TSTP Solution File: ITP010+2 by iProverMo---2.5-0.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProverMo---2.5-0.1
% Problem : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : iprover_modulo %s %d
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 23:08:59 EDT 2022
% Result : Theorem 0.21s 0.46s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : ERROR: Analysing output (Could not find formula named input)
% Comments :
%------------------------------------------------------------------------------
% Axioms transformation by autotheo
% Orienting (remaining) axiom formulas using strategy Equiv(ClausalAll)
% Orienting axioms whose shape is orientable
fof(conj_thm_2Esat_2Edc__neg,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
<=> ~ p(V1q) )
<=> ( ( p(V0p)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V0p) ) ) ) ) ),
input ).
fof(conj_thm_2Esat_2Edc__neg_0,plain,
! [V0p] :
( ~ mem(V0p,bool)
| ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
<=> ~ p(V1q) )
<=> ( ( p(V0p)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V0p) ) ) ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Esat_2Edc__neg]) ).
fof(conj_thm_2Esat_2Edc__eq,axiom,
! [V0p] :
( mem(V0p,bool)
=> ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) )
<=> ( ( p(V0p)
| p(V1q)
| p(V2r) )
& ( p(V0p)
| ~ p(V2r)
| ~ p(V1q) )
& ( p(V1q)
| ~ p(V2r)
| ~ p(V0p) )
& ( p(V2r)
| ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ),
input ).
fof(conj_thm_2Esat_2Edc__eq_0,plain,
! [V0p] :
( ~ mem(V0p,bool)
| ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) )
<=> ( ( p(V0p)
| p(V1q)
| p(V2r) )
& ( p(V0p)
| ~ p(V2r)
| ~ p(V1q) )
& ( p(V1q)
| ~ p(V2r)
| ~ p(V0p) )
& ( p(V2r)
| ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Esat_2Edc__eq]) ).
fof(conj_thm_2Esat_2EAND__INV2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( ( ~ p(V0A)
=> $false )
=> ( ( p(V0A)
=> $false )
=> $false ) ) ),
input ).
fof(conj_thm_2Esat_2EAND__INV2_0,plain,
! [V0A] :
( ~ mem(V0A,bool)
| ( ( ~ p(V0A)
=> $false )
=> ( ( p(V0A)
=> $false )
=> $false ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Esat_2EAND__INV2]) ).
fof(conj_thm_2Esat_2EOR__DUAL3,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( ~ p(V0A)
| p(V1B) )
=> $false )
<=> ( p(V0A)
=> ( ~ p(V1B)
=> $false ) ) ) ) ),
input ).
fof(conj_thm_2Esat_2EOR__DUAL3_0,plain,
! [V0A] :
( ~ mem(V0A,bool)
| ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( ~ p(V0A)
| p(V1B) )
=> $false )
<=> ( p(V0A)
=> ( ~ p(V1B)
=> $false ) ) ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Esat_2EOR__DUAL3]) ).
fof(conj_thm_2Esat_2EOR__DUAL2,axiom,
! [V0A] :
( mem(V0A,bool)
=> ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
| p(V1B) )
=> $false )
<=> ( ( p(V0A)
=> $false )
=> ( ~ p(V1B)
=> $false ) ) ) ) ),
input ).
fof(conj_thm_2Esat_2EOR__DUAL2_0,plain,
! [V0A] :
( ~ mem(V0A,bool)
| ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
| p(V1B) )
=> $false )
<=> ( ( p(V0A)
=> $false )
=> ( ~ p(V1B)
=> $false ) ) ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Esat_2EOR__DUAL2]) ).
fof(conj_thm_2Esat_2EAND__INV__IMP,axiom,
! [V0A] :
( mem(V0A,bool)
=> ( p(V0A)
=> ( ~ p(V0A)
=> $false ) ) ),
input ).
fof(conj_thm_2Esat_2EAND__INV__IMP_0,plain,
! [V0A] :
( ~ mem(V0A,bool)
| ( p(V0A)
=> ( ~ p(V0A)
=> $false ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Esat_2EAND__INV__IMP]) ).
fof(conj_thm_2Esat_2ENOT__NOT,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ~ ~ p(V0t)
<=> p(V0t) ) ),
input ).
fof(conj_thm_2Esat_2ENOT__NOT_0,plain,
! [V0t] :
( ~ mem(V0t,bool)
| ( ~ ~ p(V0t)
<=> p(V0t) ) ),
inference(orientation,[status(thm)],[conj_thm_2Esat_2ENOT__NOT]) ).
fof(conj_thm_2Ecardinal_2ECARD__LE__TOTAL,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
| p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b,A_27a),V1t),V0s)) ) ) ) ) ),
input ).
fof(conj_thm_2Ecardinal_2ECARD__LE__TOTAL_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
| p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b,A_27a),V1t),V0s)) ) ) ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Ecardinal_2ECARD__LE__TOTAL]) ).
fof(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
<=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
<=> $true )
<=> p(V0t) )
& ( ( $false
<=> p(V0t) )
<=> ~ p(V0t) )
& ( ( p(V0t)
<=> $false )
<=> ~ p(V0t) ) ) ),
input ).
fof(conj_thm_2Ebool_2EEQ__CLAUSES_0,plain,
! [V0t] :
( ~ mem(V0t,bool)
| ( ( ( $true
<=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
<=> $true )
<=> p(V0t) )
& ( ( $false
<=> p(V0t) )
<=> ~ p(V0t) )
& ( ( p(V0t)
<=> $false )
<=> ~ p(V0t) ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2EEQ__CLAUSES]) ).
fof(conj_thm_2Ebool_2EREFL__CLAUSE,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0x] :
( mem(V0x,A_27a)
=> ( V0x = V0x
<=> $true ) ) ),
input ).
fof(conj_thm_2Ebool_2EREFL__CLAUSE_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [V0x] :
( mem(V0x,A_27a)
=> ( V0x = V0x
<=> $true ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2EREFL__CLAUSE]) ).
fof(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
( ! [V0t] :
( mem(V0t,bool)
=> ( ~ ~ p(V0t)
<=> p(V0t) ) )
& ( ~ $true
<=> $false )
& ( ~ $false
<=> $true ) ),
input ).
fof(conj_thm_2Ebool_2ENOT__CLAUSES_0,plain,
! [V0t] :
( ~ mem(V0t,bool)
| ( ~ ~ p(V0t)
<=> p(V0t) ) ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES]) ).
fof(conj_thm_2Ebool_2ENOT__CLAUSES_1,plain,
( $false
| $true ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES]) ).
fof(conj_thm_2Ebool_2ENOT__CLAUSES_2,plain,
( ~ $false
| ~ $true ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES]) ).
fof(conj_thm_2Ebool_2ENOT__CLAUSES_3,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES]) ).
fof(conj_thm_2Ebool_2ENOT__CLAUSES_4,plain,
( ~ $true
| ~ $false ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES]) ).
fof(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( ( ( $true
=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
=> $true )
<=> $true )
& ( ( $false
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> $false )
<=> ~ p(V0t) ) ) ),
input ).
fof(conj_thm_2Ebool_2EIMP__CLAUSES_0,plain,
! [V0t] :
( ~ mem(V0t,bool)
| ( ( ( $true
=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
=> $true )
<=> $true )
& ( ( $false
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> $false )
<=> ~ p(V0t) ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2EIMP__CLAUSES]) ).
fof(conj_thm_2Ebool_2EFORALL__SIMP,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,bool)
=> ( ! [V1x] :
( mem(V1x,A_27a)
=> p(V0t) )
<=> p(V0t) ) ) ),
input ).
fof(conj_thm_2Ebool_2EFORALL__SIMP_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [V0t] :
( mem(V0t,bool)
=> ( ! [V1x] :
( mem(V1x,A_27a)
=> p(V0t) )
<=> p(V0t) ) ) ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2EFORALL__SIMP]) ).
fof(conj_thm_2Ebool_2EFALSITY,axiom,
! [V0t] :
( mem(V0t,bool)
=> ( $false
=> p(V0t) ) ),
input ).
fof(conj_thm_2Ebool_2EFALSITY_0,plain,
! [V0t] :
( ~ mem(V0t,bool)
| ( $false
=> p(V0t) ) ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2EFALSITY]) ).
fof(conj_thm_2Ebool_2ETRUTH,axiom,
$true,
input ).
fof(conj_thm_2Ebool_2ETRUTH_0,plain,
( $true
| $false ),
inference(orientation,[status(thm)],[conj_thm_2Ebool_2ETRUTH]) ).
fof(ax_all_p,axiom,
! [A] :
( ne(A)
=> ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ),
input ).
fof(ax_all_p_0,plain,
! [A] :
( ~ ne(A)
| ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ),
inference(orientation,[status(thm)],[ax_all_p]) ).
fof(mem_c_2Ebool_2E_21,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ),
input ).
fof(mem_c_2Ebool_2E_21_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_21]) ).
fof(ax_eq_p,axiom,
! [A] :
( ne(A)
=> ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ),
input ).
fof(ax_eq_p_0,plain,
! [A] :
( ~ ne(A)
| ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ),
inference(orientation,[status(thm)],[ax_eq_p]) ).
fof(mem_c_2Emin_2E_3D,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ),
input ).
fof(mem_c_2Emin_2E_3D_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ),
inference(orientation,[status(thm)],[mem_c_2Emin_2E_3D]) ).
fof(ax_neg_p,axiom,
! [Q] :
( mem(Q,bool)
=> ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
input ).
fof(ax_neg_p_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
inference(orientation,[status(thm)],[ax_neg_p]) ).
fof(mem_c_2Ebool_2E_7E,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
input ).
fof(mem_c_2Ebool_2E_7E_0,plain,
( mem(c_2Ebool_2E_7E,arr(bool,bool))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_7E]) ).
fof(ax_and_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ),
input ).
fof(ax_and_p_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ),
inference(orientation,[status(thm)],[ax_and_p]) ).
fof(mem_c_2Ebool_2E_2F_5C,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
input ).
fof(mem_c_2Ebool_2E_2F_5C_0,plain,
( mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool)))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_2F_5C]) ).
fof(ax_or_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ),
input ).
fof(ax_or_p_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ),
inference(orientation,[status(thm)],[ax_or_p]) ).
fof(mem_c_2Ebool_2E_5C_2F,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))),
input ).
fof(mem_c_2Ebool_2E_5C_2F_0,plain,
( mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool)))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2E_5C_2F]) ).
fof(ax_imp_p,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ),
input ).
fof(ax_imp_p_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ),
inference(orientation,[status(thm)],[ax_imp_p]) ).
fof(mem_c_2Emin_2E_3D_3D_3E,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
input ).
fof(mem_c_2Emin_2E_3D_3D_3E_0,plain,
( mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool)))
| $false ),
inference(orientation,[status(thm)],[mem_c_2Emin_2E_3D_3D_3E]) ).
fof(ax_false_p,axiom,
~ p(c_2Ebool_2EF),
input ).
fof(ax_false_p_0,plain,
( ~ p(c_2Ebool_2EF)
| $false ),
inference(orientation,[status(thm)],[ax_false_p]) ).
fof(mem_c_2Ebool_2EF,axiom,
mem(c_2Ebool_2EF,bool),
input ).
fof(mem_c_2Ebool_2EF_0,plain,
( mem(c_2Ebool_2EF,bool)
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2EF]) ).
fof(mem_c_2Ecardinal_2Ecardleq,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ecardinal_2Ecardleq(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool))) ) ),
input ).
fof(mem_c_2Ecardinal_2Ecardleq_0,plain,
! [A_27a] :
( ~ ne(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ecardinal_2Ecardleq(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool))) ) ),
inference(orientation,[status(thm)],[mem_c_2Ecardinal_2Ecardleq]) ).
fof(ax_true_p,axiom,
p(c_2Ebool_2ET),
input ).
fof(ax_true_p_0,plain,
( p(c_2Ebool_2ET)
| $false ),
inference(orientation,[status(thm)],[ax_true_p]) ).
fof(mem_c_2Ebool_2ET,axiom,
mem(c_2Ebool_2ET,bool),
input ).
fof(mem_c_2Ebool_2ET_0,plain,
( mem(c_2Ebool_2ET,bool)
| $false ),
inference(orientation,[status(thm)],[mem_c_2Ebool_2ET]) ).
fof(ibeta,axiom,
! [A,X] :
( mem(X,A)
=> ap(i(A),X) = X ),
input ).
fof(ibeta_0,plain,
! [A,X] :
( ~ mem(X,A)
| ap(i(A),X) = X ),
inference(orientation,[status(thm)],[ibeta]) ).
fof(kbeta,axiom,
! [A,Y,X] :
( mem(X,A)
=> ap(k(A,Y),X) = Y ),
input ).
fof(kbeta_0,plain,
! [A,X,Y] :
( ~ mem(X,A)
| ap(k(A,Y),X) = Y ),
inference(orientation,[status(thm)],[kbeta]) ).
fof(funcext,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [G] :
( mem(G,arr(A,B))
=> ( ! [X] :
( mem(X,A)
=> ap(F,X) = ap(G,X) )
=> F = G ) ) ),
input ).
fof(funcext_0,plain,
! [A,B,F] :
( ~ mem(F,arr(A,B))
| ! [G] :
( mem(G,arr(A,B))
=> ( ! [X] :
( mem(X,A)
=> ap(F,X) = ap(G,X) )
=> F = G ) ) ),
inference(orientation,[status(thm)],[funcext]) ).
fof(boolext,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> Q = R ) ) ),
input ).
fof(boolext_0,plain,
! [Q] :
( ~ mem(Q,bool)
| ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> Q = R ) ) ),
inference(orientation,[status(thm)],[boolext]) ).
fof(ap_tp,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
input ).
fof(ap_tp_0,plain,
! [A,B,F] :
( ~ mem(F,arr(A,B))
| ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
inference(orientation,[status(thm)],[ap_tp]) ).
fof(arr_ne,axiom,
! [A] :
( ne(A)
=> ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
input ).
fof(arr_ne_0,plain,
! [A] :
( ~ ne(A)
| ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
inference(orientation,[status(thm)],[arr_ne]) ).
fof(ind_ne,axiom,
ne(ind),
input ).
fof(ind_ne_0,plain,
( ne(ind)
| $false ),
inference(orientation,[status(thm)],[ind_ne]) ).
fof(bool_ne,axiom,
ne(bool),
input ).
fof(bool_ne_0,plain,
( ne(bool)
| $false ),
inference(orientation,[status(thm)],[bool_ne]) ).
fof(def_lhs_atom1,axiom,
( lhs_atom1
<=> ne(bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_0,plain,
( lhs_atom1
| $false ),
inference(fold_definition,[status(thm)],[bool_ne_0,def_lhs_atom1]) ).
fof(def_lhs_atom2,axiom,
( lhs_atom2
<=> ne(ind) ),
inference(definition,[],]) ).
fof(to_be_clausified_1,plain,
( lhs_atom2
| $false ),
inference(fold_definition,[status(thm)],[ind_ne_0,def_lhs_atom2]) ).
fof(def_lhs_atom3,axiom,
! [A] :
( lhs_atom3(A)
<=> ~ ne(A) ),
inference(definition,[],]) ).
fof(to_be_clausified_2,plain,
! [A] :
( lhs_atom3(A)
| ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
inference(fold_definition,[status(thm)],[arr_ne_0,def_lhs_atom3]) ).
fof(def_lhs_atom4,axiom,
! [F,B,A] :
( lhs_atom4(F,B,A)
<=> ~ mem(F,arr(A,B)) ),
inference(definition,[],]) ).
fof(to_be_clausified_3,plain,
! [A,B,F] :
( lhs_atom4(F,B,A)
| ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
inference(fold_definition,[status(thm)],[ap_tp_0,def_lhs_atom4]) ).
fof(def_lhs_atom5,axiom,
! [Q] :
( lhs_atom5(Q)
<=> ~ mem(Q,bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_4,plain,
! [Q] :
( lhs_atom5(Q)
| ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> Q = R ) ) ),
inference(fold_definition,[status(thm)],[boolext_0,def_lhs_atom5]) ).
fof(to_be_clausified_5,plain,
! [A,B,F] :
( lhs_atom4(F,B,A)
| ! [G] :
( mem(G,arr(A,B))
=> ( ! [X] :
( mem(X,A)
=> ap(F,X) = ap(G,X) )
=> F = G ) ) ),
inference(fold_definition,[status(thm)],[funcext_0,def_lhs_atom4]) ).
fof(def_lhs_atom6,axiom,
! [X,A] :
( lhs_atom6(X,A)
<=> ~ mem(X,A) ),
inference(definition,[],]) ).
fof(to_be_clausified_6,plain,
! [A,X,Y] :
( lhs_atom6(X,A)
| ap(k(A,Y),X) = Y ),
inference(fold_definition,[status(thm)],[kbeta_0,def_lhs_atom6]) ).
fof(to_be_clausified_7,plain,
! [A,X] :
( lhs_atom6(X,A)
| ap(i(A),X) = X ),
inference(fold_definition,[status(thm)],[ibeta_0,def_lhs_atom6]) ).
fof(def_lhs_atom7,axiom,
( lhs_atom7
<=> mem(c_2Ebool_2ET,bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_8,plain,
( lhs_atom7
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2ET_0,def_lhs_atom7]) ).
fof(def_lhs_atom8,axiom,
( lhs_atom8
<=> p(c_2Ebool_2ET) ),
inference(definition,[],]) ).
fof(to_be_clausified_9,plain,
( lhs_atom8
| $false ),
inference(fold_definition,[status(thm)],[ax_true_p_0,def_lhs_atom8]) ).
fof(def_lhs_atom9,axiom,
! [A_27a] :
( lhs_atom9(A_27a)
<=> ~ ne(A_27a) ),
inference(definition,[],]) ).
fof(to_be_clausified_10,plain,
! [A_27a] :
( lhs_atom9(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> mem(c_2Ecardinal_2Ecardleq(A_27a,A_27b),arr(arr(A_27a,bool),arr(arr(A_27b,bool),bool))) ) ),
inference(fold_definition,[status(thm)],[mem_c_2Ecardinal_2Ecardleq_0,def_lhs_atom9]) ).
fof(def_lhs_atom10,axiom,
( lhs_atom10
<=> mem(c_2Ebool_2EF,bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_11,plain,
( lhs_atom10
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2EF_0,def_lhs_atom10]) ).
fof(def_lhs_atom11,axiom,
( lhs_atom11
<=> ~ p(c_2Ebool_2EF) ),
inference(definition,[],]) ).
fof(to_be_clausified_12,plain,
( lhs_atom11
| $false ),
inference(fold_definition,[status(thm)],[ax_false_p_0,def_lhs_atom11]) ).
fof(def_lhs_atom12,axiom,
( lhs_atom12
<=> mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) ),
inference(definition,[],]) ).
fof(to_be_clausified_13,plain,
( lhs_atom12
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Emin_2E_3D_3D_3E_0,def_lhs_atom12]) ).
fof(to_be_clausified_14,plain,
! [Q] :
( lhs_atom5(Q)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
<=> ( p(Q)
=> p(R) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_imp_p_0,def_lhs_atom5]) ).
fof(def_lhs_atom13,axiom,
( lhs_atom13
<=> mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) ),
inference(definition,[],]) ).
fof(to_be_clausified_15,plain,
( lhs_atom13
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_5C_2F_0,def_lhs_atom13]) ).
fof(to_be_clausified_16,plain,
! [Q] :
( lhs_atom5(Q)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
<=> ( p(Q)
| p(R) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_or_p_0,def_lhs_atom5]) ).
fof(def_lhs_atom14,axiom,
( lhs_atom14
<=> mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) ),
inference(definition,[],]) ).
fof(to_be_clausified_17,plain,
( lhs_atom14
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_2F_5C_0,def_lhs_atom14]) ).
fof(to_be_clausified_18,plain,
! [Q] :
( lhs_atom5(Q)
| ! [R] :
( mem(R,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
<=> ( p(Q)
& p(R) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_and_p_0,def_lhs_atom5]) ).
fof(def_lhs_atom15,axiom,
( lhs_atom15
<=> mem(c_2Ebool_2E_7E,arr(bool,bool)) ),
inference(definition,[],]) ).
fof(to_be_clausified_19,plain,
( lhs_atom15
| $false ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_7E_0,def_lhs_atom15]) ).
fof(to_be_clausified_20,plain,
! [Q] :
( lhs_atom5(Q)
| ( p(ap(c_2Ebool_2E_7E,Q))
<=> ~ p(Q) ) ),
inference(fold_definition,[status(thm)],[ax_neg_p_0,def_lhs_atom5]) ).
fof(to_be_clausified_21,plain,
! [A_27a] :
( lhs_atom9(A_27a)
| mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ),
inference(fold_definition,[status(thm)],[mem_c_2Emin_2E_3D_0,def_lhs_atom9]) ).
fof(to_be_clausified_22,plain,
! [A] :
( lhs_atom3(A)
| ! [X] :
( mem(X,A)
=> ! [Y] :
( mem(Y,A)
=> ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
<=> X = Y ) ) ) ),
inference(fold_definition,[status(thm)],[ax_eq_p_0,def_lhs_atom3]) ).
fof(to_be_clausified_23,plain,
! [A_27a] :
( lhs_atom9(A_27a)
| mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ),
inference(fold_definition,[status(thm)],[mem_c_2Ebool_2E_21_0,def_lhs_atom9]) ).
fof(to_be_clausified_24,plain,
! [A] :
( lhs_atom3(A)
| ! [Q] :
( mem(Q,arr(A,bool))
=> ( p(ap(c_2Ebool_2E_21(A),Q))
<=> ! [X] :
( mem(X,A)
=> p(ap(Q,X)) ) ) ) ),
inference(fold_definition,[status(thm)],[ax_all_p_0,def_lhs_atom3]) ).
fof(def_lhs_atom16,axiom,
( lhs_atom16
<=> $true ),
inference(definition,[],]) ).
fof(to_be_clausified_25,plain,
( lhs_atom16
| $false ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2ETRUTH_0,def_lhs_atom16]) ).
fof(def_lhs_atom17,axiom,
! [V0t] :
( lhs_atom17(V0t)
<=> ~ mem(V0t,bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_26,plain,
! [V0t] :
( lhs_atom17(V0t)
| ( $false
=> p(V0t) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2EFALSITY_0,def_lhs_atom17]) ).
fof(to_be_clausified_27,plain,
! [A_27a] :
( lhs_atom9(A_27a)
| ! [V0t] :
( mem(V0t,bool)
=> ( ! [V1x] :
( mem(V1x,A_27a)
=> p(V0t) )
<=> p(V0t) ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2EFORALL__SIMP_0,def_lhs_atom9]) ).
fof(to_be_clausified_28,plain,
! [V0t] :
( lhs_atom17(V0t)
| ( ( ( $true
=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
=> $true )
<=> $true )
& ( ( $false
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> p(V0t) )
<=> $true )
& ( ( p(V0t)
=> $false )
<=> ~ p(V0t) ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2EIMP__CLAUSES_0,def_lhs_atom17]) ).
fof(def_lhs_atom18,axiom,
( lhs_atom18
<=> ~ $true ),
inference(definition,[],]) ).
fof(to_be_clausified_29,plain,
( lhs_atom18
| ~ $false ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES_4,def_lhs_atom18]) ).
fof(to_be_clausified_30,plain,
( lhs_atom16
| $false ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES_3,def_lhs_atom16]) ).
fof(def_lhs_atom19,axiom,
( lhs_atom19
<=> ~ $false ),
inference(definition,[],]) ).
fof(to_be_clausified_31,plain,
( lhs_atom19
| ~ $true ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES_2,def_lhs_atom19]) ).
fof(def_lhs_atom20,axiom,
( lhs_atom20
<=> $false ),
inference(definition,[],]) ).
fof(to_be_clausified_32,plain,
( lhs_atom20
| $true ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES_1,def_lhs_atom20]) ).
fof(to_be_clausified_33,plain,
! [V0t] :
( lhs_atom17(V0t)
| ( ~ ~ p(V0t)
<=> p(V0t) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2ENOT__CLAUSES_0,def_lhs_atom17]) ).
fof(to_be_clausified_34,plain,
! [A_27a] :
( lhs_atom9(A_27a)
| ! [V0x] :
( mem(V0x,A_27a)
=> ( V0x = V0x
<=> $true ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2EREFL__CLAUSE_0,def_lhs_atom9]) ).
fof(to_be_clausified_35,plain,
! [V0t] :
( lhs_atom17(V0t)
| ( ( ( $true
<=> p(V0t) )
<=> p(V0t) )
& ( ( p(V0t)
<=> $true )
<=> p(V0t) )
& ( ( $false
<=> p(V0t) )
<=> ~ p(V0t) )
& ( ( p(V0t)
<=> $false )
<=> ~ p(V0t) ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Ebool_2EEQ__CLAUSES_0,def_lhs_atom17]) ).
fof(to_be_clausified_36,plain,
! [A_27a] :
( lhs_atom9(A_27a)
| ! [A_27b] :
( ne(A_27b)
=> ! [V0s] :
( mem(V0s,arr(A_27a,bool))
=> ! [V1t] :
( mem(V1t,arr(A_27b,bool))
=> ( p(ap(ap(c_2Ecardinal_2Ecardleq(A_27a,A_27b),V0s),V1t))
| p(ap(ap(c_2Ecardinal_2Ecardleq(A_27b,A_27a),V1t),V0s)) ) ) ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Ecardinal_2ECARD__LE__TOTAL_0,def_lhs_atom9]) ).
fof(to_be_clausified_37,plain,
! [V0t] :
( lhs_atom17(V0t)
| ( ~ ~ p(V0t)
<=> p(V0t) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Esat_2ENOT__NOT_0,def_lhs_atom17]) ).
fof(def_lhs_atom21,axiom,
! [V0A] :
( lhs_atom21(V0A)
<=> ~ mem(V0A,bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_38,plain,
! [V0A] :
( lhs_atom21(V0A)
| ( p(V0A)
=> ( ~ p(V0A)
=> $false ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Esat_2EAND__INV__IMP_0,def_lhs_atom21]) ).
fof(to_be_clausified_39,plain,
! [V0A] :
( lhs_atom21(V0A)
| ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( p(V0A)
| p(V1B) )
=> $false )
<=> ( ( p(V0A)
=> $false )
=> ( ~ p(V1B)
=> $false ) ) ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Esat_2EOR__DUAL2_0,def_lhs_atom21]) ).
fof(to_be_clausified_40,plain,
! [V0A] :
( lhs_atom21(V0A)
| ! [V1B] :
( mem(V1B,bool)
=> ( ( ~ ( ~ p(V0A)
| p(V1B) )
=> $false )
<=> ( p(V0A)
=> ( ~ p(V1B)
=> $false ) ) ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Esat_2EOR__DUAL3_0,def_lhs_atom21]) ).
fof(to_be_clausified_41,plain,
! [V0A] :
( lhs_atom21(V0A)
| ( ( ~ p(V0A)
=> $false )
=> ( ( p(V0A)
=> $false )
=> $false ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Esat_2EAND__INV2_0,def_lhs_atom21]) ).
fof(def_lhs_atom22,axiom,
! [V0p] :
( lhs_atom22(V0p)
<=> ~ mem(V0p,bool) ),
inference(definition,[],]) ).
fof(to_be_clausified_42,plain,
! [V0p] :
( lhs_atom22(V0p)
| ! [V1q] :
( mem(V1q,bool)
=> ! [V2r] :
( mem(V2r,bool)
=> ( ( p(V0p)
<=> ( p(V1q)
<=> p(V2r) ) )
<=> ( ( p(V0p)
| p(V1q)
| p(V2r) )
& ( p(V0p)
| ~ p(V2r)
| ~ p(V1q) )
& ( p(V1q)
| ~ p(V2r)
| ~ p(V0p) )
& ( p(V2r)
| ~ p(V1q)
| ~ p(V0p) ) ) ) ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Esat_2Edc__eq_0,def_lhs_atom22]) ).
fof(to_be_clausified_43,plain,
! [V0p] :
( lhs_atom22(V0p)
| ! [V1q] :
( mem(V1q,bool)
=> ( ( p(V0p)
<=> ~ p(V1q) )
<=> ( ( p(V0p)
| p(V1q) )
& ( ~ p(V1q)
| ~ p(V0p) ) ) ) ) ),
inference(fold_definition,[status(thm)],[conj_thm_2Esat_2Edc__neg_0,def_lhs_atom22]) ).
% Start CNF derivation
fof(c_0_0,axiom,
! [X3,X2,X1] :
( lhs_atom4(X3,X2,X1)
| ! [X7] :
( mem(X7,arr(X1,X2))
=> ( ! [X4] :
( mem(X4,X1)
=> ap(X3,X4) = ap(X7,X4) )
=> X3 = X7 ) ) ),
file('<stdin>',to_be_clausified_5) ).
fof(c_0_1,axiom,
! [X9] :
( lhs_atom9(X9)
| ! [X10] :
( ne(X10)
=> ! [X14] :
( mem(X14,arr(X9,bool))
=> ! [X15] :
( mem(X15,arr(X10,bool))
=> ( p(ap(ap(c_2Ecardinal_2Ecardleq(X9,X10),X14),X15))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X10,X9),X15),X14)) ) ) ) ) ),
file('<stdin>',to_be_clausified_36) ).
fof(c_0_2,axiom,
! [X9] :
( lhs_atom9(X9)
| ! [X10] :
( ne(X10)
=> mem(c_2Ecardinal_2Ecardleq(X9,X10),arr(arr(X9,bool),arr(arr(X10,bool),bool))) ) ),
file('<stdin>',to_be_clausified_10) ).
fof(c_0_3,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_21(X1),X5))
<=> ! [X4] :
( mem(X4,X1)
=> p(ap(X5,X4)) ) ) ) ),
file('<stdin>',to_be_clausified_24) ).
fof(c_0_4,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X4] :
( mem(X4,X1)
=> ! [X8] :
( mem(X8,X1)
=> ( p(ap(ap(c_2Emin_2E_3D(X1),X4),X8))
<=> X4 = X8 ) ) ) ),
file('<stdin>',to_be_clausified_22) ).
fof(c_0_5,axiom,
! [X18] :
( lhs_atom22(X18)
| ! [X19] :
( mem(X19,bool)
=> ! [X20] :
( mem(X20,bool)
=> ( ( p(X18)
<=> ( p(X19)
<=> p(X20) ) )
<=> ( ( p(X18)
| p(X19)
| p(X20) )
& ( p(X18)
| ~ p(X20)
| ~ p(X19) )
& ( p(X19)
| ~ p(X20)
| ~ p(X18) )
& ( p(X20)
| ~ p(X19)
| ~ p(X18) ) ) ) ) ) ),
file('<stdin>',to_be_clausified_42) ).
fof(c_0_6,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X5),X6))
<=> ( p(X5)
=> p(X6) ) ) ) ),
file('<stdin>',to_be_clausified_14) ).
fof(c_0_7,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,X5),X6))
<=> ( p(X5)
| p(X6) ) ) ) ),
file('<stdin>',to_be_clausified_16) ).
fof(c_0_8,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,X5),X6))
<=> ( p(X5)
& p(X6) ) ) ) ),
file('<stdin>',to_be_clausified_18) ).
fof(c_0_9,axiom,
! [X3,X2,X1] :
( lhs_atom4(X3,X2,X1)
| ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
file('<stdin>',to_be_clausified_3) ).
fof(c_0_10,axiom,
! [X9] :
( lhs_atom9(X9)
| mem(c_2Emin_2E_3D(X9),arr(X9,arr(X9,bool))) ),
file('<stdin>',to_be_clausified_21) ).
fof(c_0_11,axiom,
! [X9] :
( lhs_atom9(X9)
| mem(c_2Ebool_2E_21(X9),arr(arr(X9,bool),bool)) ),
file('<stdin>',to_be_clausified_23) ).
fof(c_0_12,axiom,
! [X9] :
( lhs_atom9(X9)
| ! [X11] :
( mem(X11,bool)
=> ( ! [X12] :
( mem(X12,X9)
=> p(X11) )
<=> p(X11) ) ) ),
file('<stdin>',to_be_clausified_27) ).
fof(c_0_13,axiom,
! [X8,X4,X1] :
( lhs_atom6(X4,X1)
| ap(k(X1,X8),X4) = X8 ),
file('<stdin>',to_be_clausified_6) ).
fof(c_0_14,axiom,
! [X5] :
( lhs_atom5(X5)
| ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
file('<stdin>',to_be_clausified_20) ).
fof(c_0_15,axiom,
! [X18] :
( lhs_atom22(X18)
| ! [X19] :
( mem(X19,bool)
=> ( ( p(X18)
<=> ~ p(X19) )
<=> ( ( p(X18)
| p(X19) )
& ( ~ p(X19)
| ~ p(X18) ) ) ) ) ),
file('<stdin>',to_be_clausified_43) ).
fof(c_0_16,axiom,
! [X16] :
( lhs_atom21(X16)
| ! [X17] :
( mem(X17,bool)
=> ( ( ~ ( ~ p(X16)
| p(X17) )
=> ~ $true )
<=> ( p(X16)
=> ( ~ p(X17)
=> ~ $true ) ) ) ) ),
file('<stdin>',to_be_clausified_40) ).
fof(c_0_17,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X2] :
( ne(X2)
=> ne(arr(X1,X2)) ) ),
file('<stdin>',to_be_clausified_2) ).
fof(c_0_18,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> X5 = X6 ) ) ),
file('<stdin>',to_be_clausified_4) ).
fof(c_0_19,axiom,
! [X16] :
( lhs_atom21(X16)
| ! [X17] :
( mem(X17,bool)
=> ( ( ~ ( p(X16)
| p(X17) )
=> ~ $true )
<=> ( ( p(X16)
=> ~ $true )
=> ( ~ p(X17)
=> ~ $true ) ) ) ) ),
file('<stdin>',to_be_clausified_39) ).
fof(c_0_20,axiom,
! [X4,X1] :
( lhs_atom6(X4,X1)
| ap(i(X1),X4) = X4 ),
file('<stdin>',to_be_clausified_7) ).
fof(c_0_21,axiom,
! [X9] :
( lhs_atom9(X9)
| ! [X13] :
( mem(X13,X9)
=> ( X13 = X13
<=> $true ) ) ),
file('<stdin>',to_be_clausified_34) ).
fof(c_0_22,axiom,
! [X16] :
( lhs_atom21(X16)
| ( ( ~ p(X16)
=> ~ $true )
=> ( ( p(X16)
=> ~ $true )
=> ~ $true ) ) ),
file('<stdin>',to_be_clausified_41) ).
fof(c_0_23,axiom,
! [X16] :
( lhs_atom21(X16)
| ( p(X16)
=> ( ~ p(X16)
=> ~ $true ) ) ),
file('<stdin>',to_be_clausified_38) ).
fof(c_0_24,axiom,
! [X11] :
( lhs_atom17(X11)
| ( ~ ~ p(X11)
<=> p(X11) ) ),
file('<stdin>',to_be_clausified_37) ).
fof(c_0_25,axiom,
! [X11] :
( lhs_atom17(X11)
| ( ( ( $true
<=> p(X11) )
<=> p(X11) )
& ( ( p(X11)
<=> $true )
<=> p(X11) )
& ( ( ~ $true
<=> p(X11) )
<=> ~ p(X11) )
& ( ( p(X11)
<=> ~ $true )
<=> ~ p(X11) ) ) ),
file('<stdin>',to_be_clausified_35) ).
fof(c_0_26,axiom,
! [X11] :
( lhs_atom17(X11)
| ( ~ ~ p(X11)
<=> p(X11) ) ),
file('<stdin>',to_be_clausified_33) ).
fof(c_0_27,axiom,
( lhs_atom20
| $true ),
file('<stdin>',to_be_clausified_32) ).
fof(c_0_28,axiom,
( lhs_atom19
| ~ $true ),
file('<stdin>',to_be_clausified_31) ).
fof(c_0_29,axiom,
( lhs_atom16
| ~ $true ),
file('<stdin>',to_be_clausified_30) ).
fof(c_0_30,axiom,
( lhs_atom18
| ~ ~ $true ),
file('<stdin>',to_be_clausified_29) ).
fof(c_0_31,axiom,
! [X11] :
( lhs_atom17(X11)
| ( ( ( $true
=> p(X11) )
<=> p(X11) )
& ( ( p(X11)
=> $true )
<=> $true )
& ( ( ~ $true
=> p(X11) )
<=> $true )
& ( ( p(X11)
=> p(X11) )
<=> $true )
& ( ( p(X11)
=> ~ $true )
<=> ~ p(X11) ) ) ),
file('<stdin>',to_be_clausified_28) ).
fof(c_0_32,axiom,
! [X11] :
( lhs_atom17(X11)
| ( ~ $true
=> p(X11) ) ),
file('<stdin>',to_be_clausified_26) ).
fof(c_0_33,axiom,
( lhs_atom16
| ~ $true ),
file('<stdin>',to_be_clausified_25) ).
fof(c_0_34,axiom,
( lhs_atom15
| ~ $true ),
file('<stdin>',to_be_clausified_19) ).
fof(c_0_35,axiom,
( lhs_atom14
| ~ $true ),
file('<stdin>',to_be_clausified_17) ).
fof(c_0_36,axiom,
( lhs_atom13
| ~ $true ),
file('<stdin>',to_be_clausified_15) ).
fof(c_0_37,axiom,
( lhs_atom12
| ~ $true ),
file('<stdin>',to_be_clausified_13) ).
fof(c_0_38,axiom,
( lhs_atom11
| ~ $true ),
file('<stdin>',to_be_clausified_12) ).
fof(c_0_39,axiom,
( lhs_atom10
| ~ $true ),
file('<stdin>',to_be_clausified_11) ).
fof(c_0_40,axiom,
( lhs_atom8
| ~ $true ),
file('<stdin>',to_be_clausified_9) ).
fof(c_0_41,axiom,
( lhs_atom7
| ~ $true ),
file('<stdin>',to_be_clausified_8) ).
fof(c_0_42,axiom,
( lhs_atom2
| ~ $true ),
file('<stdin>',to_be_clausified_1) ).
fof(c_0_43,axiom,
( lhs_atom1
| ~ $true ),
file('<stdin>',to_be_clausified_0) ).
fof(c_0_44,plain,
! [X20,X19,X18] :
( epred1_3(X18,X19,X20)
<=> ( ( p(X18)
| ~ p(X20)
| ~ p(X19) )
& ( p(X19)
| ~ p(X20)
| ~ p(X18) )
& ( p(X20)
| ~ p(X19)
| ~ p(X18) ) ) ),
introduced(definition) ).
fof(c_0_45,axiom,
! [X3,X2,X1] :
( lhs_atom4(X3,X2,X1)
| ! [X7] :
( mem(X7,arr(X1,X2))
=> ( ! [X4] :
( mem(X4,X1)
=> ap(X3,X4) = ap(X7,X4) )
=> X3 = X7 ) ) ),
c_0_0 ).
fof(c_0_46,axiom,
! [X9] :
( lhs_atom9(X9)
| ! [X10] :
( ne(X10)
=> ! [X14] :
( mem(X14,arr(X9,bool))
=> ! [X15] :
( mem(X15,arr(X10,bool))
=> ( p(ap(ap(c_2Ecardinal_2Ecardleq(X9,X10),X14),X15))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X10,X9),X15),X14)) ) ) ) ) ),
c_0_1 ).
fof(c_0_47,axiom,
! [X9] :
( lhs_atom9(X9)
| ! [X10] :
( ne(X10)
=> mem(c_2Ecardinal_2Ecardleq(X9,X10),arr(arr(X9,bool),arr(arr(X10,bool),bool))) ) ),
c_0_2 ).
fof(c_0_48,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X5] :
( mem(X5,arr(X1,bool))
=> ( p(ap(c_2Ebool_2E_21(X1),X5))
<=> ! [X4] :
( mem(X4,X1)
=> p(ap(X5,X4)) ) ) ) ),
c_0_3 ).
fof(c_0_49,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X4] :
( mem(X4,X1)
=> ! [X8] :
( mem(X8,X1)
=> ( p(ap(ap(c_2Emin_2E_3D(X1),X4),X8))
<=> X4 = X8 ) ) ) ),
c_0_4 ).
fof(c_0_50,plain,
! [X18] :
( lhs_atom22(X18)
| ! [X19] :
( mem(X19,bool)
=> ! [X20] :
( mem(X20,bool)
=> ( ( p(X18)
<=> ( p(X19)
<=> p(X20) ) )
<=> ( ( p(X18)
| p(X19)
| p(X20) )
& epred1_3(X18,X19,X20) ) ) ) ) ),
inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_5]),c_0_44,theory(equality,[symmetry])]) ).
fof(c_0_51,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Emin_2E_3D_3D_3E,X5),X6))
<=> ( p(X5)
=> p(X6) ) ) ) ),
c_0_6 ).
fof(c_0_52,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Ebool_2E_5C_2F,X5),X6))
<=> ( p(X5)
| p(X6) ) ) ) ),
c_0_7 ).
fof(c_0_53,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( p(ap(ap(c_2Ebool_2E_2F_5C,X5),X6))
<=> ( p(X5)
& p(X6) ) ) ) ),
c_0_8 ).
fof(c_0_54,axiom,
! [X3,X2,X1] :
( lhs_atom4(X3,X2,X1)
| ! [X4] :
( mem(X4,X1)
=> mem(ap(X3,X4),X2) ) ),
c_0_9 ).
fof(c_0_55,plain,
! [X20,X19,X18] :
( epred1_3(X18,X19,X20)
<=> ( ( p(X18)
| ~ p(X20)
| ~ p(X19) )
& ( p(X19)
| ~ p(X20)
| ~ p(X18) )
& ( p(X20)
| ~ p(X19)
| ~ p(X18) ) ) ),
c_0_44 ).
fof(c_0_56,axiom,
! [X9] :
( lhs_atom9(X9)
| mem(c_2Emin_2E_3D(X9),arr(X9,arr(X9,bool))) ),
c_0_10 ).
fof(c_0_57,axiom,
! [X9] :
( lhs_atom9(X9)
| mem(c_2Ebool_2E_21(X9),arr(arr(X9,bool),bool)) ),
c_0_11 ).
fof(c_0_58,axiom,
! [X9] :
( lhs_atom9(X9)
| ! [X11] :
( mem(X11,bool)
=> ( ! [X12] :
( mem(X12,X9)
=> p(X11) )
<=> p(X11) ) ) ),
c_0_12 ).
fof(c_0_59,axiom,
! [X8,X4,X1] :
( lhs_atom6(X4,X1)
| ap(k(X1,X8),X4) = X8 ),
c_0_13 ).
fof(c_0_60,plain,
! [X5] :
( lhs_atom5(X5)
| ( p(ap(c_2Ebool_2E_7E,X5))
<=> ~ p(X5) ) ),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_61,plain,
! [X18] :
( lhs_atom22(X18)
| ! [X19] :
( mem(X19,bool)
=> ( ( p(X18)
<=> ~ p(X19) )
<=> ( ( p(X18)
| p(X19) )
& ( ~ p(X19)
| ~ p(X18) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_15]) ).
fof(c_0_62,plain,
! [X16] :
( lhs_atom21(X16)
| ! [X17] :
( mem(X17,bool)
=> ( ~ ~ ( ~ p(X16)
| p(X17) )
<=> ( p(X16)
=> p(X17) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_16]) ).
fof(c_0_63,axiom,
! [X1] :
( lhs_atom3(X1)
| ! [X2] :
( ne(X2)
=> ne(arr(X1,X2)) ) ),
c_0_17 ).
fof(c_0_64,axiom,
! [X5] :
( lhs_atom5(X5)
| ! [X6] :
( mem(X6,bool)
=> ( ( p(X5)
<=> p(X6) )
=> X5 = X6 ) ) ),
c_0_18 ).
fof(c_0_65,plain,
! [X16] :
( lhs_atom21(X16)
| ! [X17] :
( mem(X17,bool)
=> ( ~ ~ ( p(X16)
| p(X17) )
<=> ( ~ p(X16)
=> p(X17) ) ) ) ),
inference(fof_simplification,[status(thm)],[c_0_19]) ).
fof(c_0_66,axiom,
! [X4,X1] :
( lhs_atom6(X4,X1)
| ap(i(X1),X4) = X4 ),
c_0_20 ).
fof(c_0_67,plain,
! [X9] :
( lhs_atom9(X9)
| ! [X13] :
( mem(X13,X9)
=> X13 = X13 ) ),
inference(fof_simplification,[status(thm)],[c_0_21]) ).
fof(c_0_68,plain,
! [X16] : $true,
inference(fof_simplification,[status(thm)],[c_0_22]) ).
fof(c_0_69,plain,
! [X16] : $true,
inference(fof_simplification,[status(thm)],[c_0_23]) ).
fof(c_0_70,plain,
! [X11] : $true,
inference(fof_simplification,[status(thm)],[c_0_24]) ).
fof(c_0_71,plain,
! [X11] : $true,
inference(fof_simplification,[status(thm)],[c_0_25]) ).
fof(c_0_72,plain,
! [X11] : $true,
inference(fof_simplification,[status(thm)],[c_0_26]) ).
fof(c_0_73,plain,
$true,
inference(fof_simplification,[status(thm)],[c_0_27]) ).
fof(c_0_74,plain,
lhs_atom19,
inference(fof_simplification,[status(thm)],[c_0_28]) ).
fof(c_0_75,plain,
lhs_atom16,
inference(fof_simplification,[status(thm)],[c_0_29]) ).
fof(c_0_76,plain,
$true,
inference(fof_simplification,[status(thm)],[c_0_30]) ).
fof(c_0_77,plain,
! [X11] : $true,
inference(fof_simplification,[status(thm)],[c_0_31]) ).
fof(c_0_78,plain,
! [X11] : $true,
inference(fof_simplification,[status(thm)],[c_0_32]) ).
fof(c_0_79,plain,
lhs_atom16,
inference(fof_simplification,[status(thm)],[c_0_33]) ).
fof(c_0_80,plain,
lhs_atom15,
inference(fof_simplification,[status(thm)],[c_0_34]) ).
fof(c_0_81,plain,
lhs_atom14,
inference(fof_simplification,[status(thm)],[c_0_35]) ).
fof(c_0_82,plain,
lhs_atom13,
inference(fof_simplification,[status(thm)],[c_0_36]) ).
fof(c_0_83,plain,
lhs_atom12,
inference(fof_simplification,[status(thm)],[c_0_37]) ).
fof(c_0_84,plain,
lhs_atom11,
inference(fof_simplification,[status(thm)],[c_0_38]) ).
fof(c_0_85,plain,
lhs_atom10,
inference(fof_simplification,[status(thm)],[c_0_39]) ).
fof(c_0_86,plain,
lhs_atom8,
inference(fof_simplification,[status(thm)],[c_0_40]) ).
fof(c_0_87,plain,
lhs_atom7,
inference(fof_simplification,[status(thm)],[c_0_41]) ).
fof(c_0_88,plain,
lhs_atom2,
inference(fof_simplification,[status(thm)],[c_0_42]) ).
fof(c_0_89,plain,
lhs_atom1,
inference(fof_simplification,[status(thm)],[c_0_43]) ).
fof(c_0_90,plain,
! [X8,X9,X10,X11] :
( ( mem(esk1_4(X8,X9,X10,X11),X10)
| X8 = X11
| ~ mem(X11,arr(X10,X9))
| lhs_atom4(X8,X9,X10) )
& ( ap(X8,esk1_4(X8,X9,X10,X11)) != ap(X11,esk1_4(X8,X9,X10,X11))
| X8 = X11
| ~ mem(X11,arr(X10,X9))
| lhs_atom4(X8,X9,X10) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_45])])])])]) ).
fof(c_0_91,plain,
! [X16,X17,X18,X19] :
( lhs_atom9(X16)
| ~ ne(X17)
| ~ mem(X18,arr(X16,bool))
| ~ mem(X19,arr(X17,bool))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X16,X17),X18),X19))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X17,X16),X19),X18)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_46])])]) ).
fof(c_0_92,plain,
! [X11,X12] :
( lhs_atom9(X11)
| ~ ne(X12)
| mem(c_2Ecardinal_2Ecardleq(X11,X12),arr(arr(X11,bool),arr(arr(X12,bool),bool))) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_47])])]) ).
fof(c_0_93,plain,
! [X6,X7,X8] :
( ( ~ p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X8,X6)
| p(ap(X7,X8))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) )
& ( mem(esk2_2(X6,X7),X6)
| p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) )
& ( ~ p(ap(X7,esk2_2(X6,X7)))
| p(ap(c_2Ebool_2E_21(X6),X7))
| ~ mem(X7,arr(X6,bool))
| lhs_atom3(X6) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_48])])])])]) ).
fof(c_0_94,plain,
! [X9,X10,X11] :
( ( ~ p(ap(ap(c_2Emin_2E_3D(X9),X10),X11))
| X10 = X11
| ~ mem(X11,X9)
| ~ mem(X10,X9)
| lhs_atom3(X9) )
& ( X10 != X11
| p(ap(ap(c_2Emin_2E_3D(X9),X10),X11))
| ~ mem(X11,X9)
| ~ mem(X10,X9)
| lhs_atom3(X9) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_49])])])]) ).
fof(c_0_95,plain,
! [X21,X22,X23] :
( ( p(X21)
| p(X22)
| p(X23)
| ~ p(X22)
| ~ p(X23)
| ~ p(X21)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( epred1_3(X21,X22,X23)
| ~ p(X22)
| ~ p(X23)
| ~ p(X21)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( p(X21)
| p(X22)
| p(X23)
| p(X22)
| p(X23)
| ~ p(X21)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( epred1_3(X21,X22,X23)
| p(X22)
| p(X23)
| ~ p(X21)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( p(X21)
| p(X22)
| p(X23)
| ~ p(X22)
| p(X23)
| p(X21)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( epred1_3(X21,X22,X23)
| ~ p(X22)
| p(X23)
| p(X21)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( p(X21)
| p(X22)
| p(X23)
| ~ p(X23)
| p(X22)
| p(X21)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( epred1_3(X21,X22,X23)
| ~ p(X23)
| p(X22)
| p(X21)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X22)
| p(X23)
| ~ p(X21)
| ~ p(X21)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X23)
| p(X22)
| ~ p(X21)
| ~ p(X21)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X22)
| ~ p(X23)
| p(X21)
| ~ p(X21)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( p(X22)
| p(X23)
| p(X21)
| ~ p(X21)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X22)
| p(X23)
| ~ p(X21)
| ~ p(X22)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X23)
| p(X22)
| ~ p(X21)
| ~ p(X22)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X22)
| ~ p(X23)
| p(X21)
| ~ p(X22)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( p(X22)
| p(X23)
| p(X21)
| ~ p(X22)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X22)
| p(X23)
| ~ p(X21)
| ~ p(X23)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X23)
| p(X22)
| ~ p(X21)
| ~ p(X23)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( ~ p(X22)
| ~ p(X23)
| p(X21)
| ~ p(X23)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) )
& ( p(X22)
| p(X23)
| p(X21)
| ~ p(X23)
| ~ epred1_3(X21,X22,X23)
| ~ mem(X23,bool)
| ~ mem(X22,bool)
| lhs_atom22(X21) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_50])])])]) ).
fof(c_0_96,plain,
! [X7,X8] :
( ( ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ p(X7)
| p(X8)
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( p(X7)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( ~ p(X8)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_51])])])]) ).
fof(c_0_97,plain,
! [X7,X8] :
( ( ~ p(ap(ap(c_2Ebool_2E_5C_2F,X7),X8))
| p(X7)
| p(X8)
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( ~ p(X7)
| p(ap(ap(c_2Ebool_2E_5C_2F,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( ~ p(X8)
| p(ap(ap(c_2Ebool_2E_5C_2F,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_52])])])]) ).
fof(c_0_98,plain,
! [X7,X8] :
( ( p(X7)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( p(X8)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( ~ p(X7)
| ~ p(X8)
| p(ap(ap(c_2Ebool_2E_2F_5C,X7),X8))
| ~ mem(X8,bool)
| lhs_atom5(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
fof(c_0_99,plain,
! [X5,X6,X7,X8] :
( lhs_atom4(X5,X6,X7)
| ~ mem(X8,X7)
| mem(ap(X5,X8),X6) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_54])])]) ).
fof(c_0_100,plain,
! [X21,X22,X23,X24,X25,X26] :
( ( p(X23)
| ~ p(X21)
| ~ p(X22)
| ~ epred1_3(X23,X22,X21) )
& ( p(X22)
| ~ p(X21)
| ~ p(X23)
| ~ epred1_3(X23,X22,X21) )
& ( p(X21)
| ~ p(X22)
| ~ p(X23)
| ~ epred1_3(X23,X22,X21) )
& ( ~ p(X24)
| ~ p(X25)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| ~ p(X25)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| ~ p(X25)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( ~ p(X24)
| p(X24)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| p(X24)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| p(X24)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( ~ p(X24)
| p(X26)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| p(X26)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| p(X26)
| ~ p(X26)
| epred1_3(X26,X25,X24) )
& ( ~ p(X24)
| ~ p(X25)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| ~ p(X25)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| ~ p(X25)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( ~ p(X24)
| p(X24)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| p(X24)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| p(X24)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( ~ p(X24)
| p(X26)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| p(X26)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| p(X26)
| p(X24)
| epred1_3(X26,X25,X24) )
& ( ~ p(X24)
| ~ p(X25)
| p(X25)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| ~ p(X25)
| p(X25)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| ~ p(X25)
| p(X25)
| epred1_3(X26,X25,X24) )
& ( ~ p(X24)
| p(X24)
| p(X25)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| p(X24)
| p(X25)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| p(X24)
| p(X25)
| epred1_3(X26,X25,X24) )
& ( ~ p(X24)
| p(X26)
| p(X25)
| epred1_3(X26,X25,X24) )
& ( p(X25)
| p(X26)
| p(X25)
| epred1_3(X26,X25,X24) )
& ( p(X26)
| p(X26)
| p(X25)
| epred1_3(X26,X25,X24) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_55])])])])]) ).
fof(c_0_101,plain,
! [X10] :
( lhs_atom9(X10)
| mem(c_2Emin_2E_3D(X10),arr(X10,arr(X10,bool))) ),
inference(variable_rename,[status(thm)],[c_0_56]) ).
fof(c_0_102,plain,
! [X10] :
( lhs_atom9(X10)
| mem(c_2Ebool_2E_21(X10),arr(arr(X10,bool),bool)) ),
inference(variable_rename,[status(thm)],[c_0_57]) ).
fof(c_0_103,plain,
! [X13,X14,X16] :
( ( mem(esk3_2(X13,X14),X13)
| p(X14)
| ~ mem(X14,bool)
| lhs_atom9(X13) )
& ( ~ p(X14)
| p(X14)
| ~ mem(X14,bool)
| lhs_atom9(X13) )
& ( ~ p(X14)
| ~ mem(X16,X13)
| p(X14)
| ~ mem(X14,bool)
| lhs_atom9(X13) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_58])])])])])]) ).
fof(c_0_104,plain,
! [X9,X10,X11] :
( lhs_atom6(X10,X11)
| ap(k(X11,X9),X10) = X9 ),
inference(variable_rename,[status(thm)],[c_0_59]) ).
fof(c_0_105,plain,
! [X6] :
( ( ~ p(ap(c_2Ebool_2E_7E,X6))
| ~ p(X6)
| lhs_atom5(X6) )
& ( p(X6)
| p(ap(c_2Ebool_2E_7E,X6))
| lhs_atom5(X6) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).
fof(c_0_106,plain,
! [X20,X21] :
( ( p(X20)
| p(X21)
| ~ p(X20)
| p(X21)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( ~ p(X21)
| ~ p(X20)
| ~ p(X20)
| p(X21)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( p(X20)
| p(X21)
| p(X20)
| ~ p(X21)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( ~ p(X21)
| ~ p(X20)
| p(X20)
| ~ p(X21)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( ~ p(X20)
| ~ p(X21)
| p(X21)
| ~ p(X20)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( p(X21)
| p(X20)
| p(X21)
| ~ p(X20)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( ~ p(X20)
| ~ p(X21)
| p(X20)
| ~ p(X20)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( p(X21)
| p(X20)
| p(X20)
| ~ p(X20)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( ~ p(X20)
| ~ p(X21)
| p(X21)
| ~ p(X21)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( p(X21)
| p(X20)
| p(X21)
| ~ p(X21)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( ~ p(X20)
| ~ p(X21)
| p(X20)
| ~ p(X21)
| ~ mem(X21,bool)
| lhs_atom22(X20) )
& ( p(X21)
| p(X20)
| p(X20)
| ~ p(X21)
| ~ mem(X21,bool)
| lhs_atom22(X20) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_61])])])]) ).
fof(c_0_107,plain,
! [X18,X19] :
( ( p(X18)
| ~ p(X18)
| p(X19)
| ~ mem(X19,bool)
| lhs_atom21(X18) )
& ( ~ p(X19)
| ~ p(X18)
| p(X19)
| ~ mem(X19,bool)
| lhs_atom21(X18) )
& ( p(X18)
| ~ p(X18)
| p(X19)
| ~ mem(X19,bool)
| lhs_atom21(X18) )
& ( ~ p(X19)
| ~ p(X18)
| p(X19)
| ~ mem(X19,bool)
| lhs_atom21(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_62])])])]) ).
fof(c_0_108,plain,
! [X3,X4] :
( lhs_atom3(X3)
| ~ ne(X4)
| ne(arr(X3,X4)) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_63])])]) ).
fof(c_0_109,plain,
! [X7,X8] :
( ( ~ p(X7)
| ~ p(X8)
| X7 = X8
| ~ mem(X8,bool)
| lhs_atom5(X7) )
& ( p(X7)
| p(X8)
| X7 = X8
| ~ mem(X8,bool)
| lhs_atom5(X7) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_64])])])]) ).
fof(c_0_110,plain,
! [X18,X19] :
( ( ~ p(X18)
| p(X18)
| p(X19)
| ~ mem(X19,bool)
| lhs_atom21(X18) )
& ( ~ p(X19)
| p(X18)
| p(X19)
| ~ mem(X19,bool)
| lhs_atom21(X18) )
& ( ~ p(X18)
| p(X18)
| p(X19)
| ~ mem(X19,bool)
| lhs_atom21(X18) )
& ( ~ p(X19)
| p(X18)
| p(X19)
| ~ mem(X19,bool)
| lhs_atom21(X18) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])])]) ).
fof(c_0_111,plain,
! [X5,X6] :
( lhs_atom6(X5,X6)
| ap(i(X6),X5) = X5 ),
inference(variable_rename,[status(thm)],[c_0_66]) ).
fof(c_0_112,plain,
! [X14,X15] :
( lhs_atom9(X14)
| ~ mem(X15,X14)
| X15 = X15 ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_67])])]) ).
fof(c_0_113,plain,
! [X17] : $true,
inference(variable_rename,[status(thm)],[c_0_68]) ).
fof(c_0_114,plain,
! [X17] : $true,
inference(variable_rename,[status(thm)],[c_0_69]) ).
fof(c_0_115,plain,
! [X12] : $true,
inference(variable_rename,[status(thm)],[c_0_70]) ).
fof(c_0_116,plain,
! [X12] : $true,
inference(variable_rename,[status(thm)],[c_0_71]) ).
fof(c_0_117,plain,
! [X12] : $true,
inference(variable_rename,[status(thm)],[c_0_72]) ).
fof(c_0_118,plain,
$true,
c_0_73 ).
fof(c_0_119,plain,
lhs_atom19,
c_0_74 ).
fof(c_0_120,plain,
lhs_atom16,
c_0_75 ).
fof(c_0_121,plain,
$true,
c_0_76 ).
fof(c_0_122,plain,
! [X12] : $true,
inference(variable_rename,[status(thm)],[c_0_77]) ).
fof(c_0_123,plain,
! [X12] : $true,
inference(variable_rename,[status(thm)],[c_0_78]) ).
fof(c_0_124,plain,
lhs_atom16,
c_0_79 ).
fof(c_0_125,plain,
lhs_atom15,
c_0_80 ).
fof(c_0_126,plain,
lhs_atom14,
c_0_81 ).
fof(c_0_127,plain,
lhs_atom13,
c_0_82 ).
fof(c_0_128,plain,
lhs_atom12,
c_0_83 ).
fof(c_0_129,plain,
lhs_atom11,
c_0_84 ).
fof(c_0_130,plain,
lhs_atom10,
c_0_85 ).
fof(c_0_131,plain,
lhs_atom8,
c_0_86 ).
fof(c_0_132,plain,
lhs_atom7,
c_0_87 ).
fof(c_0_133,plain,
lhs_atom2,
c_0_88 ).
fof(c_0_134,plain,
lhs_atom1,
c_0_89 ).
cnf(c_0_135,plain,
( lhs_atom4(X1,X2,X3)
| X1 = X4
| ~ mem(X4,arr(X3,X2))
| ap(X1,esk1_4(X1,X2,X3,X4)) != ap(X4,esk1_4(X1,X2,X3,X4)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_136,plain,
( lhs_atom4(X1,X2,X3)
| X1 = X4
| mem(esk1_4(X1,X2,X3,X4),X3)
| ~ mem(X4,arr(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_90]) ).
cnf(c_0_137,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X3),X4))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X1),X4),X3))
| lhs_atom9(X2)
| ~ mem(X3,arr(X1,bool))
| ~ mem(X4,arr(X2,bool))
| ~ ne(X1) ),
inference(split_conjunct,[status(thm)],[c_0_91]) ).
cnf(c_0_138,plain,
( mem(c_2Ecardinal_2Ecardleq(X1,X2),arr(arr(X1,bool),arr(arr(X2,bool),bool)))
| lhs_atom9(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_92]) ).
cnf(c_0_139,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,esk2_2(X1,X2))) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_140,plain,
( lhs_atom3(X1)
| X2 = X3
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| ~ p(ap(ap(c_2Emin_2E_3D(X1),X2),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_141,plain,
( lhs_atom3(X1)
| p(ap(X2,X3))
| ~ mem(X2,arr(X1,bool))
| ~ mem(X3,X1)
| ~ p(ap(c_2Ebool_2E_21(X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_142,plain,
( lhs_atom3(X1)
| p(ap(ap(c_2Emin_2E_3D(X1),X2),X3))
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| X2 != X3 ),
inference(split_conjunct,[status(thm)],[c_0_94]) ).
cnf(c_0_143,plain,
( lhs_atom22(X1)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_144,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X1)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_145,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_146,plain,
( lhs_atom22(X1)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_147,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_148,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X3)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_149,plain,
( lhs_atom22(X1)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_150,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X1)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_151,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X3)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_152,plain,
( lhs_atom5(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_153,plain,
( lhs_atom5(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_154,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_155,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_156,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_157,plain,
( lhs_atom5(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_158,plain,
( lhs_atom5(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_159,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| mem(esk2_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool)) ),
inference(split_conjunct,[status(thm)],[c_0_93]) ).
cnf(c_0_160,plain,
( lhs_atom22(X1)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_161,plain,
( mem(ap(X1,X2),X3)
| lhs_atom4(X1,X3,X4)
| ~ mem(X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_99]) ).
cnf(c_0_162,plain,
( lhs_atom22(X1)
| p(X3)
| p(X2)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_163,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_164,plain,
( lhs_atom22(X1)
| p(X1)
| p(X2)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_165,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_98]) ).
cnf(c_0_166,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_167,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_97]) ).
cnf(c_0_168,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_169,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| p(X1)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_96]) ).
cnf(c_0_170,plain,
( p(X1)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_171,plain,
( p(X2)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_172,plain,
( p(X3)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_173,plain,
( mem(c_2Emin_2E_3D(X1),arr(X1,arr(X1,bool)))
| lhs_atom9(X1) ),
inference(split_conjunct,[status(thm)],[c_0_101]) ).
cnf(c_0_174,plain,
( mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool))
| lhs_atom9(X1) ),
inference(split_conjunct,[status(thm)],[c_0_102]) ).
cnf(c_0_175,plain,
( lhs_atom22(X1)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_176,plain,
( epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X2)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_177,plain,
( lhs_atom22(X1)
| p(X3)
| p(X2)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_178,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_179,plain,
( lhs_atom22(X1)
| p(X1)
| p(X2)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_95]) ).
cnf(c_0_180,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_181,plain,
( epred1_3(X1,X2,X3)
| p(X1)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_182,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| ~ p(X1)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_183,plain,
( epred1_3(X1,X2,X3)
| p(X1)
| ~ p(X1)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_184,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| ~ p(X2)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_185,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| ~ p(X2)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_186,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_187,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_188,plain,
( epred1_3(X1,X2,X3)
| p(X1)
| p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_189,plain,
( epred1_3(X1,X2,X3)
| p(X1)
| p(X1)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_190,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X2)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_191,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_192,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_193,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_194,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X2)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_195,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_196,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_197,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| ~ p(X3) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_198,plain,
( lhs_atom9(X1)
| p(X2)
| mem(esk3_2(X1,X2),X1)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_199,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_200,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_201,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_202,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_203,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_204,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_205,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_206,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_100]) ).
cnf(c_0_207,plain,
( lhs_atom9(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_208,plain,
( ap(k(X1,X2),X3) = X2
| lhs_atom6(X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_104]) ).
cnf(c_0_209,plain,
( lhs_atom5(X1)
| ~ p(X1)
| ~ p(ap(c_2Ebool_2E_7E,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_210,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_211,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_212,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_213,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_214,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_215,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_216,plain,
( lhs_atom22(X1)
| p(X2)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_217,plain,
( lhs_atom22(X1)
| p(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_218,plain,
( lhs_atom22(X1)
| p(X2)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_219,plain,
( lhs_atom22(X1)
| p(X1)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_220,plain,
( lhs_atom22(X1)
| p(X2)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_221,plain,
( lhs_atom22(X1)
| p(X1)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_106]) ).
cnf(c_0_222,plain,
( lhs_atom21(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_223,plain,
( lhs_atom21(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_224,plain,
( ne(arr(X1,X2))
| lhs_atom3(X1)
| ~ ne(X2) ),
inference(split_conjunct,[status(thm)],[c_0_108]) ).
cnf(c_0_225,plain,
( lhs_atom5(X1)
| X1 = X2
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_226,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_227,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_107]) ).
cnf(c_0_228,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_229,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_230,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_231,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_110]) ).
cnf(c_0_232,plain,
( lhs_atom9(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_103]) ).
cnf(c_0_233,plain,
( lhs_atom5(X1)
| p(ap(c_2Ebool_2E_7E,X1))
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_105]) ).
cnf(c_0_234,plain,
( lhs_atom5(X1)
| X1 = X2
| p(X2)
| p(X1)
| ~ mem(X2,bool) ),
inference(split_conjunct,[status(thm)],[c_0_109]) ).
cnf(c_0_235,plain,
( ap(i(X1),X2) = X2
| lhs_atom6(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_111]) ).
cnf(c_0_236,plain,
( X1 = X1
| lhs_atom9(X2)
| ~ mem(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_112]) ).
cnf(c_0_237,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_113]) ).
cnf(c_0_238,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_114]) ).
cnf(c_0_239,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_115]) ).
cnf(c_0_240,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_116]) ).
cnf(c_0_241,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_117]) ).
cnf(c_0_242,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_118]) ).
cnf(c_0_243,plain,
lhs_atom19,
inference(split_conjunct,[status(thm)],[c_0_119]) ).
cnf(c_0_244,plain,
lhs_atom16,
inference(split_conjunct,[status(thm)],[c_0_120]) ).
cnf(c_0_245,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_121]) ).
cnf(c_0_246,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_122]) ).
cnf(c_0_247,plain,
$true,
inference(split_conjunct,[status(thm)],[c_0_123]) ).
cnf(c_0_248,plain,
lhs_atom16,
inference(split_conjunct,[status(thm)],[c_0_124]) ).
cnf(c_0_249,plain,
lhs_atom15,
inference(split_conjunct,[status(thm)],[c_0_125]) ).
cnf(c_0_250,plain,
lhs_atom14,
inference(split_conjunct,[status(thm)],[c_0_126]) ).
cnf(c_0_251,plain,
lhs_atom13,
inference(split_conjunct,[status(thm)],[c_0_127]) ).
cnf(c_0_252,plain,
lhs_atom12,
inference(split_conjunct,[status(thm)],[c_0_128]) ).
cnf(c_0_253,plain,
lhs_atom11,
inference(split_conjunct,[status(thm)],[c_0_129]) ).
cnf(c_0_254,plain,
lhs_atom10,
inference(split_conjunct,[status(thm)],[c_0_130]) ).
cnf(c_0_255,plain,
lhs_atom8,
inference(split_conjunct,[status(thm)],[c_0_131]) ).
cnf(c_0_256,plain,
lhs_atom7,
inference(split_conjunct,[status(thm)],[c_0_132]) ).
cnf(c_0_257,plain,
lhs_atom2,
inference(split_conjunct,[status(thm)],[c_0_133]) ).
cnf(c_0_258,plain,
lhs_atom1,
inference(split_conjunct,[status(thm)],[c_0_134]) ).
cnf(c_0_259,plain,
( lhs_atom4(X1,X2,X3)
| X1 = X4
| ~ mem(X4,arr(X3,X2))
| ap(X1,esk1_4(X1,X2,X3,X4)) != ap(X4,esk1_4(X1,X2,X3,X4)) ),
c_0_135,
[final] ).
cnf(c_0_260,plain,
( lhs_atom4(X1,X2,X3)
| X1 = X4
| mem(esk1_4(X1,X2,X3,X4),X3)
| ~ mem(X4,arr(X3,X2)) ),
c_0_136,
[final] ).
cnf(c_0_261,plain,
( p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X3),X4))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X1),X4),X3))
| lhs_atom9(X2)
| ~ mem(X3,arr(X1,bool))
| ~ mem(X4,arr(X2,bool))
| ~ ne(X1) ),
c_0_137,
[final] ).
cnf(c_0_262,plain,
( mem(c_2Ecardinal_2Ecardleq(X1,X2),arr(arr(X1,bool),arr(arr(X2,bool),bool)))
| lhs_atom9(X1)
| ~ ne(X2) ),
c_0_138,
[final] ).
cnf(c_0_263,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,esk2_2(X1,X2))) ),
c_0_139,
[final] ).
cnf(c_0_264,plain,
( lhs_atom3(X1)
| X2 = X3
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| ~ p(ap(ap(c_2Emin_2E_3D(X1),X2),X3)) ),
c_0_140,
[final] ).
cnf(c_0_265,plain,
( lhs_atom3(X1)
| p(ap(X2,X3))
| ~ mem(X2,arr(X1,bool))
| ~ mem(X3,X1)
| ~ p(ap(c_2Ebool_2E_21(X1),X2)) ),
c_0_141,
[final] ).
cnf(c_0_266,plain,
( lhs_atom3(X1)
| p(ap(ap(c_2Emin_2E_3D(X1),X2),X3))
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| X2 != X3 ),
c_0_142,
[final] ).
cnf(c_0_267,plain,
( lhs_atom22(X1)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X1)
| ~ p(X2) ),
c_0_143,
[final] ).
cnf(c_0_268,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X1)
| ~ p(X3) ),
c_0_144,
[final] ).
cnf(c_0_269,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
c_0_145,
[final] ).
cnf(c_0_270,plain,
( lhs_atom22(X1)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X1)
| ~ p(X2) ),
c_0_146,
[final] ).
cnf(c_0_271,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) ),
c_0_147,
[final] ).
cnf(c_0_272,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X3)
| ~ p(X2) ),
c_0_148,
[final] ).
cnf(c_0_273,plain,
( lhs_atom22(X1)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X1)
| ~ p(X2) ),
c_0_149,
[final] ).
cnf(c_0_274,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X1)
| ~ p(X3) ),
c_0_150,
[final] ).
cnf(c_0_275,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X3)
| ~ p(X2) ),
c_0_151,
[final] ).
cnf(c_0_276,plain,
( lhs_atom5(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2)) ),
c_0_152,
[final] ).
cnf(c_0_277,plain,
( lhs_atom5(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2)) ),
c_0_153,
[final] ).
cnf(c_0_278,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1) ),
c_0_154,
[final] ).
cnf(c_0_279,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2) ),
c_0_155,
[final] ).
cnf(c_0_280,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3) ),
c_0_156,
[final] ).
cnf(c_0_281,plain,
( lhs_atom5(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
c_0_157,
[final] ).
cnf(c_0_282,plain,
( lhs_atom5(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
c_0_158,
[final] ).
cnf(c_0_283,plain,
( lhs_atom3(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| mem(esk2_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool)) ),
c_0_159,
[final] ).
cnf(c_0_284,plain,
( lhs_atom22(X1)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
c_0_160,
[final] ).
cnf(c_0_285,plain,
( mem(ap(X1,X2),X3)
| lhs_atom4(X1,X3,X4)
| ~ mem(X2,X4) ),
c_0_161,
[final] ).
cnf(c_0_286,plain,
( lhs_atom22(X1)
| p(X3)
| p(X2)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1) ),
c_0_162,
[final] ).
cnf(c_0_287,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X2) ),
c_0_163,
[final] ).
cnf(c_0_288,plain,
( lhs_atom22(X1)
| p(X1)
| p(X2)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X3) ),
c_0_164,
[final] ).
cnf(c_0_289,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
c_0_165,
[final] ).
cnf(c_0_290,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_166,
[final] ).
cnf(c_0_291,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_167,
[final] ).
cnf(c_0_292,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_168,
[final] ).
cnf(c_0_293,plain,
( lhs_atom5(X1)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| p(X1)
| ~ mem(X2,bool) ),
c_0_169,
[final] ).
cnf(c_0_294,plain,
( p(X1)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X3) ),
c_0_170,
[final] ).
cnf(c_0_295,plain,
( p(X2)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X3) ),
c_0_171,
[final] ).
cnf(c_0_296,plain,
( p(X3)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X2) ),
c_0_172,
[final] ).
cnf(c_0_297,plain,
( mem(c_2Emin_2E_3D(X1),arr(X1,arr(X1,bool)))
| lhs_atom9(X1) ),
c_0_173,
[final] ).
cnf(c_0_298,plain,
( mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool))
| lhs_atom9(X1) ),
c_0_174,
[final] ).
cnf(c_0_299,plain,
( lhs_atom22(X1)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
c_0_175,
[final] ).
cnf(c_0_300,plain,
( epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X2)
| ~ p(X3) ),
c_0_176,
[final] ).
cnf(c_0_301,plain,
( lhs_atom22(X1)
| p(X3)
| p(X2)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1) ),
c_0_177,
[final] ).
cnf(c_0_302,plain,
( lhs_atom22(X1)
| p(X1)
| p(X3)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X2) ),
c_0_178,
[final] ).
cnf(c_0_303,plain,
( lhs_atom22(X1)
| p(X1)
| p(X2)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X3) ),
c_0_179,
[final] ).
cnf(c_0_304,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| ~ p(X1)
| ~ p(X2) ),
c_0_180,
[final] ).
cnf(c_0_305,plain,
( epred1_3(X1,X2,X3)
| p(X1)
| ~ p(X1)
| ~ p(X2) ),
c_0_181,
[final] ).
cnf(c_0_306,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| ~ p(X1)
| ~ p(X3) ),
c_0_182,
[final] ).
cnf(c_0_307,plain,
( epred1_3(X1,X2,X3)
| p(X1)
| ~ p(X1)
| ~ p(X3) ),
c_0_183,
[final] ).
cnf(c_0_308,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| ~ p(X2)
| ~ p(X3) ),
c_0_184,
[final] ).
cnf(c_0_309,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| ~ p(X2)
| ~ p(X3) ),
c_0_185,
[final] ).
cnf(c_0_310,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X2)
| ~ p(X1) ),
c_0_186,
[final] ).
cnf(c_0_311,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X1) ),
c_0_187,
[final] ).
cnf(c_0_312,plain,
( epred1_3(X1,X2,X3)
| p(X1)
| p(X2)
| ~ p(X1) ),
c_0_188,
[final] ).
cnf(c_0_313,plain,
( epred1_3(X1,X2,X3)
| p(X1)
| p(X1)
| ~ p(X1) ),
c_0_189,
[final] ).
cnf(c_0_314,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X2)
| ~ p(X2) ),
c_0_190,
[final] ).
cnf(c_0_315,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X2) ),
c_0_191,
[final] ).
cnf(c_0_316,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| ~ p(X3) ),
c_0_192,
[final] ).
cnf(c_0_317,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X3) ),
c_0_193,
[final] ).
cnf(c_0_318,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X2)
| ~ p(X2) ),
c_0_194,
[final] ).
cnf(c_0_319,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| ~ p(X2) ),
c_0_195,
[final] ).
cnf(c_0_320,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| ~ p(X3) ),
c_0_196,
[final] ).
cnf(c_0_321,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| ~ p(X3) ),
c_0_197,
[final] ).
cnf(c_0_322,plain,
( lhs_atom9(X1)
| p(X2)
| mem(esk3_2(X1,X2),X1)
| ~ mem(X2,bool) ),
c_0_198,
[final] ).
cnf(c_0_323,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| p(X2) ),
c_0_199,
[final] ).
cnf(c_0_324,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| p(X1) ),
c_0_200,
[final] ).
cnf(c_0_325,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| p(X2) ),
c_0_201,
[final] ).
cnf(c_0_326,plain,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| p(X1) ),
c_0_202,
[final] ).
cnf(c_0_327,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| p(X2) ),
c_0_203,
[final] ).
cnf(c_0_328,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| p(X1) ),
c_0_204,
[final] ).
cnf(c_0_329,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| p(X2) ),
c_0_205,
[final] ).
cnf(c_0_330,plain,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| p(X1) ),
c_0_206,
[final] ).
cnf(c_0_331,plain,
( lhs_atom9(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,X1)
| ~ p(X2) ),
c_0_207,
[final] ).
cnf(c_0_332,plain,
( ap(k(X1,X2),X3) = X2
| lhs_atom6(X3,X1) ),
c_0_208,
[final] ).
cnf(c_0_333,plain,
( lhs_atom5(X1)
| ~ p(X1)
| ~ p(ap(c_2Ebool_2E_7E,X1)) ),
c_0_209,
[final] ).
cnf(c_0_334,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X1)
| ~ p(X2) ),
c_0_210,
[final] ).
cnf(c_0_335,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1)
| ~ p(X2) ),
c_0_211,
[final] ).
cnf(c_0_336,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2)
| ~ p(X1) ),
c_0_212,
[final] ).
cnf(c_0_337,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2)
| ~ p(X1) ),
c_0_213,
[final] ).
cnf(c_0_338,plain,
( lhs_atom22(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X2)
| ~ p(X1) ),
c_0_214,
[final] ).
cnf(c_0_339,plain,
( lhs_atom22(X1)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X2)
| ~ p(X1) ),
c_0_215,
[final] ).
cnf(c_0_340,plain,
( lhs_atom22(X1)
| p(X2)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_216,
[final] ).
cnf(c_0_341,plain,
( lhs_atom22(X1)
| p(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_217,
[final] ).
cnf(c_0_342,plain,
( lhs_atom22(X1)
| p(X2)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_218,
[final] ).
cnf(c_0_343,plain,
( lhs_atom22(X1)
| p(X1)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_219,
[final] ).
cnf(c_0_344,plain,
( lhs_atom22(X1)
| p(X2)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_220,
[final] ).
cnf(c_0_345,plain,
( lhs_atom22(X1)
| p(X1)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_221,
[final] ).
cnf(c_0_346,plain,
( lhs_atom21(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2) ),
c_0_222,
[final] ).
cnf(c_0_347,plain,
( lhs_atom21(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2) ),
c_0_223,
[final] ).
cnf(c_0_348,plain,
( ne(arr(X1,X2))
| lhs_atom3(X1)
| ~ ne(X2) ),
c_0_224,
[final] ).
cnf(c_0_349,plain,
( lhs_atom5(X1)
| X1 = X2
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
c_0_225,
[final] ).
cnf(c_0_350,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_226,
[final] ).
cnf(c_0_351,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_227,
[final] ).
cnf(c_0_352,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_228,
[final] ).
cnf(c_0_353,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_229,
[final] ).
cnf(c_0_354,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
c_0_230,
[final] ).
cnf(c_0_355,plain,
( lhs_atom21(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_231,
[final] ).
cnf(c_0_356,plain,
( lhs_atom9(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
c_0_232,
[final] ).
cnf(c_0_357,plain,
( lhs_atom5(X1)
| p(ap(c_2Ebool_2E_7E,X1))
| p(X1) ),
c_0_233,
[final] ).
cnf(c_0_358,plain,
( lhs_atom5(X1)
| X1 = X2
| p(X2)
| p(X1)
| ~ mem(X2,bool) ),
c_0_234,
[final] ).
cnf(c_0_359,plain,
( ap(i(X1),X2) = X2
| lhs_atom6(X2,X1) ),
c_0_235,
[final] ).
cnf(c_0_360,plain,
( X1 = X1
| lhs_atom9(X2)
| ~ mem(X1,X2) ),
c_0_236,
[final] ).
cnf(c_0_361,plain,
$true,
c_0_237,
[final] ).
cnf(c_0_362,plain,
$true,
c_0_238,
[final] ).
cnf(c_0_363,plain,
$true,
c_0_239,
[final] ).
cnf(c_0_364,plain,
$true,
c_0_240,
[final] ).
cnf(c_0_365,plain,
$true,
c_0_241,
[final] ).
cnf(c_0_366,plain,
$true,
c_0_242,
[final] ).
cnf(c_0_367,plain,
lhs_atom19,
c_0_243,
[final] ).
cnf(c_0_368,plain,
lhs_atom16,
c_0_244,
[final] ).
cnf(c_0_369,plain,
$true,
c_0_245,
[final] ).
cnf(c_0_370,plain,
$true,
c_0_246,
[final] ).
cnf(c_0_371,plain,
$true,
c_0_247,
[final] ).
cnf(c_0_372,plain,
lhs_atom16,
c_0_248,
[final] ).
cnf(c_0_373,plain,
lhs_atom15,
c_0_249,
[final] ).
cnf(c_0_374,plain,
lhs_atom14,
c_0_250,
[final] ).
cnf(c_0_375,plain,
lhs_atom13,
c_0_251,
[final] ).
cnf(c_0_376,plain,
lhs_atom12,
c_0_252,
[final] ).
cnf(c_0_377,plain,
lhs_atom11,
c_0_253,
[final] ).
cnf(c_0_378,plain,
lhs_atom10,
c_0_254,
[final] ).
cnf(c_0_379,plain,
lhs_atom8,
c_0_255,
[final] ).
cnf(c_0_380,plain,
lhs_atom7,
c_0_256,
[final] ).
cnf(c_0_381,plain,
lhs_atom2,
c_0_257,
[final] ).
cnf(c_0_382,plain,
lhs_atom1,
c_0_258,
[final] ).
% End CNF derivation
cnf(c_0_259_0,axiom,
( ~ mem(X1,arr(X3,X2))
| X1 = X4
| ~ mem(X4,arr(X3,X2))
| ap(X1,sk1_esk1_4(X1,X2,X3,X4)) != ap(X4,sk1_esk1_4(X1,X2,X3,X4)) ),
inference(unfold_definition,[status(thm)],[c_0_259,def_lhs_atom4]) ).
cnf(c_0_260_0,axiom,
( ~ mem(X1,arr(X3,X2))
| X1 = X4
| mem(sk1_esk1_4(X1,X2,X3,X4),X3)
| ~ mem(X4,arr(X3,X2)) ),
inference(unfold_definition,[status(thm)],[c_0_260,def_lhs_atom4]) ).
cnf(c_0_261_0,axiom,
( ~ ne(X2)
| p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X3),X4))
| p(ap(ap(c_2Ecardinal_2Ecardleq(X2,X1),X4),X3))
| ~ mem(X3,arr(X1,bool))
| ~ mem(X4,arr(X2,bool))
| ~ ne(X1) ),
inference(unfold_definition,[status(thm)],[c_0_261,def_lhs_atom9]) ).
cnf(c_0_262_0,axiom,
( ~ ne(X1)
| mem(c_2Ecardinal_2Ecardleq(X1,X2),arr(arr(X1,bool),arr(arr(X2,bool),bool)))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_262,def_lhs_atom9]) ).
cnf(c_0_263_0,axiom,
( ~ ne(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| ~ mem(X2,arr(X1,bool))
| ~ p(ap(X2,sk1_esk2_2(X1,X2))) ),
inference(unfold_definition,[status(thm)],[c_0_263,def_lhs_atom3]) ).
cnf(c_0_264_0,axiom,
( ~ ne(X1)
| X2 = X3
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| ~ p(ap(ap(c_2Emin_2E_3D(X1),X2),X3)) ),
inference(unfold_definition,[status(thm)],[c_0_264,def_lhs_atom3]) ).
cnf(c_0_265_0,axiom,
( ~ ne(X1)
| p(ap(X2,X3))
| ~ mem(X2,arr(X1,bool))
| ~ mem(X3,X1)
| ~ p(ap(c_2Ebool_2E_21(X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_265,def_lhs_atom3]) ).
cnf(c_0_266_0,axiom,
( ~ ne(X1)
| p(ap(ap(c_2Emin_2E_3D(X1),X2),X3))
| ~ mem(X2,X1)
| ~ mem(X3,X1)
| X2 != X3 ),
inference(unfold_definition,[status(thm)],[c_0_266,def_lhs_atom3]) ).
cnf(c_0_267_0,axiom,
( ~ mem(X1,bool)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_267,def_lhs_atom22]) ).
cnf(c_0_268_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X1)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_268,def_lhs_atom22]) ).
cnf(c_0_269_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_269,def_lhs_atom22]) ).
cnf(c_0_270_0,axiom,
( ~ mem(X1,bool)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_270,def_lhs_atom22]) ).
cnf(c_0_271_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X1)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_271,def_lhs_atom22]) ).
cnf(c_0_272_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2)
| ~ p(X3)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_272,def_lhs_atom22]) ).
cnf(c_0_273_0,axiom,
( ~ mem(X1,bool)
| p(X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_273,def_lhs_atom22]) ).
cnf(c_0_274_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X1)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_274,def_lhs_atom22]) ).
cnf(c_0_275_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3)
| ~ p(X3)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_275,def_lhs_atom22]) ).
cnf(c_0_276_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_276,def_lhs_atom5]) ).
cnf(c_0_277_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_277,def_lhs_atom5]) ).
cnf(c_0_278_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_278,def_lhs_atom22]) ).
cnf(c_0_279_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_279,def_lhs_atom22]) ).
cnf(c_0_280_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X3)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ epred1_3(X1,X2,X3)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_280,def_lhs_atom22]) ).
cnf(c_0_281_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_281,def_lhs_atom5]) ).
cnf(c_0_282_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2)) ),
inference(unfold_definition,[status(thm)],[c_0_282,def_lhs_atom5]) ).
cnf(c_0_283_0,axiom,
( ~ ne(X1)
| p(ap(c_2Ebool_2E_21(X1),X2))
| mem(sk1_esk2_2(X1,X2),X1)
| ~ mem(X2,arr(X1,bool)) ),
inference(unfold_definition,[status(thm)],[c_0_283,def_lhs_atom3]) ).
cnf(c_0_284_0,axiom,
( ~ mem(X1,bool)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_284,def_lhs_atom22]) ).
cnf(c_0_285_0,axiom,
( ~ mem(X1,arr(X4,X3))
| mem(ap(X1,X2),X3)
| ~ mem(X2,X4) ),
inference(unfold_definition,[status(thm)],[c_0_285,def_lhs_atom4]) ).
cnf(c_0_286_0,axiom,
( ~ mem(X1,bool)
| p(X3)
| p(X2)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_286,def_lhs_atom22]) ).
cnf(c_0_287_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X3)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_287,def_lhs_atom22]) ).
cnf(c_0_288_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X2)
| epred1_3(X1,X2,X3)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_288,def_lhs_atom22]) ).
cnf(c_0_289_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Ebool_2E_2F_5C,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_289,def_lhs_atom5]) ).
cnf(c_0_290_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_290,def_lhs_atom5]) ).
cnf(c_0_291_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Ebool_2E_5C_2F,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_291,def_lhs_atom5]) ).
cnf(c_0_292_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_292,def_lhs_atom5]) ).
cnf(c_0_293_0,axiom,
( ~ mem(X1,bool)
| p(ap(ap(c_2Emin_2E_3D_3D_3E,X1),X2))
| p(X1)
| ~ mem(X2,bool) ),
inference(unfold_definition,[status(thm)],[c_0_293,def_lhs_atom5]) ).
cnf(c_0_294_0,axiom,
( ~ epred1_3(X1,X2,X3)
| p(X1)
| ~ p(X2)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_294,def_epred1_3]) ).
cnf(c_0_295_0,axiom,
( ~ epred1_3(X1,X2,X3)
| p(X2)
| ~ p(X1)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_295,def_epred1_3]) ).
cnf(c_0_296_0,axiom,
( ~ epred1_3(X1,X2,X3)
| p(X3)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_296,def_epred1_3]) ).
cnf(c_0_297_0,axiom,
( ~ ne(X1)
| mem(c_2Emin_2E_3D(X1),arr(X1,arr(X1,bool))) ),
inference(unfold_definition,[status(thm)],[c_0_297,def_lhs_atom9]) ).
cnf(c_0_298_0,axiom,
( ~ ne(X1)
| mem(c_2Ebool_2E_21(X1),arr(arr(X1,bool),bool)) ),
inference(unfold_definition,[status(thm)],[c_0_298,def_lhs_atom9]) ).
cnf(c_0_299_0,axiom,
( ~ mem(X1,bool)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1)
| ~ p(X3)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_299,def_lhs_atom22]) ).
cnf(c_0_300_0,axiom,
( epred1_3(X1,X2,X3)
| ~ p(X1)
| ~ p(X2)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_300,def_epred1_3]) ).
cnf(c_0_301_0,axiom,
( ~ mem(X1,bool)
| p(X3)
| p(X2)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_301,def_lhs_atom22]) ).
cnf(c_0_302_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X3)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_302,def_lhs_atom22]) ).
cnf(c_0_303_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X2)
| p(X3)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ mem(X3,bool)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_303,def_lhs_atom22]) ).
cnf(c_0_304_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_304,def_epred1_3]) ).
cnf(c_0_305_0,axiom,
( epred1_3(X1,X2,X3)
| p(X1)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_305,def_epred1_3]) ).
cnf(c_0_306_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| ~ p(X1)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_306,def_epred1_3]) ).
cnf(c_0_307_0,axiom,
( epred1_3(X1,X2,X3)
| p(X1)
| ~ p(X1)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_307,def_epred1_3]) ).
cnf(c_0_308_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| ~ p(X2)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_308,def_epred1_3]) ).
cnf(c_0_309_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| ~ p(X2)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_309,def_epred1_3]) ).
cnf(c_0_310_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_310,def_epred1_3]) ).
cnf(c_0_311_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_311,def_epred1_3]) ).
cnf(c_0_312_0,axiom,
( epred1_3(X1,X2,X3)
| p(X1)
| p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_312,def_epred1_3]) ).
cnf(c_0_313_0,axiom,
( epred1_3(X1,X2,X3)
| p(X1)
| p(X1)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_313,def_epred1_3]) ).
cnf(c_0_314_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X2)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_314,def_epred1_3]) ).
cnf(c_0_315_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_315,def_epred1_3]) ).
cnf(c_0_316_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_316,def_epred1_3]) ).
cnf(c_0_317_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_317,def_epred1_3]) ).
cnf(c_0_318_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X2)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_318,def_epred1_3]) ).
cnf(c_0_319_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_319,def_epred1_3]) ).
cnf(c_0_320_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_320,def_epred1_3]) ).
cnf(c_0_321_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| ~ p(X3) ),
inference(unfold_definition,[status(thm)],[c_0_321,def_epred1_3]) ).
cnf(c_0_322_0,axiom,
( ~ ne(X1)
| p(X2)
| mem(sk1_esk3_2(X1,X2),X1)
| ~ mem(X2,bool) ),
inference(unfold_definition,[status(thm)],[c_0_322,def_lhs_atom9]) ).
cnf(c_0_323_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_323,def_epred1_3]) ).
cnf(c_0_324_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X3)
| p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_324,def_epred1_3]) ).
cnf(c_0_325_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_325,def_epred1_3]) ).
cnf(c_0_326_0,axiom,
( epred1_3(X1,X2,X3)
| p(X3)
| p(X1)
| p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_326,def_epred1_3]) ).
cnf(c_0_327_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_327,def_epred1_3]) ).
cnf(c_0_328_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X3)
| p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_328,def_epred1_3]) ).
cnf(c_0_329_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_329,def_epred1_3]) ).
cnf(c_0_330_0,axiom,
( epred1_3(X1,X2,X3)
| p(X2)
| p(X1)
| p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_330,def_epred1_3]) ).
cnf(c_0_331_0,axiom,
( ~ ne(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ mem(X3,X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_331,def_lhs_atom9]) ).
cnf(c_0_332_0,axiom,
( ~ mem(X3,X1)
| ap(k(X1,X2),X3) = X2 ),
inference(unfold_definition,[status(thm)],[c_0_332,def_lhs_atom6]) ).
cnf(c_0_333_0,axiom,
( ~ mem(X1,bool)
| ~ p(X1)
| ~ p(ap(c_2Ebool_2E_7E,X1)) ),
inference(unfold_definition,[status(thm)],[c_0_333,def_lhs_atom5]) ).
cnf(c_0_334_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_334,def_lhs_atom22]) ).
cnf(c_0_335_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_335,def_lhs_atom22]) ).
cnf(c_0_336_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_336,def_lhs_atom22]) ).
cnf(c_0_337_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_337,def_lhs_atom22]) ).
cnf(c_0_338_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_338,def_lhs_atom22]) ).
cnf(c_0_339_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_339,def_lhs_atom22]) ).
cnf(c_0_340_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_340,def_lhs_atom22]) ).
cnf(c_0_341_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_341,def_lhs_atom22]) ).
cnf(c_0_342_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_342,def_lhs_atom22]) ).
cnf(c_0_343_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_343,def_lhs_atom22]) ).
cnf(c_0_344_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_344,def_lhs_atom22]) ).
cnf(c_0_345_0,axiom,
( ~ mem(X1,bool)
| p(X1)
| p(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_345,def_lhs_atom22]) ).
cnf(c_0_346_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_346,def_lhs_atom21]) ).
cnf(c_0_347_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X1)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_347,def_lhs_atom21]) ).
cnf(c_0_348_0,axiom,
( ~ ne(X1)
| ne(arr(X1,X2))
| ~ ne(X2) ),
inference(unfold_definition,[status(thm)],[c_0_348,def_lhs_atom3]) ).
cnf(c_0_349_0,axiom,
( ~ mem(X1,bool)
| X1 = X2
| ~ mem(X2,bool)
| ~ p(X2)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_349,def_lhs_atom5]) ).
cnf(c_0_350_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_350,def_lhs_atom21]) ).
cnf(c_0_351_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_351,def_lhs_atom21]) ).
cnf(c_0_352_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_352,def_lhs_atom21]) ).
cnf(c_0_353_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_353,def_lhs_atom21]) ).
cnf(c_0_354_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_354,def_lhs_atom21]) ).
cnf(c_0_355_0,axiom,
( ~ mem(X1,bool)
| p(X2)
| p(X1)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_355,def_lhs_atom21]) ).
cnf(c_0_356_0,axiom,
( ~ ne(X1)
| p(X2)
| ~ mem(X2,bool)
| ~ p(X2) ),
inference(unfold_definition,[status(thm)],[c_0_356,def_lhs_atom9]) ).
cnf(c_0_357_0,axiom,
( ~ mem(X1,bool)
| p(ap(c_2Ebool_2E_7E,X1))
| p(X1) ),
inference(unfold_definition,[status(thm)],[c_0_357,def_lhs_atom5]) ).
cnf(c_0_358_0,axiom,
( ~ mem(X1,bool)
| X1 = X2
| p(X2)
| p(X1)
| ~ mem(X2,bool) ),
inference(unfold_definition,[status(thm)],[c_0_358,def_lhs_atom5]) ).
cnf(c_0_359_0,axiom,
( ~ mem(X2,X1)
| ap(i(X1),X2) = X2 ),
inference(unfold_definition,[status(thm)],[c_0_359,def_lhs_atom6]) ).
cnf(c_0_360_0,axiom,
( ~ ne(X2)
| X1 = X1
| ~ mem(X1,X2) ),
inference(unfold_definition,[status(thm)],[c_0_360,def_lhs_atom9]) ).
cnf(c_0_361_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_361,def_true]) ).
cnf(c_0_362_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_362,def_true]) ).
cnf(c_0_363_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_363,def_true]) ).
cnf(c_0_364_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_364,def_true]) ).
cnf(c_0_365_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_365,def_true]) ).
cnf(c_0_366_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_366,def_true]) ).
cnf(c_0_367_0,axiom,
~ $false,
inference(unfold_definition,[status(thm)],[c_0_367,def_lhs_atom19]) ).
cnf(c_0_368_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_368,def_lhs_atom16]) ).
cnf(c_0_369_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_369,def_true]) ).
cnf(c_0_370_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_370,def_true]) ).
cnf(c_0_371_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_371,def_true]) ).
cnf(c_0_372_0,axiom,
$true,
inference(unfold_definition,[status(thm)],[c_0_372,def_lhs_atom16]) ).
cnf(c_0_373_0,axiom,
mem(c_2Ebool_2E_7E,arr(bool,bool)),
inference(unfold_definition,[status(thm)],[c_0_373,def_lhs_atom15]) ).
cnf(c_0_374_0,axiom,
mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))),
inference(unfold_definition,[status(thm)],[c_0_374,def_lhs_atom14]) ).
cnf(c_0_375_0,axiom,
mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))),
inference(unfold_definition,[status(thm)],[c_0_375,def_lhs_atom13]) ).
cnf(c_0_376_0,axiom,
mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))),
inference(unfold_definition,[status(thm)],[c_0_376,def_lhs_atom12]) ).
cnf(c_0_377_0,axiom,
~ p(c_2Ebool_2EF),
inference(unfold_definition,[status(thm)],[c_0_377,def_lhs_atom11]) ).
cnf(c_0_378_0,axiom,
mem(c_2Ebool_2EF,bool),
inference(unfold_definition,[status(thm)],[c_0_378,def_lhs_atom10]) ).
cnf(c_0_379_0,axiom,
p(c_2Ebool_2ET),
inference(unfold_definition,[status(thm)],[c_0_379,def_lhs_atom8]) ).
cnf(c_0_380_0,axiom,
mem(c_2Ebool_2ET,bool),
inference(unfold_definition,[status(thm)],[c_0_380,def_lhs_atom7]) ).
cnf(c_0_381_0,axiom,
ne(ind),
inference(unfold_definition,[status(thm)],[c_0_381,def_lhs_atom2]) ).
cnf(c_0_382_0,axiom,
ne(bool),
inference(unfold_definition,[status(thm)],[c_0_382,def_lhs_atom1]) ).
% Orienting (remaining) axiom formulas using strategy ClausalAll
% CNF of (remaining) axioms:
% Start CNF derivation
% End CNF derivation
% Generating one_way clauses for all literals in the CNF.
% CNF of non-axioms
% Start CNF derivation
fof(c_0_0_001,conjecture,
! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ! [X4] :
( mem(X4,arr(X2,bool))
=> ( ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X3),X4))
<=> ~ p(ap(ap(c_2Ecardinal_2Ecardleq(X1,X2),X3),X4)) ) ) ) ) ),
file('<stdin>',conj_thm_2Ecardinal_2ECARD__NOT__LE) ).
fof(c_0_1_002,negated_conjecture,
~ ! [X1] :
( ne(X1)
=> ! [X2] :
( ne(X2)
=> ! [X3] :
( mem(X3,arr(X1,bool))
=> ! [X4] : $true ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[c_0_0])]) ).
fof(c_0_2_003,negated_conjecture,
( ne(esk1_0)
& ne(esk2_0)
& mem(esk3_0,arr(esk1_0,bool))
& ~ $true ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])]) ).
cnf(c_0_3_004,negated_conjecture,
mem(esk3_0,arr(esk1_0,bool)),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4_005,negated_conjecture,
ne(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5_006,negated_conjecture,
ne(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6_007,negated_conjecture,
$false,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_7_008,negated_conjecture,
mem(esk3_0,arr(esk1_0,bool)),
c_0_3,
[final] ).
cnf(c_0_8_009,negated_conjecture,
ne(esk1_0),
c_0_4,
[final] ).
cnf(c_0_9_010,negated_conjecture,
ne(esk2_0),
c_0_5,
[final] ).
cnf(c_0_10_011,negated_conjecture,
$false,
c_0_6,
[final] ).
% End CNF derivation
%-------------------------------------------------------------
% Proof by iprover
cnf(c_124,negated_conjecture,
$false,
file('/export/starexec/sandbox/tmp/iprover_modulo_afeafd.p',c_0_10) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ITP010+2 : TPTP v8.1.0. Bugfixed v7.5.0.
% 0.06/0.13 % Command : iprover_modulo %s %d
% 0.14/0.34 % Computer : n019.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Fri Jun 3 03:11:40 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % Running in mono-core mode
% 0.21/0.42 % Orienting using strategy Equiv(ClausalAll)
% 0.21/0.42 % FOF problem with conjecture
% 0.21/0.42 % Executing iprover_moduloopt --modulo true --schedule none --sub_typing false --res_to_prop_solver none --res_prop_simpl_given false --res_lit_sel kbo_max --large_theory_mode false --res_time_limit 1000 --res_orphan_elimination false --prep_sem_filter none --prep_unflatten false --comb_res_mult 1000 --comb_inst_mult 300 --clausifier .//eprover --clausifier_options "--tstp-format " --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_03febf.s --tptp_safe_out true --time_out_real 150 /export/starexec/sandbox/tmp/iprover_modulo_afeafd.p | tee /export/starexec/sandbox/tmp/iprover_modulo_out_45e508 | grep -v "SZS"
% 0.21/0.45
% 0.21/0.45 %---------------- iProver v2.5 (CASC-J8 2016) ----------------%
% 0.21/0.45
% 0.21/0.45 %
% 0.21/0.45 % ------ iProver source info
% 0.21/0.45
% 0.21/0.45 % git: sha1: 57accf6c58032223c7708532cf852a99fa48c1b3
% 0.21/0.45 % git: non_committed_changes: true
% 0.21/0.45 % git: last_make_outside_of_git: true
% 0.21/0.45
% 0.21/0.45 %
% 0.21/0.45 % ------ Input Options
% 0.21/0.45
% 0.21/0.45 % --out_options all
% 0.21/0.45 % --tptp_safe_out true
% 0.21/0.45 % --problem_path ""
% 0.21/0.45 % --include_path ""
% 0.21/0.45 % --clausifier .//eprover
% 0.21/0.45 % --clausifier_options --tstp-format
% 0.21/0.45 % --stdin false
% 0.21/0.45 % --dbg_backtrace false
% 0.21/0.45 % --dbg_dump_prop_clauses false
% 0.21/0.45 % --dbg_dump_prop_clauses_file -
% 0.21/0.45 % --dbg_out_stat false
% 0.21/0.45
% 0.21/0.45 % ------ General Options
% 0.21/0.45
% 0.21/0.45 % --fof false
% 0.21/0.45 % --time_out_real 150.
% 0.21/0.45 % --time_out_prep_mult 0.2
% 0.21/0.45 % --time_out_virtual -1.
% 0.21/0.45 % --schedule none
% 0.21/0.45 % --ground_splitting input
% 0.21/0.45 % --splitting_nvd 16
% 0.21/0.45 % --non_eq_to_eq false
% 0.21/0.45 % --prep_gs_sim true
% 0.21/0.45 % --prep_unflatten false
% 0.21/0.45 % --prep_res_sim true
% 0.21/0.45 % --prep_upred true
% 0.21/0.45 % --res_sim_input true
% 0.21/0.45 % --clause_weak_htbl true
% 0.21/0.45 % --gc_record_bc_elim false
% 0.21/0.45 % --symbol_type_check false
% 0.21/0.45 % --clausify_out false
% 0.21/0.45 % --large_theory_mode false
% 0.21/0.45 % --prep_sem_filter none
% 0.21/0.45 % --prep_sem_filter_out false
% 0.21/0.45 % --preprocessed_out false
% 0.21/0.45 % --sub_typing false
% 0.21/0.45 % --brand_transform false
% 0.21/0.45 % --pure_diseq_elim true
% 0.21/0.45 % --min_unsat_core false
% 0.21/0.45 % --pred_elim true
% 0.21/0.45 % --add_important_lit false
% 0.21/0.45 % --soft_assumptions false
% 0.21/0.45 % --reset_solvers false
% 0.21/0.45 % --bc_imp_inh []
% 0.21/0.45 % --conj_cone_tolerance 1.5
% 0.21/0.45 % --prolific_symb_bound 500
% 0.21/0.45 % --lt_threshold 2000
% 0.21/0.45
% 0.21/0.45 % ------ SAT Options
% 0.21/0.45
% 0.21/0.45 % --sat_mode false
% 0.21/0.45 % --sat_fm_restart_options ""
% 0.21/0.45 % --sat_gr_def false
% 0.21/0.45 % --sat_epr_types true
% 0.21/0.45 % --sat_non_cyclic_types false
% 0.21/0.45 % --sat_finite_models false
% 0.21/0.45 % --sat_fm_lemmas false
% 0.21/0.45 % --sat_fm_prep false
% 0.21/0.45 % --sat_fm_uc_incr true
% 0.21/0.45 % --sat_out_model small
% 0.21/0.45 % --sat_out_clauses false
% 0.21/0.45
% 0.21/0.45 % ------ QBF Options
% 0.21/0.45
% 0.21/0.45 % --qbf_mode false
% 0.21/0.45 % --qbf_elim_univ true
% 0.21/0.45 % --qbf_sk_in true
% 0.21/0.45 % --qbf_pred_elim true
% 0.21/0.45 % --qbf_split 32
% 0.21/0.45
% 0.21/0.45 % ------ BMC1 Options
% 0.21/0.45
% 0.21/0.45 % --bmc1_incremental false
% 0.21/0.45 % --bmc1_axioms reachable_all
% 0.21/0.45 % --bmc1_min_bound 0
% 0.21/0.45 % --bmc1_max_bound -1
% 0.21/0.45 % --bmc1_max_bound_default -1
% 0.21/0.45 % --bmc1_symbol_reachability true
% 0.21/0.45 % --bmc1_property_lemmas false
% 0.21/0.45 % --bmc1_k_induction false
% 0.21/0.45 % --bmc1_non_equiv_states false
% 0.21/0.45 % --bmc1_deadlock false
% 0.21/0.45 % --bmc1_ucm false
% 0.21/0.45 % --bmc1_add_unsat_core none
% 0.21/0.45 % --bmc1_unsat_core_children false
% 0.21/0.45 % --bmc1_unsat_core_extrapolate_axioms false
% 0.21/0.45 % --bmc1_out_stat full
% 0.21/0.45 % --bmc1_ground_init false
% 0.21/0.45 % --bmc1_pre_inst_next_state false
% 0.21/0.45 % --bmc1_pre_inst_state false
% 0.21/0.45 % --bmc1_pre_inst_reach_state false
% 0.21/0.45 % --bmc1_out_unsat_core false
% 0.21/0.45 % --bmc1_aig_witness_out false
% 0.21/0.45 % --bmc1_verbose false
% 0.21/0.45 % --bmc1_dump_clauses_tptp false
% 0.21/0.45 % --bmc1_dump_unsat_core_tptp false
% 0.21/0.45 % --bmc1_dump_file -
% 0.21/0.45 % --bmc1_ucm_expand_uc_limit 128
% 0.21/0.45 % --bmc1_ucm_n_expand_iterations 6
% 0.21/0.45 % --bmc1_ucm_extend_mode 1
% 0.21/0.45 % --bmc1_ucm_init_mode 2
% 0.21/0.45 % --bmc1_ucm_cone_mode none
% 0.21/0.45 % --bmc1_ucm_reduced_relation_type 0
% 0.21/0.45 % --bmc1_ucm_relax_model 4
% 0.21/0.45 % --bmc1_ucm_full_tr_after_sat true
% 0.21/0.45 % --bmc1_ucm_expand_neg_assumptions false
% 0.21/0.45 % --bmc1_ucm_layered_model none
% 0.21/0.45 % --bmc1_ucm_max_lemma_size 10
% 0.21/0.45
% 0.21/0.45 % ------ AIG Options
% 0.21/0.45
% 0.21/0.45 % --aig_mode false
% 0.21/0.45
% 0.21/0.45 % ------ Instantiation Options
% 0.21/0.45
% 0.21/0.45 % --instantiation_flag true
% 0.21/0.45 % --inst_lit_sel [+prop;+sign;+ground;-num_var;-num_symb]
% 0.21/0.45 % --inst_solver_per_active 750
% 0.21/0.45 % --inst_solver_calls_frac 0.5
% 0.21/0.45 % --inst_passive_queue_type priority_queues
% 0.21/0.45 % --inst_passive_queues [[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]
% 0.21/0.45 % --inst_passive_queues_freq [25;2]
% 0.21/0.45 % --inst_dismatching true
% 0.21/0.45 % --inst_eager_unprocessed_to_passive true
% 0.21/0.45 % --inst_prop_sim_given true
% 0.21/0.45 % --inst_prop_sim_new false
% 0.21/0.45 % --inst_orphan_elimination true
% 0.21/0.45 % --inst_learning_loop_flag true
% 0.21/0.45 % --inst_learning_start 3000
% 0.21/0.45 % --inst_learning_factor 2
% 0.21/0.45 % --inst_start_prop_sim_after_learn 3
% 0.21/0.45 % --inst_sel_renew solver
% 0.21/0.45 % --inst_lit_activity_flag true
% 0.21/0.45 % --inst_out_proof true
% 0.21/0.45
% 0.21/0.45 % ------ Resolution Options
% 0.21/0.45
% 0.21/0.45 % --resolution_flag true
% 0.21/0.45 % --res_lit_sel kbo_max
% 0.21/0.45 % --res_to_prop_solver none
% 0.21/0.45 % --res_prop_simpl_new false
% 0.21/0.45 % --res_prop_simpl_given false
% 0.21/0.45 % --res_passive_queue_type priority_queues
% 0.21/0.45 % --res_passive_queues [[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]
% 0.21/0.45 % --res_passive_queues_freq [15;5]
% 0.21/0.45 % --res_forward_subs full
% 0.21/0.45 % --res_backward_subs full
% 0.21/0.45 % --res_forward_subs_resolution true
% 0.21/0.45 % --res_backward_subs_resolution true
% 0.21/0.45 % --res_orphan_elimination false
% 0.21/0.45 % --res_time_limit 1000.
% 0.21/0.45 % --res_out_proof true
% 0.21/0.45 % --proof_out_file /export/starexec/sandbox/tmp/iprover_proof_03febf.s
% 0.21/0.45 % --modulo true
% 0.21/0.45
% 0.21/0.45 % ------ Combination Options
% 0.21/0.45
% 0.21/0.45 % --comb_res_mult 1000
% 0.21/0.45 % --comb_inst_mult 300
% 0.21/0.45 % ------
% 0.21/0.45
% 0.21/0.45 % ------ Parsing...%
% 0.21/0.45
% 0.21/0.45
% 0.21/0.45 % Resolution empty clause
% 0.21/0.45
% 0.21/0.45 % ------ Statistics
% 0.21/0.45
% 0.21/0.45 % ------ General
% 0.21/0.45
% 0.21/0.45 % num_of_input_clauses: 125
% 0.21/0.45 % num_of_input_neg_conjectures: 1
% 0.21/0.45 % num_of_splits: 0
% 0.21/0.45 % num_of_split_atoms: 0
% 0.21/0.45 % num_of_sem_filtered_clauses: 0
% 0.21/0.45 % num_of_subtypes: 0
% 0.21/0.45 % monotx_restored_types: 0
% 0.21/0.45 % sat_num_of_epr_types: 0
% 0.21/0.45 % sat_num_of_non_cyclic_types: 0
% 0.21/0.45 % sat_guarded_non_collapsed_types: 0
% 0.21/0.45 % is_epr: 0
% 0.21/0.45 % is_horn: 0
% 0.21/0.45 % has_eq: 0
% 0.21/0.45 % num_pure_diseq_elim: 0
% 0.21/0.45 % simp_replaced_by: 0
% 0.21/0.45 % res_preprocessed: 0
% 0.21/0.45 % prep_upred: 0
% 0.21/0.45 % prep_unflattend: 0
% 0.21/0.45 % pred_elim_cands: 0
% 0.21/0.45 % pred_elim: 0
% 0.21/0.45 % pred_elim_cl: 0
% 0.21/0.45 % pred_elim_cycles: 0
% 0.21/0.45 % forced_gc_time: 0
% 0.21/0.45 % gc_basic_clause_elim: 0
% 0.21/0.45 % parsing_time: 0.
% 0.21/0.45 % sem_filter_time: 0.
% 0.21/0.45 % pred_elim_time: 0.
% 0.21/0.45 % out_proof_time: 0.
% 0.21/0.45 % monotx_time: 0.
% 0.21/0.45 % subtype_inf_time: 0.
% 0.21/0.45 % unif_index_cands_time: 0.
% 0.21/0.45 % unif_index_add_time: 0.
% 0.21/0.45 % total_time: 0.024
% 0.21/0.45 % num_of_symbols: 47
% 0.21/0.45 % num_of_terms: 228
% 0.21/0.45
% 0.21/0.45 % ------ Propositional Solver
% 0.21/0.45
% 0.21/0.45 % prop_solver_calls: 0
% 0.21/0.45 % prop_fast_solver_calls: 0
% 0.21/0.45 % prop_num_of_clauses: 0
% 0.21/0.45 % prop_preprocess_simplified: 0
% 0.21/0.45 % prop_fo_subsumed: 0
% 0.21/0.45 % prop_solver_time: 0.
% 0.21/0.45 % prop_fast_solver_time: 0.
% 0.21/0.45 % prop_unsat_core_time: 0.
% 0.21/0.45
% 0.21/0.45 % ------ QBF
% 0.21/0.45
% 0.21/0.45 % qbf_q_res: 0
% 0.21/0.45 % qbf_num_tautologies: 0
% 0.21/0.45 % qbf_prep_cycles: 0
% 0.21/0.45
% 0.21/0.45 % ------ BMC1
% 0.21/0.45
% 0.21/0.45 % bmc1_current_bound: -1
% 0.21/0.45 % bmc1_last_solved_bound: -1
% 0.21/0.45 % bmc1_unsat_core_size: -1
% 0.21/0.45 % bmc1_unsat_core_parents_size: -1
% 0.21/0.45 % bmc1_merge_next_fun: 0
% 0.21/0.45 % bmc1_unsat_core_clauses_time: 0.
% 0.21/0.45
% 0.21/0.45 % ------ Instantiation
% 0.21/0.45
% 0.21/0.45 % inst_num_of_clauses: undef
% 0.21/0.45 % inst_num_in_passive: undef
% 0.21/0.45 % inst_num_in_active: 0
% 0.21/0.45 % inst_num_in_unprocessed: 0
% 0.21/0.45 % inst_num_of_loops: 0
% 0.21/0.45 % inst_num_of_learning_restarts: 0
% 0.21/0.45 % inst_num_moves_active_passive: 0
% 0.21/0.45 % inst_lit_activity: 0
% 0.21/0.45 % inst_lit_activity_moves: 0
% 0.21/0.45 % inst_num_tautologies: 0
% 0.21/0.45 % inst_num_prop_implied: 0
% 0.21/0.45 % inst_num_existing_simplified: 0
% 0.21/0.45 % inst_num_eq_res_simplified: 0
% 0.21/0.45 % inst_num_child_elim: 0
% 0.21/0.45 % inst_num_of_dismatching_blockings: 0
% 0.21/0.45 % inst_num_of_non_proper_insts: 0
% 0.21/0.45 % inst_num_of_duplicates: 0
% 0.21/0.45 % inst_inst_num_from_inst_to_res: 0
% 0.21/0.45 % inst_dismatching_checking_time: 0.
% 0.21/0.45
% 0.21/0.45 % ------ Resolution
% 0.21/0.45
% 0.21/0.45 % res_num_of_clauses: undef
% 0.21/0.45 % res_num_in_passive: undef
% 0.21/0.45 % res_num_in_active: 0
% 0.21/0.45 % res_num_of_loops: 0
% 0.21/0.45 % res_forward_subset_subsumed: 0
% 0.21/0.45 % res_backward_subset_subsumed: 0
% 0.21/0.45 % res_forward_subsumed: 0
% 0.21/0.45 % res_backward_subsumed: 0
% 0.21/0.45 % res_forward_subsumption_resolution: 0
% 0.21/0.45 % res_backward_subsumption_resolution: 0
% 0.21/0.45 % res_clause_to_clause_subsumption: 0
% 0.21/0.45 % res_orphan_elimination: 0
% 0.21/0.45 % res_tautology_del: 0
% 0.21/0.45 % res_num_eq_res_simplified: 0
% 0.21/0.45 % res_num_sel_changes: 0
% 0.21/0.45 % res_moves_from_active_to_pass: 0
% 0.21/0.45
% 0.21/0.46 % Status Unsatisfiable
% 0.21/0.46 % SZS status Theorem
% 0.21/0.46 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------