TSTP Solution File: ITP011+2 by Beagle---0.9.51
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%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : ITP011+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n007.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 : 300s
% DateTime : Tue Aug 22 10:43:10 EDT 2023
% Result : Theorem 105.32s 81.75s
% Output : CNFRefutation 105.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 55
% Syntax : Number of formulae : 577 ( 253 unt; 38 typ; 0 def)
% Number of atoms : 1343 ( 222 equ)
% Maximal formula atoms : 57 ( 2 avg)
% Number of connectives : 1551 ( 747 ~; 709 |; 28 &)
% ( 12 <=>; 55 =>; 0 <=; 0 <~>)
% Maximal formula depth : 33 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 47 ( 26 >; 21 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 35 ( 35 usr; 12 con; 0-5 aty)
% Number of variables : 464 (; 461 !; 3 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ mem > p > ne > k > c_2Eoption_2Eoption__CASE > c_2Eoption_2EOPTREL > c_2Eoption_2EOPTION__MAP > arr > ap > #nlpp > ty_2Eoption_2Eoption > i > c_2Eoption_2ETHE > c_2Eoption_2ESOME > c_2Eoption_2EOPTION__JOIN > c_2Eoption_2ENONE > c_2Eoption_2EIS__SOME > c_2Eoption_2EIS__NONE > c_2Emin_2E_3D > c_2Ebool_2E_3F > c_2Ebool_2E_21 > ind > c_2Emin_2E_3D_3D_3E > c_2Ebool_2E_7E > c_2Ebool_2E_5C_2F > c_2Ebool_2E_2F_5C > c_2Ebool_2ET > c_2Ebool_2EF > bool > #skF_6 > #skF_7 > #skF_5 > #skF_3 > #skF_10 > #skF_9 > #skF_8 > #skF_2 > #skF_1 > #skF_4
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(arr,type,
arr: ( $i * $i ) > $i ).
tff(ne,type,
ne: $i > $o ).
tff(c_2Ebool_2EF,type,
c_2Ebool_2EF: $i ).
tff(c_2Eoption_2EOPTREL,type,
c_2Eoption_2EOPTREL: ( $i * $i ) > $i ).
tff(i,type,
i: $i > $i ).
tff(c_2Ebool_2E_21,type,
c_2Ebool_2E_21: $i > $i ).
tff(ty_2Eoption_2Eoption,type,
ty_2Eoption_2Eoption: $i > $i ).
tff(c_2Eoption_2EIS__NONE,type,
c_2Eoption_2EIS__NONE: $i > $i ).
tff(bool,type,
bool: $i ).
tff('#skF_6',type,
'#skF_6': ( $i * $i * $i * $i * $i ) > $i ).
tff(mem,type,
mem: ( $i * $i ) > $o ).
tff('#skF_7',type,
'#skF_7': $i ).
tff(ap,type,
ap: ( $i * $i ) > $i ).
tff('#skF_5',type,
'#skF_5': ( $i * $i * $i * $i * $i ) > $i ).
tff('#skF_3',type,
'#skF_3': ( $i * $i ) > $i ).
tff(c_2Eoption_2EIS__SOME,type,
c_2Eoption_2EIS__SOME: $i > $i ).
tff('#skF_10',type,
'#skF_10': $i ).
tff(p,type,
p: $i > $o ).
tff(ind,type,
ind: $i ).
tff(c_2Eoption_2Eoption__CASE,type,
c_2Eoption_2Eoption__CASE: ( $i * $i ) > $i ).
tff(c_2Ebool_2E_3F,type,
c_2Ebool_2E_3F: $i > $i ).
tff(c_2Emin_2E_3D_3D_3E,type,
c_2Emin_2E_3D_3D_3E: $i ).
tff(c_2Ebool_2E_5C_2F,type,
c_2Ebool_2E_5C_2F: $i ).
tff(c_2Eoption_2ESOME,type,
c_2Eoption_2ESOME: $i > $i ).
tff('#skF_9',type,
'#skF_9': $i ).
tff(c_2Ebool_2E_7E,type,
c_2Ebool_2E_7E: $i ).
tff('#skF_8',type,
'#skF_8': $i ).
tff(c_2Ebool_2ET,type,
c_2Ebool_2ET: $i ).
tff(k,type,
k: ( $i * $i ) > $i ).
tff(c_2Eoption_2EOPTION__MAP,type,
c_2Eoption_2EOPTION__MAP: ( $i * $i ) > $i ).
tff('#skF_2',type,
'#skF_2': ( $i * $i ) > $i ).
tff(c_2Eoption_2ETHE,type,
c_2Eoption_2ETHE: $i > $i ).
tff('#skF_1',type,
'#skF_1': ( $i * $i * $i * $i ) > $i ).
tff(c_2Emin_2E_3D,type,
c_2Emin_2E_3D: $i > $i ).
tff(c_2Ebool_2E_2F_5C,type,
c_2Ebool_2E_2F_5C: $i ).
tff(c_2Eoption_2EOPTION__JOIN,type,
c_2Eoption_2EOPTION__JOIN: $i > $i ).
tff('#skF_4',type,
'#skF_4': ( $i * $i ) > $i ).
tff(c_2Eoption_2ENONE,type,
c_2Eoption_2ENONE: $i > $i ).
tff(f_579,negated_conjecture,
~ ! [A_27a] :
( ne(A_27a)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27a,bool)))
=> ! [V1x] :
( mem(V1x,A_27a)
=> ! [V2y] :
( mem(V2y,A_27a)
=> ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27a),V0R),c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ENONE(A_27a)))
<=> $true )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27a),V0R),ap(c_2Eoption_2ESOME(A_27a),V1x)),c_2Eoption_2ENONE(A_27a)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27a),V0R),c_2Eoption_2ENONE(A_27a)),ap(c_2Eoption_2ESOME(A_27a),V2y)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27a),V0R),ap(c_2Eoption_2ESOME(A_27a),V1x)),ap(c_2Eoption_2ESOME(A_27a),V2y)))
<=> p(ap(ap(V0R,V1x),V2y)) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Equotient__option_2EOPTION__REL__def) ).
tff(f_163,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2ESOME(A_27a),arr(A_27a,ty_2Eoption_2Eoption(A_27a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ESOME) ).
tff(f_67,axiom,
! [A,B,F] :
( mem(F,arr(A,B))
=> ! [X] :
( mem(X,A)
=> mem(ap(F,X),B) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',ap_tp) ).
tff(f_143,axiom,
p(c_2Ebool_2ET),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_true_p) ).
tff(f_104,axiom,
! [A0] :
( ne(A0)
=> ne(ty_2Eoption_2Eoption(A0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ne_ty_2Eoption_2Eoption) ).
tff(f_142,axiom,
mem(c_2Ebool_2ET,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2ET) ).
tff(f_52,axiom,
ne(bool),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',bool_ne) ).
tff(f_60,axiom,
! [A] :
( ne(A)
=> ! [B] :
( ne(B)
=> ne(arr(A,B)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',arr_ne) ).
tff(f_183,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2ENONE(A_27a),ty_2Eoption_2Eoption(A_27a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ENONE) ).
tff(f_522,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0e] :
( mem(V0e,A_27b)
=> ! [V1f] :
( mem(V1f,arr(A_27a,A_27b))
=> ! [V2e] :
( mem(V2e,ty_2Eoption_2Eoption(A_27a))
=> ( ! [V3x] :
( mem(V3x,A_27a)
=> ! [V4y] :
( mem(V4y,A_27a)
=> ( ( ap(c_2Eoption_2ESOME(A_27a),V3x) = ap(c_2Eoption_2ESOME(A_27a),V4y) )
<=> ( V3x = V4y ) ) ) )
& ! [V5x] :
( mem(V5x,A_27a)
=> ( ap(c_2Eoption_2ETHE(A_27a),ap(c_2Eoption_2ESOME(A_27a),V5x)) = V5x ) )
& ! [V6x] :
( mem(V6x,A_27a)
=> ( c_2Eoption_2ENONE(A_27a) != ap(c_2Eoption_2ESOME(A_27a),V6x) ) )
& ! [V7x] :
( mem(V7x,A_27a)
=> ( ap(c_2Eoption_2ESOME(A_27a),V7x) != c_2Eoption_2ENONE(A_27a) ) )
& ! [V8x] :
( mem(V8x,A_27a)
=> ( p(ap(c_2Eoption_2EIS__SOME(A_27a),ap(c_2Eoption_2ESOME(A_27a),V8x)))
<=> $true ) )
& ( p(ap(c_2Eoption_2EIS__SOME(A_27a),c_2Eoption_2ENONE(A_27a)))
<=> $false )
& ! [V9x] :
( mem(V9x,ty_2Eoption_2Eoption(A_27a))
=> ( p(ap(c_2Eoption_2EIS__NONE(A_27a),V9x))
<=> ( V9x = c_2Eoption_2ENONE(A_27a) ) ) )
& ! [V10x] :
( mem(V10x,ty_2Eoption_2Eoption(A_27a))
=> ( ~ p(ap(c_2Eoption_2EIS__SOME(A_27a),V10x))
<=> ( V10x = c_2Eoption_2ENONE(A_27a) ) ) )
& ! [V11x] :
( mem(V11x,ty_2Eoption_2Eoption(A_27a))
=> ( p(ap(c_2Eoption_2EIS__SOME(A_27a),V11x))
=> ( ap(c_2Eoption_2ESOME(A_27a),ap(c_2Eoption_2ETHE(A_27a),V11x)) = V11x ) ) )
& ! [V12x] :
( mem(V12x,ty_2Eoption_2Eoption(A_27a))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V12x),c_2Eoption_2ENONE(A_27a)),c_2Eoption_2ESOME(A_27a)) = V12x ) )
& ! [V13x] :
( mem(V13x,ty_2Eoption_2Eoption(A_27a))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V13x),V13x),c_2Eoption_2ESOME(A_27a)) = V13x ) )
& ! [V14x] :
( mem(V14x,ty_2Eoption_2Eoption(A_27a))
=> ( p(ap(c_2Eoption_2EIS__NONE(A_27a),V14x))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V14x),V0e),V1f) = V0e ) ) )
& ! [V15x] :
( mem(V15x,ty_2Eoption_2Eoption(A_27a))
=> ( p(ap(c_2Eoption_2EIS__SOME(A_27a),V15x))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),V15x),V0e),V1f) = ap(V1f,ap(c_2Eoption_2ETHE(A_27a),V15x)) ) ) )
& ! [V16x] :
( mem(V16x,ty_2Eoption_2Eoption(A_27a))
=> ( p(ap(c_2Eoption_2EIS__SOME(A_27a),V16x))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,ty_2Eoption_2Eoption(A_27a)),V16x),V2e),c_2Eoption_2ESOME(A_27a)) = V16x ) ) )
& ! [V17v] :
( mem(V17v,A_27b)
=> ! [V18f] :
( mem(V18f,arr(A_27a,A_27b))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),c_2Eoption_2ENONE(A_27a)),V17v),V18f) = V17v ) ) )
& ! [V19x] :
( mem(V19x,A_27a)
=> ! [V20v] :
( mem(V20v,A_27b)
=> ! [V21f] :
( mem(V21f,arr(A_27a,A_27b))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(A_27a,A_27b),ap(c_2Eoption_2ESOME(A_27a),V19x)),V20v),V21f) = ap(V21f,V19x) ) ) ) )
& ! [V22f] :
( mem(V22f,arr(A_27a,A_27b))
=> ! [V23x] :
( mem(V23x,A_27a)
=> ( ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V22f),ap(c_2Eoption_2ESOME(A_27a),V23x)) = ap(c_2Eoption_2ESOME(A_27b),ap(V22f,V23x)) ) ) )
& ! [V24f] :
( mem(V24f,arr(A_27a,A_27b))
=> ( ap(ap(c_2Eoption_2EOPTION__MAP(A_27a,A_27b),V24f),c_2Eoption_2ENONE(A_27a)) = c_2Eoption_2ENONE(A_27b) ) )
& ( ap(c_2Eoption_2EOPTION__JOIN(A_27a),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a))) = c_2Eoption_2ENONE(A_27a) )
& ! [V25x] :
( mem(V25x,ty_2Eoption_2Eoption(A_27a))
=> ( ap(c_2Eoption_2EOPTION__JOIN(A_27a),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(A_27a)),V25x)) = V25x ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eoption_2Eoption__CLAUSES) ).
tff(f_282,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [V0t] :
( mem(V0t,bool)
=> ( ? [V1x] :
( mem(V1x,A_27a)
& p(V0t) )
<=> p(V0t) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Ebool_2EEXISTS__SIMP) ).
tff(f_141,axiom,
~ p(c_2Ebool_2EF),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_false_p) ).
tff(f_147,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2EIS__SOME(A_27a),arr(ty_2Eoption_2Eoption(A_27a),bool)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EIS__SOME) ).
tff(f_108,axiom,
! [A_27a] :
( ne(A_27a)
=> mem(c_2Eoption_2EOPTION__JOIN(A_27a),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption(A_27a)),ty_2Eoption_2Eoption(A_27a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2EOPTION__JOIN) ).
tff(f_139,axiom,
mem(c_2Ebool_2EF,bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Ebool_2EF) ).
tff(f_78,axiom,
! [Q] :
( mem(Q,bool)
=> ! [R] :
( mem(R,bool)
=> ( ( p(Q)
<=> p(R) )
=> ( Q = R ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/ITP001/ITP001+2.ax',boolext) ).
tff(f_554,axiom,
! [A_27a] :
( ne(A_27a)
=> ! [A_27b] :
( ne(A_27b)
=> ! [V0R] :
( mem(V0R,arr(A_27a,arr(A_27b,bool)))
=> ! [V1x] :
( mem(V1x,ty_2Eoption_2Eoption(A_27a))
=> ! [V2y] :
( mem(V2y,ty_2Eoption_2Eoption(A_27b))
=> ( p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a,A_27b),V0R),V1x),V2y))
<=> ( ( ( V1x = c_2Eoption_2ENONE(A_27a) )
& ( V2y = c_2Eoption_2ENONE(A_27b) ) )
| ? [V3x0] :
( mem(V3x0,A_27a)
& ? [V4y0] :
( mem(V4y0,A_27b)
& ( V1x = ap(c_2Eoption_2ESOME(A_27a),V3x0) )
& ( V2y = ap(c_2Eoption_2ESOME(A_27b),V4y0) )
& p(ap(ap(V0R,V3x0),V4y0)) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EOPTREL__def) ).
tff(c_224,plain,
ne('#skF_7'),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_62,plain,
! [A_27a_40] :
( mem(c_2Eoption_2ESOME(A_27a_40),arr(A_27a_40,ty_2Eoption_2Eoption(A_27a_40)))
| ~ ne(A_27a_40) ),
inference(cnfTransformation,[status(thm)],[f_163]) ).
tff(c_218,plain,
mem('#skF_10','#skF_7'),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_343724,plain,
! [F_6884,X_6885,B_6886,A_6887] :
( mem(ap(F_6884,X_6885),B_6886)
| ~ mem(X_6885,A_6887)
| ~ mem(F_6884,arr(A_6887,B_6886)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_343780,plain,
! [F_6884,B_6886] :
( mem(ap(F_6884,'#skF_10'),B_6886)
| ~ mem(F_6884,arr('#skF_7',B_6886)) ),
inference(resolution,[status(thm)],[c_218,c_343724]) ).
tff(c_220,plain,
mem('#skF_9','#skF_7'),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_343781,plain,
! [F_6884,B_6886] :
( mem(ap(F_6884,'#skF_9'),B_6886)
| ~ mem(F_6884,arr('#skF_7',B_6886)) ),
inference(resolution,[status(thm)],[c_220,c_343724]) ).
tff(c_222,plain,
mem('#skF_8',arr('#skF_7',arr('#skF_7',bool))),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_50,plain,
p(c_2Ebool_2ET),
inference(cnfTransformation,[status(thm)],[f_143]) ).
tff(c_26,plain,
! [A0_25] :
( ne(ty_2Eoption_2Eoption(A0_25))
| ~ ne(A0_25) ),
inference(cnfTransformation,[status(thm)],[f_104]) ).
tff(c_48,plain,
mem(c_2Ebool_2ET,bool),
inference(cnfTransformation,[status(thm)],[f_142]) ).
tff(c_2,plain,
ne(bool),
inference(cnfTransformation,[status(thm)],[f_52]) ).
tff(c_6,plain,
! [A_1,B_3] :
( ne(arr(A_1,B_3))
| ~ ne(B_3)
| ~ ne(A_1) ),
inference(cnfTransformation,[status(thm)],[f_60]) ).
tff(c_72,plain,
! [A_27a_52] :
( mem(c_2Eoption_2ENONE(A_27a_52),ty_2Eoption_2Eoption(A_27a_52))
| ~ ne(A_27a_52) ),
inference(cnfTransformation,[status(thm)],[f_183]) ).
tff(c_351257,plain,
! [A_27b_7281,A_27a_7284,V0e_7283,V2e_7282,V1f_7285] :
( ( ap(c_2Eoption_2EOPTION__JOIN(A_27a_7284),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a_7284))) = c_2Eoption_2ENONE(A_27a_7284) )
| ~ mem(V2e_7282,ty_2Eoption_2Eoption(A_27a_7284))
| ~ mem(V1f_7285,arr(A_27a_7284,A_27b_7281))
| ~ mem(V0e_7283,A_27b_7281)
| ~ ne(A_27b_7281)
| ~ ne(A_27a_7284) ),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_426450,plain,
! [A_27a_8717,V1f_8718,A_27b_8719,V0e_8720] :
( ( ap(c_2Eoption_2EOPTION__JOIN(A_27a_8717),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a_8717))) = c_2Eoption_2ENONE(A_27a_8717) )
| ~ mem(V1f_8718,arr(A_27a_8717,A_27b_8719))
| ~ mem(V0e_8720,A_27b_8719)
| ~ ne(A_27b_8719)
| ~ ne(A_27a_8717) ),
inference(resolution,[status(thm)],[c_72,c_351257]) ).
tff(c_426624,plain,
! [V0e_8720] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_8720,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_426450]) ).
tff(c_426790,plain,
! [V0e_8720] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_8720,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_426624]) ).
tff(c_426909,plain,
~ ne(arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_426790]) ).
tff(c_426912,plain,
( ~ ne(bool)
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_6,c_426909]) ).
tff(c_426916,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_2,c_426912]) ).
tff(c_426918,plain,
ne(arr('#skF_7',bool)),
inference(splitRight,[status(thm)],[c_426790]) ).
tff(c_130,plain,
! [A_27a_85,V0t_91] :
( mem('#skF_4'(A_27a_85,V0t_91),A_27a_85)
| ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(A_27a_85) ),
inference(cnfTransformation,[status(thm)],[f_282]) ).
tff(c_426917,plain,
! [V0e_8720] :
( ~ mem(V0e_8720,arr('#skF_7',bool))
| ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_426790]) ).
tff(c_427593,plain,
! [V0e_8726] : ~ mem(V0e_8726,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_426917]) ).
tff(c_427709,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_427593]) ).
tff(c_427895,plain,
! [V0t_8729] :
( ~ p(V0t_8729)
| ~ mem(V0t_8729,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_426918,c_427709]) ).
tff(c_428124,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_427895]) ).
tff(c_428213,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_428124]) ).
tff(c_428214,plain,
ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_426917]) ).
tff(c_343772,plain,
! [F_6884,A_27a_52,B_6886] :
( mem(ap(F_6884,c_2Eoption_2ENONE(A_27a_52)),B_6886)
| ~ mem(F_6884,arr(ty_2Eoption_2Eoption(A_27a_52),B_6886))
| ~ ne(A_27a_52) ),
inference(resolution,[status(thm)],[c_72,c_343724]) ).
tff(c_428220,plain,
! [B_6886] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_6886)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_6886))
| ~ ne(ty_2Eoption_2Eoption('#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_428214,c_343772]) ).
tff(c_428343,plain,
~ ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_428220]) ).
tff(c_428346,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_26,c_428343]) ).
tff(c_428350,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_428346]) ).
tff(c_428352,plain,
ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_428220]) ).
tff(c_46,plain,
~ p(c_2Ebool_2EF),
inference(cnfTransformation,[status(thm)],[f_141]) ).
tff(c_52,plain,
! [A_27a_37] :
( mem(c_2Eoption_2EIS__SOME(A_27a_37),arr(ty_2Eoption_2Eoption(A_27a_37),bool))
| ~ ne(A_27a_37) ),
inference(cnfTransformation,[status(thm)],[f_147]) ).
tff(c_28,plain,
! [A_27a_26] :
( mem(c_2Eoption_2EOPTION__JOIN(A_27a_26),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption(A_27a_26)),ty_2Eoption_2Eoption(A_27a_26)))
| ~ ne(A_27a_26) ),
inference(cnfTransformation,[status(thm)],[f_108]) ).
tff(c_429035,plain,
! [B_8734] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_8734)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_8734)) ),
inference(splitRight,[status(thm)],[c_428220]) ).
tff(c_429039,plain,
( mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_28,c_429035]) ).
tff(c_429042,plain,
mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_429039]) ).
tff(c_8,plain,
! [F_6,X_8,B_5,A_4] :
( mem(ap(F_6,X_8),B_5)
| ~ mem(X_8,A_4)
| ~ mem(F_6,arr(A_4,B_5)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_429247,plain,
! [F_8736,B_8737] :
( mem(ap(F_8736,c_2Eoption_2ENONE('#skF_7')),B_8737)
| ~ mem(F_8736,arr(ty_2Eoption_2Eoption('#skF_7'),B_8737)) ),
inference(resolution,[status(thm)],[c_429042,c_8]) ).
tff(c_44,plain,
mem(c_2Ebool_2EF,bool),
inference(cnfTransformation,[status(thm)],[f_139]) ).
tff(c_15402,plain,
! [Q_2009,R_2010] :
( p(Q_2009)
| p(R_2010)
| ( R_2010 = Q_2009 )
| ~ mem(R_2010,bool)
| ~ mem(Q_2009,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_15406,plain,
! [Q_2009] :
( p(Q_2009)
| p(c_2Ebool_2EF)
| ( c_2Ebool_2EF = Q_2009 )
| ~ mem(Q_2009,bool) ),
inference(resolution,[status(thm)],[c_44,c_15402]) ).
tff(c_15411,plain,
! [Q_2009] :
( p(Q_2009)
| ( c_2Ebool_2EF = Q_2009 )
| ~ mem(Q_2009,bool) ),
inference(negUnitSimplification,[status(thm)],[c_46,c_15406]) ).
tff(c_439048,plain,
! [F_8865] :
( p(ap(F_8865,c_2Eoption_2ENONE('#skF_7')))
| ( ap(F_8865,c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ mem(F_8865,arr(ty_2Eoption_2Eoption('#skF_7'),bool)) ),
inference(resolution,[status(thm)],[c_429247,c_15411]) ).
tff(c_439180,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_52,c_439048]) ).
tff(c_439229,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF ) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_439180]) ).
tff(c_439356,plain,
ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF,
inference(splitLeft,[status(thm)],[c_439229]) ).
tff(c_366700,plain,
! [A_27a_7709,V1f_7710,A_27b_7711,V0e_7712] :
( ( ap(c_2Eoption_2EOPTION__JOIN(A_27a_7709),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a_7709))) = c_2Eoption_2ENONE(A_27a_7709) )
| ~ mem(V1f_7710,arr(A_27a_7709,A_27b_7711))
| ~ mem(V0e_7712,A_27b_7711)
| ~ ne(A_27b_7711)
| ~ ne(A_27a_7709) ),
inference(resolution,[status(thm)],[c_72,c_351257]) ).
tff(c_366874,plain,
! [V0e_7712] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_7712,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_366700]) ).
tff(c_367040,plain,
! [V0e_7712] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_7712,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_366874]) ).
tff(c_367154,plain,
~ ne(arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_367040]) ).
tff(c_367157,plain,
( ~ ne(bool)
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_6,c_367154]) ).
tff(c_367161,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_2,c_367157]) ).
tff(c_367163,plain,
ne(arr('#skF_7',bool)),
inference(splitRight,[status(thm)],[c_367040]) ).
tff(c_367162,plain,
! [V0e_7712] :
( ~ mem(V0e_7712,arr('#skF_7',bool))
| ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_367040]) ).
tff(c_368365,plain,
! [V0e_7719] : ~ mem(V0e_7719,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_367162]) ).
tff(c_368481,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_368365]) ).
tff(c_368773,plain,
! [V0t_7722] :
( ~ p(V0t_7722)
| ~ mem(V0t_7722,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_367163,c_368481]) ).
tff(c_369005,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_368773]) ).
tff(c_369095,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_369005]) ).
tff(c_369096,plain,
ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_367162]) ).
tff(c_369102,plain,
! [B_6886] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_6886)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_6886))
| ~ ne(ty_2Eoption_2Eoption('#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_369096,c_343772]) ).
tff(c_369149,plain,
~ ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_369102]) ).
tff(c_369268,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_26,c_369149]) ).
tff(c_369272,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_369268]) ).
tff(c_369274,plain,
ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_369102]) ).
tff(c_369275,plain,
! [B_7725] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_7725)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_7725)) ),
inference(splitRight,[status(thm)],[c_369102]) ).
tff(c_369279,plain,
( mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_28,c_369275]) ).
tff(c_369282,plain,
mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_369279]) ).
tff(c_369366,plain,
! [F_7726,B_7727] :
( mem(ap(F_7726,c_2Eoption_2ENONE('#skF_7')),B_7727)
| ~ mem(F_7726,arr(ty_2Eoption_2Eoption('#skF_7'),B_7727)) ),
inference(resolution,[status(thm)],[c_369282,c_8]) ).
tff(c_15439,plain,
! [R_2014,Q_2015] :
( ~ p(R_2014)
| ~ p(Q_2015)
| ( R_2014 = Q_2015 )
| ~ mem(R_2014,bool)
| ~ mem(Q_2015,bool) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_15444,plain,
! [Q_2015] :
( ~ p(c_2Ebool_2ET)
| ~ p(Q_2015)
| ( c_2Ebool_2ET = Q_2015 )
| ~ mem(Q_2015,bool) ),
inference(resolution,[status(thm)],[c_48,c_15439]) ).
tff(c_15452,plain,
! [Q_2015] :
( ~ p(Q_2015)
| ( c_2Ebool_2ET = Q_2015 )
| ~ mem(Q_2015,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_50,c_15444]) ).
tff(c_381535,plain,
! [F_7885] :
( ~ p(ap(F_7885,c_2Eoption_2ENONE('#skF_7')))
| ( ap(F_7885,c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET )
| ~ mem(F_7885,arr(ty_2Eoption_2Eoption('#skF_7'),bool)) ),
inference(resolution,[status(thm)],[c_369366,c_15452]) ).
tff(c_381671,plain,
( ~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET )
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_52,c_381535]) ).
tff(c_381721,plain,
( ~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET ) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_381671]) ).
tff(c_381753,plain,
~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7'))),
inference(splitLeft,[status(thm)],[c_381721]) ).
tff(c_381771,plain,
! [F_7890] :
( p(ap(F_7890,c_2Eoption_2ENONE('#skF_7')))
| ( ap(F_7890,c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ mem(F_7890,arr(ty_2Eoption_2Eoption('#skF_7'),bool)) ),
inference(resolution,[status(thm)],[c_369366,c_15411]) ).
tff(c_381907,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_52,c_381771]) ).
tff(c_381958,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF ) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_381907]) ).
tff(c_381959,plain,
ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_381753,c_381958]) ).
tff(c_15190,plain,
! [A_27a_1962,A_27b_1963,V0R_1964] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_1962,A_27b_1963),V0R_1964),c_2Eoption_2ENONE(A_27a_1962)),c_2Eoption_2ENONE(A_27b_1963)))
| ~ mem(c_2Eoption_2ENONE(A_27b_1963),ty_2Eoption_2Eoption(A_27b_1963))
| ~ mem(c_2Eoption_2ENONE(A_27a_1962),ty_2Eoption_2Eoption(A_27a_1962))
| ~ mem(V0R_1964,arr(A_27a_1962,arr(A_27b_1963,bool)))
| ~ ne(A_27b_1963)
| ~ ne(A_27a_1962) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_226,plain,
( ~ p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7')))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),c_2Eoption_2ENONE('#skF_7'))) ),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_268,plain,
~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),c_2Eoption_2ENONE('#skF_7'))),
inference(splitLeft,[status(thm)],[c_226]) ).
tff(c_15195,plain,
( ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_15190,c_268]) ).
tff(c_15199,plain,
~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_15195]) ).
tff(c_15202,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_72,c_15199]) ).
tff(c_15206,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_15202]) ).
tff(c_15208,plain,
p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),c_2Eoption_2ENONE('#skF_7'))),
inference(splitRight,[status(thm)],[c_226]) ).
tff(c_232,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7')))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),c_2Eoption_2ENONE('#skF_7'))) ),
inference(cnfTransformation,[status(thm)],[f_579]) ).
tff(c_246,plain,
~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),c_2Eoption_2ENONE('#skF_7'))),
inference(splitLeft,[status(thm)],[c_232]) ).
tff(c_15283,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_15208,c_246]) ).
tff(c_15285,plain,
p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),c_2Eoption_2ENONE('#skF_7'))),
inference(splitRight,[status(thm)],[c_232]) ).
tff(c_15293,plain,
~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),c_2Eoption_2ENONE('#skF_7'))),
inference(splitLeft,[status(thm)],[c_226]) ).
tff(c_15382,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_15285,c_15293]) ).
tff(c_15383,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| ~ p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'))) ),
inference(splitRight,[status(thm)],[c_226]) ).
tff(c_346817,plain,
~ p(ap(ap('#skF_8','#skF_9'),'#skF_10')),
inference(splitLeft,[status(thm)],[c_15383]) ).
tff(c_169172,plain,
! [V2e_4405,A_27a_4407,A_27b_4404,V1f_4408,V0e_4406] :
( ( ap(c_2Eoption_2EOPTION__JOIN(A_27a_4407),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a_4407))) = c_2Eoption_2ENONE(A_27a_4407) )
| ~ mem(V2e_4405,ty_2Eoption_2Eoption(A_27a_4407))
| ~ mem(V1f_4408,arr(A_27a_4407,A_27b_4404))
| ~ mem(V0e_4406,A_27b_4404)
| ~ ne(A_27b_4404)
| ~ ne(A_27a_4407) ),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_281185,plain,
! [A_27a_6067,V1f_6068,A_27b_6069,V0e_6070] :
( ( ap(c_2Eoption_2EOPTION__JOIN(A_27a_6067),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a_6067))) = c_2Eoption_2ENONE(A_27a_6067) )
| ~ mem(V1f_6068,arr(A_27a_6067,A_27b_6069))
| ~ mem(V0e_6070,A_27b_6069)
| ~ ne(A_27b_6069)
| ~ ne(A_27a_6067) ),
inference(resolution,[status(thm)],[c_72,c_169172]) ).
tff(c_281359,plain,
! [V0e_6070] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_6070,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_281185]) ).
tff(c_281525,plain,
! [V0e_6070] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_6070,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_281359]) ).
tff(c_281649,plain,
~ ne(arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_281525]) ).
tff(c_281652,plain,
( ~ ne(bool)
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_6,c_281649]) ).
tff(c_281656,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_2,c_281652]) ).
tff(c_281658,plain,
ne(arr('#skF_7',bool)),
inference(splitRight,[status(thm)],[c_281525]) ).
tff(c_281657,plain,
! [V0e_6070] :
( ~ mem(V0e_6070,arr('#skF_7',bool))
| ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_281525]) ).
tff(c_282914,plain,
! [V0e_6077] : ~ mem(V0e_6077,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_281657]) ).
tff(c_283030,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_282914]) ).
tff(c_283206,plain,
! [V0t_6079] :
( ~ p(V0t_6079)
| ~ mem(V0t_6079,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_281658,c_283030]) ).
tff(c_283438,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_283206]) ).
tff(c_283528,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_283438]) ).
tff(c_283529,plain,
ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_281657]) ).
tff(c_15474,plain,
! [F_2017,X_2018,B_2019,A_2020] :
( mem(ap(F_2017,X_2018),B_2019)
| ~ mem(X_2018,A_2020)
| ~ mem(F_2017,arr(A_2020,B_2019)) ),
inference(cnfTransformation,[status(thm)],[f_67]) ).
tff(c_15522,plain,
! [F_2017,A_27a_52,B_2019] :
( mem(ap(F_2017,c_2Eoption_2ENONE(A_27a_52)),B_2019)
| ~ mem(F_2017,arr(ty_2Eoption_2Eoption(A_27a_52),B_2019))
| ~ ne(A_27a_52) ),
inference(resolution,[status(thm)],[c_72,c_15474]) ).
tff(c_283536,plain,
! [B_2019] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_2019)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_2019))
| ~ ne(ty_2Eoption_2Eoption('#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_283529,c_15522]) ).
tff(c_283711,plain,
~ ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_283536]) ).
tff(c_283714,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_26,c_283711]) ).
tff(c_283718,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_283714]) ).
tff(c_283720,plain,
ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_283536]) ).
tff(c_187316,plain,
! [A_27a_4877,V1f_4878,A_27b_4879,V0e_4880] :
( ( ap(c_2Eoption_2EOPTION__JOIN(A_27a_4877),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a_4877))) = c_2Eoption_2ENONE(A_27a_4877) )
| ~ mem(V1f_4878,arr(A_27a_4877,A_27b_4879))
| ~ mem(V0e_4880,A_27b_4879)
| ~ ne(A_27b_4879)
| ~ ne(A_27a_4877) ),
inference(resolution,[status(thm)],[c_72,c_169172]) ).
tff(c_187490,plain,
! [V0e_4880] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_4880,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_187316]) ).
tff(c_187656,plain,
! [V0e_4880] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_4880,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_187490]) ).
tff(c_187780,plain,
~ ne(arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_187656]) ).
tff(c_187783,plain,
( ~ ne(bool)
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_6,c_187780]) ).
tff(c_187787,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_2,c_187783]) ).
tff(c_187789,plain,
ne(arr('#skF_7',bool)),
inference(splitRight,[status(thm)],[c_187656]) ).
tff(c_187788,plain,
! [V0e_4880] :
( ~ mem(V0e_4880,arr('#skF_7',bool))
| ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_187656]) ).
tff(c_189035,plain,
! [V0e_4887] : ~ mem(V0e_4887,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_187788]) ).
tff(c_189151,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_189035]) ).
tff(c_189443,plain,
! [V0t_4890] :
( ~ p(V0t_4890)
| ~ mem(V0t_4890,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_187789,c_189151]) ).
tff(c_189675,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_189443]) ).
tff(c_189765,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_189675]) ).
tff(c_189766,plain,
ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_187788]) ).
tff(c_189772,plain,
! [B_2019] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_2019)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_2019))
| ~ ne(ty_2Eoption_2Eoption('#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_189766,c_15522]) ).
tff(c_189819,plain,
~ ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_189772]) ).
tff(c_189938,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_26,c_189819]) ).
tff(c_189942,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_189938]) ).
tff(c_189944,plain,
ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_189772]) ).
tff(c_189945,plain,
! [B_4895] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_4895)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_4895)) ),
inference(splitRight,[status(thm)],[c_189772]) ).
tff(c_189949,plain,
( mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_28,c_189945]) ).
tff(c_189952,plain,
mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_189949]) ).
tff(c_190036,plain,
! [F_4896,B_4897] :
( mem(ap(F_4896,c_2Eoption_2ENONE('#skF_7')),B_4897)
| ~ mem(F_4896,arr(ty_2Eoption_2Eoption('#skF_7'),B_4897)) ),
inference(resolution,[status(thm)],[c_189952,c_8]) ).
tff(c_201744,plain,
! [F_5041] :
( ~ p(ap(F_5041,c_2Eoption_2ENONE('#skF_7')))
| ( ap(F_5041,c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET )
| ~ mem(F_5041,arr(ty_2Eoption_2Eoption('#skF_7'),bool)) ),
inference(resolution,[status(thm)],[c_190036,c_15452]) ).
tff(c_201876,plain,
( ~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET )
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_52,c_201744]) ).
tff(c_201925,plain,
( ~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET ) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_201876]) ).
tff(c_201957,plain,
~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7'))),
inference(splitLeft,[status(thm)],[c_201925]) ).
tff(c_202342,plain,
! [F_5049] :
( p(ap(F_5049,c_2Eoption_2ENONE('#skF_7')))
| ( ap(F_5049,c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ mem(F_5049,arr(ty_2Eoption_2Eoption('#skF_7'),bool)) ),
inference(resolution,[status(thm)],[c_190036,c_15411]) ).
tff(c_202474,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_52,c_202342]) ).
tff(c_202524,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF ) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_202474]) ).
tff(c_202525,plain,
ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_201957,c_202524]) ).
tff(c_15531,plain,
! [F_2017,B_2019] :
( mem(ap(F_2017,'#skF_9'),B_2019)
| ~ mem(F_2017,arr('#skF_7',B_2019)) ),
inference(resolution,[status(thm)],[c_220,c_15474]) ).
tff(c_15284,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'))) ),
inference(splitRight,[status(thm)],[c_232]) ).
tff(c_15454,plain,
p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'))),
inference(splitLeft,[status(thm)],[c_15284]) ).
tff(c_23202,plain,
! [V1f_2416,V0e_2414,V2e_2413,A_27a_2415,A_27b_2412] :
( ( ap(c_2Eoption_2EOPTION__JOIN(A_27a_2415),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a_2415))) = c_2Eoption_2ENONE(A_27a_2415) )
| ~ mem(V2e_2413,ty_2Eoption_2Eoption(A_27a_2415))
| ~ mem(V1f_2416,arr(A_27a_2415,A_27b_2412))
| ~ mem(V0e_2414,A_27b_2412)
| ~ ne(A_27b_2412)
| ~ ne(A_27a_2415) ),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_40463,plain,
! [A_27a_2891,V1f_2892,A_27b_2893,V0e_2894] :
( ( ap(c_2Eoption_2EOPTION__JOIN(A_27a_2891),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(A_27a_2891))) = c_2Eoption_2ENONE(A_27a_2891) )
| ~ mem(V1f_2892,arr(A_27a_2891,A_27b_2893))
| ~ mem(V0e_2894,A_27b_2893)
| ~ ne(A_27b_2893)
| ~ ne(A_27a_2891) ),
inference(resolution,[status(thm)],[c_72,c_23202]) ).
tff(c_40637,plain,
! [V0e_2894] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_2894,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_40463]) ).
tff(c_40803,plain,
! [V0e_2894] :
( ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(V0e_2894,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_40637]) ).
tff(c_40923,plain,
~ ne(arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_40803]) ).
tff(c_40926,plain,
( ~ ne(bool)
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_6,c_40923]) ).
tff(c_40930,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_2,c_40926]) ).
tff(c_40932,plain,
ne(arr('#skF_7',bool)),
inference(splitRight,[status(thm)],[c_40803]) ).
tff(c_40931,plain,
! [V0e_2894] :
( ~ mem(V0e_2894,arr('#skF_7',bool))
| ( ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_40803]) ).
tff(c_42185,plain,
! [V0e_2901] : ~ mem(V0e_2901,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_40931]) ).
tff(c_42301,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_42185]) ).
tff(c_42593,plain,
! [V0t_2904] :
( ~ p(V0t_2904)
| ~ mem(V0t_2904,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_40932,c_42301]) ).
tff(c_42825,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_42593]) ).
tff(c_42915,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_42825]) ).
tff(c_42916,plain,
ap(c_2Eoption_2EOPTION__JOIN('#skF_7'),c_2Eoption_2ENONE(ty_2Eoption_2Eoption('#skF_7'))) = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_40931]) ).
tff(c_42922,plain,
! [B_2019] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_2019)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_2019))
| ~ ne(ty_2Eoption_2Eoption('#skF_7')) ),
inference(superposition,[status(thm),theory(equality)],[c_42916,c_15522]) ).
tff(c_42969,plain,
~ ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_42922]) ).
tff(c_43088,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_26,c_42969]) ).
tff(c_43092,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_43088]) ).
tff(c_43094,plain,
ne(ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_42922]) ).
tff(c_43095,plain,
! [B_2909] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_2909)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_2909)) ),
inference(splitRight,[status(thm)],[c_42922]) ).
tff(c_43099,plain,
( mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_28,c_43095]) ).
tff(c_43102,plain,
mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_43099]) ).
tff(c_43186,plain,
! [F_2910,B_2911] :
( mem(ap(F_2910,c_2Eoption_2ENONE('#skF_7')),B_2911)
| ~ mem(F_2910,arr(ty_2Eoption_2Eoption('#skF_7'),B_2911)) ),
inference(resolution,[status(thm)],[c_43102,c_8]) ).
tff(c_52805,plain,
! [F_3028] :
( ~ p(ap(F_3028,c_2Eoption_2ENONE('#skF_7')))
| ( ap(F_3028,c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET )
| ~ mem(F_3028,arr(ty_2Eoption_2Eoption('#skF_7'),bool)) ),
inference(resolution,[status(thm)],[c_43186,c_15452]) ).
tff(c_52937,plain,
( ~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET )
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_52,c_52805]) ).
tff(c_52986,plain,
( ~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET ) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_52937]) ).
tff(c_53373,plain,
~ p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7'))),
inference(splitLeft,[status(thm)],[c_52986]) ).
tff(c_54765,plain,
! [F_3051] :
( p(ap(F_3051,c_2Eoption_2ENONE('#skF_7')))
| ( ap(F_3051,c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ mem(F_3051,arr(ty_2Eoption_2Eoption('#skF_7'),bool)) ),
inference(resolution,[status(thm)],[c_43186,c_15411]) ).
tff(c_54897,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_52,c_54765]) ).
tff(c_54947,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF ) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_54897]) ).
tff(c_54948,plain,
ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_53373,c_54947]) ).
tff(c_18451,plain,
~ p(ap(ap('#skF_8','#skF_9'),'#skF_10')),
inference(splitLeft,[status(thm)],[c_15383]) ).
tff(c_15592,plain,
! [F_2025,B_2026] :
( mem(ap(F_2025,'#skF_10'),B_2026)
| ~ mem(F_2025,arr('#skF_7',B_2026)) ),
inference(resolution,[status(thm)],[c_218,c_15474]) ).
tff(c_18513,plain,
! [F_2208] :
( p(ap(F_2208,'#skF_10'))
| ( ap(F_2208,'#skF_10') = c_2Ebool_2EF )
| ~ mem(F_2208,arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_15592,c_15411]) ).
tff(c_31140,plain,
! [F_2667] :
( p(ap(ap(F_2667,'#skF_9'),'#skF_10'))
| ( ap(ap(F_2667,'#skF_9'),'#skF_10') = c_2Ebool_2EF )
| ~ mem(F_2667,arr('#skF_7',arr('#skF_7',bool))) ),
inference(resolution,[status(thm)],[c_15531,c_18513]) ).
tff(c_31223,plain,
( p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| ( ap(ap('#skF_8','#skF_9'),'#skF_10') = c_2Ebool_2EF ) ),
inference(resolution,[status(thm)],[c_222,c_31140]) ).
tff(c_31262,plain,
ap(ap('#skF_8','#skF_9'),'#skF_10') = c_2Ebool_2EF,
inference(negUnitSimplification,[status(thm)],[c_18451,c_31223]) ).
tff(c_23610,plain,
! [V5x_2435,A_27b_2433,V1f_2438,V0e_2436,V2e_2434,A_27a_2437] :
( ( ap(c_2Eoption_2ETHE(A_27a_2437),ap(c_2Eoption_2ESOME(A_27a_2437),V5x_2435)) = V5x_2435 )
| ~ mem(V5x_2435,A_27a_2437)
| ~ mem(V2e_2434,ty_2Eoption_2Eoption(A_27a_2437))
| ~ mem(V1f_2438,arr(A_27a_2437,A_27b_2433))
| ~ mem(V0e_2436,A_27b_2433)
| ~ ne(A_27b_2433)
| ~ ne(A_27a_2437) ),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_46446,plain,
! [V5x_2958,V0e_2959,A_27b_2960,A_27a_2957,V1f_2961] :
( ( ap(c_2Eoption_2ETHE(A_27a_2957),ap(c_2Eoption_2ESOME(A_27a_2957),V5x_2958)) = V5x_2958 )
| ~ mem(V5x_2958,A_27a_2957)
| ~ mem(V1f_2961,arr(A_27a_2957,A_27b_2960))
| ~ mem(V0e_2959,A_27b_2960)
| ~ ne(A_27b_2960)
| ~ ne(A_27a_2957) ),
inference(resolution,[status(thm)],[c_72,c_23610]) ).
tff(c_46626,plain,
! [V5x_2958,V0e_2959] :
( ( ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V5x_2958)) = V5x_2958 )
| ~ mem(V5x_2958,'#skF_7')
| ~ mem(V0e_2959,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_46446]) ).
tff(c_46796,plain,
! [V5x_2958,V0e_2959] :
( ( ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V5x_2958)) = V5x_2958 )
| ~ mem(V5x_2958,'#skF_7')
| ~ mem(V0e_2959,arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_40932,c_46626]) ).
tff(c_46952,plain,
! [V0e_2963] : ~ mem(V0e_2963,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_46796]) ).
tff(c_47072,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_46952]) ).
tff(c_47390,plain,
! [V0t_2969] :
( ~ p(V0t_2969)
| ~ mem(V0t_2969,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_40932,c_47072]) ).
tff(c_47629,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_47390]) ).
tff(c_47721,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_47629]) ).
tff(c_47722,plain,
! [V5x_2958] :
( ( ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V5x_2958)) = V5x_2958 )
| ~ mem(V5x_2958,'#skF_7') ),
inference(splitRight,[status(thm)],[c_46796]) ).
tff(c_31404,plain,
! [V1x_2673,V0R_2670,A_27a_2672,V2y_2669,A_27b_2671] :
( ( c_2Eoption_2ENONE(A_27a_2672) = V1x_2673 )
| mem('#skF_5'(V2y_2669,V0R_2670,A_27b_2671,A_27a_2672,V1x_2673),A_27a_2672)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_2672,A_27b_2671),V0R_2670),V1x_2673),V2y_2669))
| ~ mem(V2y_2669,ty_2Eoption_2Eoption(A_27b_2671))
| ~ mem(V1x_2673,ty_2Eoption_2Eoption(A_27a_2672))
| ~ mem(V0R_2670,arr(A_27a_2672,arr(A_27b_2671,bool)))
| ~ ne(A_27b_2671)
| ~ ne(A_27a_2672) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_31408,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_15454,c_31404]) ).
tff(c_31415,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_31408]) ).
tff(c_93271,plain,
~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_31415]) ).
tff(c_93275,plain,
~ mem(c_2Eoption_2ESOME('#skF_7'),arr('#skF_7',ty_2Eoption_2Eoption('#skF_7'))),
inference(resolution,[status(thm)],[c_15531,c_93271]) ).
tff(c_93278,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_62,c_93275]) ).
tff(c_93282,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_93278]) ).
tff(c_93284,plain,
mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_31415]) ).
tff(c_15530,plain,
! [F_2017,B_2019] :
( mem(ap(F_2017,'#skF_10'),B_2019)
| ~ mem(F_2017,arr('#skF_7',B_2019)) ),
inference(resolution,[status(thm)],[c_218,c_15474]) ).
tff(c_93283,plain,
( ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_31415]) ).
tff(c_94537,plain,
~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_93283]) ).
tff(c_94541,plain,
~ mem(c_2Eoption_2ESOME('#skF_7'),arr('#skF_7',ty_2Eoption_2Eoption('#skF_7'))),
inference(resolution,[status(thm)],[c_15530,c_94537]) ).
tff(c_94544,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_62,c_94541]) ).
tff(c_94548,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_94544]) ).
tff(c_94550,plain,
mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_93283]) ).
tff(c_31701,plain,
! [A_27a_2684,A_27b_2683,V0R_2682,V2y_2681,V1x_2685] :
( ( c_2Eoption_2ENONE(A_27b_2683) = V2y_2681 )
| mem('#skF_6'(V2y_2681,V0R_2682,A_27b_2683,A_27a_2684,V1x_2685),A_27b_2683)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_2684,A_27b_2683),V0R_2682),V1x_2685),V2y_2681))
| ~ mem(V2y_2681,ty_2Eoption_2Eoption(A_27b_2683))
| ~ mem(V1x_2685,ty_2Eoption_2Eoption(A_27a_2684))
| ~ mem(V0R_2682,arr(A_27a_2684,arr(A_27b_2683,bool)))
| ~ ne(A_27b_2683)
| ~ ne(A_27a_2684) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_31705,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_15454,c_31701]) ).
tff(c_31712,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_31705]) ).
tff(c_96014,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_93284,c_94550,c_31712]) ).
tff(c_96015,plain,
mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7'),
inference(splitLeft,[status(thm)],[c_96014]) ).
tff(c_34874,plain,
! [V1x_2785,A_27a_2784,V2y_2781,A_27b_2783,V0R_2782] :
( ( c_2Eoption_2ENONE(A_27b_2783) = V2y_2781 )
| ( ap(c_2Eoption_2ESOME(A_27b_2783),'#skF_6'(V2y_2781,V0R_2782,A_27b_2783,A_27a_2784,V1x_2785)) = V2y_2781 )
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_2784,A_27b_2783),V0R_2782),V1x_2785),V2y_2781))
| ~ mem(V2y_2781,ty_2Eoption_2Eoption(A_27b_2783))
| ~ mem(V1x_2785,ty_2Eoption_2Eoption(A_27a_2784))
| ~ mem(V0R_2782,arr(A_27a_2784,arr(A_27b_2783,bool)))
| ~ ne(A_27b_2783)
| ~ ne(A_27a_2784) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_34878,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') )
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_15454,c_34874]) ).
tff(c_34885,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') )
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_34878]) ).
tff(c_128755,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_93284,c_94550,c_34885]) ).
tff(c_128756,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),
inference(splitLeft,[status(thm)],[c_128755]) ).
tff(c_132281,plain,
( ( '#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')) = ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')) )
| ~ mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_128756,c_47722]) ).
tff(c_132302,plain,
'#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')) = ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')),
inference(demodulation,[status(thm),theory(equality)],[c_96015,c_132281]) ).
tff(c_94549,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(splitRight,[status(thm)],[c_93283]) ).
tff(c_95398,plain,
mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7'),
inference(splitLeft,[status(thm)],[c_94549]) ).
tff(c_34310,plain,
! [A_27a_2753,A_27b_2752,V2y_2750,V0R_2751,V1x_2754] :
( ( c_2Eoption_2ENONE(A_27a_2753) = V1x_2754 )
| ( ap(c_2Eoption_2ESOME(A_27a_2753),'#skF_5'(V2y_2750,V0R_2751,A_27b_2752,A_27a_2753,V1x_2754)) = V1x_2754 )
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_2753,A_27b_2752),V0R_2751),V1x_2754),V2y_2750))
| ~ mem(V2y_2750,ty_2Eoption_2Eoption(A_27b_2752))
| ~ mem(V1x_2754,ty_2Eoption_2Eoption(A_27a_2753))
| ~ mem(V0R_2751,arr(A_27a_2753,arr(A_27b_2752,bool)))
| ~ ne(A_27b_2752)
| ~ ne(A_27a_2753) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_34314,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') )
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_15454,c_34310]) ).
tff(c_34321,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') )
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_34314]) ).
tff(c_116406,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_93284,c_94550,c_34321]) ).
tff(c_116407,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),
inference(splitLeft,[status(thm)],[c_116406]) ).
tff(c_116453,plain,
( ( '#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')) = ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')) )
| ~ mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_116407,c_47722]) ).
tff(c_116474,plain,
'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')) = ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),
inference(demodulation,[status(thm),theory(equality)],[c_95398,c_116453]) ).
tff(c_36398,plain,
! [V1x_2819,A_27a_2818,A_27b_2817,V2y_2815,V0R_2816] :
( ( c_2Eoption_2ENONE(A_27a_2818) = V1x_2819 )
| p(ap(ap(V0R_2816,'#skF_5'(V2y_2815,V0R_2816,A_27b_2817,A_27a_2818,V1x_2819)),'#skF_6'(V2y_2815,V0R_2816,A_27b_2817,A_27a_2818,V1x_2819)))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_2818,A_27b_2817),V0R_2816),V1x_2819),V2y_2815))
| ~ mem(V2y_2815,ty_2Eoption_2Eoption(A_27b_2817))
| ~ mem(V1x_2819,ty_2Eoption_2Eoption(A_27a_2818))
| ~ mem(V0R_2816,arr(A_27a_2818,arr(A_27b_2817,bool)))
| ~ ne(A_27b_2817)
| ~ ne(A_27a_2818) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_36402,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| p(ap(ap('#skF_8','#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))),'#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_15454,c_36398]) ).
tff(c_36409,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| p(ap(ap('#skF_8','#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))),'#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_36402]) ).
tff(c_162705,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| p(ap(ap('#skF_8',ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))),ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))) ),
inference(demodulation,[status(thm),theory(equality)],[c_93284,c_94550,c_132302,c_116474,c_36409]) ).
tff(c_162706,plain,
p(ap(ap('#skF_8',ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))),ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))),
inference(splitLeft,[status(thm)],[c_162705]) ).
tff(c_162711,plain,
( p(ap(ap('#skF_8','#skF_9'),ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'))))
| ~ mem('#skF_9','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_47722,c_162706]) ).
tff(c_162717,plain,
p(ap(ap('#skF_8','#skF_9'),ap(c_2Eoption_2ETHE('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_162711]) ).
tff(c_162724,plain,
( p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| ~ mem('#skF_10','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_47722,c_162717]) ).
tff(c_162727,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_31262,c_162724]) ).
tff(c_162729,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_162727]) ).
tff(c_162730,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_162705]) ).
tff(c_24446,plain,
! [A_27b_2467,V1f_2472,V8x_2471,A_27a_2470,V2e_2468,V0e_2469] :
( p(ap(c_2Eoption_2EIS__SOME(A_27a_2470),ap(c_2Eoption_2ESOME(A_27a_2470),V8x_2471)))
| ~ mem(V8x_2471,A_27a_2470)
| ~ mem(V2e_2468,ty_2Eoption_2Eoption(A_27a_2470))
| ~ mem(V1f_2472,arr(A_27a_2470,A_27b_2467))
| ~ mem(V0e_2469,A_27b_2467)
| ~ ne(A_27b_2467)
| ~ ne(A_27a_2470) ),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_44791,plain,
! [V1f_2942,V0e_2941,V8x_2943,A_27a_2939,A_27b_2940] :
( p(ap(c_2Eoption_2EIS__SOME(A_27a_2939),ap(c_2Eoption_2ESOME(A_27a_2939),V8x_2943)))
| ~ mem(V8x_2943,A_27a_2939)
| ~ mem(V1f_2942,arr(A_27a_2939,A_27b_2940))
| ~ mem(V0e_2941,A_27b_2940)
| ~ ne(A_27b_2940)
| ~ ne(A_27a_2939) ),
inference(resolution,[status(thm)],[c_72,c_24446]) ).
tff(c_44971,plain,
! [V8x_2943,V0e_2941] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_2943)))
| ~ mem(V8x_2943,'#skF_7')
| ~ mem(V0e_2941,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_44791]) ).
tff(c_45141,plain,
! [V8x_2943,V0e_2941] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_2943)))
| ~ mem(V8x_2943,'#skF_7')
| ~ mem(V0e_2941,arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_40932,c_44971]) ).
tff(c_45264,plain,
! [V0e_2945] : ~ mem(V0e_2945,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_45141]) ).
tff(c_45384,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_45264]) ).
tff(c_45988,plain,
! [V0t_2952] :
( ~ p(V0t_2952)
| ~ mem(V0t_2952,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_40932,c_45384]) ).
tff(c_46227,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_45988]) ).
tff(c_46319,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_46227]) ).
tff(c_46320,plain,
! [V8x_2943] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_2943)))
| ~ mem(V8x_2943,'#skF_7') ),
inference(splitRight,[status(thm)],[c_45141]) ).
tff(c_116456,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')))
| ~ mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_116407,c_46320]) ).
tff(c_116476,plain,
p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))),
inference(demodulation,[status(thm),theory(equality)],[c_95398,c_116456]) ).
tff(c_162740,plain,
p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7'))),
inference(demodulation,[status(thm),theory(equality)],[c_162730,c_116476]) ).
tff(c_162750,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_54948,c_162740]) ).
tff(c_162752,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_162750]) ).
tff(c_162753,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_128755]) ).
tff(c_162829,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_10','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_162753,c_46320]) ).
tff(c_162909,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_54948,c_162829]) ).
tff(c_162911,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_162909]) ).
tff(c_162912,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_116406]) ).
tff(c_162968,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_9','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_162912,c_46320]) ).
tff(c_163050,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_54948,c_162968]) ).
tff(c_163052,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_163050]) ).
tff(c_163053,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_96014]) ).
tff(c_163091,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_10','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_163053,c_46320]) ).
tff(c_163170,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_54948,c_163091]) ).
tff(c_163172,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_163170]) ).
tff(c_163173,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_94549]) ).
tff(c_163205,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_9','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_163173,c_46320]) ).
tff(c_163286,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_54948,c_163205]) ).
tff(c_163288,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_163286]) ).
tff(c_163289,plain,
ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_52986]) ).
tff(c_171,plain,
! [V1f_970,A_27b_598,V0e_846,V2e_1032,A_27a_102] :
( ~ p(ap(c_2Eoption_2EIS__SOME(A_27a_102),c_2Eoption_2ENONE(A_27a_102)))
| ~ mem(V2e_1032,ty_2Eoption_2Eoption(A_27a_102))
| ~ mem(V1f_970,arr(A_27a_102,A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598)
| ~ ne(A_27a_102) ),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_163299,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ p(c_2Ebool_2ET)
| ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598)
| ~ ne('#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_163289,c_171]) ).
tff(c_163311,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_50,c_163299]) ).
tff(c_164295,plain,
! [V1f_4178,A_27b_4179,V0e_4180] :
( ~ mem(V1f_4178,arr('#skF_7',A_27b_4179))
| ~ mem(V0e_4180,A_27b_4179)
| ~ ne(A_27b_4179) ),
inference(splitLeft,[status(thm)],[c_163311]) ).
tff(c_164402,plain,
! [V0e_4180] :
( ~ mem(V0e_4180,ty_2Eoption_2Eoption('#skF_7'))
| ~ ne(ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_62,c_164295]) ).
tff(c_164465,plain,
! [V0e_4180] : ~ mem(V0e_4180,ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_43094,c_164402]) ).
tff(c_164470,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_164465,c_43102]) ).
tff(c_164471,plain,
! [V2e_1032] : ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_163311]) ).
tff(c_164473,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_164471,c_43102]) ).
tff(c_164474,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7'))) ),
inference(splitRight,[status(thm)],[c_15383]) ).
tff(c_180818,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7'))) ),
inference(demodulation,[status(thm),theory(equality)],[c_15454,c_164474]) ).
tff(c_180819,plain,
p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7'))),
inference(splitLeft,[status(thm)],[c_180818]) ).
tff(c_216,plain,
! [V0R_1261,V1x_1289,A_27b_1205,A_27a_1093,V2y_1303] :
( ( c_2Eoption_2ENONE(A_27a_1093) = V1x_1289 )
| mem('#skF_5'(V2y_1303,V0R_1261,A_27b_1205,A_27a_1093,V1x_1289),A_27a_1093)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_1093,A_27b_1205),V0R_1261),V1x_1289),V2y_1303))
| ~ mem(V2y_1303,ty_2Eoption_2Eoption(A_27b_1205))
| ~ mem(V1x_1289,ty_2Eoption_2Eoption(A_27a_1093))
| ~ mem(V0R_1261,arr(A_27a_1093,arr(A_27b_1205,bool)))
| ~ ne(A_27b_1205)
| ~ ne(A_27a_1093) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_180829,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_180819,c_216]) ).
tff(c_180854,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_180829]) ).
tff(c_225162,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_189952,c_180854]) ).
tff(c_225163,plain,
~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_225162]) ).
tff(c_225167,plain,
~ mem(c_2Eoption_2ESOME('#skF_7'),arr('#skF_7',ty_2Eoption_2Eoption('#skF_7'))),
inference(resolution,[status(thm)],[c_15531,c_225163]) ).
tff(c_225170,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_62,c_225167]) ).
tff(c_225174,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_225170]) ).
tff(c_225176,plain,
mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_225162]) ).
tff(c_212,plain,
! [V0R_1261,V1x_1289,A_27b_1205,A_27a_1093,V2y_1303] :
( ( c_2Eoption_2ENONE(A_27a_1093) = V1x_1289 )
| mem('#skF_6'(V2y_1303,V0R_1261,A_27b_1205,A_27a_1093,V1x_1289),A_27b_1205)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_1093,A_27b_1205),V0R_1261),V1x_1289),V2y_1303))
| ~ mem(V2y_1303,ty_2Eoption_2Eoption(A_27b_1205))
| ~ mem(V1x_1289,ty_2Eoption_2Eoption(A_27a_1093))
| ~ mem(V0R_1261,arr(A_27a_1093,arr(A_27b_1205,bool)))
| ~ ne(A_27b_1205)
| ~ ne(A_27a_1093) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_180835,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_180819,c_212]) ).
tff(c_180865,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_180835]) ).
tff(c_225915,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_225176,c_189952,c_180865]) ).
tff(c_225916,plain,
mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7'),
inference(splitLeft,[status(thm)],[c_225915]) ).
tff(c_225175,plain,
( mem('#skF_5'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_225162]) ).
tff(c_249269,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7'),
inference(splitLeft,[status(thm)],[c_225175]) ).
tff(c_169756,plain,
! [V2e_4435,A_27a_4437,V0e_4436,V1f_4439,V8x_4438,A_27b_4434] :
( p(ap(c_2Eoption_2EIS__SOME(A_27a_4437),ap(c_2Eoption_2ESOME(A_27a_4437),V8x_4438)))
| ~ mem(V8x_4438,A_27a_4437)
| ~ mem(V2e_4435,ty_2Eoption_2Eoption(A_27a_4437))
| ~ mem(V1f_4439,arr(A_27a_4437,A_27b_4434))
| ~ mem(V0e_4436,A_27b_4434)
| ~ ne(A_27b_4434)
| ~ ne(A_27a_4437) ),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_193357,plain,
! [V0e_4947,V8x_4946,A_27a_4943,V1f_4945,A_27b_4944] :
( p(ap(c_2Eoption_2EIS__SOME(A_27a_4943),ap(c_2Eoption_2ESOME(A_27a_4943),V8x_4946)))
| ~ mem(V8x_4946,A_27a_4943)
| ~ mem(V1f_4945,arr(A_27a_4943,A_27b_4944))
| ~ mem(V0e_4947,A_27b_4944)
| ~ ne(A_27b_4944)
| ~ ne(A_27a_4943) ),
inference(resolution,[status(thm)],[c_72,c_169756]) ).
tff(c_193537,plain,
! [V8x_4946,V0e_4947] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_4946)))
| ~ mem(V8x_4946,'#skF_7')
| ~ mem(V0e_4947,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_193357]) ).
tff(c_193707,plain,
! [V8x_4946,V0e_4947] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_4946)))
| ~ mem(V8x_4946,'#skF_7')
| ~ mem(V0e_4947,arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_187789,c_193537]) ).
tff(c_193834,plain,
! [V0e_4949] : ~ mem(V0e_4949,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_193707]) ).
tff(c_193954,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_193834]) ).
tff(c_194272,plain,
! [V0t_4955] :
( ~ p(V0t_4955)
| ~ mem(V0t_4955,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_187789,c_193954]) ).
tff(c_194511,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_194272]) ).
tff(c_194603,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_194511]) ).
tff(c_194604,plain,
! [V8x_4946] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_4946)))
| ~ mem(V8x_4946,'#skF_7') ),
inference(splitRight,[status(thm)],[c_193707]) ).
tff(c_249323,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_9','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_249269,c_194604]) ).
tff(c_249403,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_202525,c_249323]) ).
tff(c_249405,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_249403]) ).
tff(c_249407,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') != c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_225175]) ).
tff(c_204,plain,
! [V0R_1261,V1x_1289,A_27b_1205,A_27a_1093,V2y_1303] :
( ( c_2Eoption_2ENONE(A_27a_1093) = V1x_1289 )
| ( ap(c_2Eoption_2ESOME(A_27b_1205),'#skF_6'(V2y_1303,V0R_1261,A_27b_1205,A_27a_1093,V1x_1289)) = V2y_1303 )
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_1093,A_27b_1205),V0R_1261),V1x_1289),V2y_1303))
| ~ mem(V2y_1303,ty_2Eoption_2Eoption(A_27b_1205))
| ~ mem(V1x_1289,ty_2Eoption_2Eoption(A_27a_1093))
| ~ mem(V0R_1261,arr(A_27a_1093,arr(A_27b_1205,bool)))
| ~ ne(A_27b_1205)
| ~ ne(A_27a_1093) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_180823,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_180819,c_204]) ).
tff(c_180843,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_180823]) ).
tff(c_250125,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_225176,c_189952,c_180843]) ).
tff(c_250126,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = c_2Eoption_2ENONE('#skF_7'),
inference(negUnitSimplification,[status(thm)],[c_249407,c_250125]) ).
tff(c_250130,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_250126,c_194604]) ).
tff(c_250151,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_225916,c_202525,c_250130]) ).
tff(c_250153,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_250151]) ).
tff(c_250154,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_225915]) ).
tff(c_250177,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_9','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_250154,c_194604]) ).
tff(c_250257,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_202525,c_250177]) ).
tff(c_250259,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_250257]) ).
tff(c_250260,plain,
ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_201925]) ).
tff(c_250270,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ p(c_2Ebool_2ET)
| ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598)
| ~ ne('#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_250260,c_171]) ).
tff(c_250282,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_50,c_250270]) ).
tff(c_250424,plain,
! [V1f_5655,A_27b_5656,V0e_5657] :
( ~ mem(V1f_5655,arr('#skF_7',A_27b_5656))
| ~ mem(V0e_5657,A_27b_5656)
| ~ ne(A_27b_5656) ),
inference(splitLeft,[status(thm)],[c_250282]) ).
tff(c_250531,plain,
! [V0e_5657] :
( ~ mem(V0e_5657,ty_2Eoption_2Eoption('#skF_7'))
| ~ ne(ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_62,c_250424]) ).
tff(c_250594,plain,
! [V0e_5657] : ~ mem(V0e_5657,ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_189944,c_250531]) ).
tff(c_250599,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_250594,c_189952]) ).
tff(c_250600,plain,
! [V2e_1032] : ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_250282]) ).
tff(c_250631,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_250600,c_189952]) ).
tff(c_250633,plain,
~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7'))),
inference(splitRight,[status(thm)],[c_180818]) ).
tff(c_283721,plain,
! [B_6084] :
( mem(c_2Eoption_2ENONE('#skF_7'),B_6084)
| ~ mem(c_2Eoption_2EOPTION__JOIN('#skF_7'),arr(ty_2Eoption_2Eoption(ty_2Eoption_2Eoption('#skF_7')),B_6084)) ),
inference(splitRight,[status(thm)],[c_283536]) ).
tff(c_283725,plain,
( mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_28,c_283721]) ).
tff(c_283728,plain,
mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_283725]) ).
tff(c_250632,plain,
p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'))),
inference(splitRight,[status(thm)],[c_180818]) ).
tff(c_214,plain,
! [V0R_1261,V1x_1289,A_27b_1205,A_27a_1093,V2y_1303] :
( ( c_2Eoption_2ENONE(A_27b_1205) = V2y_1303 )
| mem('#skF_5'(V2y_1303,V0R_1261,A_27b_1205,A_27a_1093,V1x_1289),A_27a_1093)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_1093,A_27b_1205),V0R_1261),V1x_1289),V2y_1303))
| ~ mem(V2y_1303,ty_2Eoption_2Eoption(A_27b_1205))
| ~ mem(V1x_1289,ty_2Eoption_2Eoption(A_27a_1093))
| ~ mem(V0R_1261,arr(A_27a_1093,arr(A_27b_1205,bool)))
| ~ ne(A_27b_1205)
| ~ ne(A_27a_1093) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_250645,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_250632,c_214]) ).
tff(c_250672,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_250645]) ).
tff(c_323003,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_283728,c_250672]) ).
tff(c_323004,plain,
~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_323003]) ).
tff(c_323008,plain,
~ mem(c_2Eoption_2ESOME('#skF_7'),arr('#skF_7',ty_2Eoption_2Eoption('#skF_7'))),
inference(resolution,[status(thm)],[c_15530,c_323004]) ).
tff(c_323011,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_62,c_323008]) ).
tff(c_323015,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_323011]) ).
tff(c_323016,plain,
( mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_323003]) ).
tff(c_338646,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7'),
inference(splitLeft,[status(thm)],[c_323016]) ).
tff(c_338652,plain,
p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7'))),
inference(demodulation,[status(thm),theory(equality)],[c_338646,c_15454]) ).
tff(c_338656,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_250633,c_338652]) ).
tff(c_338657,plain,
mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7'),
inference(splitRight,[status(thm)],[c_323016]) ).
tff(c_283825,plain,
! [F_6087,B_6088] :
( mem(ap(F_6087,c_2Eoption_2ENONE('#skF_7')),B_6088)
| ~ mem(F_6087,arr(ty_2Eoption_2Eoption('#skF_7'),B_6088)) ),
inference(resolution,[status(thm)],[c_283728,c_8]) ).
tff(c_286445,plain,
! [F_6128] :
( p(ap(F_6128,c_2Eoption_2ENONE('#skF_7')))
| ( ap(F_6128,c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ mem(F_6128,arr(ty_2Eoption_2Eoption('#skF_7'),bool)) ),
inference(resolution,[status(thm)],[c_283825,c_15411]) ).
tff(c_286573,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF )
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_52,c_286445]) ).
tff(c_286621,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ( ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF ) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_286573]) ).
tff(c_286973,plain,
ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2EF,
inference(splitLeft,[status(thm)],[c_286621]) ).
tff(c_338658,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') != c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_323016]) ).
tff(c_323017,plain,
mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_323003]) ).
tff(c_206,plain,
! [V0R_1261,V1x_1289,A_27b_1205,A_27a_1093,V2y_1303] :
( ( c_2Eoption_2ENONE(A_27b_1205) = V2y_1303 )
| ( ap(c_2Eoption_2ESOME(A_27a_1093),'#skF_5'(V2y_1303,V0R_1261,A_27b_1205,A_27a_1093,V1x_1289)) = V1x_1289 )
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_1093,A_27b_1205),V0R_1261),V1x_1289),V2y_1303))
| ~ mem(V2y_1303,ty_2Eoption_2Eoption(A_27b_1205))
| ~ mem(V1x_1289,ty_2Eoption_2Eoption(A_27a_1093))
| ~ mem(V0R_1261,arr(A_27a_1093,arr(A_27b_1205,bool)))
| ~ ne(A_27b_1205)
| ~ ne(A_27a_1093) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_250639,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_250632,c_206]) ).
tff(c_250662,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_250639]) ).
tff(c_340389,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_283728,c_323017,c_250662]) ).
tff(c_340390,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7'))) = c_2Eoption_2ENONE('#skF_7'),
inference(negUnitSimplification,[status(thm)],[c_338658,c_340389]) ).
tff(c_286622,plain,
! [V0e_6133,A_27a_6129,V8x_6132,V1f_6131,A_27b_6130] :
( p(ap(c_2Eoption_2EIS__SOME(A_27a_6129),ap(c_2Eoption_2ESOME(A_27a_6129),V8x_6132)))
| ~ mem(V8x_6132,A_27a_6129)
| ~ mem(V1f_6131,arr(A_27a_6129,A_27b_6130))
| ~ mem(V0e_6133,A_27b_6130)
| ~ ne(A_27b_6130)
| ~ ne(A_27a_6129) ),
inference(resolution,[status(thm)],[c_72,c_169756]) ).
tff(c_286802,plain,
! [V8x_6132,V0e_6133] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_6132)))
| ~ mem(V8x_6132,'#skF_7')
| ~ mem(V0e_6133,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_286622]) ).
tff(c_286972,plain,
! [V8x_6132,V0e_6133] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_6132)))
| ~ mem(V8x_6132,'#skF_7')
| ~ mem(V0e_6133,arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_281658,c_286802]) ).
tff(c_287009,plain,
! [V0e_6135] : ~ mem(V0e_6135,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_286972]) ).
tff(c_287129,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_287009]) ).
tff(c_287447,plain,
! [V0t_6141] :
( ~ p(V0t_6141)
| ~ mem(V0t_6141,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_281658,c_287129]) ).
tff(c_287686,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_287447]) ).
tff(c_287778,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_287686]) ).
tff(c_287779,plain,
! [V8x_6132] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_6132)))
| ~ mem(V8x_6132,'#skF_7') ),
inference(splitRight,[status(thm)],[c_286972]) ).
tff(c_340397,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_340390,c_287779]) ).
tff(c_340417,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_338657,c_286973,c_340397]) ).
tff(c_340419,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_340417]) ).
tff(c_340420,plain,
p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7'))),
inference(splitRight,[status(thm)],[c_286621]) ).
tff(c_340423,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598)
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_340420,c_171]) ).
tff(c_340428,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_340423]) ).
tff(c_343528,plain,
! [V1f_6880,A_27b_6881,V0e_6882] :
( ~ mem(V1f_6880,arr('#skF_7',A_27b_6881))
| ~ mem(V0e_6882,A_27b_6881)
| ~ ne(A_27b_6881) ),
inference(splitLeft,[status(thm)],[c_340428]) ).
tff(c_343632,plain,
! [V0e_6882] :
( ~ mem(V0e_6882,ty_2Eoption_2Eoption('#skF_7'))
| ~ ne(ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_62,c_343528]) ).
tff(c_343694,plain,
! [V0e_6882] : ~ mem(V0e_6882,ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_283720,c_343632]) ).
tff(c_343699,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_343694,c_283728]) ).
tff(c_343700,plain,
! [V2e_1032] : ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_340428]) ).
tff(c_343702,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_343700,c_283728]) ).
tff(c_343703,plain,
( p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7'))) ),
inference(splitRight,[status(thm)],[c_15284]) ).
tff(c_356233,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10')))
| p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7'))) ),
inference(negUnitSimplification,[status(thm)],[c_346817,c_343703]) ).
tff(c_356234,plain,
p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),c_2Eoption_2ENONE('#skF_7'))),
inference(splitLeft,[status(thm)],[c_356233]) ).
tff(c_358309,plain,
! [V0R_7507,A_27b_7508,V1x_7510,A_27a_7509,V2y_7506] :
( ( c_2Eoption_2ENONE(A_27a_7509) = V1x_7510 )
| mem('#skF_5'(V2y_7506,V0R_7507,A_27b_7508,A_27a_7509,V1x_7510),A_27a_7509)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_7509,A_27b_7508),V0R_7507),V1x_7510),V2y_7506))
| ~ mem(V2y_7506,ty_2Eoption_2Eoption(A_27b_7508))
| ~ mem(V1x_7510,ty_2Eoption_2Eoption(A_27a_7509))
| ~ mem(V0R_7507,arr(A_27a_7509,arr(A_27b_7508,bool)))
| ~ ne(A_27b_7508)
| ~ ne(A_27a_7509) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_358311,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_356234,c_358309]) ).
tff(c_358318,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_358311]) ).
tff(c_403037,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_369282,c_358318]) ).
tff(c_403038,plain,
~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_403037]) ).
tff(c_403042,plain,
~ mem(c_2Eoption_2ESOME('#skF_7'),arr('#skF_7',ty_2Eoption_2Eoption('#skF_7'))),
inference(resolution,[status(thm)],[c_343781,c_403038]) ).
tff(c_403045,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_62,c_403042]) ).
tff(c_403049,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_403045]) ).
tff(c_403051,plain,
mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_403037]) ).
tff(c_359388,plain,
! [V0R_7544,V2y_7543,A_27a_7546,V1x_7547,A_27b_7545] :
( ( c_2Eoption_2ENONE(A_27a_7546) = V1x_7547 )
| mem('#skF_6'(V2y_7543,V0R_7544,A_27b_7545,A_27a_7546,V1x_7547),A_27b_7545)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_7546,A_27b_7545),V0R_7544),V1x_7547),V2y_7543))
| ~ mem(V2y_7543,ty_2Eoption_2Eoption(A_27b_7545))
| ~ mem(V1x_7547,ty_2Eoption_2Eoption(A_27a_7546))
| ~ mem(V0R_7544,arr(A_27a_7546,arr(A_27b_7545,bool)))
| ~ ne(A_27b_7545)
| ~ ne(A_27a_7546) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_359390,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_356234,c_359388]) ).
tff(c_359397,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_359390]) ).
tff(c_404194,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_403051,c_369282,c_359397]) ).
tff(c_404195,plain,
mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7'),
inference(splitLeft,[status(thm)],[c_404194]) ).
tff(c_403050,plain,
( mem('#skF_5'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7')
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_403037]) ).
tff(c_410222,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7'),
inference(splitLeft,[status(thm)],[c_403050]) ).
tff(c_351977,plain,
! [V1f_7312,A_27b_7307,V8x_7311,A_27a_7310,V2e_7308,V0e_7309] :
( p(ap(c_2Eoption_2EIS__SOME(A_27a_7310),ap(c_2Eoption_2ESOME(A_27a_7310),V8x_7311)))
| ~ mem(V8x_7311,A_27a_7310)
| ~ mem(V2e_7308,ty_2Eoption_2Eoption(A_27a_7310))
| ~ mem(V1f_7312,arr(A_27a_7310,A_27b_7307))
| ~ mem(V0e_7309,A_27b_7307)
| ~ ne(A_27b_7307)
| ~ ne(A_27a_7310) ),
inference(cnfTransformation,[status(thm)],[f_522]) ).
tff(c_374426,plain,
! [V8x_7783,A_27b_7786,V0e_7785,V1f_7784,A_27a_7782] :
( p(ap(c_2Eoption_2EIS__SOME(A_27a_7782),ap(c_2Eoption_2ESOME(A_27a_7782),V8x_7783)))
| ~ mem(V8x_7783,A_27a_7782)
| ~ mem(V1f_7784,arr(A_27a_7782,A_27b_7786))
| ~ mem(V0e_7785,A_27b_7786)
| ~ ne(A_27b_7786)
| ~ ne(A_27a_7782) ),
inference(resolution,[status(thm)],[c_72,c_351977]) ).
tff(c_374606,plain,
! [V8x_7783,V0e_7785] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_7783)))
| ~ mem(V8x_7783,'#skF_7')
| ~ mem(V0e_7785,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_374426]) ).
tff(c_374776,plain,
! [V8x_7783,V0e_7785] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_7783)))
| ~ mem(V8x_7783,'#skF_7')
| ~ mem(V0e_7785,arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_367163,c_374606]) ).
tff(c_374924,plain,
! [V0e_7792] : ~ mem(V0e_7792,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_374776]) ).
tff(c_375044,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_374924]) ).
tff(c_375362,plain,
! [V0t_7798] :
( ~ p(V0t_7798)
| ~ mem(V0t_7798,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_367163,c_375044]) ).
tff(c_375601,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_375362]) ).
tff(c_375693,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_375601]) ).
tff(c_375694,plain,
! [V8x_7783] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_7783)))
| ~ mem(V8x_7783,'#skF_7') ),
inference(splitRight,[status(thm)],[c_374776]) ).
tff(c_410246,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_9','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_410222,c_375694]) ).
tff(c_410326,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_381959,c_410246]) ).
tff(c_410328,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_410326]) ).
tff(c_410330,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') != c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_403050]) ).
tff(c_363182,plain,
! [A_27b_7645,V0R_7644,A_27a_7646,V2y_7643,V1x_7647] :
( ( c_2Eoption_2ENONE(A_27a_7646) = V1x_7647 )
| ( ap(c_2Eoption_2ESOME(A_27b_7645),'#skF_6'(V2y_7643,V0R_7644,A_27b_7645,A_27a_7646,V1x_7647)) = V2y_7643 )
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_7646,A_27b_7645),V0R_7644),V1x_7647),V2y_7643))
| ~ mem(V2y_7643,ty_2Eoption_2Eoption(A_27b_7645))
| ~ mem(V1x_7647,ty_2Eoption_2Eoption(A_27a_7646))
| ~ mem(V0R_7644,arr(A_27a_7646,arr(A_27b_7645,bool)))
| ~ ne(A_27b_7645)
| ~ ne(A_27a_7646) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_363184,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_356234,c_363182]) ).
tff(c_363191,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_363184]) ).
tff(c_414074,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_403051,c_369282,c_363191]) ).
tff(c_414075,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'))) = c_2Eoption_2ENONE('#skF_7'),
inference(negUnitSimplification,[status(thm)],[c_410330,c_414074]) ).
tff(c_414079,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_6'(c_2Eoption_2ENONE('#skF_7'),'#skF_8','#skF_7','#skF_7',ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_414075,c_375694]) ).
tff(c_414100,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_404195,c_381959,c_414079]) ).
tff(c_414102,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_414100]) ).
tff(c_414103,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9') = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_404194]) ).
tff(c_414121,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_9','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_414103,c_375694]) ).
tff(c_414201,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_220,c_381959,c_414121]) ).
tff(c_414203,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_414201]) ).
tff(c_414204,plain,
ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')) = c_2Ebool_2ET,
inference(splitRight,[status(thm)],[c_381721]) ).
tff(c_414214,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ p(c_2Ebool_2ET)
| ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598)
| ~ ne('#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_414204,c_171]) ).
tff(c_414226,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_50,c_414214]) ).
tff(c_414242,plain,
! [V1f_8416,A_27b_8417,V0e_8418] :
( ~ mem(V1f_8416,arr('#skF_7',A_27b_8417))
| ~ mem(V0e_8418,A_27b_8417)
| ~ ne(A_27b_8417) ),
inference(splitLeft,[status(thm)],[c_414226]) ).
tff(c_414352,plain,
! [V0e_8418] :
( ~ mem(V0e_8418,ty_2Eoption_2Eoption('#skF_7'))
| ~ ne(ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_62,c_414242]) ).
tff(c_414416,plain,
! [V0e_8418] : ~ mem(V0e_8418,ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_369274,c_414352]) ).
tff(c_414421,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_414416,c_369282]) ).
tff(c_414422,plain,
! [V2e_1032] : ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_414226]) ).
tff(c_414434,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_414422,c_369282]) ).
tff(c_414435,plain,
p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),c_2Eoption_2ENONE('#skF_7')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'))),
inference(splitRight,[status(thm)],[c_356233]) ).
tff(c_417604,plain,
! [V0R_8525,V1x_8528,V2y_8524,A_27a_8527,A_27b_8526] :
( ( c_2Eoption_2ENONE(A_27b_8526) = V2y_8524 )
| mem('#skF_6'(V2y_8524,V0R_8525,A_27b_8526,A_27a_8527,V1x_8528),A_27b_8526)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_8527,A_27b_8526),V0R_8525),V1x_8528),V2y_8524))
| ~ mem(V2y_8524,ty_2Eoption_2Eoption(A_27b_8526))
| ~ mem(V1x_8528,ty_2Eoption_2Eoption(A_27a_8527))
| ~ mem(V0R_8525,arr(A_27a_8527,arr(A_27b_8526,bool)))
| ~ ne(A_27b_8526)
| ~ ne(A_27a_8527) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_417606,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_414435,c_417604]) ).
tff(c_417613,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_417606]) ).
tff(c_463295,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_429042,c_417613]) ).
tff(c_463296,plain,
~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_463295]) ).
tff(c_463300,plain,
~ mem(c_2Eoption_2ESOME('#skF_7'),arr('#skF_7',ty_2Eoption_2Eoption('#skF_7'))),
inference(resolution,[status(thm)],[c_343780,c_463296]) ).
tff(c_463303,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_62,c_463300]) ).
tff(c_463307,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_463303]) ).
tff(c_463309,plain,
mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_463295]) ).
tff(c_416884,plain,
! [A_27a_8510,V1x_8511,V0R_8508,A_27b_8509,V2y_8507] :
( ( c_2Eoption_2ENONE(A_27b_8509) = V2y_8507 )
| mem('#skF_5'(V2y_8507,V0R_8508,A_27b_8509,A_27a_8510,V1x_8511),A_27a_8510)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_8510,A_27b_8509),V0R_8508),V1x_8511),V2y_8507))
| ~ mem(V2y_8507,ty_2Eoption_2Eoption(A_27b_8509))
| ~ mem(V1x_8511,ty_2Eoption_2Eoption(A_27a_8510))
| ~ mem(V0R_8508,arr(A_27a_8510,arr(A_27b_8509,bool)))
| ~ ne(A_27b_8509)
| ~ ne(A_27a_8510) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_416886,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_414435,c_416884]) ).
tff(c_416893,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_416886]) ).
tff(c_464731,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7') ),
inference(demodulation,[status(thm),theory(equality)],[c_429042,c_463309,c_416893]) ).
tff(c_464732,plain,
mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7'),
inference(splitLeft,[status(thm)],[c_464731]) ).
tff(c_463308,plain,
( mem('#skF_6'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7')
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') ) ),
inference(splitRight,[status(thm)],[c_463295]) ).
tff(c_471809,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7'),
inference(splitLeft,[status(thm)],[c_463308]) ).
tff(c_433476,plain,
! [A_27b_8792,V1f_8790,A_27a_8788,V0e_8791,V8x_8789] :
( p(ap(c_2Eoption_2EIS__SOME(A_27a_8788),ap(c_2Eoption_2ESOME(A_27a_8788),V8x_8789)))
| ~ mem(V8x_8789,A_27a_8788)
| ~ mem(V1f_8790,arr(A_27a_8788,A_27b_8792))
| ~ mem(V0e_8791,A_27b_8792)
| ~ ne(A_27b_8792)
| ~ ne(A_27a_8788) ),
inference(resolution,[status(thm)],[c_72,c_351977]) ).
tff(c_433656,plain,
! [V8x_8789,V0e_8791] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_8789)))
| ~ mem(V8x_8789,'#skF_7')
| ~ mem(V0e_8791,arr('#skF_7',bool))
| ~ ne(arr('#skF_7',bool))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_222,c_433476]) ).
tff(c_433826,plain,
! [V8x_8789,V0e_8791] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_8789)))
| ~ mem(V8x_8789,'#skF_7')
| ~ mem(V0e_8791,arr('#skF_7',bool)) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_426918,c_433656]) ).
tff(c_433839,plain,
! [V0e_8793] : ~ mem(V0e_8793,arr('#skF_7',bool)),
inference(splitLeft,[status(thm)],[c_433826]) ).
tff(c_433959,plain,
! [V0t_91] :
( ~ p(V0t_91)
| ~ mem(V0t_91,bool)
| ~ ne(arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_130,c_433839]) ).
tff(c_434277,plain,
! [V0t_8799] :
( ~ p(V0t_8799)
| ~ mem(V0t_8799,bool) ),
inference(demodulation,[status(thm),theory(equality)],[c_426918,c_433959]) ).
tff(c_434516,plain,
~ p(c_2Ebool_2ET),
inference(resolution,[status(thm)],[c_48,c_434277]) ).
tff(c_434608,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_50,c_434516]) ).
tff(c_434609,plain,
! [V8x_8789] :
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),ap(c_2Eoption_2ESOME('#skF_7'),V8x_8789)))
| ~ mem(V8x_8789,'#skF_7') ),
inference(splitRight,[status(thm)],[c_433826]) ).
tff(c_471978,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_10','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_471809,c_434609]) ).
tff(c_472058,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_439356,c_471978]) ).
tff(c_472060,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_472058]) ).
tff(c_472062,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') != c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_463308]) ).
tff(c_419252,plain,
! [A_27b_8574,V1x_8576,V0R_8573,A_27a_8575,V2y_8572] :
( ( c_2Eoption_2ENONE(A_27b_8574) = V2y_8572 )
| ( ap(c_2Eoption_2ESOME(A_27a_8575),'#skF_5'(V2y_8572,V0R_8573,A_27b_8574,A_27a_8575,V1x_8576)) = V1x_8576 )
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_8575,A_27b_8574),V0R_8573),V1x_8576),V2y_8572))
| ~ mem(V2y_8572,ty_2Eoption_2Eoption(A_27b_8574))
| ~ mem(V1x_8576,ty_2Eoption_2Eoption(A_27a_8575))
| ~ mem(V0R_8573,arr(A_27a_8575,arr(A_27b_8574,bool)))
| ~ ne(A_27b_8574)
| ~ ne(A_27a_8575) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_419254,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_414435,c_419252]) ).
tff(c_419261,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') )
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(c_2Eoption_2ENONE('#skF_7'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_419254]) ).
tff(c_477042,plain,
( ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7') )
| ( ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7'))) = c_2Eoption_2ENONE('#skF_7') ) ),
inference(demodulation,[status(thm),theory(equality)],[c_429042,c_463309,c_419261]) ).
tff(c_477043,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7'))) = c_2Eoption_2ENONE('#skF_7'),
inference(negUnitSimplification,[status(thm)],[c_472062,c_477042]) ).
tff(c_477047,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_5'(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),'#skF_8','#skF_7','#skF_7',c_2Eoption_2ENONE('#skF_7')),'#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_477043,c_434609]) ).
tff(c_477068,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_464732,c_439356,c_477047]) ).
tff(c_477070,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_477068]) ).
tff(c_477071,plain,
ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10') = c_2Eoption_2ENONE('#skF_7'),
inference(splitRight,[status(thm)],[c_464731]) ).
tff(c_477097,plain,
( p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7')))
| ~ mem('#skF_10','#skF_7') ),
inference(superposition,[status(thm),theory(equality)],[c_477071,c_434609]) ).
tff(c_477177,plain,
p(c_2Ebool_2EF),
inference(demodulation,[status(thm),theory(equality)],[c_218,c_439356,c_477097]) ).
tff(c_477179,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_46,c_477177]) ).
tff(c_477180,plain,
p(ap(c_2Eoption_2EIS__SOME('#skF_7'),c_2Eoption_2ENONE('#skF_7'))),
inference(splitRight,[status(thm)],[c_439229]) ).
tff(c_477183,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598)
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_477180,c_171]) ).
tff(c_477188,plain,
! [V2e_1032,V1f_970,A_27b_598,V0e_846] :
( ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(V1f_970,arr('#skF_7',A_27b_598))
| ~ mem(V0e_846,A_27b_598)
| ~ ne(A_27b_598) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_477183]) ).
tff(c_477317,plain,
! [V1f_9462,A_27b_9463,V0e_9464] :
( ~ mem(V1f_9462,arr('#skF_7',A_27b_9463))
| ~ mem(V0e_9464,A_27b_9463)
| ~ ne(A_27b_9463) ),
inference(splitLeft,[status(thm)],[c_477188]) ).
tff(c_477424,plain,
! [V0e_9464] :
( ~ mem(V0e_9464,ty_2Eoption_2Eoption('#skF_7'))
| ~ ne(ty_2Eoption_2Eoption('#skF_7'))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_62,c_477317]) ).
tff(c_477487,plain,
! [V0e_9464] : ~ mem(V0e_9464,ty_2Eoption_2Eoption('#skF_7')),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_428352,c_477424]) ).
tff(c_477492,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_477487,c_429042]) ).
tff(c_477493,plain,
! [V2e_1032] : ~ mem(V2e_1032,ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_477188]) ).
tff(c_477495,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_477493,c_429042]) ).
tff(c_477497,plain,
p(ap(ap('#skF_8','#skF_9'),'#skF_10')),
inference(splitRight,[status(thm)],[c_15383]) ).
tff(c_343843,plain,
! [F_6894,B_6895] :
( mem(ap(F_6894,'#skF_10'),B_6895)
| ~ mem(F_6894,arr('#skF_7',B_6895)) ),
inference(resolution,[status(thm)],[c_218,c_343724]) ).
tff(c_477550,plain,
! [F_9481] :
( ~ p(ap(F_9481,'#skF_10'))
| ( ap(F_9481,'#skF_10') = c_2Ebool_2ET )
| ~ mem(F_9481,arr('#skF_7',bool)) ),
inference(resolution,[status(thm)],[c_343843,c_15452]) ).
tff(c_489588,plain,
! [F_9934] :
( ~ p(ap(ap(F_9934,'#skF_9'),'#skF_10'))
| ( ap(ap(F_9934,'#skF_9'),'#skF_10') = c_2Ebool_2ET )
| ~ mem(F_9934,arr('#skF_7',arr('#skF_7',bool))) ),
inference(resolution,[status(thm)],[c_343781,c_477550]) ).
tff(c_489671,plain,
( ~ p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| ( ap(ap('#skF_8','#skF_9'),'#skF_10') = c_2Ebool_2ET ) ),
inference(resolution,[status(thm)],[c_222,c_489588]) ).
tff(c_489710,plain,
ap(ap('#skF_8','#skF_9'),'#skF_10') = c_2Ebool_2ET,
inference(demodulation,[status(thm),theory(equality)],[c_477497,c_489671]) ).
tff(c_495531,plain,
! [A_27b_10105,V3x0_10104,A_27a_10107,V0R_10103,V4y0_10106] :
( ~ p(ap(ap(V0R_10103,V3x0_10104),V4y0_10106))
| ~ mem(V4y0_10106,A_27b_10105)
| ~ mem(V3x0_10104,A_27a_10107)
| p(ap(ap(ap(c_2Eoption_2EOPTREL(A_27a_10107,A_27b_10105),V0R_10103),ap(c_2Eoption_2ESOME(A_27a_10107),V3x0_10104)),ap(c_2Eoption_2ESOME(A_27b_10105),V4y0_10106)))
| ~ mem(ap(c_2Eoption_2ESOME(A_27b_10105),V4y0_10106),ty_2Eoption_2Eoption(A_27b_10105))
| ~ mem(ap(c_2Eoption_2ESOME(A_27a_10107),V3x0_10104),ty_2Eoption_2Eoption(A_27a_10107))
| ~ mem(V0R_10103,arr(A_27a_10107,arr(A_27b_10105,bool)))
| ~ ne(A_27b_10105)
| ~ ne(A_27a_10107) ),
inference(cnfTransformation,[status(thm)],[f_554]) ).
tff(c_343704,plain,
~ p(ap(ap(ap(c_2Eoption_2EOPTREL('#skF_7','#skF_7'),'#skF_8'),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9')),ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'))),
inference(splitRight,[status(thm)],[c_15284]) ).
tff(c_495556,plain,
( ~ p(ap(ap('#skF_8','#skF_9'),'#skF_10'))
| ~ mem('#skF_10','#skF_7')
| ~ mem('#skF_9','#skF_7')
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem('#skF_8',arr('#skF_7',arr('#skF_7',bool)))
| ~ ne('#skF_7') ),
inference(resolution,[status(thm)],[c_495531,c_343704]) ).
tff(c_495570,plain,
( ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7'))
| ~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')) ),
inference(demodulation,[status(thm),theory(equality)],[c_224,c_222,c_220,c_218,c_50,c_489710,c_495556]) ).
tff(c_496126,plain,
~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_9'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitLeft,[status(thm)],[c_495570]) ).
tff(c_496130,plain,
~ mem(c_2Eoption_2ESOME('#skF_7'),arr('#skF_7',ty_2Eoption_2Eoption('#skF_7'))),
inference(resolution,[status(thm)],[c_343781,c_496126]) ).
tff(c_496133,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_62,c_496130]) ).
tff(c_496137,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_496133]) ).
tff(c_496138,plain,
~ mem(ap(c_2Eoption_2ESOME('#skF_7'),'#skF_10'),ty_2Eoption_2Eoption('#skF_7')),
inference(splitRight,[status(thm)],[c_495570]) ).
tff(c_496144,plain,
~ mem(c_2Eoption_2ESOME('#skF_7'),arr('#skF_7',ty_2Eoption_2Eoption('#skF_7'))),
inference(resolution,[status(thm)],[c_343780,c_496138]) ).
tff(c_496228,plain,
~ ne('#skF_7'),
inference(resolution,[status(thm)],[c_62,c_496144]) ).
tff(c_496232,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_224,c_496228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP011+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.00/0.14 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 3 18:32:38 EDT 2023
% 0.13/0.36 % CPUTime :
% 105.32/81.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 105.54/81.81
% 105.54/81.81 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 105.95/81.88
% 105.95/81.88 Inference rules
% 105.95/81.88 ----------------------
% 105.95/81.88 #Ref : 11
% 105.95/81.88 #Sup : 106497
% 105.95/81.88 #Fact : 13
% 105.95/81.88 #Define : 0
% 105.95/81.88 #Split : 670
% 105.95/81.88 #Chain : 0
% 105.95/81.88 #Close : 0
% 105.95/81.88
% 105.95/81.88 Ordering : KBO
% 105.95/81.88
% 105.95/81.88 Simplification rules
% 105.95/81.88 ----------------------
% 105.95/81.88 #Subsume : 12785
% 105.95/81.88 #Demod : 40472
% 105.95/81.88 #Tautology : 6560
% 105.95/81.88 #SimpNegUnit : 13378
% 105.95/81.88 #BackRed : 11748
% 105.95/81.88
% 105.95/81.88 #Partial instantiations: 0
% 105.95/81.88 #Strategies tried : 1
% 105.95/81.88
% 105.95/81.88 Timing (in seconds)
% 105.95/81.88 ----------------------
% 105.95/81.89 Preprocessing : 0.75
% 105.95/81.89 Parsing : 0.24
% 105.95/81.89 CNF conversion : 0.09
% 105.95/81.89 Main loop : 79.98
% 105.95/81.89 Inferencing : 13.02
% 105.95/81.89 Reduction : 33.59
% 105.95/81.89 Demodulation : 26.62
% 105.95/81.89 BG Simplification : 0.85
% 105.95/81.89 Subsumption : 25.88
% 105.95/81.89 Abstraction : 1.33
% 105.95/81.89 MUC search : 0.00
% 105.95/81.89 Cooper : 0.00
% 105.95/81.89 Total : 80.88
% 105.95/81.89 Index Insertion : 0.00
% 105.95/81.89 Index Deletion : 0.00
% 105.95/81.89 Index Matching : 0.00
% 105.95/81.89 BG Taut test : 0.00
%------------------------------------------------------------------------------