ~ sP46_prd(X) ) ),
inference(NNF_transformation,[status(thm)],[f462]) ).
fof(f498,plain,
( ! [X] :
( ( ~ s(X,f(X))
& ~ g(X)
& e(X) )
| sP46_prd(X) )
& ! [X] :
( s(X,f(X))
| g(X)
| ~ e(X)
| ~ sP46_prd(X) ) ),
inference(miniscoping,[status(thm)],[f497]) ).
fof(f499,plain,
! [X0] :
( s(X0,f(X0))
| g(X0)
| ~ e(X0)
| ~ sP46_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f498]) ).
fof(f503,plain,
! [X2] :
( ( ( ~ c(f(X2))
& ~ g(X2)
& e(X2) )
| sP47_prd(X2) )
& ( c(f(X2))
| g(X2)
| ~ e(X2)
| ~ sP47_prd(X2) ) ),
inference(NNF_transformation,[status(thm)],[f463]) ).
fof(f504,plain,
( ! [X2] :
( ( ~ c(f(X2))
& ~ g(X2)
& e(X2) )
| sP47_prd(X2) )
& ! [X2] :
( c(f(X2))
| g(X2)
| ~ e(X2)
| ~ sP47_prd(X2) ) ),
inference(miniscoping,[status(thm)],[f503]) ).
fof(f505,plain,
! [X0] :
( c(f(X0))
| g(X0)
| ~ e(X0)
| ~ sP47_prd(X0) ),
inference(cnf_transformation,[status(thm)],[f504]) ).
fof(f509,plain,
! [A,Y] :
( ( ( ~ p1(Y)
& s(A,Y) )
| sP48_prd(Y,A) )
& ( p1(Y)
| ~ s(A,Y)
| ~ sP48_prd(Y,A) ) ),
inference(NNF_transformation,[status(thm)],[f464]) ).
fof(f510,plain,
( ! [A,Y] :
( ( ~ p1(Y)
& s(A,Y) )
| sP48_prd(Y,A) )
& ! [A,Y] :
( p1(Y)
| ~ s(A,Y)
| ~ sP48_prd(Y,A) ) ),
inference(miniscoping,[status(thm)],[f509]) ).
fof(f511,plain,
! [X0,X1] :
( p1(X0)
| ~ s(X1,X0)
| ~ sP48_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f510]) ).
fof(f514,definition,
( sP51_prd
<=> ( ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) )
& ! [Z] : q1(f(Z)) ) ) ),
introduced(definition,[new_symbols(definition,[sP51_prd])],[]) ).
fof(f515,plain,
( sP49_prd
<=> ( ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| sP51_prd ) ),
inference(formula_renaming,[status(thm)],[f486,f514]) ).
fof(f516,plain,
( ( ( ! [B,C] :
( ? [X,Y] :
( q1(X)
& ( ( ( ( r1(C)
& r1(B) )
| ~ r1(Y) )
& p1(X) )
| ~ p1(f(Y)) ) )
| ~ q1(f(B)) )
& ~ sP51_prd )
| sP49_prd )
& ( ? [B,C] :
( ! [X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) )
& q1(f(B)) )
| sP51_prd
| ~ sP49_prd ) ),
inference(NNF_transformation,[status(thm)],[f515]) ).
fof(f517,plain,
( ( ( ! [B] :
( ! [C] :
? [X] :
( q1(X)
& ( ( ( ( r1(C)
& r1(B) )
| ? [Y] : ~ r1(Y) )
& p1(X) )
| ? [Y] : ~ p1(f(Y)) ) )
| ~ q1(f(B)) )
& ~ sP51_prd )
| sP49_prd )
& ( ? [B] :
( ? [C] :
! [X] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& ! [Y] : r1(Y) )
| ~ p1(X) )
& ! [Y] : p1(f(Y)) ) )
& q1(f(B)) )
| sP51_prd
| ~ sP49_prd ) ),
inference(miniscoping,[status(thm)],[f516]) ).
fof(f518,plain,
( ( ( ! [B] :
( ! [C] :
( q1(sK138_skl(C,B))
& ( ( ( ( r1(C)
& r1(B) )
| ~ r1(sK140_skl(C,B)) )
& p1(sK138_skl(C,B)) )
| ~ p1(f(sK139_skl(C,B))) ) )
| ~ q1(f(B)) )
& ~ sP51_prd )
| sP49_prd )
& ( ( ! [X] :
( ~ q1(X)
| ( ( ( ( ~ r1(sK137_skl)
| ~ r1(sK136_skl) )
& ! [Y] : r1(Y) )
| ~ p1(X) )
& ! [Y] : p1(f(Y)) ) )
& q1(f(sK136_skl)) )
| sP51_prd
| ~ sP49_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK136_skl,sK137_skl,sK138_skl,sK139_skl,sK140_skl]),skolemize(B,sK136_skl),skolemize(C,sK137_skl),skolemize(X,sK138_skl(C,B)),skolemize(Y,sK139_skl(C,B)),skolemize(Y,sK140_skl(C,B))],[f517]) ).
fof(f519,plain,
( q1(f(sK136_skl))
| sP51_prd
| ~ sP49_prd ),
inference(cnf_transformation,[status(thm)],[f518]) ).
fof(f520,plain,
! [X0,X1] :
( ~ q1(X1)
| p1(f(X0))
| sP51_prd
| ~ sP49_prd ),
inference(cnf_transformation,[status(thm)],[f518]) ).
fof(f521,plain,
! [X0,X1] :
( ~ q1(X0)
| r1(X1)
| ~ p1(X0)
| sP51_prd
| ~ sP49_prd ),
inference(cnf_transformation,[status(thm)],[f518]) ).
fof(f522,plain,
! [X0] :
( ~ q1(X0)
| ~ r1(sK137_skl)
| ~ r1(sK136_skl)
| ~ p1(X0)
| sP51_prd
| ~ sP49_prd ),
inference(cnf_transformation,[status(thm)],[f518]) ).
fof(f528,plain,
( ( ! [X] :
( b(X)
| ~ a1(X) )
| ? [X] :
( ~ c(X)
& ~ b(X)
& a1(X) )
| sP50_prd )
& ( ( ? [X] :
( ~ b(X)
& a1(X) )
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ~ sP50_prd ) ),
inference(NNF_transformation,[status(thm)],[f488]) ).
fof(f529,plain,
( ( ! [X] :
( b(X)
| ~ a1(X) )
| ( ~ c(sK142_skl)
& ~ b(sK142_skl)
& a1(sK142_skl) )
| sP50_prd )
& ( ( ~ b(sK141_skl)
& a1(sK141_skl)
& ! [X] :
( c(X)
| b(X)
| ~ a1(X) ) )
| ~ sP50_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK141_skl,sK142_skl]),skolemize(X,sK141_skl),skolemize(X,sK142_skl)],[f528]) ).
fof(f530,plain,
! [X0] :
( c(X0)
| b(X0)
| ~ a1(X0)
| ~ sP50_prd ),
inference(cnf_transformation,[status(thm)],[f529]) ).
fof(f531,plain,
( a1(sK141_skl)
| ~ sP50_prd ),
inference(cnf_transformation,[status(thm)],[f529]) ).
fof(f532,plain,
( ~ b(sK141_skl)
| ~ sP50_prd ),
inference(cnf_transformation,[status(thm)],[f529]) ).
fof(f536,definition,
! [C,B,X,Y] :
( sP52_prd(Y,X,B,C)
<=> ( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) ) ) ),
introduced(definition,[new_symbols(definition,[sP52_prd])],[]) ).
fof(f537,definition,
! [B,C,X,Y] :
( sP53_prd(Y,X,C,B)
<=> ( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) ) ) ),
introduced(definition,[new_symbols(definition,[sP53_prd])],[]) ).
fof(f538,plain,
( sP51_prd
<=> ( ? [B,C] :
( ! [X,Y] : sP53_prd(Y,X,C,B)
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] : sP52_prd(Y,X,B,C)
& ! [Z] : q1(f(Z)) ) ) ),
inference(formula_renaming,[status(thm)],[f514,f537,f536]) ).
fof(f539,plain,
( ( ( ! [B,C] :
( ? [X,Y] : ~ sP53_prd(Y,X,C,B)
| ? [Z] : ~ q1(f(Z)) )
& ! [C,B] :
( ? [X,Y] : ~ sP52_prd(Y,X,B,C)
| ? [Z] : ~ q1(f(Z)) ) )
| sP51_prd )
& ( ? [B,C] :
( ! [X,Y] : sP53_prd(Y,X,C,B)
& ! [Z] : q1(f(Z)) )
| ? [C,B] :
( ! [X,Y] : sP52_prd(Y,X,B,C)
& ! [Z] : q1(f(Z)) )
| ~ sP51_prd ) ),
inference(NNF_transformation,[status(thm)],[f538]) ).
fof(f540,plain,
( ( ( ( ! [B,C] :
? [X,Y] : ~ sP53_prd(Y,X,C,B)
| ? [Z] : ~ q1(f(Z)) )
& ( ! [C,B] :
? [X,Y] : ~ sP52_prd(Y,X,B,C)
| ? [Z] : ~ q1(f(Z)) ) )
| sP51_prd )
& ( ( ? [B,C] :
! [X,Y] : sP53_prd(Y,X,C,B)
& ! [Z] : q1(f(Z)) )
| ( ? [C,B] :
! [X,Y] : sP52_prd(Y,X,B,C)
& ! [Z] : q1(f(Z)) )
| ~ sP51_prd ) ),
inference(miniscoping,[status(thm)],[f539]) ).
fof(f541,plain,
( ( ( ( ! [B,C] : ~ sP53_prd(sK152_skl(C,B),sK151_skl(C,B),C,B)
| ~ q1(f(sK150_skl)) )
& ( ! [C,B] : ~ sP52_prd(sK149_skl(B,C),sK148_skl(B,C),B,C)
| ~ q1(f(sK147_skl)) ) )
| sP51_prd )
& ( ( ! [X,Y] : sP53_prd(Y,X,sK146_skl,sK145_skl)
& ! [Z] : q1(f(Z)) )
| ( ! [X,Y] : sP52_prd(Y,X,sK144_skl,sK143_skl)
& ! [Z] : q1(f(Z)) )
| ~ sP51_prd ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK143_skl,sK144_skl,sK145_skl,sK146_skl,sK147_skl,sK148_skl,sK149_skl,sK150_skl,sK151_skl,sK152_skl]),skolemize(C,sK143_skl),skolemize(B,sK144_skl),skolemize(B,sK145_skl),skolemize(C,sK146_skl),skolemize(Z,sK147_skl),skolemize(X,sK148_skl(B,C)),skolemize(Y,sK149_skl(B,C)),skolemize(Z,sK150_skl),skolemize(X,sK151_skl(C,B)),skolemize(Y,sK152_skl(C,B))],[f540]) ).
fof(f542,plain,
! [X0,X1] :
( q1(f(X1))
| q1(f(X0))
| ~ sP51_prd ),
inference(cnf_transformation,[status(thm)],[f541]) ).
fof(f545,plain,
! [X0,X1,X2,X3] :
( sP53_prd(X2,X3,sK146_skl,sK145_skl)
| sP52_prd(X0,X1,sK144_skl,sK143_skl)
| ~ sP51_prd ),
inference(cnf_transformation,[status(thm)],[f541]) ).
fof(f548,plain,
! [C,B,X,Y] :
( ( ( q1(X)
& ( ( r1(C)
& r1(B) )
| ~ r1(Y) )
& ( p1(X)
| ~ p1(f(Y)) ) )
| sP52_prd(Y,X,B,C) )
& ( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) )
| ~ sP52_prd(Y,X,B,C) ) ),
inference(NNF_transformation,[status(thm)],[f536]) ).
fof(f549,plain,
( ! [C,B,X,Y] :
( ( q1(X)
& ( ( r1(C)
& r1(B) )
| ~ r1(Y) )
& ( p1(X)
| ~ p1(f(Y)) ) )
| sP52_prd(Y,X,B,C) )
& ! [C,B,X,Y] :
( ~ q1(X)
| ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ( ~ p1(X)
& p1(f(Y)) )
| ~ sP52_prd(Y,X,B,C) ) ),
inference(miniscoping,[status(thm)],[f548]) ).
fof(f550,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| r1(X0)
| p1(f(X0))
| ~ sP52_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f549]) ).
fof(f551,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| ~ r1(X3)
| ~ r1(X2)
| p1(f(X0))
| ~ sP52_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f549]) ).
fof(f552,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| r1(X0)
| ~ p1(X1)
| ~ sP52_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f549]) ).
fof(f553,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| ~ r1(X3)
| ~ r1(X2)
| ~ p1(X1)
| ~ sP52_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f549]) ).
fof(f558,plain,
! [B,C,X,Y] :
( ( ( q1(X)
& ( ( ( ( r1(C)
& r1(B) )
| ~ r1(Y) )
& p1(X) )
| ~ p1(f(Y)) ) )
| sP53_prd(Y,X,C,B) )
& ( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) )
| ~ sP53_prd(Y,X,C,B) ) ),
inference(NNF_transformation,[status(thm)],[f537]) ).
fof(f559,plain,
( ! [B,C,X,Y] :
( ( q1(X)
& ( ( ( ( r1(C)
& r1(B) )
| ~ r1(Y) )
& p1(X) )
| ~ p1(f(Y)) ) )
| sP53_prd(Y,X,C,B) )
& ! [B,C,X,Y] :
( ~ q1(X)
| ( ( ( ( ~ r1(C)
| ~ r1(B) )
& r1(Y) )
| ~ p1(X) )
& p1(f(Y)) )
| ~ sP53_prd(Y,X,C,B) ) ),
inference(miniscoping,[status(thm)],[f558]) ).
fof(f560,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| p1(f(X0))
| ~ sP53_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f561,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| r1(X0)
| ~ p1(X1)
| ~ sP53_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f562,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| ~ r1(X2)
| ~ r1(X3)
| ~ p1(X1)
| ~ sP53_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f559]) ).
fof(f567,plain,
! [X0] :
( q1(X0)
| sP0_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f8,f10]) ).
fof(f568,plain,
( ~ q1(sK0_skl)
| sP0_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f9,f11]) ).
fof(f569,plain,
! [X0] :
( p(f(X0),X0)
| ~ r1(X0)
| sP1_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f17,f11]) ).
fof(f572,plain,
! [X0,X1] :
( ~ q(X0,X1)
| ~ p(X0,X1)
| sP1_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f19,f575]) ).
fof(f573,plain,
! [X0,X1] :
( q(f(sK2_skl),sK2_skl)
| ~ p(X0,X1)
| sP1_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f18,f575]) ).
fof(f574,plain,
! [X0] :
( p(f(X0),X0)
| r1(sK2_skl)
| sP1_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f16,f575]) ).
fof(f575,plain,
sP0_prd,
inference(forward_subsumption_resolution,[status(thm)],[f568,f567]) ).
fof(f578,plain,
! [X0,X1] :
( p(X0,X1)
| sP2_prd
| ~ sP1_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f33,f34]) ).
fof(f579,plain,
( sP4_prd
| ~ sP2_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f43,f580]) ).
fof(f580,plain,
( ~ b0
| sP4_prd
| ~ sP2_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f42]) ).
fof(f581,plain,
( sP34_prd
| ~ sP33_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f346,f345]) ).
fof(f582,plain,
( sP6_prd
| ~ sP4_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f65,f583]) ).
fof(f583,plain,
( b0
| sP6_prd
| ~ sP4_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f62,f64]) ).
fof(f584,plain,
( sP7_prd
| ~ sP6_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f83]) ).
fof(f585,plain,
( sP9_prd
| ~ sP8_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f100,f101]) ).
fof(f586,plain,
( sP10_prd
| ~ sP9_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f108,f107]) ).
fof(f587,plain,
( sP12_prd
| ~ sP11_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f125]) ).
fof(f588,plain,
( sP16_prd
| ~ sP14_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f156]) ).
fof(f589,plain,
( sP22_prd
| ~ sP20_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f219]) ).
fof(f590,plain,
( sP27_prd
| ~ sP26_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f270,f272]) ).
fof(f591,plain,
( sP40_prd
| ~ sP39_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f417,f415]) ).
fof(f592,plain,
( sP41_prd
| ~ sP40_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f428,f426]) ).
fof(f593,plain,
( sP8_prd
| ~ sP7_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f92]) ).
fof(f594,plain,
( sP2_prd
| ~ sP1_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f35,f578]) ).
fof(f595,plain,
! [X0] :
( sP44_prd(X0)
| p1(X0)
| ~ sP38_prd(X0) ),
inference(resolution,[status(thm)],[f407,f484]) ).
fof(f597,plain,
! [X0] :
( sP44_prd(X0)
| ~ sP38_prd(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f595,f485]) ).
fof(f602,plain,
! [X0] :
( p1(X0)
| sP17_prd
| ~ sP16_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f173,f172]) ).
fof(f603,plain,
( sP28_prd
| ~ sP27_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f279,f604]) ).
fof(f604,plain,
! [X0] :
( ~ a1(X0)
| sP28_prd
| ~ sP27_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f281,f280]) ).
fof(f605,plain,
( sP31_prd
| ~ sP30_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f311,f606]) ).
fof(f606,plain,
! [X0] :
( ~ a1(X0)
| sP31_prd
| ~ sP30_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f310,f312]) ).
fof(f607,plain,
! [X0] :
( p1(X0)
| sP32_prd
| ~ sP31_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f322,f321]) ).
fof(f608,plain,
( sP33_prd
| ~ sP32_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f337,f609]) ).
fof(f609,plain,
! [X0] :
( q1(X0)
| sP33_prd
| ~ sP32_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f335,f336]) ).
fof(f610,plain,
! [X0] :
( p1(X0)
| sP36_prd
| ~ sP35_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f369,f368]) ).
fof(f612,plain,
( ~ p1(sK36_skl)
| sP17_prd
| ~ sP16_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f176,f602]) ).
fof(f614,plain,
! [X0] :
( ~ b0
| ~ p1(X0)
| sP35_prd
| ~ sP34_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f356,f355]) ).
fof(f615,plain,
! [X0] :
( q0
| ~ p1(X0)
| sP35_prd
| ~ sP34_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f357,f614]) ).
fof(f616,plain,
! [X0] :
( ~ p1(X0)
| sP35_prd
| ~ sP34_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f615,f617]) ).
fof(f617,plain,
! [X0] :
( ~ q0
| ~ p1(X0)
| sP35_prd
| ~ sP34_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f358,f614]) ).
fof(f618,plain,
( sP35_prd
| ~ sP34_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f353,f616]) ).
fof(f621,plain,
( ~ p1(sK56_skl)
| sP24_prd
| ~ sP23_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f242,f241]) ).
fof(f622,plain,
( ~ p1(sK59_skl)
| sP25_prd
| ~ sP24_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f252,f251]) ).
fof(f623,plain,
( b(sK78_skl)
| sP30_prd
| ~ sP29_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f300,f301]) ).
fof(f624,plain,
( ~ p1(sK85_skl)
| sP32_prd
| ~ sP31_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f325,f607]) ).
fof(f625,plain,
( ~ p1(sK96_skl)
| sP36_prd
| ~ sP35_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f372,f610]) ).
fof(f626,plain,
( sP39_prd
| ~ sP37_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f402]) ).
fof(f627,plain,
( ~ p1(sK119_skl)
| sP42_prd
| ~ sP41_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f438,f437]) ).
fof(f640,plain,
( r1(sK2_skl)
| sP1_prd
| q(f(sK2_skl),sK2_skl)
| sP1_prd ),
inference(resolution,[status(thm)],[f573,f574]) ).
fof(f641,plain,
( r1(sK2_skl)
| q(f(sK2_skl),sK2_skl)
| sP1_prd ),
inference(duplicate_literals_removal,[status(thm)],[f640]) ).
fof(f644,plain,
( ~ p(f(sK2_skl),sK2_skl)
| sP1_prd
| r1(sK2_skl)
| sP1_prd ),
inference(resolution,[status(thm)],[f641,f572]) ).
fof(f645,plain,
( ~ p(f(sK2_skl),sK2_skl)
| r1(sK2_skl)
| sP1_prd ),
inference(duplicate_literals_removal,[status(thm)],[f644]) ).
fof(f646,plain,
( r1(sK2_skl)
| sP1_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f645,f574]) ).
fof(f651,plain,
( p(f(sK2_skl),sK2_skl)
| sP1_prd
| sP1_prd ),
inference(resolution,[status(thm)],[f646,f569]) ).
fof(f652,plain,
( p(f(sK2_skl),sK2_skl)
| sP1_prd ),
inference(duplicate_literals_removal,[status(thm)],[f651]) ).
fof(f653,plain,
( q(f(sK2_skl),sK2_skl)
| sP1_prd
| sP1_prd ),
inference(resolution,[status(thm)],[f652,f573]) ).
fof(f656,plain,
( q(f(sK2_skl),sK2_skl)
| sP1_prd ),
inference(duplicate_literals_removal,[status(thm)],[f653]) ).
fof(f659,plain,
( ~ p(f(sK2_skl),sK2_skl)
| sP1_prd
| sP1_prd ),
inference(resolution,[status(thm)],[f656,f572]) ).
fof(f660,plain,
( ~ p(f(sK2_skl),sK2_skl)
| sP1_prd ),
inference(duplicate_literals_removal,[status(thm)],[f659]) ).
fof(f661,plain,
sP1_prd,
inference(forward_subsumption_resolution,[status(thm)],[f660,f652]) ).
fof(f662,plain,
sP2_prd,
inference(backward_subsumption_resolution,[status(thm)],[f594,f661]) ).
fof(f663,plain,
sP4_prd,
inference(backward_subsumption_resolution,[status(thm)],[f579,f662]) ).
fof(f664,plain,
sP6_prd,
inference(backward_subsumption_resolution,[status(thm)],[f582,f663]) ).
fof(f665,plain,
sP7_prd,
inference(backward_subsumption_resolution,[status(thm)],[f584,f664]) ).
fof(f666,plain,
sP8_prd,
inference(backward_subsumption_resolution,[status(thm)],[f593,f665]) ).
fof(f667,plain,
sP9_prd,
inference(backward_subsumption_resolution,[status(thm)],[f585,f666]) ).
fof(f668,plain,
sP10_prd,
inference(backward_subsumption_resolution,[status(thm)],[f586,f667]) ).
fof(f669,plain,
! [X0] :
( ~ p(X0,sK21_skl)
| sP11_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f116,f668]) ).
fof(f670,plain,
! [X0] :
( p(sK20_skl,X0)
| sP11_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f115,f668]) ).
fof(f671,plain,
( sP11_prd
| sP11_prd ),
inference(resolution,[status(thm)],[f670,f669]) ).
fof(f675,plain,
sP11_prd,
inference(duplicate_literals_removal,[status(thm)],[f671]) ).
fof(f676,plain,
sP12_prd,
inference(backward_subsumption_resolution,[status(thm)],[f587,f675]) ).
fof(f677,plain,
! [X0,X1] :
( r1(X1)
| ~ p1(X0)
| sP13_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f133,f676]) ).
fof(f678,plain,
( ~ r1(sK27_skl)
| sP13_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f135,f676]) ).
fof(f679,plain,
( p1(sK26_skl)
| sP13_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f134,f676]) ).
fof(f690,plain,
! [X0] :
( sP13_prd
| r1(X0)
| sP13_prd ),
inference(resolution,[status(thm)],[f677,f679]) ).
fof(f691,plain,
! [X0] :
( r1(X0)
| sP13_prd ),
inference(duplicate_literals_removal,[status(thm)],[f690]) ).
fof(f692,plain,
sP13_prd,
inference(backward_subsumption_resolution,[status(thm)],[f678,f691]) ).
fof(f697,plain,
! [X0] :
( p1(X0)
| ~ r1(X0)
| sP14_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f146,f692]) ).
fof(f698,plain,
( ~ q1(sK30_skl)
| sP14_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f147,f692]) ).
fof(f699,plain,
( sP15_prd(sK30_skl)
| sP14_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f145,f692]) ).
fof(f700,plain,
! [X0] :
( q1(X0)
| ~ p1(X0)
| sP14_prd ),
inference(resolution,[status(thm)],[f699,f163]) ).
fof(f701,plain,
( r1(sK30_skl)
| sP14_prd ),
inference(resolution,[status(thm)],[f699,f164]) ).
fof(f705,plain,
( sP14_prd
| p1(sK30_skl)
| sP14_prd ),
inference(resolution,[status(thm)],[f697,f701]) ).
fof(f706,plain,
( p1(sK30_skl)
| sP14_prd ),
inference(duplicate_literals_removal,[status(thm)],[f705]) ).
fof(f717,plain,
( sP14_prd
| q1(sK30_skl)
| sP14_prd ),
inference(resolution,[status(thm)],[f700,f706]) ).
fof(f718,plain,
( q1(sK30_skl)
| sP14_prd ),
inference(duplicate_literals_removal,[status(thm)],[f717]) ).
fof(f719,plain,
sP14_prd,
inference(forward_subsumption_resolution,[status(thm)],[f718,f698]) ).
fof(f720,plain,
sP16_prd,
inference(backward_subsumption_resolution,[status(thm)],[f588,f719]) ).
fof(f721,plain,
( ~ p1(sK36_skl)
| sP17_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f612,f720]) ).
fof(f723,plain,
! [X0] :
( p1(X0)
| sP17_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f602,f720]) ).
fof(f767,plain,
! [X0,X1] :
( ~ sP19_prd(sK39_skl(X1,X0),X1,X0)
| eq(X0,X1)
| sP18_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f190,f771]) ).
fof(f768,plain,
! [X0,X1,X2] :
( sP19_prd(X2,X1,X0)
| ~ eq(X0,X1)
| sP18_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f189,f771]) ).
fof(f769,plain,
( ~ eq(sK41_skl,sK40_skl)
| sP18_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f192,f771]) ).
fof(f770,plain,
( eq(sK40_skl,sK41_skl)
| sP18_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f191,f771]) ).
fof(f771,plain,
sP17_prd,
inference(forward_subsumption_resolution,[status(thm)],[f721,f723]) ).
fof(f774,plain,
! [X0] :
( sP18_prd
| sP19_prd(X0,sK41_skl,sK40_skl)
| sP18_prd ),
inference(resolution,[status(thm)],[f768,f770]) ).
fof(f775,plain,
! [X0] :
( sP19_prd(X0,sK41_skl,sK40_skl)
| sP18_prd ),
inference(duplicate_literals_removal,[status(thm)],[f774]) ).
fof(f776,plain,
! [X0] :
( ~ a_member_of(X0,sK41_skl)
| a_member_of(X0,sK40_skl)
| sP18_prd ),
inference(resolution,[status(thm)],[f775,f211]) ).
fof(f777,plain,
! [X0] :
( a_member_of(X0,sK41_skl)
| ~ a_member_of(X0,sK40_skl)
| sP18_prd ),
inference(resolution,[status(thm)],[f775,f210]) ).
fof(f785,plain,
! [X0,X1] :
( a_member_of(sK39_skl(X1,X0),X1)
| a_member_of(sK39_skl(X1,X0),X0)
| eq(X0,X1)
| sP18_prd ),
inference(resolution,[status(thm)],[f767,f213]) ).
fof(f795,plain,
! [X0] :
( ~ q1(X0)
| ~ r1(sK137_skl)
| ~ p1(X0)
| sP51_prd
| ~ sP49_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f521]) ).
fof(f804,plain,
! [X0] :
( a_member_of(sK39_skl(X0,sK41_skl),sK40_skl)
| sP18_prd
| a_member_of(sK39_skl(X0,sK41_skl),X0)
| eq(sK41_skl,X0)
| sP18_prd ),
inference(resolution,[status(thm)],[f785,f776]) ).
fof(f814,plain,
! [X0] :
( a_member_of(sK39_skl(X0,sK41_skl),sK40_skl)
| a_member_of(sK39_skl(X0,sK41_skl),X0)
| eq(sK41_skl,X0)
| sP18_prd ),
inference(duplicate_literals_removal,[status(thm)],[f804]) ).
fof(f867,plain,
( a_member_of(sK39_skl(sK40_skl,sK41_skl),sK41_skl)
| sP18_prd
| eq(sK41_skl,sK40_skl)
| sP18_prd ),
inference(resolution,[status(thm)],[f814,f777]) ).
fof(f875,plain,
( a_member_of(sK39_skl(sK40_skl,sK41_skl),sK41_skl)
| eq(sK41_skl,sK40_skl)
| sP18_prd ),
inference(duplicate_literals_removal,[status(thm)],[f867]) ).
fof(f876,plain,
( a_member_of(sK39_skl(sK40_skl,sK41_skl),sK41_skl)
| sP18_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f875,f769]) ).
fof(f883,plain,
! [X0] :
( ~ a_member_of(sK39_skl(sK40_skl,sK41_skl),X0)
| sP19_prd(sK39_skl(sK40_skl,sK41_skl),X0,sK41_skl)
| sP18_prd ),
inference(resolution,[status(thm)],[f876,f212]) ).
fof(f906,plain,
( eq(sK41_skl,sK40_skl)
| sP18_prd
| sP19_prd(sK39_skl(sK40_skl,sK41_skl),sK40_skl,sK41_skl)
| sP18_prd ),
inference(resolution,[status(thm)],[f883,f814]) ).
fof(f914,plain,
( eq(sK41_skl,sK40_skl)
| sP19_prd(sK39_skl(sK40_skl,sK41_skl),sK40_skl,sK41_skl)
| sP18_prd ),
inference(duplicate_literals_removal,[status(thm)],[f906]) ).
fof(f915,plain,
( eq(sK41_skl,sK40_skl)
| sP18_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f914,f767]) ).
fof(f922,plain,
! [X0,X1] :
( ~ p(X0,sK45_skl(X1))
| sP21_prd(X0,sK45_skl(X1))
| sP20_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f204,f925]) ).
fof(f923,plain,
! [X0,X1] :
( p(X0,X1)
| sP21_prd(X0,sK45_skl(X1))
| sP20_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f203,f925]) ).
fof(f924,plain,
! [X0,X1] :
( p(X1,X0)
| sP21_prd(X0,sK45_skl(X1))
| sP20_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f202,f925]) ).
fof(f925,plain,
sP18_prd,
inference(forward_subsumption_resolution,[status(thm)],[f915,f769]) ).
fof(f926,plain,
! [X0,X1,X2] :
( ~ p(X2,X0)
| p(X0,X1)
| sP20_prd ),
inference(resolution,[status(thm)],[f923,f226]) ).
fof(f929,plain,
! [X0,X1] :
( p(X1,sK45_skl(X0))
| p(X0,X1)
| sP20_prd ),
inference(resolution,[status(thm)],[f924,f225]) ).
fof(f930,plain,
! [X0,X1] :
( p(X0,sK45_skl(X1))
| sP20_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f929,f926]) ).
fof(f931,plain,
! [X0,X1] :
( sP21_prd(X0,sK45_skl(X1))
| sP20_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f922,f930]) ).
fof(f936,plain,
! [X0,X1] :
( ~ p(X0,X1)
| sP20_prd ),
inference(resolution,[status(thm)],[f931,f226]) ).
fof(f938,plain,
sP20_prd,
inference(backward_subsumption_resolution,[status(thm)],[f930,f936]) ).
fof(f939,plain,
sP22_prd,
inference(backward_subsumption_resolution,[status(thm)],[f589,f938]) ).
fof(f940,plain,
! [X0,X1] :
( ~ p1(X1)
| ~ p1(X0)
| sP23_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f233,f939]) ).
fof(f941,plain,
( p1(sK52_skl)
| p1(sK51_skl)
| sP23_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f232,f939]) ).
fof(f943,plain,
! [X0] :
( ~ p1(X0)
| sP23_prd
| p1(sK51_skl)
| sP23_prd ),
inference(resolution,[status(thm)],[f941,f940]) ).
fof(f948,plain,
! [X0] :
( ~ p1(X0)
| p1(sK51_skl)
| sP23_prd ),
inference(duplicate_literals_removal,[status(thm)],[f943]) ).
fof(f949,plain,
! [X0] :
( ~ p1(X0)
| sP23_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f948,f940]) ).
fof(f951,plain,
( ~ p1(sK56_skl)
| sP24_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f621,f949]) ).
fof(f952,plain,
( p1(sK52_skl)
| sP23_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f941,f949]) ).
fof(f953,plain,
sP23_prd,
inference(forward_subsumption_resolution,[status(thm)],[f952,f949]) ).
fof(f954,plain,
! [X0] :
( p1(X0)
| sP24_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f241,f953]) ).
fof(f955,plain,
! [X0] :
( p1(X0)
| sP25_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f251,f954]) ).
fof(f978,plain,
( sP25_prd
| ~ sP24_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f622,f955]) ).
fof(f1000,plain,
sP24_prd,
inference(forward_subsumption_resolution,[status(thm)],[f951,f954]) ).
fof(f1001,plain,
! [X0,X1,X2,X3] :
( ~ a(X2,X3)
| ~ a(X0,X1)
| sP26_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f261,f1003]) ).
fof(f1002,plain,
( a(sK64_skl,sK63_skl)
| a(sK61_skl,sK62_skl)
| sP26_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f260,f1003]) ).
fof(f1003,plain,
sP25_prd,
inference(forward_subsumption_resolution,[status(thm)],[f978,f1000]) ).
fof(f1004,plain,
! [X0,X1] :
( ~ a(X0,X1)
| sP26_prd
| a(sK61_skl,sK62_skl)
| sP26_prd ),
inference(resolution,[status(thm)],[f1002,f1001]) ).
fof(f1005,plain,
! [X0,X1] :
( ~ a(X0,X1)
| a(sK61_skl,sK62_skl)
| sP26_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1004]) ).
fof(f1006,plain,
! [X0,X1] :
( ~ a(X0,X1)
| sP26_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1005,f1001]) ).
fof(f1007,plain,
( a(sK64_skl,sK63_skl)
| sP26_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f1002,f1006]) ).
fof(f1008,plain,
sP26_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1007,f1006]) ).
fof(f1009,plain,
sP27_prd,
inference(backward_subsumption_resolution,[status(thm)],[f590,f1008]) ).
fof(f1010,plain,
sP28_prd,
inference(backward_subsumption_resolution,[status(thm)],[f603,f1009]) ).
fof(f1011,plain,
! [X0] :
( ~ a(X0,X0)
| ~ a(X0,sK75_skl)
| sP29_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f290,f1010]) ).
fof(f1012,plain,
! [X0] :
( a(X0,X0)
| a(X0,sK75_skl)
| sP29_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f291,f1010]) ).
fof(f1014,plain,
( ~ a(sK75_skl,sK75_skl)
| sP29_prd
| sP29_prd ),
inference(resolution,[status(thm)],[f1012,f1011]) ).
fof(f1019,plain,
( ~ a(sK75_skl,sK75_skl)
| sP29_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1014]) ).
fof(f1021,plain,
( sP29_prd
| sP29_prd ),
inference(resolution,[status(thm)],[f1019,f1012]) ).
fof(f1025,plain,
sP29_prd,
inference(duplicate_literals_removal,[status(thm)],[f1021]) ).
fof(f1031,plain,
! [X0] :
( ~ b(X0)
| sP30_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f302,f1025]) ).
fof(f1032,plain,
( b(sK78_skl)
| sP30_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f623,f1025]) ).
fof(f1038,plain,
sP31_prd,
inference(backward_subsumption_resolution,[status(thm)],[f605,f1039]) ).
fof(f1039,plain,
sP30_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1032,f1031]) ).
fof(f1040,plain,
( ~ p1(sK85_skl)
| sP32_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f624,f1038]) ).
fof(f1042,plain,
! [X0] :
( p1(X0)
| sP32_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f607,f1038]) ).
fof(f1075,plain,
sP33_prd,
inference(backward_subsumption_resolution,[status(thm)],[f608,f1076]) ).
fof(f1076,plain,
sP32_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1040,f1042]) ).
fof(f1077,plain,
sP34_prd,
inference(backward_subsumption_resolution,[status(thm)],[f581,f1075]) ).
fof(f1078,plain,
sP35_prd,
inference(backward_subsumption_resolution,[status(thm)],[f618,f1077]) ).
fof(f1079,plain,
( ~ p1(sK96_skl)
| sP36_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f625,f1078]) ).
fof(f1081,plain,
! [X0] :
( p1(X0)
| sP36_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f610,f1078]) ).
fof(f1102,plain,
! [X0] :
( sP38_prd(X0)
| sP36_prd ),
inference(resolution,[status(thm)],[f1081,f409]) ).
fof(f1106,plain,
! [X0] :
( sP38_prd(X0)
| sP37_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f388,f1102]) ).
fof(f1110,plain,
! [X0] :
( sP44_prd(X0)
| sP37_prd ),
inference(resolution,[status(thm)],[f1106,f597]) ).
fof(f1112,plain,
! [X0,X1] :
( q(X0,X1)
| ~ r(X0,X1)
| sP37_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f389,f1117]) ).
fof(f1113,plain,
! [X0,X1] :
( ~ q(X0,X1)
| ~ p1(X0)
| sP37_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f390,f1117]) ).
fof(f1114,plain,
( r(sK99_skl,sK101_skl)
| sP37_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f387,f1117]) ).
fof(f1115,plain,
( s1(sK99_skl)
| sP37_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f386,f1117]) ).
fof(f1117,plain,
sP36_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1079,f1081]) ).
fof(f1122,plain,
( p1(sK99_skl)
| ~ sP44_prd(sK99_skl)
| sP37_prd ),
inference(resolution,[status(thm)],[f1115,f483]) ).
fof(f1128,plain,
( p1(sK99_skl)
| sP37_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1122,f1110]) ).
fof(f1148,plain,
( q(sK99_skl,sK101_skl)
| sP37_prd
| sP37_prd ),
inference(resolution,[status(thm)],[f1114,f1112]) ).
fof(f1150,plain,
( q(sK99_skl,sK101_skl)
| sP37_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1148]) ).
fof(f1151,plain,
( ~ p1(sK99_skl)
| sP37_prd
| sP37_prd ),
inference(resolution,[status(thm)],[f1150,f1113]) ).
fof(f1153,plain,
( ~ p1(sK99_skl)
| sP37_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1151]) ).
fof(f1154,plain,
sP37_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1153,f1128]) ).
fof(f1156,plain,
sP39_prd,
inference(backward_subsumption_resolution,[status(thm)],[f626,f1154]) ).
fof(f1157,plain,
sP40_prd,
inference(backward_subsumption_resolution,[status(thm)],[f591,f1156]) ).
fof(f1158,plain,
sP41_prd,
inference(backward_subsumption_resolution,[status(thm)],[f592,f1157]) ).
fof(f1159,plain,
( ~ p1(sK119_skl)
| sP42_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f627,f1158]) ).
fof(f1160,plain,
! [X0] :
( p1(X0)
| sP42_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f437,f1158]) ).
fof(f1169,plain,
! [X0] :
( sP44_prd(X0)
| sP42_prd ),
inference(resolution,[status(thm)],[f1160,f485]) ).
fof(f1171,plain,
! [X0] :
( sP44_prd(X0)
| sP43_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f452,f1169]) ).
fof(f1176,plain,
! [X0,X1] :
( q(X0,X1)
| ~ r(X0,X1)
| sP43_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f453,f1181]) ).
fof(f1177,plain,
! [X0,X1] :
( ~ q(X0,X1)
| ~ p1(X0)
| sP43_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f454,f1181]) ).
fof(f1178,plain,
( r(sK121_skl,sK123_skl)
| sP43_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f451,f1181]) ).
fof(f1179,plain,
( s1(sK121_skl)
| sP43_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f450,f1181]) ).
fof(f1181,plain,
sP42_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1159,f1160]) ).
fof(f1184,plain,
( p1(sK121_skl)
| ~ sP44_prd(sK121_skl)
| sP43_prd ),
inference(resolution,[status(thm)],[f1179,f483]) ).
fof(f1186,plain,
( p1(sK121_skl)
| sP43_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1184,f1171]) ).
fof(f1198,plain,
( q(sK121_skl,sK123_skl)
| sP43_prd
| sP43_prd ),
inference(resolution,[status(thm)],[f1178,f1176]) ).
fof(f1199,plain,
( q(sK121_skl,sK123_skl)
| sP43_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1198]) ).
fof(f1200,plain,
( ~ p1(sK121_skl)
| sP43_prd
| sP43_prd ),
inference(resolution,[status(thm)],[f1199,f1177]) ).
fof(f1201,plain,
( ~ p1(sK121_skl)
| sP43_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1200]) ).
fof(f1202,plain,
sP43_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1201,f1186]) ).
fof(f1203,plain,
! [X0] :
( ~ c(X0)
| ~ p1(X0)
| sP45_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f475,f1202]) ).
fof(f1204,plain,
! [X0] :
( ~ g(X0)
| ~ p1(X0)
| sP45_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f474,f1202]) ).
fof(f1205,plain,
! [X0] :
( sP48_prd(X0,sK129_skl)
| sP45_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f473,f1202]) ).
fof(f1206,plain,
( e(sK129_skl)
| sP45_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f470,f1202]) ).
fof(f1207,plain,
( p1(sK129_skl)
| sP45_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f469,f1202]) ).
fof(f1208,plain,
! [X0] :
( sP47_prd(X0)
| sP45_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f472,f1202]) ).
fof(f1209,plain,
! [X0] :
( sP46_prd(X0)
| sP45_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f471,f1202]) ).
fof(f1212,plain,
( s(sK129_skl,f(sK129_skl))
| g(sK129_skl)
| ~ sP46_prd(sK129_skl)
| sP45_prd ),
inference(resolution,[status(thm)],[f1206,f499]) ).
fof(f1213,plain,
( c(f(sK129_skl))
| g(sK129_skl)
| ~ sP47_prd(sK129_skl)
| sP45_prd ),
inference(resolution,[status(thm)],[f1206,f505]) ).
fof(f1214,plain,
( s(sK129_skl,f(sK129_skl))
| g(sK129_skl)
| sP45_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1212,f1209]) ).
fof(f1215,plain,
( c(f(sK129_skl))
| g(sK129_skl)
| sP45_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1213,f1208]) ).
fof(f1222,plain,
( ~ p1(f(sK129_skl))
| sP45_prd
| g(sK129_skl)
| sP45_prd ),
inference(resolution,[status(thm)],[f1215,f1203]) ).
fof(f1224,plain,
( ~ p1(f(sK129_skl))
| g(sK129_skl)
| sP45_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1222]) ).
fof(f1226,plain,
( p1(f(sK129_skl))
| ~ sP48_prd(f(sK129_skl),sK129_skl)
| g(sK129_skl)
| sP45_prd ),
inference(resolution,[status(thm)],[f1214,f511]) ).
fof(f1227,plain,
( p1(f(sK129_skl))
| g(sK129_skl)
| sP45_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1226,f1205]) ).
fof(f1228,plain,
( g(sK129_skl)
| sP45_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1227,f1224]) ).
fof(f1229,plain,
( ~ p1(sK129_skl)
| sP45_prd
| sP45_prd ),
inference(resolution,[status(thm)],[f1228,f1204]) ).
fof(f1232,plain,
( ~ p1(sK129_skl)
| sP45_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1229]) ).
fof(f1233,plain,
sP45_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1232,f1207]) ).
fof(f1234,plain,
! [X0] :
( ~ c(X0)
| ~ a1(X0)
| sP49_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f493,f1233]) ).
fof(f1235,plain,
( sP50_prd
| sP49_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f492,f1233]) ).
fof(f1236,plain,
( a1(sK141_skl)
| sP49_prd ),
inference(resolution,[status(thm)],[f1235,f531]) ).
fof(f1238,plain,
( c(sK141_skl)
| b(sK141_skl)
| ~ sP50_prd
| sP49_prd ),
inference(resolution,[status(thm)],[f1236,f530]) ).
fof(f1239,plain,
( c(sK141_skl)
| b(sK141_skl)
| sP49_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1238,f1235]) ).
fof(f1240,plain,
( ~ a1(sK141_skl)
| sP49_prd
| b(sK141_skl)
| sP49_prd ),
inference(resolution,[status(thm)],[f1239,f1234]) ).
fof(f1241,plain,
( ~ a1(sK141_skl)
| b(sK141_skl)
| sP49_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1240]) ).
fof(f1242,plain,
( b(sK141_skl)
| sP49_prd ),
inference(forward_subsumption_resolution,[status(thm)],[f1241,f1236]) ).
fof(f1243,plain,
( ~ sP50_prd
| sP49_prd ),
inference(resolution,[status(thm)],[f1242,f532]) ).
fof(f1244,plain,
sP49_prd,
inference(forward_subsumption_resolution,[status(thm)],[f1243,f1235]) ).
fof(f1245,plain,
! [X0] :
( ~ q1(X0)
| ~ r1(sK137_skl)
| ~ p1(X0)
| sP51_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f795,f1244]) ).
fof(f1246,plain,
! [X0,X1] :
( ~ q1(X0)
| r1(X1)
| ~ p1(X0)
| sP51_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f521,f1244]) ).
fof(f1247,plain,
! [X0,X1] :
( ~ q1(X1)
| p1(f(X0))
| sP51_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f520,f1244]) ).
fof(f1248,plain,
( q1(f(sK136_skl))
| sP51_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f519,f1244]) ).
fof(f1250,plain,
! [X0] :
( ~ q1(X0)
| ~ p1(X0)
| sP51_prd ),
inference(backward_subsumption_resolution,[status(thm)],[f1245,f1246]) ).
fof(f1253,plain,
( sP51_prd
| ~ p1(f(sK136_skl))
| sP51_prd ),
inference(resolution,[status(thm)],[f1250,f1248]) ).
fof(f1254,plain,
( ~ p1(f(sK136_skl))
| sP51_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1253]) ).
fof(f1255,plain,
! [X0] :
( sP51_prd
| p1(f(X0))
| sP51_prd ),
inference(resolution,[status(thm)],[f1247,f1248]) ).
fof(f1256,plain,
! [X0] :
( p1(f(X0))
| sP51_prd ),
inference(duplicate_literals_removal,[status(thm)],[f1255]) ).
fof(f1257,plain,
sP51_prd,
inference(backward_subsumption_resolution,[status(thm)],[f1254,f1256]) ).
fof(f1265,plain,
! [X0,X1,X2,X3] :
( sP53_prd(X2,X3,sK146_skl,sK145_skl)
| sP52_prd(X0,X1,sK144_skl,sK143_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f545,f1257]) ).
fof(f1268,plain,
! [X0,X1] :
( q1(f(X1))
| q1(f(X0)) ),
inference(backward_subsumption_resolution,[status(thm)],[f542,f1257]) ).
fof(f1272,plain,
! [X0] : q1(f(X0)),
inference(factoring,[status(thm)],[f1268]) ).
fof(f1275,plain,
! [X0,X1,X2] :
( ~ q1(X2)
| ~ r1(sK143_skl)
| ~ r1(sK144_skl)
| ~ p1(X2)
| sP53_prd(X0,X1,sK146_skl,sK145_skl) ),
inference(resolution,[status(thm)],[f1265,f553]) ).
fof(f1277,plain,
! [X0,X1,X2,X3] :
( ~ q1(X2)
| r1(X3)
| ~ p1(X2)
| sP53_prd(X0,X1,sK146_skl,sK145_skl) ),
inference(resolution,[status(thm)],[f1265,f552]) ).
fof(f1280,plain,
! [X0,X1,X2,X3] :
( ~ q1(X3)
| p1(f(X2))
| sP52_prd(X0,X1,sK144_skl,sK143_skl) ),
inference(resolution,[status(thm)],[f1265,f560]) ).
fof(f1287,plain,
! [X0,X1,X2] :
( p1(f(X2))
| sP52_prd(X0,X1,sK144_skl,sK143_skl) ),
inference(resolution,[status(thm)],[f1280,f1272]) ).
fof(f1290,plain,
! [X0,X1,X2] :
( ~ q1(X2)
| r1(X1)
| p1(f(X1))
| p1(f(X0)) ),
inference(resolution,[status(thm)],[f1287,f550]) ).
fof(f1291,plain,
! [X0,X1,X2] :
( ~ q1(X1)
| r1(X2)
| ~ p1(X1)
| p1(f(X0)) ),
inference(resolution,[status(thm)],[f1287,f552]) ).
fof(f1309,plain,
! [X0,X1,X2] :
( r1(X2)
| ~ p1(f(X1))
| p1(f(X0)) ),
inference(resolution,[status(thm)],[f1291,f1272]) ).
fof(f1321,plain,
! [X0,X1] :
( ~ q1(X1)
| r1(X0)
| p1(f(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1290,f1309]) ).
fof(f1322,plain,
! [X0] :
( r1(X0)
| p1(f(X0)) ),
inference(resolution,[status(thm)],[f1321,f1272]) ).
fof(f1326,plain,
! [X0,X1,X2] :
( r1(X2)
| p1(f(X1))
| r1(X0) ),
inference(resolution,[status(thm)],[f1322,f1309]) ).
fof(f1373,plain,
! [X0,X1] :
( p1(f(X1))
| r1(X0) ),
inference(factoring,[status(thm)],[f1326]) ).
fof(f1374,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| ~ r1(X3)
| p1(f(X0))
| ~ sP52_prd(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f551,f1373]) ).
fof(f1386,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| p1(f(X0))
| ~ sP52_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1374,f1373]) ).
fof(f1414,plain,
! [X0,X1,X2] :
( p1(f(X2))
| ~ q1(X1)
| p1(f(X0)) ),
inference(resolution,[status(thm)],[f1386,f1287]) ).
fof(f1457,plain,
! [X0,X1] :
( p1(f(X1))
| p1(f(X0)) ),
inference(resolution,[status(thm)],[f1414,f1272]) ).
fof(f1473,plain,
! [X0] : p1(f(X0)),
inference(factoring,[status(thm)],[f1457]) ).
fof(f1483,plain,
! [X0,X1,X2] :
( ~ q1(X2)
| ~ r1(sK143_skl)
| ~ p1(X2)
| sP53_prd(X0,X1,sK146_skl,sK145_skl) ),
inference(backward_subsumption_resolution,[status(thm)],[f1275,f1277]) ).
fof(f1484,plain,
! [X0,X1,X2,X3] :
( r1(X3)
| ~ p1(f(X2))
| sP53_prd(X0,X1,sK146_skl,sK145_skl) ),
inference(resolution,[status(thm)],[f1277,f1272]) ).
fof(f1485,plain,
! [X0,X1,X2] :
( ~ q1(X2)
| ~ p1(X2)
| sP53_prd(X0,X1,sK146_skl,sK145_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1483,f1277]) ).
fof(f1486,plain,
! [X0,X1,X2] :
( r1(X2)
| sP53_prd(X0,X1,sK146_skl,sK145_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1484,f1473]) ).
fof(f1488,plain,
! [X0,X1,X2] :
( ~ q1(X1)
| r1(X2)
| ~ p1(X1)
| r1(X0) ),
inference(resolution,[status(thm)],[f1486,f561]) ).
fof(f1494,plain,
! [X0,X1,X2] :
( r1(X2)
| ~ p1(f(X1))
| r1(X0) ),
inference(resolution,[status(thm)],[f1488,f1272]) ).
fof(f1495,plain,
! [X0,X1] :
( r1(X1)
| r1(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1494,f1473]) ).
fof(f1504,plain,
! [X0] : r1(X0),
inference(factoring,[status(thm)],[f1495]) ).
fof(f1506,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| ~ r1(X3)
| ~ p1(X1)
| ~ sP53_prd(X0,X1,X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f562,f1504]) ).
fof(f1512,plain,
! [X0,X1,X2,X3] :
( ~ q1(X1)
| ~ p1(X1)
| ~ sP53_prd(X0,X1,X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1506,f1504]) ).
fof(f1526,plain,
! [X0,X1,X2] :
( ~ p1(f(X2))
| sP53_prd(X0,X1,sK146_skl,sK145_skl) ),
inference(resolution,[status(thm)],[f1485,f1272]) ).
fof(f1527,plain,
! [X0,X1] : sP53_prd(X0,X1,sK146_skl,sK145_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1526,f1473]) ).
fof(f1528,plain,
! [X0] :
( ~ q1(X0)
| ~ p1(X0) ),
inference(resolution,[status(thm)],[f1527,f1512]) ).
fof(f1530,plain,
! [X0] : ~ p1(f(X0)),
inference(resolution,[status(thm)],[f1528,f1272]) ).
fof(f1531,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1530,f1473]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN938+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 11:28:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.39 % Drodi V4.1.1
% 0.72/0.62 % Refutation found
% 0.72/0.62 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.72/0.62 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.72/0.64 % Elapsed time: 0.269598 seconds
% 0.72/0.64 % CPU time: 1.697058 seconds
% 0.72/0.64 % Total memory used: 48.912 MB
% 0.72/0.64 % Net memory used: 47.220 MB
%------------------------------------------------------------------------------