%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP011_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 11:28:02 AM UTC 2026
% Result : Theorem 4.85s 1.82s
% Output : Refutation 6.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 33
% Syntax : Number of formulae : 253 ( 33 unt; 0 typ; 27 def)
% Number of atoms : 2360 ( 223 equ)
% Maximal formula atoms : 55 ( 9 avg)
% Number of connectives : 1513 ( 575 ~; 563 |; 211 &)
% ( 56 <=>; 107 =>; 0 <=; 1 <~>)
% Maximal formula depth : 33 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1169 (1169 fml; 0 var)
% Number of types : 4 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 36 ( 33 usr; 27 prp; 0-5 aty)
% Number of functors : 30 ( 30 usr; 5 con; 0-5 aty)
% Number of variables : 499 ( 0 sgn 481 !; 18 ?; 499 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
del: $tType ).
tff(type_def_6,type,
tp__o: $tType ).
tff(func_def_0,type,
bool: del ).
tff(func_def_1,type,
ind: del ).
tff(func_def_2,type,
arr: ( del * del ) > del ).
tff(func_def_4,type,
k: ( del * $i ) > $i ).
tff(func_def_5,type,
i: del > $i ).
tff(func_def_6,type,
ty_2Eoption_2Eoption: del > del ).
tff(func_def_7,type,
c_2Eoption_2EOPTION__JOIN: del > $i ).
tff(func_def_8,type,
c_2Eoption_2EOPTION__MAP: ( del * del ) > $i ).
tff(func_def_9,type,
c_2Eoption_2Eoption__CASE: ( del * del ) > $i ).
tff(func_def_10,type,
inj__o: tp__o > $i ).
tff(func_def_11,type,
surj__o: $i > tp__o ).
tff(func_def_13,type,
fo__c_2Emin_2E_3D_3D_3E: ( tp__o * tp__o ) > tp__o ).
tff(func_def_14,type,
c_2Eoption_2EIS__NONE: del > $i ).
tff(func_def_16,type,
fo__c_2Ebool_2EF: tp__o ).
tff(func_def_18,type,
fo__c_2Ebool_2ET: tp__o ).
tff(func_def_19,type,
c_2Eoption_2EIS__SOME: del > $i ).
tff(func_def_21,type,
fo__c_2Ebool_2E_7E: tp__o > tp__o ).
tff(func_def_22,type,
c_2Eoption_2ETHE: del > $i ).
tff(func_def_23,type,
c_2Eoption_2ESOME: del > $i ).
tff(func_def_24,type,
c_2Ebool_2E_3F: del > $i ).
tff(func_def_25,type,
c_2Eoption_2ENONE: del > $i ).
tff(func_def_27,type,
fo__c_2Ebool_2E_2F_5C: ( tp__o * tp__o ) > tp__o ).
tff(func_def_29,type,
fo__c_2Ebool_2E_5C_2F: ( tp__o * tp__o ) > tp__o ).
tff(func_def_30,type,
c_2Eoption_2EOPTREL: ( del * del ) > $i ).
tff(func_def_31,type,
c_2Emin_2E_3D: del > $i ).
tff(func_def_32,type,
c_2Ebool_2E_21: del > $i ).
tff(func_def_33,type,
sK5: del ).
tff(func_def_37,type,
sK9: ( del * del * $i * $i * $i ) > $i ).
tff(func_def_38,type,
sK10: ( del * del * $i * $i * $i ) > $i ).
tff(func_def_39,type,
sK11: ( del * $i * $i ) > $i ).
tff(pred_def_1,type,
mem: ( $i * del ) > $o ).
tff(pred_def_3,type,
sP0: ( del * del * $i * $i * $i ) > $o ).
tff(pred_def_4,type,
sP1: del > $o ).
tff(pred_def_5,type,
sP2: del > $o ).
tff(pred_def_6,type,
sP3: del > $o ).
tff(pred_def_7,type,
sP4: ( del * $i * $i * del * $i ) > $o ).
tff(f1,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,X1))
=> ! [X3: $i] :
( mem(X3,X0)
=> mem(ap(X2,X3),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap_tp) ).
tff(f27,axiom,
! [X0: del] : mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ESOME) ).
tff(f30,axiom,
! [X0: del] : mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mem_c_2Eoption_2ENONE) ).
tff(f51,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,X1)
=> ! [X3: $i] :
( mem(X3,arr(X0,X1))
=> ! [X4: $i] :
( mem(X4,ty_2Eoption_2Eoption(X0))
=> ( ! [X5: $i] :
( mem(X5,X0)
=> ! [X6: $i] :
( mem(X6,X0)
=> ( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6) )
<=> ( X5 = X6 ) ) ) )
& ! [X7: $i] :
( mem(X7,X0)
=> ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 ) )
& ! [X8: $i] :
( mem(X8,X0)
=> ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) ) )
& ! [X9: $i] :
( mem(X9,X0)
=> ( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) ) )
& ! [X10: $i] :
( mem(X10,X0)
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
<=> $true ) )
& ( p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
<=> $false )
& ! [X11: $i] :
( mem(X11,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> ( X11 = c_2Eoption_2ENONE(X0) ) ) )
& ! [X12: $i] :
( mem(X12,ty_2Eoption_2Eoption(X0))
=> ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> ( X12 = c_2Eoption_2ENONE(X0) ) ) )
& ! [X13: $i] :
( mem(X13,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X13))
=> ( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 ) ) )
& ! [X14: $i] :
( mem(X14,ty_2Eoption_2Eoption(X0))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 ) )
& ! [X15: $i] :
( mem(X15,ty_2Eoption_2Eoption(X0))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 ) )
& ! [X16: $i] :
( mem(X16,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X16))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 ) ) )
& ! [X17: $i] :
( mem(X17,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X17))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) ) ) )
& ! [X18: $i] :
( mem(X18,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X18))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 ) ) )
& ! [X19: $i] :
( mem(X19,X1)
=> ! [X20: $i] :
( mem(X20,arr(X0,X1))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 ) ) )
& ! [X21: $i] :
( mem(X21,X0)
=> ! [X22: $i] :
( mem(X22,X1)
=> ! [X23: $i] :
( mem(X23,arr(X0,X1))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) ) ) ) )
& ! [X24: $i] :
( mem(X24,arr(X0,X1))
=> ! [X25: $i] :
( mem(X25,X0)
=> ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) ) ) )
& ! [X26: $i] :
( mem(X26,arr(X0,X1))
=> ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) ) )
& ( ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0) )
& ! [X27: $i] :
( mem(X27,ty_2Eoption_2Eoption(X0))
=> ( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Eoption_2Eoption__CLAUSES) ).
tff(f52,axiom,
! [X0: del,X1: del,X2: $i] :
( mem(X2,arr(X0,arr(X1,bool)))
=> ! [X3: $i] :
( mem(X3,ty_2Eoption_2Eoption(X0))
=> ! [X4: $i] :
( mem(X4,ty_2Eoption_2Eoption(X1))
=> ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
<=> ( ( ( X3 = c_2Eoption_2ENONE(X0) )
& ( X4 = c_2Eoption_2ENONE(X1) ) )
| ? [X5: $i] :
( mem(X5,X0)
& ? [X6: $i] :
( mem(X6,X1)
& ( X3 = ap(c_2Eoption_2ESOME(X0),X5) )
& ( X4 = ap(c_2Eoption_2ESOME(X1),X6) )
& p(ap(ap(X2,X5),X6)) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax_thm_2Eoption_2EOPTREL__def) ).
tff(f53,conjecture,
! [X0: del,X1: $i] :
( mem(X1,arr(X0,arr(X0,bool)))
=> ! [X2: $i] :
( mem(X2,X0)
=> ! [X3: $i] :
( mem(X3,X0)
=> ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
<=> $true )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> p(ap(ap(X1,X2),X3)) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_thm_2Equotient__option_2EOPTION__REL__def) ).
tff(f54,negated_conjecture,
~ ! [X0: del,X1: $i] :
( mem(X1,arr(X0,arr(X0,bool)))
=> ! [X2: $i] :
( mem(X2,X0)
=> ! [X3: $i] :
( mem(X3,X0)
=> ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
<=> $true )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> $false )
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> p(ap(ap(X1,X2),X3)) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
tff(f55,plain,
~ ! [X0: del,X1: $i] :
( mem(X1,arr(X0,arr(X0,bool)))
=> ! [X2: $i] :
( mem(X2,X0)
=> ! [X3: $i] :
( mem(X3,X0)
=> ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
& ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
& ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> p(ap(ap(X1,X2),X3)) ) ) ) ) ),
inference(true_and_false_elimination,[],[f54]) ).
tff(f56,plain,
~ ! [X0: del,X1: $i] :
( mem(X1,arr(X0,arr(X0,bool)))
=> ! [X2: $i] :
( mem(X2,X0)
=> ! [X3: $i] :
( mem(X3,X0)
=> ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
& ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
& ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
& ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<=> p(ap(ap(X1,X2),X3)) ) ) ) ) ),
inference(flattening,[],[f55]) ).
tff(f57,plain,
! [X0: del,X1: del,X2: $i] :
( mem(X2,X1)
=> ! [X3: $i] :
( mem(X3,arr(X0,X1))
=> ! [X4: $i] :
( mem(X4,ty_2Eoption_2Eoption(X0))
=> ( ! [X5: $i] :
( mem(X5,X0)
=> ! [X6: $i] :
( mem(X6,X0)
=> ( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6) )
<=> ( X5 = X6 ) ) ) )
& ! [X7: $i] :
( mem(X7,X0)
=> ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 ) )
& ! [X8: $i] :
( mem(X8,X0)
=> ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) ) )
& ! [X9: $i] :
( mem(X9,X0)
=> ( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) ) )
& ! [X10: $i] :
( mem(X10,X0)
=> p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10))) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& ! [X11: $i] :
( mem(X11,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> ( X11 = c_2Eoption_2ENONE(X0) ) ) )
& ! [X12: $i] :
( mem(X12,ty_2Eoption_2Eoption(X0))
=> ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> ( X12 = c_2Eoption_2ENONE(X0) ) ) )
& ! [X13: $i] :
( mem(X13,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X13))
=> ( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 ) ) )
& ! [X14: $i] :
( mem(X14,ty_2Eoption_2Eoption(X0))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 ) )
& ! [X15: $i] :
( mem(X15,ty_2Eoption_2Eoption(X0))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 ) )
& ! [X16: $i] :
( mem(X16,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X16))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 ) ) )
& ! [X17: $i] :
( mem(X17,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X17))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) ) ) )
& ! [X18: $i] :
( mem(X18,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X18))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 ) ) )
& ! [X19: $i] :
( mem(X19,X1)
=> ! [X20: $i] :
( mem(X20,arr(X0,X1))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 ) ) )
& ! [X21: $i] :
( mem(X21,X0)
=> ! [X22: $i] :
( mem(X22,X1)
=> ! [X23: $i] :
( mem(X23,arr(X0,X1))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) ) ) ) )
& ! [X24: $i] :
( mem(X24,arr(X0,X1))
=> ! [X25: $i] :
( mem(X25,X0)
=> ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) ) ) )
& ! [X26: $i] :
( mem(X26,arr(X0,X1))
=> ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) ) )
& ( ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0) )
& ! [X27: $i] :
( mem(X27,ty_2Eoption_2Eoption(X0))
=> ( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 ) ) ) ) ) ),
inference(true_and_false_elimination,[],[f51]) ).
tff(f58,plain,
! [X0: del,X1: del,X2: $i] :
( mem(X2,X1)
=> ! [X3: $i] :
( mem(X3,arr(X0,X1))
=> ! [X4: $i] :
( mem(X4,ty_2Eoption_2Eoption(X0))
=> ( ! [X5: $i] :
( mem(X5,X0)
=> ! [X6: $i] :
( mem(X6,X0)
=> ( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6) )
<=> ( X5 = X6 ) ) ) )
& ! [X7: $i] :
( mem(X7,X0)
=> ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 ) )
& ! [X8: $i] :
( mem(X8,X0)
=> ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) ) )
& ! [X9: $i] :
( mem(X9,X0)
=> ( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) ) )
& ! [X10: $i] :
( mem(X10,X0)
=> p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10))) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& ! [X11: $i] :
( mem(X11,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> ( X11 = c_2Eoption_2ENONE(X0) ) ) )
& ! [X12: $i] :
( mem(X12,ty_2Eoption_2Eoption(X0))
=> ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> ( X12 = c_2Eoption_2ENONE(X0) ) ) )
& ! [X13: $i] :
( mem(X13,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X13))
=> ( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 ) ) )
& ! [X14: $i] :
( mem(X14,ty_2Eoption_2Eoption(X0))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 ) )
& ! [X15: $i] :
( mem(X15,ty_2Eoption_2Eoption(X0))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 ) )
& ! [X16: $i] :
( mem(X16,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__NONE(X0),X16))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 ) ) )
& ! [X17: $i] :
( mem(X17,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X17))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) ) ) )
& ! [X18: $i] :
( mem(X18,ty_2Eoption_2Eoption(X0))
=> ( p(ap(c_2Eoption_2EIS__SOME(X0),X18))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 ) ) )
& ! [X19: $i] :
( mem(X19,X1)
=> ! [X20: $i] :
( mem(X20,arr(X0,X1))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 ) ) )
& ! [X21: $i] :
( mem(X21,X0)
=> ! [X22: $i] :
( mem(X22,X1)
=> ! [X23: $i] :
( mem(X23,arr(X0,X1))
=> ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) ) ) ) )
& ! [X24: $i] :
( mem(X24,arr(X0,X1))
=> ! [X25: $i] :
( mem(X25,X0)
=> ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) ) ) )
& ! [X26: $i] :
( mem(X26,arr(X0,X1))
=> ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) ) )
& ( ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0) )
& ! [X27: $i] :
( mem(X27,ty_2Eoption_2Eoption(X0))
=> ( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 ) ) ) ) ) ),
inference(flattening,[],[f57]) ).
tff(f60,plain,
? [X0: del,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
| ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3)))
<~> p(ap(ap(X1,X2),X3)) ) )
& mem(X3,X0) )
& mem(X2,X0) )
& mem(X1,arr(X0,arr(X0,bool))) ),
inference(ennf_transformation,[],[f56]) ).
tff(f61,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( mem(ap(X2,X3),X1)
| ~ mem(X3,X0) )
| ~ mem(X2,arr(X0,X1)) ),
inference(ennf_transformation,[],[f1]) ).
tff(f62,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
<=> ( ( ( X3 = c_2Eoption_2ENONE(X0) )
& ( X4 = c_2Eoption_2ENONE(X1) ) )
| ? [X5: $i] :
( mem(X5,X0)
& ? [X6: $i] :
( mem(X6,X1)
& ( X3 = ap(c_2Eoption_2ESOME(X0),X5) )
& ( X4 = ap(c_2Eoption_2ESOME(X1),X6) )
& p(ap(ap(X2,X5),X6)) ) ) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(ennf_transformation,[],[f52]) ).
tff(f63,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ! [X5: $i] :
( ! [X6: $i] :
( ( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6) )
<=> ( X5 = X6 ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
& ! [X7: $i] :
( ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 )
| ~ mem(X7,X0) )
& ! [X8: $i] :
( ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) )
| ~ mem(X8,X0) )
& ! [X9: $i] :
( ( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) )
| ~ mem(X9,X0) )
& ! [X10: $i] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
| ~ mem(X10,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& ! [X11: $i] :
( ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> ( X11 = c_2Eoption_2ENONE(X0) ) )
| ~ mem(X11,ty_2Eoption_2Eoption(X0)) )
& ! [X12: $i] :
( ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> ( X12 = c_2Eoption_2ENONE(X0) ) )
| ~ mem(X12,ty_2Eoption_2Eoption(X0)) )
& ! [X13: $i] :
( ( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 )
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 )
| ~ mem(X15,ty_2Eoption_2Eoption(X0)) )
& ! [X16: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 )
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X16))
| ~ mem(X16,ty_2Eoption_2Eoption(X0)) )
& ! [X17: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X17))
| ~ mem(X17,ty_2Eoption_2Eoption(X0)) )
& ! [X18: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X18))
| ~ mem(X18,ty_2Eoption_2Eoption(X0)) )
& ! [X19: $i] :
( ! [X20: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 )
| ~ mem(X20,arr(X0,X1)) )
| ~ mem(X19,X1) )
& ! [X21: $i] :
( ! [X22: $i] :
( ! [X23: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) )
| ~ mem(X23,arr(X0,X1)) )
| ~ mem(X22,X1) )
| ~ mem(X21,X0) )
& ! [X24: $i] :
( ! [X25: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) )
| ~ mem(X25,X0) )
| ~ mem(X24,arr(X0,X1)) )
& ! [X26: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) )
| ~ mem(X26,arr(X0,X1)) )
& ( ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0) )
& ! [X27: $i] :
( ( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 )
| ~ mem(X27,ty_2Eoption_2Eoption(X0)) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,X1) ),
inference(ennf_transformation,[],[f58]) ).
tff(f64,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ! [X5: $i] :
( ! [X6: $i] :
( ( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6) )
<=> ( X5 = X6 ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
& ! [X7: $i] :
( ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 )
| ~ mem(X7,X0) )
& ! [X8: $i] :
( ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) )
| ~ mem(X8,X0) )
& ! [X9: $i] :
( ( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) )
| ~ mem(X9,X0) )
& ! [X10: $i] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
| ~ mem(X10,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& ! [X11: $i] :
( ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> ( X11 = c_2Eoption_2ENONE(X0) ) )
| ~ mem(X11,ty_2Eoption_2Eoption(X0)) )
& ! [X12: $i] :
( ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> ( X12 = c_2Eoption_2ENONE(X0) ) )
| ~ mem(X12,ty_2Eoption_2Eoption(X0)) )
& ! [X13: $i] :
( ( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 )
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 )
| ~ mem(X15,ty_2Eoption_2Eoption(X0)) )
& ! [X16: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 )
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X16))
| ~ mem(X16,ty_2Eoption_2Eoption(X0)) )
& ! [X17: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X17))
| ~ mem(X17,ty_2Eoption_2Eoption(X0)) )
& ! [X18: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X18))
| ~ mem(X18,ty_2Eoption_2Eoption(X0)) )
& ! [X19: $i] :
( ! [X20: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 )
| ~ mem(X20,arr(X0,X1)) )
| ~ mem(X19,X1) )
& ! [X21: $i] :
( ! [X22: $i] :
( ! [X23: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) )
| ~ mem(X23,arr(X0,X1)) )
| ~ mem(X22,X1) )
| ~ mem(X21,X0) )
& ! [X24: $i] :
( ! [X25: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) )
| ~ mem(X25,X0) )
| ~ mem(X24,arr(X0,X1)) )
& ! [X26: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) )
| ~ mem(X26,arr(X0,X1)) )
& ( ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0) )
& ! [X27: $i] :
( ( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 )
| ~ mem(X27,ty_2Eoption_2Eoption(X0)) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,X1) ),
inference(flattening,[],[f63]) ).
tff(f70,definition,
! [X0: del,X1: del,X3: $i,X4: $i,X2: $i] :
( sP0(X0,X1,X3,X4,X2)
<=> ? [X5: $i] :
( mem(X5,X0)
& ? [X6: $i] :
( mem(X6,X1)
& ( X3 = ap(c_2Eoption_2ESOME(X0),X5) )
& ( X4 = ap(c_2Eoption_2ESOME(X1),X6) )
& p(ap(ap(X2,X5),X6)) ) ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
tff(f71,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
<=> ( ( ( X3 = c_2Eoption_2ENONE(X0) )
& ( X4 = c_2Eoption_2ENONE(X1) ) )
| sP0(X0,X1,X3,X4,X2) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(definition_folding,[],[f62,f70]) ).
tff(f72,definition,
! [X0: del] :
( ! [X12: $i] :
( ( ~ p(ap(c_2Eoption_2EIS__SOME(X0),X12))
<=> ( X12 = c_2Eoption_2ENONE(X0) ) )
| ~ mem(X12,ty_2Eoption_2Eoption(X0)) )
| ~ sP1(X0) ),
introduced(definition,[new_symbols(definition,[sP1])],[predicate_definition_introduction]) ).
tff(f73,definition,
! [X0: del] :
( ! [X11: $i] :
( ( p(ap(c_2Eoption_2EIS__NONE(X0),X11))
<=> ( X11 = c_2Eoption_2ENONE(X0) ) )
| ~ mem(X11,ty_2Eoption_2Eoption(X0)) )
| ~ sP2(X0) ),
introduced(definition,[new_symbols(definition,[sP2])],[predicate_definition_introduction]) ).
tff(f74,definition,
! [X0: del] :
( ! [X5: $i] :
( ! [X6: $i] :
( ( ( ap(c_2Eoption_2ESOME(X0),X5) = ap(c_2Eoption_2ESOME(X0),X6) )
<=> ( X5 = X6 ) )
| ~ mem(X6,X0) )
| ~ mem(X5,X0) )
| ~ sP3(X0) ),
introduced(definition,[new_symbols(definition,[sP3])],[predicate_definition_introduction]) ).
tff(f75,definition,
! [X0: del,X2: $i,X3: $i,X1: del,X4: $i] :
( ( sP3(X0)
& ! [X7: $i] :
( ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 )
| ~ mem(X7,X0) )
& ! [X8: $i] :
( ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) )
| ~ mem(X8,X0) )
& ! [X9: $i] :
( ( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) )
| ~ mem(X9,X0) )
& ! [X10: $i] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
| ~ mem(X10,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& sP2(X0)
& sP1(X0)
& ! [X13: $i] :
( ( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 )
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 )
| ~ mem(X15,ty_2Eoption_2Eoption(X0)) )
& ! [X16: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 )
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X16))
| ~ mem(X16,ty_2Eoption_2Eoption(X0)) )
& ! [X17: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X17))
| ~ mem(X17,ty_2Eoption_2Eoption(X0)) )
& ! [X18: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X18))
| ~ mem(X18,ty_2Eoption_2Eoption(X0)) )
& ! [X19: $i] :
( ! [X20: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 )
| ~ mem(X20,arr(X0,X1)) )
| ~ mem(X19,X1) )
& ! [X21: $i] :
( ! [X22: $i] :
( ! [X23: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) )
| ~ mem(X23,arr(X0,X1)) )
| ~ mem(X22,X1) )
| ~ mem(X21,X0) )
& ! [X24: $i] :
( ! [X25: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) )
| ~ mem(X25,X0) )
| ~ mem(X24,arr(X0,X1)) )
& ! [X26: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) )
| ~ mem(X26,arr(X0,X1)) )
& ( ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0) )
& ! [X27: $i] :
( ( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 )
| ~ mem(X27,ty_2Eoption_2Eoption(X0)) ) )
| ~ sP4(X0,X2,X3,X1,X4) ),
introduced(definition,[new_symbols(definition,[sP4])],[predicate_definition_introduction]) ).
tff(f76,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( sP4(X0,X2,X3,X1,X4)
| ~ mem(X4,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X3,arr(X0,X1)) )
| ~ mem(X2,X1) ),
inference(definition_folding,[],[f64,f75,f74,f73,f72]) ).
tff(f77,plain,
? [X0: del,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X0)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),c_2Eoption_2ENONE(X0)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),c_2Eoption_2ENONE(X0)),ap(c_2Eoption_2ESOME(X0),X3)))
| ( ( ~ p(ap(ap(X1,X2),X3))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3))) )
& ( p(ap(ap(X1,X2),X3))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X0),X1),ap(c_2Eoption_2ESOME(X0),X2)),ap(c_2Eoption_2ESOME(X0),X3))) ) ) )
& mem(X3,X0) )
& mem(X2,X0) )
& mem(X1,arr(X0,arr(X0,bool))) ),
inference(nnf_transformation,[],[f60]) ).
tff(f78,plain,
( ( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| ( ( ~ p(ap(ap(sK6,sK7),sK8))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) )
& ( p(ap(ap(sK6,sK7),sK8))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) ) ) )
& mem(sK8,sK5)
& mem(sK7,sK5)
& mem(sK6,arr(sK5,arr(sK5,bool))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7,sK8]),skolemize(X0,sK5),skolemize(X1,sK6),skolemize(X2,sK7),skolemize(X3,sK8)],[f77]) ).
tff(f79,plain,
! [X0: del,X1: del,X3: $i,X4: $i,X2: $i] :
( ( sP0(X0,X1,X3,X4,X2)
| ! [X5: $i] :
( ~ mem(X5,X0)
| ! [X6: $i] :
( ~ mem(X6,X1)
| ( ap(c_2Eoption_2ESOME(X0),X5) != X3 )
| ( ap(c_2Eoption_2ESOME(X1),X6) != X4 )
| ~ p(ap(ap(X2,X5),X6)) ) ) )
& ( ? [X5: $i] :
( mem(X5,X0)
& ? [X6: $i] :
( mem(X6,X1)
& ( X3 = ap(c_2Eoption_2ESOME(X0),X5) )
& ( X4 = ap(c_2Eoption_2ESOME(X1),X6) )
& p(ap(ap(X2,X5),X6)) ) )
| ~ sP0(X0,X1,X3,X4,X2) ) ),
inference(nnf_transformation,[],[f70]) ).
tff(f80,plain,
! [X0: del,X1: del,X2: $i,X3: $i,X4: $i] :
( ( sP0(X0,X1,X2,X3,X4)
| ! [X5: $i] :
( ~ mem(X5,X0)
| ! [X6: $i] :
( ~ mem(X6,X1)
| ( ap(c_2Eoption_2ESOME(X0),X5) != X2 )
| ( ap(c_2Eoption_2ESOME(X1),X6) != X3 )
| ~ p(ap(ap(X4,X5),X6)) ) ) )
& ( ? [X7: $i] :
( mem(X7,X0)
& ? [X8: $i] :
( mem(X8,X1)
& ( ap(c_2Eoption_2ESOME(X0),X7) = X2 )
& ( ap(c_2Eoption_2ESOME(X1),X8) = X3 )
& p(ap(ap(X4,X7),X8)) ) )
| ~ sP0(X0,X1,X2,X3,X4) ) ),
inference(rectify,[],[f79]) ).
tff(f81,plain,
! [X0: del,X1: del,X2: $i,X3: $i,X4: $i] :
( ( sP0(X0,X1,X2,X3,X4)
| ! [X5: $i] :
( ~ mem(X5,X0)
| ! [X6: $i] :
( ~ mem(X6,X1)
| ( ap(c_2Eoption_2ESOME(X0),X5) != X2 )
| ( ap(c_2Eoption_2ESOME(X1),X6) != X3 )
| ~ p(ap(ap(X4,X5),X6)) ) ) )
& ( ( mem(sK9(X0,X1,X2,X3,X4),X0)
& mem(sK10(X0,X1,X2,X3,X4),X1)
& ( ap(c_2Eoption_2ESOME(X0),sK9(X0,X1,X2,X3,X4)) = X2 )
& ( ap(c_2Eoption_2ESOME(X1),sK10(X0,X1,X2,X3,X4)) = X3 )
& p(ap(ap(X4,sK9(X0,X1,X2,X3,X4)),sK10(X0,X1,X2,X3,X4))) )
| ~ sP0(X0,X1,X2,X3,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X7,sK9(X0,X1,X2,X3,X4)),skolemize(X8,sK10(X0,X1,X2,X3,X4))],[f80]) ).
tff(f82,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| ( ( ( c_2Eoption_2ENONE(X0) != X3 )
| ( c_2Eoption_2ENONE(X1) != X4 ) )
& ~ sP0(X0,X1,X3,X4,X2) ) )
& ( ( ( X3 = c_2Eoption_2ENONE(X0) )
& ( X4 = c_2Eoption_2ENONE(X1) ) )
| sP0(X0,X1,X3,X4,X2)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4)) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(nnf_transformation,[],[f71]) ).
tff(f83,plain,
! [X0: del,X1: del,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| ( ( ( c_2Eoption_2ENONE(X0) != X3 )
| ( c_2Eoption_2ENONE(X1) != X4 ) )
& ~ sP0(X0,X1,X3,X4,X2) ) )
& ( ( ( X3 = c_2Eoption_2ENONE(X0) )
& ( X4 = c_2Eoption_2ENONE(X1) ) )
| sP0(X0,X1,X3,X4,X2)
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4)) ) )
| ~ mem(X4,ty_2Eoption_2Eoption(X1)) )
| ~ mem(X3,ty_2Eoption_2Eoption(X0)) )
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(flattening,[],[f82]) ).
tff(f84,plain,
! [X0: del,X2: $i,X3: $i,X1: del,X4: $i] :
( ( sP3(X0)
& ! [X7: $i] :
( ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X7)) = X7 )
| ~ mem(X7,X0) )
& ! [X8: $i] :
( ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X8) )
| ~ mem(X8,X0) )
& ! [X9: $i] :
( ( ap(c_2Eoption_2ESOME(X0),X9) != c_2Eoption_2ENONE(X0) )
| ~ mem(X9,X0) )
& ! [X10: $i] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X10)))
| ~ mem(X10,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& sP2(X0)
& sP1(X0)
& ! [X13: $i] :
( ( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X13)) = X13 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X14 )
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X15),X15),c_2Eoption_2ESOME(X0)) = X15 )
| ~ mem(X15,ty_2Eoption_2Eoption(X0)) )
& ! [X16: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X16),X2),X3) = X2 )
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X16))
| ~ mem(X16,ty_2Eoption_2Eoption(X0)) )
& ! [X17: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),X17),X2),X3) = ap(X3,ap(c_2Eoption_2ETHE(X0),X17)) )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X17))
| ~ mem(X17,ty_2Eoption_2Eoption(X0)) )
& ! [X18: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X18),X4),c_2Eoption_2ESOME(X0)) = X18 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X18))
| ~ mem(X18,ty_2Eoption_2Eoption(X0)) )
& ! [X19: $i] :
( ! [X20: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),c_2Eoption_2ENONE(X0)),X19),X20) = X19 )
| ~ mem(X20,arr(X0,X1)) )
| ~ mem(X19,X1) )
& ! [X21: $i] :
( ! [X22: $i] :
( ! [X23: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X1),ap(c_2Eoption_2ESOME(X0),X21)),X22),X23) = ap(X23,X21) )
| ~ mem(X23,arr(X0,X1)) )
| ~ mem(X22,X1) )
| ~ mem(X21,X0) )
& ! [X24: $i] :
( ! [X25: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X24),ap(c_2Eoption_2ESOME(X0),X25)) = ap(c_2Eoption_2ESOME(X1),ap(X24,X25)) )
| ~ mem(X25,X0) )
| ~ mem(X24,arr(X0,X1)) )
& ! [X26: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X1),X26),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X1) )
| ~ mem(X26,arr(X0,X1)) )
& ( ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0) )
& ! [X27: $i] :
( ( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X27)) = X27 )
| ~ mem(X27,ty_2Eoption_2Eoption(X0)) ) )
| ~ sP4(X0,X2,X3,X1,X4) ),
inference(nnf_transformation,[],[f75]) ).
tff(f85,plain,
! [X0: del,X1: $i,X2: $i,X3: del,X4: $i] :
( ( sP3(X0)
& ! [X5: $i] :
( ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X5)) = X5 )
| ~ mem(X5,X0) )
& ! [X6: $i] :
( ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X6) )
| ~ mem(X6,X0) )
& ! [X7: $i] :
( ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X7) )
| ~ mem(X7,X0) )
& ! [X8: $i] :
( p(ap(c_2Eoption_2EIS__SOME(X0),ap(c_2Eoption_2ESOME(X0),X8)))
| ~ mem(X8,X0) )
& ~ p(ap(c_2Eoption_2EIS__SOME(X0),c_2Eoption_2ENONE(X0)))
& sP2(X0)
& sP1(X0)
& ! [X9: $i] :
( ( ap(c_2Eoption_2ESOME(X0),ap(c_2Eoption_2ETHE(X0),X9)) = X9 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X9))
| ~ mem(X9,ty_2Eoption_2Eoption(X0)) )
& ! [X10: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X10),c_2Eoption_2ENONE(X0)),c_2Eoption_2ESOME(X0)) = X10 )
| ~ mem(X10,ty_2Eoption_2Eoption(X0)) )
& ! [X11: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X11),X11),c_2Eoption_2ESOME(X0)) = X11 )
| ~ mem(X11,ty_2Eoption_2Eoption(X0)) )
& ! [X12: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X3),X12),X1),X2) = X1 )
| ~ p(ap(c_2Eoption_2EIS__NONE(X0),X12))
| ~ mem(X12,ty_2Eoption_2Eoption(X0)) )
& ! [X13: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X3),X13),X1),X2) = ap(X2,ap(c_2Eoption_2ETHE(X0),X13)) )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X13))
| ~ mem(X13,ty_2Eoption_2Eoption(X0)) )
& ! [X14: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,ty_2Eoption_2Eoption(X0)),X14),X4),c_2Eoption_2ESOME(X0)) = X14 )
| ~ p(ap(c_2Eoption_2EIS__SOME(X0),X14))
| ~ mem(X14,ty_2Eoption_2Eoption(X0)) )
& ! [X15: $i] :
( ! [X16: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X3),c_2Eoption_2ENONE(X0)),X15),X16) = X15 )
| ~ mem(X16,arr(X0,X3)) )
| ~ mem(X15,X3) )
& ! [X17: $i] :
( ! [X18: $i] :
( ! [X19: $i] :
( ( ap(ap(ap(c_2Eoption_2Eoption__CASE(X0,X3),ap(c_2Eoption_2ESOME(X0),X17)),X18),X19) = ap(X19,X17) )
| ~ mem(X19,arr(X0,X3)) )
| ~ mem(X18,X3) )
| ~ mem(X17,X0) )
& ! [X20: $i] :
( ! [X21: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X3),X20),ap(c_2Eoption_2ESOME(X0),X21)) = ap(c_2Eoption_2ESOME(X3),ap(X20,X21)) )
| ~ mem(X21,X0) )
| ~ mem(X20,arr(X0,X3)) )
& ! [X22: $i] :
( ( ap(ap(c_2Eoption_2EOPTION__MAP(X0,X3),X22),c_2Eoption_2ENONE(X0)) = c_2Eoption_2ENONE(X3) )
| ~ mem(X22,arr(X0,X3)) )
& ( ap(c_2Eoption_2EOPTION__JOIN(X0),c_2Eoption_2ENONE(ty_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE(X0) )
& ! [X23: $i] :
( ( ap(c_2Eoption_2EOPTION__JOIN(X0),ap(c_2Eoption_2ESOME(ty_2Eoption_2Eoption(X0)),X23)) = X23 )
| ~ mem(X23,ty_2Eoption_2Eoption(X0)) ) )
| ~ sP4(X0,X1,X2,X3,X4) ),
inference(rectify,[],[f84]) ).
tff(f94,plain,
mem(sK6,arr(sK5,arr(sK5,bool))),
inference(cnf_transformation,[],[f78]) ).
tff(f95,plain,
mem(sK7,sK5),
inference(cnf_transformation,[],[f78]) ).
tff(f96,plain,
mem(sK8,sK5),
inference(cnf_transformation,[],[f78]) ).
tff(f97,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| p(ap(ap(sK6,sK7),sK8))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) ),
inference(cnf_transformation,[],[f78]) ).
tff(f98,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5)))
| p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| ~ p(ap(ap(sK6,sK7),sK8))
| ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) ),
inference(cnf_transformation,[],[f78]) ).
tff(f99,plain,
! [X2: $i,X3: $i,X0: del,X1: del] :
( ~ mem(X2,arr(X0,X1))
| ~ mem(X3,X0)
| mem(ap(X2,X3),X1) ),
inference(cnf_transformation,[],[f61]) ).
tff(f100,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( p(ap(ap(X4,sK9(X0,X1,X2,X3,X4)),sK10(X0,X1,X2,X3,X4)))
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f81]) ).
tff(f101,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( ~ sP0(X0,X1,X2,X3,X4)
| ( ap(c_2Eoption_2ESOME(X1),sK10(X0,X1,X2,X3,X4)) = X3 ) ),
inference(cnf_transformation,[],[f81]) ).
tff(f102,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( ~ sP0(X0,X1,X2,X3,X4)
| ( ap(c_2Eoption_2ESOME(X0),sK9(X0,X1,X2,X3,X4)) = X2 ) ),
inference(cnf_transformation,[],[f81]) ).
tff(f103,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( mem(sK10(X0,X1,X2,X3,X4),X1)
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f81]) ).
tff(f104,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( mem(sK9(X0,X1,X2,X3,X4),X0)
| ~ sP0(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f81]) ).
tff(f105,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( sP0(X0,X1,X2,X3,X4)
| ~ mem(X5,X0)
| ~ mem(X6,X1)
| ( ap(c_2Eoption_2ESOME(X0),X5) != X2 )
| ( ap(c_2Eoption_2ESOME(X1),X6) != X3 )
| ~ p(ap(ap(X4,X5),X6)) ),
inference(cnf_transformation,[],[f81]) ).
tff(f106,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| sP0(X0,X1,X3,X4,X2)
| ( c_2Eoption_2ENONE(X1) = X4 )
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(cnf_transformation,[],[f83]) ).
tff(f107,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| sP0(X0,X1,X3,X4,X2)
| ( c_2Eoption_2ENONE(X0) = X3 )
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(cnf_transformation,[],[f83]) ).
tff(f108,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| ~ sP0(X0,X1,X3,X4,X2)
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(cnf_transformation,[],[f83]) ).
tff(f109,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),X3),X4))
| ( c_2Eoption_2ENONE(X0) != X3 )
| ( c_2Eoption_2ENONE(X1) != X4 )
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(X3,ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(cnf_transformation,[],[f83]) ).
tff(f126,plain,
! [X2: $i,X3: del,X0: del,X1: $i,X7: $i,X4: $i] :
( ( c_2Eoption_2ENONE(X0) != ap(c_2Eoption_2ESOME(X0),X7) )
| ~ mem(X7,X0)
| ~ sP4(X0,X1,X2,X3,X4) ),
inference(cnf_transformation,[],[f85]) ).
tff(f128,plain,
! [X2: $i,X3: del,X0: del,X1: $i,X4: $i,X5: $i] :
( ~ sP4(X0,X1,X2,X3,X4)
| ~ mem(X5,X0)
| ( ap(c_2Eoption_2ETHE(X0),ap(c_2Eoption_2ESOME(X0),X5)) = X5 ) ),
inference(cnf_transformation,[],[f85]) ).
tff(f136,plain,
! [X2: $i,X3: $i,X0: del,X1: del,X4: $i] :
( sP4(X0,X2,X3,X1,X4)
| ~ mem(X4,ty_2Eoption_2Eoption(X0))
| ~ mem(X3,arr(X0,X1))
| ~ mem(X2,X1) ),
inference(cnf_transformation,[],[f76]) ).
tff(f137,plain,
! [X0: del] : mem(c_2Eoption_2ESOME(X0),arr(X0,ty_2Eoption_2Eoption(X0))),
inference(cnf_transformation,[],[f27]) ).
tff(f138,plain,
! [X0: del] : mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0)),
inference(cnf_transformation,[],[f30]) ).
tff(f151,plain,
! [X3: $i,X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( sP0(X0,X1,ap(c_2Eoption_2ESOME(X0),X5),X3,X4)
| ~ mem(X5,X0)
| ~ mem(X6,X1)
| ( ap(c_2Eoption_2ESOME(X1),X6) != X3 )
| ~ p(ap(ap(X4,X5),X6)) ),
inference(equality_resolution,[],[f105]) ).
tff(f152,plain,
! [X0: del,X1: del,X6: $i,X4: $i,X5: $i] :
( sP0(X0,X1,ap(c_2Eoption_2ESOME(X0),X5),ap(c_2Eoption_2ESOME(X1),X6),X4)
| ~ mem(X5,X0)
| ~ mem(X6,X1)
| ~ p(ap(ap(X4,X5),X6)) ),
inference(equality_resolution,[],[f151]) ).
tff(f153,plain,
! [X2: $i,X0: del,X1: del,X4: $i] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),c_2Eoption_2ENONE(X0)),X4))
| ( c_2Eoption_2ENONE(X1) != X4 )
| ~ mem(X4,ty_2Eoption_2Eoption(X1))
| ~ mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(equality_resolution,[],[f109]) ).
tff(f154,plain,
! [X2: $i,X0: del,X1: del] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X1)))
| ~ mem(c_2Eoption_2ENONE(X1),ty_2Eoption_2Eoption(X1))
| ~ mem(c_2Eoption_2ENONE(X0),ty_2Eoption_2Eoption(X0))
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(equality_resolution,[],[f153]) ).
tff(f161,plain,
! [X2: $i,X0: del,X1: del] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X1)))
| ~ mem(c_2Eoption_2ENONE(X1),ty_2Eoption_2Eoption(X1))
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(forward_subsumption_resolution,[],[f154,f138]) ).
tff(f163,definition,
( spl12_1
<=> p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8))) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
tff(f164,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| spl12_1 ),
inference(avatar_component_clause,[],[f163]) ).
tff(f165,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f163]) ).
tff(f167,definition,
( spl12_2
<=> p(ap(ap(sK6,sK7),sK8)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
tff(f168,plain,
( ~ p(ap(ap(sK6,sK7),sK8))
| spl12_2 ),
inference(avatar_component_clause,[],[f167]) ).
tff(f169,plain,
( p(ap(ap(sK6,sK7),sK8))
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f167]) ).
tff(f171,definition,
( spl12_3
<=> p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8))) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
tff(f173,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),ap(c_2Eoption_2ESOME(sK5),sK8)))
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f171]) ).
tff(f175,definition,
( spl12_4
<=> p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5))) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
tff(f177,plain,
( p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),ap(c_2Eoption_2ESOME(sK5),sK7)),c_2Eoption_2ENONE(sK5)))
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f175]) ).
tff(f179,definition,
( spl12_5
<=> p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5))) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
tff(f181,plain,
( ~ p(ap(ap(ap(c_2Eoption_2EOPTREL(sK5,sK5),sK6),c_2Eoption_2ENONE(sK5)),c_2Eoption_2ENONE(sK5)))
| spl12_5 ),
inference(avatar_component_clause,[],[f179]) ).
tff(f182,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f97,f179,f175,f171,f167,f163]) ).
tff(f183,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_3
| spl12_4
| ~ spl12_5 ),
inference(avatar_split_clause,[],[f98,f179,f175,f171,f167,f163]) ).
tff(f184,plain,
! [X2: $i,X0: del,X1: del] :
( p(ap(ap(ap(c_2Eoption_2EOPTREL(X0,X1),X2),c_2Eoption_2ENONE(X0)),c_2Eoption_2ENONE(X1)))
| ~ mem(X2,arr(X0,arr(X1,bool))) ),
inference(forward_subsumption_resolution,[],[f161,f138]) ).
tff(f189,plain,
! [X0: $i,X1: del] :
( mem(ap(c_2Eoption_2ESOME(X1),X0),ty_2Eoption_2Eoption(X1))
| ~ mem(X0,X1) ),
inference(resolution,[],[f99,f137]) ).
tff(f190,plain,
! [X0: $i] :
( mem(ap(sK6,X0),arr(sK5,bool))
| ~ mem(X0,sK5) ),
inference(resolution,[],[f99,f94]) ).
tff(f264,plain,
! [X2: $i,X3: del,X0: $i,X1: del,X4: $i,X5: $i] :
( ~ mem(X2,arr(X1,X3))
| ~ mem(X0,ty_2Eoption_2Eoption(X1))
| ~ mem(X4,X3)
| ~ mem(X5,X1)
| ( ap(c_2Eoption_2ETHE(X1),ap(c_2Eoption_2ESOME(X1),X5)) = X5 ) ),
inference(resolution,[],[f136,f128]) ).
tff(f284,plain,
( ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| spl12_5 ),
inference(resolution,[],[f184,f181]) ).
tff(f285,plain,
( $false
| spl12_5 ),
inference(forward_subsumption_resolution,[],[f284,f94]) ).
tff(f286,plain,
spl12_5,
inference(avatar_contradiction_clause,[],[f285]) ).
tff(f378,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| spl12_1 ),
inference(resolution,[],[f108,f164]) ).
tff(f379,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| spl12_1 ),
inference(forward_subsumption_resolution,[],[f378,f94]) ).
tff(f381,definition,
( spl12_10
<=> mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5)) ),
introduced(definition,[new_symbols(definition,[spl12_10])],[avatar_definition]) ).
tff(f382,plain,
( mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ spl12_10 ),
inference(avatar_component_clause,[],[f381]) ).
tff(f383,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| spl12_10 ),
inference(avatar_component_clause,[],[f381]) ).
tff(f385,definition,
( spl12_11
<=> mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5)) ),
introduced(definition,[new_symbols(definition,[spl12_11])],[avatar_definition]) ).
tff(f386,plain,
( mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ spl12_11 ),
inference(avatar_component_clause,[],[f385]) ).
tff(f387,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| spl12_11 ),
inference(avatar_component_clause,[],[f385]) ).
tff(f389,definition,
( spl12_12
<=> sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) ),
introduced(definition,[new_symbols(definition,[spl12_12])],[avatar_definition]) ).
tff(f390,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f389]) ).
tff(f391,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| spl12_12 ),
inference(avatar_component_clause,[],[f389]) ).
tff(f392,plain,
( ~ spl12_10
| ~ spl12_11
| ~ spl12_12
| spl12_1 ),
inference(avatar_split_clause,[],[f379,f163,f389,f385,f381]) ).
tff(f485,plain,
( ~ mem(sK7,sK5)
| spl12_10 ),
inference(resolution,[],[f189,f383]) ).
tff(f486,plain,
( $false
| spl12_10 ),
inference(forward_subsumption_resolution,[],[f485,f95]) ).
tff(f487,plain,
spl12_10,
inference(avatar_contradiction_clause,[],[f486]) ).
tff(f488,plain,
( ~ mem(sK8,sK5)
| spl12_11 ),
inference(resolution,[],[f387,f189]) ).
tff(f489,plain,
( $false
| spl12_11 ),
inference(forward_subsumption_resolution,[],[f488,f96]) ).
tff(f490,plain,
spl12_11,
inference(avatar_contradiction_clause,[],[f489]) ).
tff(f491,plain,
( ~ mem(sK7,sK5)
| ~ mem(sK8,sK5)
| ~ p(ap(ap(sK6,sK7),sK8))
| spl12_12 ),
inference(resolution,[],[f391,f152]) ).
tff(f492,plain,
( ~ mem(sK8,sK5)
| ~ p(ap(ap(sK6,sK7),sK8))
| spl12_12 ),
inference(forward_subsumption_resolution,[],[f491,f95]) ).
tff(f493,plain,
( ~ p(ap(ap(sK6,sK7),sK8))
| spl12_12 ),
inference(forward_subsumption_resolution,[],[f492,f96]) ).
tff(f494,plain,
( $false
| ~ spl12_2
| spl12_12 ),
inference(forward_subsumption_resolution,[],[f493,f169]) ).
tff(f495,plain,
( ~ spl12_2
| spl12_12 ),
inference(avatar_contradiction_clause,[],[f494]) ).
tff(f503,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8) )
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(c_2Eoption_2ENONE(sK5),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_3 ),
inference(resolution,[],[f173,f106]) ).
tff(f504,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8) )
| ~ mem(c_2Eoption_2ENONE(sK5),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_3
| ~ spl12_11 ),
inference(forward_subsumption_resolution,[],[f503,f386]) ).
tff(f505,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8) )
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_3
| ~ spl12_11 ),
inference(forward_subsumption_resolution,[],[f504,f138]) ).
tff(f506,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8) )
| ~ spl12_3
| ~ spl12_11 ),
inference(forward_subsumption_resolution,[],[f505,f94]) ).
tff(f508,definition,
( spl12_15
<=> ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8) ) ),
introduced(definition,[new_symbols(definition,[spl12_15])],[avatar_definition]) ).
tff(f510,plain,
( ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK8) )
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f508]) ).
tff(f512,definition,
( spl12_16
<=> sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) ),
introduced(definition,[new_symbols(definition,[spl12_16])],[avatar_definition]) ).
tff(f514,plain,
( sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f512]) ).
tff(f515,plain,
( spl12_15
| spl12_16
| ~ spl12_3
| ~ spl12_11 ),
inference(avatar_split_clause,[],[f506,f385,f171,f512,f508]) ).
tff(f525,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ( c_2Eoption_2ENONE(sK5) != c_2Eoption_2ENONE(sK5) )
| ~ mem(sK8,sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl12_15 ),
inference(superposition,[],[f126,f510]) ).
tff(f526,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ~ mem(sK8,sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl12_15 ),
inference(trivial_inequality_removal,[],[f525]) ).
tff(f527,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] : ~ sP4(sK5,X0,X1,X2,X3)
| ~ spl12_15 ),
inference(forward_subsumption_resolution,[],[f526,f96]) ).
tff(f545,definition,
( spl12_19
<=> ! [X2: del,X1: $i,X3: $i] :
( ~ mem(X1,arr(sK5,X2))
| ~ mem(X3,X2) ) ),
introduced(definition,[new_symbols(definition,[spl12_19])],[avatar_definition]) ).
tff(f546,plain,
( ! [X2: del,X3: $i,X1: $i] :
( ~ mem(X1,arr(sK5,X2))
| ~ mem(X3,X2) )
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f545]) ).
tff(f548,definition,
( spl12_20
<=> ! [X0: $i] : ~ mem(X0,ty_2Eoption_2Eoption(sK5)) ),
introduced(definition,[new_symbols(definition,[spl12_20])],[avatar_definition]) ).
tff(f549,plain,
( ! [X0: $i] : ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f548]) ).
tff(f554,plain,
( ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK9(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)) )
| ~ spl12_16 ),
inference(resolution,[],[f514,f102]) ).
tff(f561,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ( c_2Eoption_2ENONE(sK5) != c_2Eoption_2ENONE(sK5) )
| ~ mem(sK9(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl12_16 ),
inference(superposition,[],[f126,f554]) ).
tff(f562,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ~ mem(sK9(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl12_16 ),
inference(trivial_inequality_removal,[],[f561]) ).
tff(f564,definition,
( spl12_21
<=> ! [X2: del,X0: $i,X1: $i,X3: $i] : ~ sP4(sK5,X0,X1,X2,X3) ),
introduced(definition,[new_symbols(definition,[spl12_21])],[avatar_definition]) ).
tff(f565,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] : ~ sP4(sK5,X0,X1,X2,X3)
| ~ spl12_21 ),
inference(avatar_component_clause,[],[f564]) ).
tff(f567,definition,
( spl12_22
<=> mem(sK9(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5) ),
introduced(definition,[new_symbols(definition,[spl12_22])],[avatar_definition]) ).
tff(f569,plain,
( ~ mem(sK9(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| spl12_22 ),
inference(avatar_component_clause,[],[f567]) ).
tff(f570,plain,
( spl12_21
| ~ spl12_22
| ~ spl12_16 ),
inference(avatar_split_clause,[],[f562,f512,f567,f564]) ).
tff(f597,definition,
( spl12_26
<=> ! [X1: $i] : ~ mem(X1,arr(sK5,bool)) ),
introduced(definition,[new_symbols(definition,[spl12_26])],[avatar_definition]) ).
tff(f598,plain,
( ! [X1: $i] : ~ mem(X1,arr(sK5,bool))
| ~ spl12_26 ),
inference(avatar_component_clause,[],[f597]) ).
tff(f609,definition,
( spl12_29
<=> ! [X2: $i] : ~ mem(X2,sK5) ),
introduced(definition,[new_symbols(definition,[spl12_29])],[avatar_definition]) ).
tff(f610,plain,
( ! [X2: $i] : ~ mem(X2,sK5)
| ~ spl12_29 ),
inference(avatar_component_clause,[],[f609]) ).
tff(f615,plain,
( ! [X0: $i] : ~ mem(X0,sK5)
| ~ spl12_20 ),
inference(resolution,[],[f549,f189]) ).
tff(f623,plain,
( spl12_29
| ~ spl12_20 ),
inference(avatar_split_clause,[],[f615,f548,f609]) ).
tff(f655,plain,
( ! [X0: $i] : ~ mem(X0,sK5)
| ~ spl12_26 ),
inference(resolution,[],[f598,f190]) ).
tff(f659,plain,
( spl12_29
| ~ spl12_26 ),
inference(avatar_split_clause,[],[f655,f597,f609]) ).
tff(f665,plain,
( $false
| ~ spl12_29 ),
inference(resolution,[],[f610,f95]) ).
tff(f674,plain,
~ spl12_29,
inference(avatar_contradiction_clause,[],[f665]) ).
tff(f697,plain,
( ~ sP0(sK5,sK5,c_2Eoption_2ENONE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| spl12_22 ),
inference(resolution,[],[f569,f104]) ).
tff(f698,plain,
( $false
| ~ spl12_16
| spl12_22 ),
inference(forward_subsumption_resolution,[],[f697,f514]) ).
tff(f699,plain,
( ~ spl12_16
| spl12_22 ),
inference(avatar_contradiction_clause,[],[f698]) ).
tff(f700,plain,
( spl12_21
| ~ spl12_15 ),
inference(avatar_split_clause,[],[f527,f508,f564]) ).
tff(f704,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) )
| ~ mem(c_2Eoption_2ENONE(sK5),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_4 ),
inference(resolution,[],[f177,f107]) ).
tff(f706,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) )
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f704,f138]) ).
tff(f707,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) )
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_4
| ~ spl12_10 ),
inference(forward_subsumption_resolution,[],[f706,f382]) ).
tff(f708,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) )
| ~ spl12_4
| ~ spl12_10 ),
inference(forward_subsumption_resolution,[],[f707,f94]) ).
tff(f710,definition,
( spl12_31
<=> ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) ) ),
introduced(definition,[new_symbols(definition,[spl12_31])],[avatar_definition]) ).
tff(f711,plain,
( ( c_2Eoption_2ENONE(sK5) != ap(c_2Eoption_2ESOME(sK5),sK7) )
| spl12_31 ),
inference(avatar_component_clause,[],[f710]) ).
tff(f712,plain,
( ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) )
| ~ spl12_31 ),
inference(avatar_component_clause,[],[f710]) ).
tff(f714,definition,
( spl12_32
<=> sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6) ),
introduced(definition,[new_symbols(definition,[spl12_32])],[avatar_definition]) ).
tff(f716,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| ~ spl12_32 ),
inference(avatar_component_clause,[],[f714]) ).
tff(f717,plain,
( spl12_31
| spl12_32
| ~ spl12_4
| ~ spl12_10 ),
inference(avatar_split_clause,[],[f708,f381,f175,f714,f710]) ).
tff(f720,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ mem(X1,arr(sK5,X2))
| ~ mem(X3,X2) )
| ~ spl12_21 ),
inference(resolution,[],[f565,f136]) ).
tff(f742,plain,
( ! [X0: $i] : ~ mem(X0,arr(sK5,bool))
| ~ spl12_19 ),
inference(resolution,[],[f546,f94]) ).
tff(f747,plain,
( spl12_26
| ~ spl12_19 ),
inference(avatar_split_clause,[],[f742,f545,f597]) ).
tff(f749,plain,
( spl12_19
| spl12_20
| ~ spl12_21 ),
inference(avatar_split_clause,[],[f720,f564,f548,f545]) ).
tff(f762,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ( c_2Eoption_2ENONE(sK5) != c_2Eoption_2ENONE(sK5) )
| ~ mem(sK7,sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl12_31 ),
inference(superposition,[],[f126,f712]) ).
tff(f763,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ~ mem(sK7,sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl12_31 ),
inference(trivial_inequality_removal,[],[f762]) ).
tff(f764,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] : ~ sP4(sK5,X0,X1,X2,X3)
| ~ spl12_31 ),
inference(forward_subsumption_resolution,[],[f763,f95]) ).
tff(f769,plain,
( spl12_21
| ~ spl12_31 ),
inference(avatar_split_clause,[],[f764,f710,f564]) ).
tff(f773,plain,
( sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) )
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_1 ),
inference(resolution,[],[f165,f107]) ).
tff(f776,plain,
( ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK7) )
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_1
| spl12_12 ),
inference(forward_subsumption_resolution,[],[f773,f391]) ).
tff(f778,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK5),sK8),ty_2Eoption_2Eoption(sK5))
| ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_1
| spl12_12
| spl12_31 ),
inference(forward_subsumption_resolution,[],[f776,f711]) ).
tff(f780,plain,
( ~ mem(ap(c_2Eoption_2ESOME(sK5),sK7),ty_2Eoption_2Eoption(sK5))
| ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_1
| ~ spl12_11
| spl12_12
| spl12_31 ),
inference(forward_subsumption_resolution,[],[f778,f386]) ).
tff(f782,plain,
( ~ mem(sK6,arr(sK5,arr(sK5,bool)))
| ~ spl12_1
| ~ spl12_10
| ~ spl12_11
| spl12_12
| spl12_31 ),
inference(forward_subsumption_resolution,[],[f780,f382]) ).
tff(f785,plain,
( $false
| ~ spl12_1
| ~ spl12_10
| ~ spl12_11
| spl12_12
| spl12_31 ),
inference(forward_subsumption_resolution,[],[f782,f94]) ).
tff(f786,plain,
( ~ spl12_1
| ~ spl12_10
| ~ spl12_11
| spl12_12
| spl12_31 ),
inference(avatar_contradiction_clause,[],[f785]) ).
tff(f922,plain,
! [X2: $i,X0: $i,X1: $i] :
( ~ mem(X0,ty_2Eoption_2Eoption(sK5))
| ~ mem(X1,arr(sK5,bool))
| ~ mem(X2,sK5)
| ( ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),X2)) = X2 ) ),
inference(resolution,[],[f264,f94]) ).
tff(f930,definition,
( spl12_37
<=> ! [X2: $i] :
( ~ mem(X2,sK5)
| ( ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),X2)) = X2 ) ) ),
introduced(definition,[new_symbols(definition,[spl12_37])],[avatar_definition]) ).
tff(f931,plain,
( ! [X2: $i] :
( ~ mem(X2,sK5)
| ( ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),X2)) = X2 ) )
| ~ spl12_37 ),
inference(avatar_component_clause,[],[f930]) ).
tff(f932,plain,
( spl12_37
| spl12_26
| spl12_20 ),
inference(avatar_split_clause,[],[f922,f548,f597,f930]) ).
tff(f933,plain,
( ( sK7 = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK7)) )
| ~ spl12_37 ),
inference(resolution,[],[f931,f95]) ).
tff(f934,plain,
( ( sK8 = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8)) )
| ~ spl12_37 ),
inference(resolution,[],[f931,f96]) ).
tff(f1387,definition,
( spl12_53
<=> mem(sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5) ),
introduced(definition,[new_symbols(definition,[spl12_53])],[avatar_definition]) ).
tff(f1388,plain,
( mem(sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| ~ spl12_53 ),
inference(avatar_component_clause,[],[f1387]) ).
tff(f1389,plain,
( ~ mem(sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| spl12_53 ),
inference(avatar_component_clause,[],[f1387]) ).
tff(f1417,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| spl12_53 ),
inference(resolution,[],[f1389,f104]) ).
tff(f1418,plain,
( $false
| ~ spl12_12
| spl12_53 ),
inference(forward_subsumption_resolution,[],[f1417,f390]) ).
tff(f1419,plain,
( ~ spl12_12
| spl12_53 ),
inference(avatar_contradiction_clause,[],[f1418]) ).
tff(f1425,plain,
( ( c_2Eoption_2ENONE(sK5) = ap(c_2Eoption_2ESOME(sK5),sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)) )
| ~ spl12_32 ),
inference(resolution,[],[f716,f101]) ).
tff(f1462,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ( c_2Eoption_2ENONE(sK5) != c_2Eoption_2ENONE(sK5) )
| ~ mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6),sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl12_32 ),
inference(superposition,[],[f126,f1425]) ).
tff(f1465,plain,
( ! [X2: del,X3: $i,X0: $i,X1: $i] :
( ~ mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6),sK5)
| ~ sP4(sK5,X0,X1,X2,X3) )
| ~ spl12_32 ),
inference(trivial_inequality_removal,[],[f1462]) ).
tff(f1468,definition,
( spl12_60
<=> mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6),sK5) ),
introduced(definition,[new_symbols(definition,[spl12_60])],[avatar_definition]) ).
tff(f1470,plain,
( ~ mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6),sK5)
| spl12_60 ),
inference(avatar_component_clause,[],[f1468]) ).
tff(f1471,plain,
( spl12_21
| ~ spl12_60
| ~ spl12_32 ),
inference(avatar_split_clause,[],[f1465,f714,f1468,f564]) ).
tff(f1503,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),c_2Eoption_2ENONE(sK5),sK6)
| spl12_60 ),
inference(resolution,[],[f1470,f103]) ).
tff(f1504,plain,
( $false
| ~ spl12_32
| spl12_60 ),
inference(forward_subsumption_resolution,[],[f1503,f716]) ).
tff(f1505,plain,
( ~ spl12_32
| spl12_60 ),
inference(avatar_contradiction_clause,[],[f1504]) ).
tff(f1526,plain,
( ( ap(c_2Eoption_2ESOME(sK5),sK7) = ap(c_2Eoption_2ESOME(sK5),sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)) )
| ~ spl12_12 ),
inference(resolution,[],[f390,f102]) ).
tff(f1527,plain,
( ( ap(c_2Eoption_2ESOME(sK5),sK8) = ap(c_2Eoption_2ESOME(sK5),sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)) )
| ~ spl12_12 ),
inference(resolution,[],[f390,f101]) ).
tff(f1530,plain,
( ( sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6))) )
| ~ spl12_37
| ~ spl12_53 ),
inference(resolution,[],[f1388,f931]) ).
tff(f1541,plain,
( ( sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK7)) )
| ~ spl12_12
| ~ spl12_37
| ~ spl12_53 ),
inference(forward_demodulation,[],[f1530,f1526]) ).
tff(f1544,plain,
( ( sK7 = sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) )
| ~ spl12_12
| ~ spl12_37
| ~ spl12_53 ),
inference(forward_demodulation,[],[f1541,f933]) ).
tff(f1580,definition,
( spl12_70
<=> mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5) ),
introduced(definition,[new_symbols(definition,[spl12_70])],[avatar_definition]) ).
tff(f1581,plain,
( mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| ~ spl12_70 ),
inference(avatar_component_clause,[],[f1580]) ).
tff(f1582,plain,
( ~ mem(sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6),sK5)
| spl12_70 ),
inference(avatar_component_clause,[],[f1580]) ).
tff(f1597,plain,
( ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| spl12_70 ),
inference(resolution,[],[f1582,f103]) ).
tff(f1598,plain,
( $false
| ~ spl12_12
| spl12_70 ),
inference(forward_subsumption_resolution,[],[f1597,f390]) ).
tff(f1599,plain,
( ~ spl12_12
| spl12_70 ),
inference(avatar_contradiction_clause,[],[f1598]) ).
tff(f1646,plain,
( ( sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6))) )
| ~ spl12_37
| ~ spl12_70 ),
inference(resolution,[],[f1581,f931]) ).
tff(f1657,plain,
( ( sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) = ap(c_2Eoption_2ETHE(sK5),ap(c_2Eoption_2ESOME(sK5),sK8)) )
| ~ spl12_12
| ~ spl12_37
| ~ spl12_70 ),
inference(forward_demodulation,[],[f1646,f1527]) ).
tff(f1660,plain,
( ( sK8 = sK10(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6) )
| ~ spl12_12
| ~ spl12_37
| ~ spl12_70 ),
inference(forward_demodulation,[],[f1657,f934]) ).
tff(f1792,plain,
( p(ap(ap(sK6,sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)),sK8))
| ~ sP0(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)
| ~ spl12_12
| ~ spl12_37
| ~ spl12_70 ),
inference(superposition,[],[f100,f1660]) ).
tff(f1794,plain,
( p(ap(ap(sK6,sK9(sK5,sK5,ap(c_2Eoption_2ESOME(sK5),sK7),ap(c_2Eoption_2ESOME(sK5),sK8),sK6)),sK8))
| ~ spl12_12
| ~ spl12_37
| ~ spl12_70 ),
inference(forward_subsumption_resolution,[],[f1792,f390]) ).
tff(f1797,plain,
( p(ap(ap(sK6,sK7),sK8))
| ~ spl12_12
| ~ spl12_37
| ~ spl12_53
| ~ spl12_70 ),
inference(forward_demodulation,[],[f1794,f1544]) ).
tff(f1798,plain,
( $false
| spl12_2
| ~ spl12_12
| ~ spl12_37
| ~ spl12_53
| ~ spl12_70 ),
inference(forward_subsumption_resolution,[],[f1797,f168]) ).
tff(f1799,plain,
( spl12_2
| ~ spl12_12
| ~ spl12_37
| ~ spl12_53
| ~ spl12_70 ),
inference(avatar_contradiction_clause,[],[f1798]) ).
cnf(s1,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4
| ~ spl12_5 ),
inference(sat_conversion,[],[f182]) ).
cnf(s2,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_3
| spl12_4
| ~ spl12_5 ),
inference(sat_conversion,[],[f183]) ).
cnf(s5,plain,
spl12_5,
inference(sat_conversion,[],[f286]) ).
cnf(s6,plain,
( spl12_1
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(sat_conversion,[],[f392]) ).
cnf(s8,plain,
spl12_10,
inference(sat_conversion,[],[f487]) ).
cnf(s9,plain,
spl12_11,
inference(sat_conversion,[],[f490]) ).
cnf(s10,plain,
( ~ spl12_2
| spl12_12 ),
inference(sat_conversion,[],[f495]) ).
cnf(s11,plain,
( ~ spl12_3
| ~ spl12_11
| spl12_15
| spl12_16 ),
inference(sat_conversion,[],[f515]) ).
cnf(s16,plain,
( ~ spl12_16
| spl12_21
| ~ spl12_22 ),
inference(sat_conversion,[],[f570]) ).
cnf(s26,plain,
( ~ spl12_20
| spl12_29 ),
inference(sat_conversion,[],[f623]) ).
cnf(s28,plain,
( ~ spl12_26
| spl12_29 ),
inference(sat_conversion,[],[f659]) ).
cnf(s30,plain,
~ spl12_29,
inference(sat_conversion,[],[f674]) ).
cnf(s33,plain,
( ~ spl12_16
| spl12_22 ),
inference(sat_conversion,[],[f699]) ).
cnf(s34,plain,
( ~ spl12_15
| spl12_21 ),
inference(sat_conversion,[],[f700]) ).
cnf(s35,plain,
( ~ spl12_4
| ~ spl12_10
| spl12_31
| spl12_32 ),
inference(sat_conversion,[],[f717]) ).
cnf(s39,plain,
( ~ spl12_19
| spl12_26 ),
inference(sat_conversion,[],[f747]) ).
cnf(s41,plain,
( spl12_19
| spl12_20
| ~ spl12_21 ),
inference(sat_conversion,[],[f749]) ).
cnf(s42,plain,
( spl12_21
| ~ spl12_31 ),
inference(sat_conversion,[],[f769]) ).
cnf(s44,plain,
( ~ spl12_1
| ~ spl12_10
| ~ spl12_11
| spl12_12
| spl12_31 ),
inference(sat_conversion,[],[f786]) ).
cnf(s49,plain,
( spl12_20
| spl12_26
| spl12_37 ),
inference(sat_conversion,[],[f932]) ).
cnf(s70,plain,
( ~ spl12_12
| spl12_53 ),
inference(sat_conversion,[],[f1419]) ).
cnf(s72,plain,
( spl12_21
| ~ spl12_32
| ~ spl12_60 ),
inference(sat_conversion,[],[f1471]) ).
cnf(s79,plain,
( ~ spl12_32
| spl12_60 ),
inference(sat_conversion,[],[f1505]) ).
cnf(s86,plain,
( ~ spl12_12
| spl12_70 ),
inference(sat_conversion,[],[f1599]) ).
cnf(s119,plain,
( spl12_2
| ~ spl12_12
| ~ spl12_37
| ~ spl12_53
| ~ spl12_70 ),
inference(sat_conversion,[],[f1799]) ).
cnf(s133,plain,
~ spl12_26,
inference(rat,[],[s28,s30]) ).
cnf(s134,plain,
~ spl12_19,
inference(rat,[],[s39,s133]) ).
cnf(s136,plain,
~ spl12_20,
inference(rat,[],[s26,s30]) ).
cnf(s147,plain,
spl12_37,
inference(rat,[],[s49,s133,s136]) ).
cnf(s150,plain,
~ spl12_21,
inference(rat,[],[s41,s134,s136]) ).
cnf(s156,plain,
~ spl12_31,
inference(rat,[],[s42,s150]) ).
cnf(s157,plain,
~ spl12_15,
inference(rat,[],[s34,s150]) ).
cnf(s160,plain,
( ~ spl12_16
| ~ spl12_22 ),
inference(rat,[],[s16,s150]) ).
cnf(s161,plain,
( ~ spl12_3
| ~ spl12_11
| spl12_16 ),
inference(rat,[],[s11,s157]) ).
cnf(s162,plain,
( spl12_1
| ~ spl12_12 ),
inference(rat,[],[s6,s9,s8]) ).
cnf(s163,plain,
( ~ spl12_1
| ~ spl12_2
| spl12_3
| spl12_4 ),
inference(rat,[],[s2,s5]) ).
cnf(s164,plain,
( spl12_1
| spl12_2
| spl12_3
| spl12_4 ),
inference(rat,[],[s1,s5]) ).
cnf(s165,plain,
~ spl12_32,
inference(rat,[],[s72,s79,s150]) ).
cnf(s166,plain,
~ spl12_4,
inference(rat,[],[s35,s8,s156,s165]) ).
cnf(s167,plain,
~ spl12_16,
inference(rat,[],[s160,s33]) ).
cnf(s168,plain,
~ spl12_3,
inference(rat,[],[s161,s9,s167]) ).
cnf(s169,plain,
spl12_1,
inference(rat,[],[s10,s164,s162,s168,s166]) ).
cnf(s170,plain,
spl12_12,
inference(rat,[],[s44,s156,s8,s9,s169]) ).
cnf(s171,plain,
~ spl12_2,
inference(rat,[],[s163,s166,s168,s169]) ).
cnf(s172,plain,
spl12_70,
inference(rat,[],[s86,s170]) ).
cnf(s173,plain,
spl12_53,
inference(rat,[],[s70,s170]) ).
cnf(s174,plain,
$false,
inference(rat,[],[s119,s172,s173,s147,s170,s171]) ).
tff(f1800,plain,
$false,
inference(avatar_sat_refutation,[],[s174]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP011_2 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n026.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sun Sep 27 12:00:26 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.47 Running first-order theorem proving
% 0.14/0.47 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.85/1.82 % (2719364)Detected formulas, will run a generic FOF schedule.
% 4.85/1.82 % (2719369)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1704961402:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.85/1.82 % (2719373)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2275202053:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.85/1.82 % (2719374)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3100531383:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.85/1.82 % (2719371)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4214416927:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.85/1.82 % (2719370)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=644132180:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.85/1.82 % (2719372)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2195151528:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.85/1.82 % (2719372)Refutation not found, incomplete strategy
% 4.85/1.82 % (2719372)------------------------------
% 4.85/1.82 % (2719372)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.82 % (2719372)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.82 % (2719372)CaDiCaL version: 2.1.3
% 4.85/1.82 % (2719372)Termination reason: Refutation not found, incomplete strategy
% 4.85/1.82 % (2719372)Time elapsed: 0.005 s
% 4.85/1.82 % (2719372)Peak memory usage: 88 MB
% 4.85/1.82 % (2719372)Instructions burned: 3 (million)
% 4.85/1.82 % (2719375)dis-21_1_sil=8000:lcm=predicate:random_seed=330295693:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 4.85/1.82 % (2719373)Instruction limit reached!
% 4.85/1.82 % (2719373)------------------------------
% 4.85/1.82 % (2719373)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.82 % (2719373)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.82 % (2719373)CaDiCaL version: 2.1.3
% 4.85/1.82 % (2719373)Termination reason: Instruction limit
% 4.85/1.82 % (2719373)Termination phase: Saturation
% 4.85/1.82 % (2719373)Time elapsed: 0.098 s
% 4.85/1.82 % (2719373)Peak memory usage: 88 MB
% 4.85/1.82 % (2719373)Instructions burned: 119 (million)
% 4.85/1.82 % (2719374)Instruction limit reached!
% 4.85/1.82 % (2719374)------------------------------
% 4.85/1.82 % (2719374)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.82 % (2719374)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.82 % (2719374)CaDiCaL version: 2.1.3
% 4.85/1.82 % (2719374)Termination reason: Instruction limit
% 4.85/1.82 % (2719374)Termination phase: Saturation
% 4.85/1.82 % (2719374)Time elapsed: 0.139 s
% 4.85/1.82 % (2719374)Peak memory usage: 90 MB
% 4.85/1.82 % (2719374)Instructions burned: 139 (million)
% 4.85/1.82 % (2719375)Instruction limit reached!
% 4.85/1.82 % (2719375)------------------------------
% 4.85/1.82 % (2719375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.85/1.82 % (2719375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.85/1.82 % (2719375)CaDiCaL version: 2.1.3
% 4.85/1.82 % (2719375)Termination reason: Instruction limit
% 4.85/1.82 % (2719375)Termination phase: Saturation
% 4.85/1.82 % (2719375)Time elapsed: 0.128 s
% 4.85/1.82 % (2719375)Peak memory usage: 91 MB
% 4.85/1.82 % (2719375)Instructions burned: 129 (million)
% 4.85/1.82 % (2719383)lrs+10_1_sil=8000:sp=occurrence:random_seed=2522353626:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 4.85/1.82 % (2719385)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2619864818:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 4.85/1.82 % (2719384)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1902963282:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/157Mi)
% 4.85/1.82 % (2719383)First to succeed.
% 4.85/1.82 % (2719383)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2719364"
% 4.85/1.82 % (2719372)------------------------------
% 4.85/1.82 % (2719372)------------------------------
% 4.85/1.82 % (2719384)Also succeeded, but the first one will report.
% 4.85/1.82 % (2719385)Also succeeded, but the first one will report.
% 4.85/1.82 % (2719389)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2630176383:s2a=on:i=248:s2at=1.23:gtg=position_2993 on theBenchmark for (2993ds/248Mi)
% 4.85/1.82 % (2719383)Refutation found. Thanks to Tanya!
% 4.85/1.82 % SZS status Theorem for theBenchmark
% 4.85/1.82 % SZS output start Proof for theBenchmark
% See solution above
% 6.72/2.03 % (2719383)------------------------------
% 6.72/2.03 % (2719383)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.72/2.03 % (2719383)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.72/2.03 % (2719383)CaDiCaL version: 2.1.3
% 6.72/2.03 % (2719383)Termination reason: Refutation
% 6.72/2.03 % (2719383)Time elapsed: 0.083 s
% 6.72/2.03 % (2719383)Peak memory usage: 91 MB
% 6.72/2.03 % (2719383)Instructions burned: 154 (million)
% 6.72/2.03 % (2719383)------------------------------
% 6.72/2.03 % (2719383)------------------------------
% 6.72/2.03 % (2719364)Success in time 0.865 s
% 6.72/2.03 % Vampire exiting
%------------------------------------------------------------------------------