%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : ITP011_3 : 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 : n008.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 6.69s 1.95s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 23
% Syntax : Number of formulae : 167 ( 35 unt; 0 typ; 11 def)
% Number of atoms : 572 ( 276 equ)
% Maximal formula atoms : 33 ( 3 avg)
% Number of connectives : 587 ( 182 ~; 269 |; 107 &)
% ( 23 <=>; 5 =>; 0 <=; 1 <~>)
% Maximal formula depth : 30 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 12 prp; 0-2 aty)
% Number of functors : 45 ( 45 usr; 9 con; 0-5 aty)
% Number of variables : 312 ( 0 sgn 300 !; 12 ?; 312 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
tyop_2Emin_2Ebool: $tType ).
tff(type_def_6,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(type_def_7,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(type_def_8,type,
sK0: $tType ).
tff(func_def_0,type,
app_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_1,type,
combin_i_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,X0) ).
tff(func_def_2,type,
combin_k_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X0)) ).
tff(func_def_3,type,
combin_s_2E0:
!>[X0: $tType,X1: $tType,X2: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,X2)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(X0,X2))) ).
tff(func_def_4,type,
c_2Ebool_2E_21_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_5,type,
c_2Ebool_2E_21_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_6,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_7,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_8,type,
c_2Emin_2E_3D_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)) ).
tff(func_def_9,type,
c_2Emin_2E_3D_2E2:
!>[X0: $tType] : ( ( X0 * X0 ) > tyop_2Emin_2Ebool ) ).
tff(func_def_10,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_11,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_12,type,
c_2Ebool_2E_3F_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(func_def_13,type,
c_2Ebool_2E_3F_2E1:
!>[X0: $tType] : ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(func_def_14,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(func_def_15,type,
c_2Eoption_2EIS__NONE_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool) ).
tff(func_def_16,type,
c_2Eoption_2EIS__NONE_2E1:
!>[X0: $tType] : ( tyop_2Eoption_2Eoption(X0) > tyop_2Emin_2Ebool ) ).
tff(func_def_17,type,
c_2Eoption_2EIS__SOME_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool) ).
tff(func_def_18,type,
c_2Eoption_2EIS__SOME_2E1:
!>[X0: $tType] : ( tyop_2Eoption_2Eoption(X0) > tyop_2Emin_2Ebool ) ).
tff(func_def_19,type,
c_2Eoption_2ENONE_2E0:
!>[X0: $tType] : tyop_2Eoption_2Eoption(X0) ).
tff(func_def_20,type,
c_2Eoption_2EOPTION__JOIN_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)),tyop_2Eoption_2Eoption(X0)) ).
tff(func_def_21,type,
c_2Eoption_2EOPTION__JOIN_2E1:
!>[X0: $tType] : ( tyop_2Eoption_2Eoption(tyop_2Eoption_2Eoption(X0)) > tyop_2Eoption_2Eoption(X0) ) ).
tff(func_def_22,type,
c_2Eoption_2EOPTION__MAP_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Eoption_2Eoption(X1))) ).
tff(func_def_23,type,
c_2Eoption_2EOPTION__MAP_2E2:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Eoption_2Eoption(X0) ) > tyop_2Eoption_2Eoption(X1) ) ).
tff(func_def_24,type,
c_2Eoption_2EOPTREL_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool))) ).
tff(func_def_25,type,
c_2Eoption_2EOPTREL_2E3:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * tyop_2Eoption_2Eoption(X0) * tyop_2Eoption_2Eoption(X1) ) > tyop_2Emin_2Ebool ) ).
tff(func_def_26,type,
c_2Eoption_2ESOME_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(X0,tyop_2Eoption_2Eoption(X0)) ).
tff(func_def_27,type,
c_2Eoption_2ESOME_2E1:
!>[X0: $tType] : ( X0 > tyop_2Eoption_2Eoption(X0) ) ).
tff(func_def_28,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(func_def_29,type,
c_2Eoption_2ETHE_2E0:
!>[X0: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),X0) ).
tff(func_def_30,type,
c_2Eoption_2ETHE_2E1:
!>[X0: $tType] : ( tyop_2Eoption_2Eoption(X0) > X0 ) ).
tff(func_def_31,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(func_def_32,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(func_def_33,type,
c_2Eoption_2Eoption__CASE_2E0:
!>[X0: $tType,X1: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(X1,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),X1))) ).
tff(func_def_34,type,
c_2Eoption_2Eoption__CASE_2E3:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Eoption_2Eoption(X0) * X1 * tyop_2Emin_2Efun(X0,X1) ) > X1 ) ).
tff(func_def_35,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(func_def_36,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(func_def_37,type,
sK1: sK0 ).
tff(func_def_38,type,
sK2: sK0 ).
tff(func_def_39,type,
sK3: tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)) ).
tff(func_def_40,type,
sK4:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,X1) * tyop_2Emin_2Efun(X0,X1) ) > X0 ) ).
tff(func_def_41,type,
sK5:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * tyop_2Eoption_2Eoption(X0) * tyop_2Eoption_2Eoption(X1) ) > X0 ) ).
tff(func_def_42,type,
sK6:
!>[X0: $tType,X1: $tType] : ( ( tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)) * tyop_2Eoption_2Eoption(X0) * tyop_2Eoption_2Eoption(X1) ) > X1 ) ).
tff(pred_def_1,type,
p: tyop_2Emin_2Ebool > $o ).
tff(f2,axiom,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( p(X0)
<=> p(X1) )
=> ( X0 = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Eboolext) ).
tff(f3,axiom,
p(c_2Ebool_2ET_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Etruth) ).
tff(f4,axiom,
~ p(c_2Ebool_2EF_2E0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Enotfalse) ).
tff(f5,axiom,
! [X0: tyop_2Emin_2Ebool] :
( ( X0 = c_2Ebool_2ET_2E0 )
| ( X0 = c_2Ebool_2EF_2E0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eextra_2Dho_2Ebool__cases__ax) ).
tff(f21,axiom,
! [X0: $tType,X1: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2EIS__NONE_2E1(X0,X1) = app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E0(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2EIS__NONE_2E1_2Emono_2EA_27a) ).
tff(f26,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] : ( c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4) = app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2EOPTREL_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).
tff(f28,axiom,
! [X0: $tType,X1: X0] : ( c_2Eoption_2ESOME_2E1(X0,X1) = app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b) ).
tff(f32,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Eoption_2Eoption(X0),X3: X1,X4: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,X2,X3,X4) = app_2E2(tyop_2Emin_2Efun(X0,X1),X1,app_2E2(X1,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),X1),app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(X1,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),X1)),c_2Eoption_2Eoption__CASE_2E0(X0,X1),X2),X3),X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2EA_27b) ).
tff(f43,axiom,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
<=> p(X0) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
<=> p(X0) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
<=> ~ p(X0) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
<=> ~ p(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Ebool_2EEQ__CLAUSES) ).
tff(f44,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Eoption_2Eoption(X0),X4: X1] :
( ! [X5: X0,X6: X0] :
( ( c_2Eoption_2ESOME_2E1(X0,X5) = c_2Eoption_2ESOME_2E1(X0,X6) )
<=> ( X5 = X6 ) )
& ! [X7: X0] : ( c_2Eoption_2ETHE_2E1(X0,c_2Eoption_2ESOME_2E1(X0,X7)) = X7 )
& ! [X8: X0] : ( c_2Eoption_2ENONE_2E0(X0) != c_2Eoption_2ESOME_2E1(X0,X8) )
& ! [X9: X0] : ( c_2Eoption_2ESOME_2E1(X0,X9) != c_2Eoption_2ENONE_2E0(X0) )
& ! [X10: X0] : ( c_2Eoption_2EIS__SOME_2E1(X0,c_2Eoption_2ESOME_2E1(X0,X10)) = c_2Ebool_2ET_2E0 )
& ( c_2Eoption_2EIS__SOME_2E1(X0,c_2Eoption_2ENONE_2E0(X0)) = c_2Ebool_2EF_2E0 )
& ! [X11: tyop_2Eoption_2Eoption(X0)] :
( p(c_2Eoption_2EIS__NONE_2E1(X0,X11))
<=> ( X11 = c_2Eoption_2ENONE_2E0(X0) ) )
& ! [X12: tyop_2Eoption_2Eoption(X0)] :
( ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X12))
<=> ( X12 = c_2Eoption_2ENONE_2E0(X0) ) )
& ! [X13: tyop_2Eoption_2Eoption(X0)] :
( p(c_2Eoption_2EIS__SOME_2E1(X0,X13))
=> ( c_2Eoption_2ESOME_2E1(X0,c_2Eoption_2ETHE_2E1(X0,X13)) = X13 ) )
& ! [X14: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X14,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ESOME_2E0(X0)) = X14 )
& ! [X15: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X15,X15,c_2Eoption_2ESOME_2E0(X0)) = X15 )
& ! [X16: tyop_2Eoption_2Eoption(X0)] :
( p(c_2Eoption_2EIS__NONE_2E1(X0,X16))
=> ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,X16,X4,X2) = X4 ) )
& ! [X17: tyop_2Eoption_2Eoption(X0)] :
( p(c_2Eoption_2EIS__SOME_2E1(X0,X17))
=> ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,X17,X4,X2) = app_2E2(X0,X1,X2,c_2Eoption_2ETHE_2E1(X0,X17)) ) )
& ! [X18: tyop_2Eoption_2Eoption(X0)] :
( p(c_2Eoption_2EIS__SOME_2E1(X0,X18))
=> ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X18,X3,c_2Eoption_2ESOME_2E0(X0)) = X18 ) )
& ! [X19: X1,X20: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,c_2Eoption_2ENONE_2E0(X0),X19,X20) = X19 )
& ! [X21: X0,X22: X1,X23: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,c_2Eoption_2ESOME_2E1(X0,X21),X22,X23) = app_2E2(X0,X1,X23,X21) )
& ! [X24: tyop_2Emin_2Efun(X0,X1),X25: X0] : ( c_2Eoption_2EOPTION__MAP_2E2(X0,X1,X24,c_2Eoption_2ESOME_2E1(X0,X25)) = c_2Eoption_2ESOME_2E1(X1,app_2E2(X0,X1,X24,X25)) )
& ! [X26: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2EOPTION__MAP_2E2(X0,X1,X26,c_2Eoption_2ENONE_2E0(X0)) = c_2Eoption_2ENONE_2E0(X1) )
& ( c_2Eoption_2EOPTION__JOIN_2E1(X0,c_2Eoption_2ENONE_2E0(tyop_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE_2E0(X0) )
& ! [X27: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2EOPTION__JOIN_2E1(X0,c_2Eoption_2ESOME_2E1(tyop_2Eoption_2Eoption(X0),X27)) = X27 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2Eoption__CLAUSES) ).
tff(f45,axiom,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4))
<=> ( ( ( X3 = c_2Eoption_2ENONE_2E0(X0) )
& ( X4 = c_2Eoption_2ENONE_2E0(X1) ) )
| ? [X5: X0,X6: X1] :
( ( X3 = c_2Eoption_2ESOME_2E1(X0,X5) )
& ( X4 = c_2Eoption_2ESOME_2E1(X1,X6) )
& p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Eoption_2EOPTREL__def) ).
tff(f46,conjecture,
! [X0: $tType,X1: X0,X2: X0,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))] :
( ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ENONE_2E0(X0)) = c_2Ebool_2ET_2E0 )
& ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ESOME_2E1(X0,X2),c_2Eoption_2ENONE_2E0(X0)) = c_2Ebool_2EF_2E0 )
& ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ESOME_2E1(X0,X1)) = c_2Ebool_2EF_2E0 )
& ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ESOME_2E1(X0,X2),c_2Eoption_2ESOME_2E1(X0,X1)) = app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3,X2),X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm_2Equotient__option_2EOPTION__REL__def) ).
tff(f47,negated_conjecture,
~ ! [X0: $tType,X1: X0,X2: X0,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))] :
( ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ENONE_2E0(X0)) = c_2Ebool_2ET_2E0 )
& ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ESOME_2E1(X0,X2),c_2Eoption_2ENONE_2E0(X0)) = c_2Ebool_2EF_2E0 )
& ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ESOME_2E1(X0,X1)) = c_2Ebool_2EF_2E0 )
& ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ESOME_2E1(X0,X2),c_2Eoption_2ESOME_2E1(X0,X1)) = app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3,X2),X1) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
tff(f50,plain,
? [X0: $tType,X1: X0,X2: X0,X3: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))] :
( ( c_2Ebool_2ET_2E0 != c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ENONE_2E0(X0)) )
| ( c_2Ebool_2EF_2E0 != c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ESOME_2E1(X0,X2),c_2Eoption_2ENONE_2E0(X0)) )
| ( c_2Ebool_2EF_2E0 != c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ESOME_2E1(X0,X1)) )
| ( c_2Eoption_2EOPTREL_2E3(X0,X0,X3,c_2Eoption_2ESOME_2E1(X0,X2),c_2Eoption_2ESOME_2E1(X0,X1)) != app_2E2(X0,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool),X3,X2),X1) ) ),
inference(ennf_transformation,[],[f47]) ).
tff(f53,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( p(X0)
<~> p(X1) ) ),
inference(ennf_transformation,[],[f2]) ).
tff(f55,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Eoption_2Eoption(X0),X4: X1] :
( ! [X5: X0,X6: X0] :
( ( c_2Eoption_2ESOME_2E1(X0,X5) = c_2Eoption_2ESOME_2E1(X0,X6) )
<=> ( X5 = X6 ) )
& ! [X7: X0] : ( c_2Eoption_2ETHE_2E1(X0,c_2Eoption_2ESOME_2E1(X0,X7)) = X7 )
& ! [X8: X0] : ( c_2Eoption_2ENONE_2E0(X0) != c_2Eoption_2ESOME_2E1(X0,X8) )
& ! [X9: X0] : ( c_2Eoption_2ESOME_2E1(X0,X9) != c_2Eoption_2ENONE_2E0(X0) )
& ! [X10: X0] : ( c_2Eoption_2EIS__SOME_2E1(X0,c_2Eoption_2ESOME_2E1(X0,X10)) = c_2Ebool_2ET_2E0 )
& ( c_2Eoption_2EIS__SOME_2E1(X0,c_2Eoption_2ENONE_2E0(X0)) = c_2Ebool_2EF_2E0 )
& ! [X11: tyop_2Eoption_2Eoption(X0)] :
( p(c_2Eoption_2EIS__NONE_2E1(X0,X11))
<=> ( X11 = c_2Eoption_2ENONE_2E0(X0) ) )
& ! [X12: tyop_2Eoption_2Eoption(X0)] :
( ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X12))
<=> ( X12 = c_2Eoption_2ENONE_2E0(X0) ) )
& ! [X13: tyop_2Eoption_2Eoption(X0)] :
( ( c_2Eoption_2ESOME_2E1(X0,c_2Eoption_2ETHE_2E1(X0,X13)) = X13 )
| ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X13)) )
& ! [X14: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X14,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ESOME_2E0(X0)) = X14 )
& ! [X15: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X15,X15,c_2Eoption_2ESOME_2E0(X0)) = X15 )
& ! [X16: tyop_2Eoption_2Eoption(X0)] :
( ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,X16,X4,X2) = X4 )
| ~ p(c_2Eoption_2EIS__NONE_2E1(X0,X16)) )
& ! [X17: tyop_2Eoption_2Eoption(X0)] :
( ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,X17,X4,X2) = app_2E2(X0,X1,X2,c_2Eoption_2ETHE_2E1(X0,X17)) )
| ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X17)) )
& ! [X18: tyop_2Eoption_2Eoption(X0)] :
( ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X18,X3,c_2Eoption_2ESOME_2E0(X0)) = X18 )
| ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X18)) )
& ! [X19: X1,X20: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,c_2Eoption_2ENONE_2E0(X0),X19,X20) = X19 )
& ! [X21: X0,X22: X1,X23: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,c_2Eoption_2ESOME_2E1(X0,X21),X22,X23) = app_2E2(X0,X1,X23,X21) )
& ! [X24: tyop_2Emin_2Efun(X0,X1),X25: X0] : ( c_2Eoption_2EOPTION__MAP_2E2(X0,X1,X24,c_2Eoption_2ESOME_2E1(X0,X25)) = c_2Eoption_2ESOME_2E1(X1,app_2E2(X0,X1,X24,X25)) )
& ! [X26: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2EOPTION__MAP_2E2(X0,X1,X26,c_2Eoption_2ENONE_2E0(X0)) = c_2Eoption_2ENONE_2E0(X1) )
& ( c_2Eoption_2EOPTION__JOIN_2E1(X0,c_2Eoption_2ENONE_2E0(tyop_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE_2E0(X0) )
& ! [X27: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2EOPTION__JOIN_2E1(X0,c_2Eoption_2ESOME_2E1(tyop_2Eoption_2Eoption(X0),X27)) = X27 ) ),
inference(ennf_transformation,[],[f44]) ).
tff(f57,plain,
( ( c_2Ebool_2ET_2E0 != c_2Eoption_2EOPTREL_2E3(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0(sK0),c_2Eoption_2ENONE_2E0(sK0)) )
| ( c_2Ebool_2EF_2E0 != c_2Eoption_2EOPTREL_2E3(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(sK0,sK2),c_2Eoption_2ENONE_2E0(sK0)) )
| ( c_2Ebool_2EF_2E0 != c_2Eoption_2EOPTREL_2E3(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0(sK0),c_2Eoption_2ESOME_2E1(sK0,sK1)) )
| ( c_2Eoption_2EOPTREL_2E3(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(sK0,sK2),c_2Eoption_2ESOME_2E1(sK0,sK1)) != app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f50]) ).
tff(f58,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( ( ~ p(X1)
| ~ p(X0) )
& ( p(X1)
| p(X0) ) ) ),
inference(nnf_transformation,[],[f53]) ).
tff(f60,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,X1),X3: tyop_2Eoption_2Eoption(X0),X4: X1] :
( ! [X5: X0,X6: X0] :
( ( ( c_2Eoption_2ESOME_2E1(X0,X5) = c_2Eoption_2ESOME_2E1(X0,X6) )
| ( X5 != X6 ) )
& ( ( X5 = X6 )
| ( c_2Eoption_2ESOME_2E1(X0,X5) != c_2Eoption_2ESOME_2E1(X0,X6) ) ) )
& ! [X7: X0] : ( c_2Eoption_2ETHE_2E1(X0,c_2Eoption_2ESOME_2E1(X0,X7)) = X7 )
& ! [X8: X0] : ( c_2Eoption_2ENONE_2E0(X0) != c_2Eoption_2ESOME_2E1(X0,X8) )
& ! [X9: X0] : ( c_2Eoption_2ESOME_2E1(X0,X9) != c_2Eoption_2ENONE_2E0(X0) )
& ! [X10: X0] : ( c_2Eoption_2EIS__SOME_2E1(X0,c_2Eoption_2ESOME_2E1(X0,X10)) = c_2Ebool_2ET_2E0 )
& ( c_2Eoption_2EIS__SOME_2E1(X0,c_2Eoption_2ENONE_2E0(X0)) = c_2Ebool_2EF_2E0 )
& ! [X11: tyop_2Eoption_2Eoption(X0)] :
( ( p(c_2Eoption_2EIS__NONE_2E1(X0,X11))
| ( c_2Eoption_2ENONE_2E0(X0) != X11 ) )
& ( ( X11 = c_2Eoption_2ENONE_2E0(X0) )
| ~ p(c_2Eoption_2EIS__NONE_2E1(X0,X11)) ) )
& ! [X12: tyop_2Eoption_2Eoption(X0)] :
( ( ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X12))
| ( c_2Eoption_2ENONE_2E0(X0) != X12 ) )
& ( ( X12 = c_2Eoption_2ENONE_2E0(X0) )
| p(c_2Eoption_2EIS__SOME_2E1(X0,X12)) ) )
& ! [X13: tyop_2Eoption_2Eoption(X0)] :
( ( c_2Eoption_2ESOME_2E1(X0,c_2Eoption_2ETHE_2E1(X0,X13)) = X13 )
| ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X13)) )
& ! [X14: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X14,c_2Eoption_2ENONE_2E0(X0),c_2Eoption_2ESOME_2E0(X0)) = X14 )
& ! [X15: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X15,X15,c_2Eoption_2ESOME_2E0(X0)) = X15 )
& ! [X16: tyop_2Eoption_2Eoption(X0)] :
( ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,X16,X4,X2) = X4 )
| ~ p(c_2Eoption_2EIS__NONE_2E1(X0,X16)) )
& ! [X17: tyop_2Eoption_2Eoption(X0)] :
( ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,X17,X4,X2) = app_2E2(X0,X1,X2,c_2Eoption_2ETHE_2E1(X0,X17)) )
| ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X17)) )
& ! [X18: tyop_2Eoption_2Eoption(X0)] :
( ( c_2Eoption_2Eoption__CASE_2E3(X0,tyop_2Eoption_2Eoption(X0),X18,X3,c_2Eoption_2ESOME_2E0(X0)) = X18 )
| ~ p(c_2Eoption_2EIS__SOME_2E1(X0,X18)) )
& ! [X19: X1,X20: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,c_2Eoption_2ENONE_2E0(X0),X19,X20) = X19 )
& ! [X21: X0,X22: X1,X23: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,c_2Eoption_2ESOME_2E1(X0,X21),X22,X23) = app_2E2(X0,X1,X23,X21) )
& ! [X24: tyop_2Emin_2Efun(X0,X1),X25: X0] : ( c_2Eoption_2EOPTION__MAP_2E2(X0,X1,X24,c_2Eoption_2ESOME_2E1(X0,X25)) = c_2Eoption_2ESOME_2E1(X1,app_2E2(X0,X1,X24,X25)) )
& ! [X26: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2EOPTION__MAP_2E2(X0,X1,X26,c_2Eoption_2ENONE_2E0(X0)) = c_2Eoption_2ENONE_2E0(X1) )
& ( c_2Eoption_2EOPTION__JOIN_2E1(X0,c_2Eoption_2ENONE_2E0(tyop_2Eoption_2Eoption(X0))) = c_2Eoption_2ENONE_2E0(X0) )
& ! [X27: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2EOPTION__JOIN_2E1(X0,c_2Eoption_2ESOME_2E1(tyop_2Eoption_2Eoption(X0),X27)) = X27 ) ),
inference(nnf_transformation,[],[f55]) ).
tff(f61,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) ) ),
inference(nnf_transformation,[],[f43]) ).
tff(f62,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( ( c_2Ebool_2ET_2E0 = X0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2ET_2E0 )
| ~ p(X0) )
& ( p(X0)
| ( c_2Ebool_2ET_2E0 != X0 ) )
& ( ( c_2Ebool_2EF_2E0 = X0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) )
& ( ( X0 = c_2Ebool_2EF_2E0 )
| p(X0) )
& ( ~ p(X0)
| ( c_2Ebool_2EF_2E0 != X0 ) ) ),
inference(flattening,[],[f61]) ).
tff(f69,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ( p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4))
| ( ( ( c_2Eoption_2ENONE_2E0(X0) != X3 )
| ( c_2Eoption_2ENONE_2E0(X1) != X4 ) )
& ! [X5: X0,X6: X1] :
( ( c_2Eoption_2ESOME_2E1(X0,X5) != X3 )
| ( c_2Eoption_2ESOME_2E1(X1,X6) != X4 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ) ) )
& ( ( ( X3 = c_2Eoption_2ENONE_2E0(X0) )
& ( X4 = c_2Eoption_2ENONE_2E0(X1) ) )
| ? [X5: X0,X6: X1] :
( ( X3 = c_2Eoption_2ESOME_2E1(X0,X5) )
& ( X4 = c_2Eoption_2ESOME_2E1(X1,X6) )
& p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) )
| ~ p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4)) ) ),
inference(nnf_transformation,[],[f45]) ).
tff(f70,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ( p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4))
| ( ( ( c_2Eoption_2ENONE_2E0(X0) != X3 )
| ( c_2Eoption_2ENONE_2E0(X1) != X4 ) )
& ! [X5: X0,X6: X1] :
( ( c_2Eoption_2ESOME_2E1(X0,X5) != X3 )
| ( c_2Eoption_2ESOME_2E1(X1,X6) != X4 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ) ) )
& ( ( ( X3 = c_2Eoption_2ENONE_2E0(X0) )
& ( X4 = c_2Eoption_2ENONE_2E0(X1) ) )
| ? [X5: X0,X6: X1] :
( ( X3 = c_2Eoption_2ESOME_2E1(X0,X5) )
& ( X4 = c_2Eoption_2ESOME_2E1(X1,X6) )
& p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) )
| ~ p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4)) ) ),
inference(flattening,[],[f69]) ).
tff(f71,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ( p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4))
| ( ( ( c_2Eoption_2ENONE_2E0(X0) != X3 )
| ( c_2Eoption_2ENONE_2E0(X1) != X4 ) )
& ! [X5: X0,X6: X1] :
( ( c_2Eoption_2ESOME_2E1(X0,X5) != X3 )
| ( c_2Eoption_2ESOME_2E1(X1,X6) != X4 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ) ) )
& ( ( ( X3 = c_2Eoption_2ENONE_2E0(X0) )
& ( X4 = c_2Eoption_2ENONE_2E0(X1) ) )
| ? [X7: X0,X8: X1] :
( ( c_2Eoption_2ESOME_2E1(X0,X7) = X3 )
& ( c_2Eoption_2ESOME_2E1(X1,X8) = X4 )
& p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X7),X8)) )
| ~ p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4)) ) ),
inference(rectify,[],[f70]) ).
tff(f72,plain,
! [X0: $tType,X1: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ( p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4))
| ( ( ( c_2Eoption_2ENONE_2E0(X0) != X3 )
| ( c_2Eoption_2ENONE_2E0(X1) != X4 ) )
& ! [X5: X0,X6: X1] :
( ( c_2Eoption_2ESOME_2E1(X0,X5) != X3 )
| ( c_2Eoption_2ESOME_2E1(X1,X6) != X4 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ) ) )
& ( ( ( X3 = c_2Eoption_2ENONE_2E0(X0) )
& ( X4 = c_2Eoption_2ENONE_2E0(X1) ) )
| ( ( c_2Eoption_2ESOME_2E1(X0,sK5(X0,X1,X2,X3,X4)) = X3 )
& ( c_2Eoption_2ESOME_2E1(X1,sK6(X0,X1,X2,X3,X4)) = X4 )
& p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK5(X0,X1,X2,X3,X4)),sK6(X0,X1,X2,X3,X4))) )
| ~ p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X7,sK5(X0,X1,X2,X3,X4)),skolemize(X8,sK6(X0,X1,X2,X3,X4))],[f71]) ).
tff(f76,plain,
( ( c_2Ebool_2ET_2E0 != c_2Eoption_2EOPTREL_2E3(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0(sK0),c_2Eoption_2ENONE_2E0(sK0)) )
| ( c_2Ebool_2EF_2E0 != c_2Eoption_2EOPTREL_2E3(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(sK0,sK2),c_2Eoption_2ENONE_2E0(sK0)) )
| ( c_2Ebool_2EF_2E0 != c_2Eoption_2EOPTREL_2E3(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0(sK0),c_2Eoption_2ESOME_2E1(sK0,sK1)) )
| ( c_2Eoption_2EOPTREL_2E3(sK0,sK0,sK3,c_2Eoption_2ESOME_2E1(sK0,sK2),c_2Eoption_2ESOME_2E1(sK0,sK1)) != app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) ) ),
inference(cnf_transformation,[],[f57]) ).
tff(f81,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| p(X0)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f58]) ).
tff(f88,plain,
! [X1: $tType,X0: $tType,X21: X0,X22: X1,X23: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,c_2Eoption_2ESOME_2E1(X0,X21),X22,X23) = app_2E2(X0,X1,X23,X21) ),
inference(cnf_transformation,[],[f60]) ).
tff(f99,plain,
! [X0: $tType,X11: tyop_2Eoption_2Eoption(X0)] :
( p(c_2Eoption_2EIS__NONE_2E1(X0,X11))
| ( c_2Eoption_2ENONE_2E0(X0) != X11 ) ),
inference(cnf_transformation,[],[f60]) ).
tff(f102,plain,
! [X0: $tType,X9: X0] : ( c_2Eoption_2ENONE_2E0(X0) != c_2Eoption_2ESOME_2E1(X0,X9) ),
inference(cnf_transformation,[],[f60]) ).
tff(f112,plain,
! [X0: tyop_2Emin_2Ebool] :
( ~ p(X0)
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(cnf_transformation,[],[f62]) ).
tff(f152,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(cnf_transformation,[],[f5]) ).
tff(f153,plain,
~ p(c_2Ebool_2EF_2E0),
inference(cnf_transformation,[],[f4]) ).
tff(f156,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ( c_2Eoption_2ENONE_2E0(X1) = X4 )
| ( c_2Eoption_2ESOME_2E1(X0,sK5(X0,X1,X2,X3,X4)) = X3 )
| ~ p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f72]) ).
tff(f157,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ( c_2Eoption_2ENONE_2E0(X0) = X3 )
| p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK5(X0,X1,X2,X3,X4)),sK6(X0,X1,X2,X3,X4)))
| ~ p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f72]) ).
tff(f158,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ( c_2Eoption_2ENONE_2E0(X0) = X3 )
| ( c_2Eoption_2ESOME_2E1(X1,sK6(X0,X1,X2,X3,X4)) = X4 )
| ~ p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f72]) ).
tff(f159,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ( c_2Eoption_2ENONE_2E0(X0) = X3 )
| ( c_2Eoption_2ESOME_2E1(X0,sK5(X0,X1,X2,X3,X4)) = X3 )
| ~ p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4)) ),
inference(cnf_transformation,[],[f72]) ).
tff(f160,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X6: X1,X4: tyop_2Eoption_2Eoption(X1),X5: X0] :
( p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4))
| ( c_2Eoption_2ESOME_2E1(X0,X5) != X3 )
| ( c_2Eoption_2ESOME_2E1(X1,X6) != X4 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ),
inference(cnf_transformation,[],[f72]) ).
tff(f161,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( p(c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4))
| ( c_2Eoption_2ENONE_2E0(X0) != X3 )
| ( c_2Eoption_2ENONE_2E0(X1) != X4 ) ),
inference(cnf_transformation,[],[f72]) ).
tff(f162,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] : ( c_2Eoption_2EOPTREL_2E3(X0,X1,X2,X3,X4) = app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),X3),X4) ),
inference(cnf_transformation,[],[f26]) ).
tff(f165,plain,
! [X0: $tType,X1: X0] : ( c_2Eoption_2ESOME_2E1(X0,X1) = app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),X1) ),
inference(cnf_transformation,[],[f28]) ).
tff(f170,plain,
p(c_2Ebool_2ET_2E0),
inference(cnf_transformation,[],[f3]) ).
tff(f173,plain,
! [X0: $tType,X1: tyop_2Eoption_2Eoption(X0)] : ( c_2Eoption_2EIS__NONE_2E1(X0,X1) = app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E0(X0),X1) ),
inference(cnf_transformation,[],[f21]) ).
tff(f179,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Eoption_2Eoption(X0),X3: X1,X4: tyop_2Emin_2Efun(X0,X1)] : ( c_2Eoption_2Eoption__CASE_2E3(X0,X1,X2,X3,X4) = app_2E2(tyop_2Emin_2Efun(X0,X1),X1,app_2E2(X1,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),X1),app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(X1,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),X1)),c_2Eoption_2Eoption__CASE_2E0(X0,X1),X2),X3),X4) ),
inference(cnf_transformation,[],[f32]) ).
tff(f180,plain,
( ( c_2Ebool_2ET_2E0 != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),c_2Eoption_2ENONE_2E0(sK0)) )
| ( c_2Ebool_2EF_2E0 != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),c_2Eoption_2ENONE_2E0(sK0)) )
| ( c_2Ebool_2EF_2E0 != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| ( app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) ) ),
inference(definition_unfolding,[],[f76,f162,f162,f165,f162,f165,f162,f165,f165]) ).
tff(f185,plain,
! [X0: $tType,X9: X0] : ( c_2Eoption_2ENONE_2E0(X0) != app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),X9) ),
inference(definition_unfolding,[],[f102,f165]) ).
tff(f188,plain,
! [X0: $tType,X11: tyop_2Eoption_2Eoption(X0)] :
( p(app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E0(X0),X11))
| ( c_2Eoption_2ENONE_2E0(X0) != X11 ) ),
inference(definition_unfolding,[],[f99,f173]) ).
tff(f199,plain,
! [X1: $tType,X0: $tType,X21: X0,X22: X1,X23: tyop_2Emin_2Efun(X0,X1)] : ( app_2E2(X0,X1,X23,X21) = app_2E2(tyop_2Emin_2Efun(X0,X1),X1,app_2E2(X1,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),X1),app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(X1,tyop_2Emin_2Efun(tyop_2Emin_2Efun(X0,X1),X1)),c_2Eoption_2Eoption__CASE_2E0(X0,X1),app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),X21)),X22),X23) ),
inference(definition_unfolding,[],[f88,f179,f165]) ).
tff(f204,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),X3),X4))
| ( c_2Eoption_2ENONE_2E0(X0) != X3 )
| ( c_2Eoption_2ENONE_2E0(X1) != X4 ) ),
inference(definition_unfolding,[],[f161,f162]) ).
tff(f205,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X6: X1,X4: tyop_2Eoption_2Eoption(X1),X5: X0] :
( p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),X3),X4))
| ( app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),X5) != X3 )
| ( app_2E2(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E0(X1),X6) != X4 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ),
inference(definition_unfolding,[],[f160,f162,f165,f165]) ).
tff(f206,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ~ p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),X3),X4))
| ( app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),sK5(X0,X1,X2,X3,X4)) = X3 )
| ( c_2Eoption_2ENONE_2E0(X0) = X3 ) ),
inference(definition_unfolding,[],[f159,f165,f162]) ).
tff(f207,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ~ p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),X3),X4))
| ( app_2E2(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E0(X1),sK6(X0,X1,X2,X3,X4)) = X4 )
| ( c_2Eoption_2ENONE_2E0(X0) = X3 ) ),
inference(definition_unfolding,[],[f158,f165,f162]) ).
tff(f208,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ~ p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),X3),X4))
| p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,sK5(X0,X1,X2,X3,X4)),sK6(X0,X1,X2,X3,X4)))
| ( c_2Eoption_2ENONE_2E0(X0) = X3 ) ),
inference(definition_unfolding,[],[f157,f162]) ).
tff(f209,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X3: tyop_2Eoption_2Eoption(X0),X4: tyop_2Eoption_2Eoption(X1)] :
( ~ p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),X3),X4))
| ( app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),sK5(X0,X1,X2,X3,X4)) = X3 )
| ( c_2Eoption_2ENONE_2E0(X1) = X4 ) ),
inference(definition_unfolding,[],[f156,f165,f162]) ).
tff(f217,plain,
! [X0: $tType] : p(app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E0(X0),c_2Eoption_2ENONE_2E0(X0))),
inference(equality_resolution,[],[f188]) ).
tff(f223,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X4: tyop_2Eoption_2Eoption(X1)] :
( p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),c_2Eoption_2ENONE_2E0(X0)),X4))
| ( c_2Eoption_2ENONE_2E0(X1) != X4 ) ),
inference(equality_resolution,[],[f204]) ).
tff(f224,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool))] : p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),c_2Eoption_2ENONE_2E0(X0)),c_2Eoption_2ENONE_2E0(X1))),
inference(equality_resolution,[],[f223]) ).
tff(f225,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X6: X1,X4: tyop_2Eoption_2Eoption(X1),X5: X0] :
( p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),X5)),X4))
| ( app_2E2(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E0(X1),X6) != X4 )
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ),
inference(equality_resolution,[],[f205]) ).
tff(f226,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),X6: X1,X5: X0] :
( p(app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X0,X1),X2),app_2E2(X0,tyop_2Eoption_2Eoption(X0),c_2Eoption_2ESOME_2E0(X0),X5)),app_2E2(X1,tyop_2Eoption_2Eoption(X1),c_2Eoption_2ESOME_2E0(X1),X6)))
| ~ p(app_2E2(X1,tyop_2Emin_2Ebool,app_2E2(X0,tyop_2Emin_2Efun(X1,tyop_2Emin_2Ebool),X2,X5),X6)) ),
inference(equality_resolution,[],[f225]) ).
tff(f231,definition,
( spl7_1
<=> ( app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition]) ).
tff(f233,plain,
( ( app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| spl7_1 ),
inference(avatar_component_clause,[],[f231]) ).
tff(f235,definition,
( spl7_2
<=> ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition]) ).
tff(f237,plain,
( ( c_2Ebool_2EF_2E0 != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| spl7_2 ),
inference(avatar_component_clause,[],[f235]) ).
tff(f239,definition,
( spl7_3
<=> ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),c_2Eoption_2ENONE_2E0(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition]) ).
tff(f241,plain,
( ( c_2Ebool_2EF_2E0 != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),c_2Eoption_2ENONE_2E0(sK0)) )
| spl7_3 ),
inference(avatar_component_clause,[],[f239]) ).
tff(f243,definition,
( spl7_4
<=> ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),c_2Eoption_2ENONE_2E0(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition]) ).
tff(f245,plain,
( ( c_2Ebool_2ET_2E0 != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),c_2Eoption_2ENONE_2E0(sK0)) )
| spl7_4 ),
inference(avatar_component_clause,[],[f243]) ).
tff(f246,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(avatar_split_clause,[],[f180,f243,f239,f235,f231]) ).
tff(f250,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( c_2Ebool_2EF_2E0 = X1 )
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(superposition,[],[f152,f152]) ).
tff(f252,plain,
( ( c_2Ebool_2ET_2E0 != app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) )
| ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| spl7_1 ),
inference(superposition,[],[f233,f152]) ).
tff(f253,plain,
! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
| ( c_2Ebool_2EF_2E0 = X0 ) ),
inference(equality_factoring,[],[f152]) ).
tff(f255,definition,
( spl7_5
<=> ! [X0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EF_2E0 = X0 ) ),
introduced(definition,[new_symbols(definition,[spl7_5])],[avatar_definition]) ).
tff(f256,plain,
( ! [X0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EF_2E0 = X0 )
| ~ spl7_5 ),
inference(avatar_component_clause,[],[f255]) ).
tff(f258,definition,
( spl7_6
<=> ( c_2Ebool_2ET_2E0 = c_2Ebool_2EF_2E0 ) ),
introduced(definition,[new_symbols(definition,[spl7_6])],[avatar_definition]) ).
tff(f260,plain,
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
| spl7_6 ),
inference(avatar_component_clause,[],[f258]) ).
tff(f261,plain,
( spl7_5
| ~ spl7_6 ),
inference(avatar_split_clause,[],[f253,f258,f255]) ).
tff(f263,definition,
( spl7_7
<=> ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl7_7])],[avatar_definition]) ).
tff(f265,plain,
( ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| ~ spl7_7 ),
inference(avatar_component_clause,[],[f263]) ).
tff(f267,definition,
( spl7_8
<=> ( c_2Ebool_2ET_2E0 = app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) ) ),
introduced(definition,[new_symbols(definition,[spl7_8])],[avatar_definition]) ).
tff(f268,plain,
( ( c_2Ebool_2ET_2E0 = app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) )
| ~ spl7_8 ),
inference(avatar_component_clause,[],[f267]) ).
tff(f269,plain,
( ( c_2Ebool_2ET_2E0 != app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) )
| spl7_8 ),
inference(avatar_component_clause,[],[f267]) ).
tff(f270,plain,
( spl7_7
| ~ spl7_8
| spl7_1 ),
inference(avatar_split_clause,[],[f252,f231,f267,f263]) ).
tff(f271,plain,
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2ET_2E0 )
| ( c_2Ebool_2EF_2E0 = app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) )
| spl7_8 ),
inference(superposition,[],[f269,f152]) ).
tff(f272,plain,
( ( c_2Ebool_2EF_2E0 = app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) )
| spl7_8 ),
inference(trivial_inequality_removal,[],[f271]) ).
tff(f276,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( p(X1)
| ( X0 = X1 )
| ( c_2Ebool_2ET_2E0 = X0 ) ),
inference(resolution,[],[f81,f112]) ).
tff(f279,plain,
( ( c_2Ebool_2ET_2E0 != c_2Ebool_2EF_2E0 )
| spl7_8 ),
inference(superposition,[],[f269,f272]) ).
tff(f286,plain,
! [X0: $tType] : ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E0(X0),c_2Eoption_2ENONE_2E0(X0)) ),
inference(resolution,[],[f217,f112]) ).
tff(f291,plain,
! [X0: tyop_2Emin_2Ebool,X1: tyop_2Emin_2Ebool] :
( ( X0 = X1 )
| ( c_2Ebool_2ET_2E0 = X0 )
| ( c_2Ebool_2ET_2E0 = X1 ) ),
inference(resolution,[],[f276,f112]) ).
tff(f343,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 != app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1) )
| ( app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) )
| spl7_1 ),
inference(superposition,[],[f233,f250]) ).
tff(f368,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) = X0 )
| ( c_2Ebool_2EF_2E0 = X0 ) )
| spl7_1
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f343,f272]) ).
tff(f384,plain,
( ! [X0: $tType] :
( p(app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)))
| ( c_2Ebool_2EF_2E0 = app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool,c_2Eoption_2EIS__NONE_2E0(X0),c_2Eoption_2ENONE_2E0(X0)) ) )
| spl7_1
| spl7_8 ),
inference(superposition,[],[f217,f368]) ).
tff(f391,plain,
( ( c_2Ebool_2ET_2E0 = c_2Ebool_2EF_2E0 )
| p(app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)))
| spl7_1
| spl7_8 ),
inference(forward_demodulation,[],[f384,f286]) ).
tff(f393,plain,
( p(app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)))
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f391,f260]) ).
tff(f411,plain,
( ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(resolution,[],[f393,f112]) ).
tff(f999,definition,
( spl7_9
<=> ! [X3: tyop_2Emin_2Ebool] : ( c_2Ebool_2ET_2E0 = X3 ) ),
introduced(definition,[new_symbols(definition,[spl7_9])],[avatar_definition]) ).
tff(f1000,plain,
( ! [X3: tyop_2Emin_2Ebool] : ( c_2Ebool_2ET_2E0 = X3 )
| ~ spl7_9 ),
inference(avatar_component_clause,[],[f999]) ).
tff(f1012,plain,
! [X1: $tType,X0: $tType,X2: tyop_2Emin_2Efun(X1,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool))] : ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(X1,tyop_2Emin_2Efun(X0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X1),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(X0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(X1,X0),X2),c_2Eoption_2ENONE_2E0(X1)),c_2Eoption_2ENONE_2E0(X0)) ),
inference(resolution,[],[f224,f112]) ).
tff(f1982,plain,
( ( app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK5(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) )
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(resolution,[],[f206,f393]) ).
tff(f2026,plain,
( ( app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK5(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f1982,f185]) ).
tff(f2034,plain,
( ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(sK0,X0)] : ( app_2E2(sK0,X0,X1,sK5(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) = app_2E2(tyop_2Emin_2Efun(sK0,X0),X0,app_2E2(X0,tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK0,X0),X0),app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK0,X0),X0)),c_2Eoption_2Eoption__CASE_2E0(sK0,X0),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),X2),X1) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(superposition,[],[f199,f2026]) ).
tff(f2037,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Efun(sK0,X0)] : ( app_2E2(sK0,X0,X1,sK5(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) = app_2E2(sK0,X0,X1,sK2) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_demodulation,[],[f2034,f199]) ).
tff(f2040,plain,
( ( app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) )
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(resolution,[],[f207,f393]) ).
tff(f2084,plain,
( ( app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f2040,f185]) ).
tff(f2249,plain,
( ! [X0: $tType,X2: X0,X1: tyop_2Emin_2Efun(sK0,X0)] : ( app_2E2(sK0,X0,X1,sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) = app_2E2(tyop_2Emin_2Efun(sK0,X0),X0,app_2E2(X0,tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK0,X0),X0),app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(X0,tyop_2Emin_2Efun(tyop_2Emin_2Efun(sK0,X0),X0)),c_2Eoption_2Eoption__CASE_2E0(sK0,X0),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)),X2),X1) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(superposition,[],[f199,f2084]) ).
tff(f2252,plain,
( ! [X0: $tType,X1: tyop_2Emin_2Efun(sK0,X0)] : ( app_2E2(sK0,X0,X1,sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) = app_2E2(sK0,X0,X1,sK1) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_demodulation,[],[f2249,f199]) ).
tff(f2324,plain,
( ~ p(c_2Ebool_2ET_2E0)
| p(app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK5(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))),sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))))
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(superposition,[],[f208,f411]) ).
tff(f2361,plain,
( p(app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK5(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))),sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))))
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) )
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f2324,f170]) ).
tff(f2365,plain,
( p(app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK5(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))),sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))))
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f2361,f185]) ).
tff(f2368,plain,
( p(app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK5(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))),sK1))
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_demodulation,[],[f2365,f2252]) ).
tff(f2371,plain,
( p(app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1))
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_demodulation,[],[f2368,f2037]) ).
tff(f2374,plain,
( p(c_2Ebool_2EF_2E0)
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_demodulation,[],[f2371,f272]) ).
tff(f2378,plain,
( $false
| spl7_1
| spl7_6
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f2374,f153]) ).
tff(f2379,plain,
( spl7_1
| spl7_6
| spl7_8 ),
inference(avatar_contradiction_clause,[],[f2378]) ).
tff(f2381,plain,
( $false
| ~ spl7_5
| spl7_8 ),
inference(forward_subsumption_resolution,[],[f279,f256]) ).
tff(f2382,plain,
( ~ spl7_5
| spl7_8 ),
inference(avatar_contradiction_clause,[],[f2381]) ).
tff(f2635,plain,
( p(c_2Ebool_2EF_2E0)
| ~ p(app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1))
| ~ spl7_7 ),
inference(superposition,[],[f226,f265]) ).
tff(f2647,plain,
( ~ p(app_2E2(sK0,tyop_2Emin_2Ebool,app_2E2(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool),sK3,sK2),sK1))
| ~ spl7_7 ),
inference(forward_subsumption_resolution,[],[f2635,f153]) ).
tff(f2664,plain,
( ~ p(c_2Ebool_2ET_2E0)
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_demodulation,[],[f2647,f268]) ).
tff(f2668,plain,
( $false
| ~ spl7_7
| ~ spl7_8 ),
inference(forward_subsumption_resolution,[],[f2664,f170]) ).
tff(f2669,plain,
( ~ spl7_7
| ~ spl7_8 ),
inference(avatar_contradiction_clause,[],[f2668]) ).
tff(f2676,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 != X0 )
| ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| ( c_2Ebool_2ET_2E0 = X0 ) )
| spl7_2 ),
inference(superposition,[],[f237,f291]) ).
tff(f2707,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| ( c_2Ebool_2ET_2E0 = X0 ) )
| spl7_2 ),
inference(forward_subsumption_resolution,[],[f2676,f152]) ).
tff(f2709,definition,
( spl7_12
<=> ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) ) ),
introduced(definition,[new_symbols(definition,[spl7_12])],[avatar_definition]) ).
tff(f2710,plain,
( ( c_2Ebool_2ET_2E0 != app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| spl7_12 ),
inference(avatar_component_clause,[],[f2709]) ).
tff(f2711,plain,
( ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),c_2Eoption_2ENONE_2E0(sK0)),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1)) )
| ~ spl7_12 ),
inference(avatar_component_clause,[],[f2709]) ).
tff(f2717,plain,
( spl7_9
| spl7_12
| spl7_2 ),
inference(avatar_split_clause,[],[f2707,f235,f2709,f999]) ).
tff(f3254,plain,
( ~ p(c_2Ebool_2ET_2E0)
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK5(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0(sK0),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) )
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1) )
| ~ spl7_12 ),
inference(superposition,[],[f209,f2711]) ).
tff(f3258,plain,
( ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK5(sK0,sK0,sK3,c_2Eoption_2ENONE_2E0(sK0),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1))) )
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1) )
| ~ spl7_12 ),
inference(forward_subsumption_resolution,[],[f3254,f170]) ).
tff(f3263,plain,
( ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK1) )
| ~ spl7_12 ),
inference(forward_subsumption_resolution,[],[f3258,f185]) ).
tff(f3266,plain,
( $false
| ~ spl7_12 ),
inference(forward_subsumption_resolution,[],[f3263,f185]) ).
tff(f3267,plain,
~ spl7_12,
inference(avatar_contradiction_clause,[],[f3266]) ).
tff(f3268,plain,
( $false
| ~ spl7_9
| spl7_12 ),
inference(forward_subsumption_resolution,[],[f2710,f1000]) ).
tff(f3269,plain,
( ~ spl7_9
| spl7_12 ),
inference(avatar_contradiction_clause,[],[f3268]) ).
tff(f3556,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2EF_2E0 != X0 )
| ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),c_2Eoption_2ENONE_2E0(sK0)) )
| ( c_2Ebool_2ET_2E0 = X0 ) )
| spl7_3 ),
inference(superposition,[],[f241,f291]) ).
tff(f3587,plain,
( ! [X0: tyop_2Emin_2Ebool] :
( ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),c_2Eoption_2ENONE_2E0(sK0)) )
| ( c_2Ebool_2ET_2E0 = X0 ) )
| spl7_3 ),
inference(forward_subsumption_resolution,[],[f3556,f152]) ).
tff(f3589,definition,
( spl7_19
<=> ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),c_2Eoption_2ENONE_2E0(sK0)) ) ),
introduced(definition,[new_symbols(definition,[spl7_19])],[avatar_definition]) ).
tff(f3591,plain,
( ( c_2Ebool_2ET_2E0 = app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool,app_2E2(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(sK0,tyop_2Emin_2Efun(sK0,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(sK0),tyop_2Emin_2Ebool)),c_2Eoption_2EOPTREL_2E0(sK0,sK0),sK3),app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2)),c_2Eoption_2ENONE_2E0(sK0)) )
| ~ spl7_19 ),
inference(avatar_component_clause,[],[f3589]) ).
tff(f3594,plain,
( spl7_9
| spl7_19
| spl7_3 ),
inference(avatar_split_clause,[],[f3587,f239,f3589,f999]) ).
tff(f3621,plain,
( ~ p(c_2Ebool_2ET_2E0)
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),c_2Eoption_2ENONE_2E0(sK0))) )
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) )
| ~ spl7_19 ),
inference(superposition,[],[f207,f3591]) ).
tff(f3627,plain,
( ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK6(sK0,sK0,sK3,app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2),c_2Eoption_2ENONE_2E0(sK0))) )
| ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) )
| ~ spl7_19 ),
inference(forward_subsumption_resolution,[],[f3621,f170]) ).
tff(f3632,plain,
( ( c_2Eoption_2ENONE_2E0(sK0) = app_2E2(sK0,tyop_2Eoption_2Eoption(sK0),c_2Eoption_2ESOME_2E0(sK0),sK2) )
| ~ spl7_19 ),
inference(forward_subsumption_resolution,[],[f3627,f185]) ).
tff(f3634,plain,
( $false
| ~ spl7_19 ),
inference(forward_subsumption_resolution,[],[f3632,f185]) ).
tff(f3635,plain,
~ spl7_19,
inference(avatar_contradiction_clause,[],[f3634]) ).
tff(f3636,plain,
( $false
| spl7_4 ),
inference(forward_subsumption_resolution,[],[f245,f1012]) ).
tff(f3637,plain,
spl7_4,
inference(avatar_contradiction_clause,[],[f3636]) ).
cnf(s1,plain,
( ~ spl7_1
| ~ spl7_2
| ~ spl7_3
| ~ spl7_4 ),
inference(sat_conversion,[],[f246]) ).
cnf(s2,plain,
( spl7_5
| ~ spl7_6 ),
inference(sat_conversion,[],[f261]) ).
cnf(s3,plain,
( spl7_1
| spl7_7
| ~ spl7_8 ),
inference(sat_conversion,[],[f270]) ).
cnf(s8,plain,
( spl7_1
| spl7_6
| spl7_8 ),
inference(sat_conversion,[],[f2379]) ).
cnf(s10,plain,
( ~ spl7_5
| spl7_8 ),
inference(sat_conversion,[],[f2382]) ).
cnf(s13,plain,
( ~ spl7_7
| ~ spl7_8 ),
inference(sat_conversion,[],[f2669]) ).
cnf(s16,plain,
( spl7_2
| spl7_9
| spl7_12 ),
inference(sat_conversion,[],[f2717]) ).
cnf(s17,plain,
~ spl7_12,
inference(sat_conversion,[],[f3267]) ).
cnf(s18,plain,
( ~ spl7_9
| spl7_12 ),
inference(sat_conversion,[],[f3269]) ).
cnf(s34,plain,
( spl7_3
| spl7_9
| spl7_19 ),
inference(sat_conversion,[],[f3594]) ).
cnf(s35,plain,
~ spl7_19,
inference(sat_conversion,[],[f3635]) ).
cnf(s36,plain,
spl7_4,
inference(sat_conversion,[],[f3637]) ).
cnf(s37,plain,
( spl7_3
| spl7_9 ),
inference(rat,[],[s34,s35]) ).
cnf(s40,plain,
~ spl7_9,
inference(rat,[],[s18,s17]) ).
cnf(s41,plain,
spl7_3,
inference(rat,[],[s37,s40]) ).
cnf(s42,plain,
spl7_2,
inference(rat,[],[s16,s17,s40]) ).
cnf(s43,plain,
~ spl7_1,
inference(rat,[],[s1,s36,s41,s42]) ).
cnf(s44,plain,
~ spl7_8,
inference(rat,[],[s3,s13,s43]) ).
cnf(s45,plain,
~ spl7_5,
inference(rat,[],[s10,s44]) ).
cnf(s46,plain,
spl7_6,
inference(rat,[],[s8,s43,s44]) ).
cnf(s50,plain,
$false,
inference(rat,[],[s2,s46,s45]) ).
tff(f3639,plain,
$false,
inference(avatar_sat_refutation,[],[s50]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP011_3 : TPTP v9.3.1. Bugfixed v7.5.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 % Computer : n008.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Sun Sep 27 11:58:25 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 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
% 5.95/1.84 % (1097189)Detected formulas, will run a generic FOF schedule.
% 5.95/1.84 % (1097196)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=2463489848:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.95/1.84 % (1097196)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.95/1.84 % (1097198)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=611776335:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.95/1.84 % (1097199)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3746964430:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.95/1.84 % (1097197)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1969576296:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.95/1.84 % (1097195)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=643323523:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.95/1.84 % (1097194)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=1458954047:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.95/1.84 % (1097200)dis-21_1_sil=8000:lcm=predicate:random_seed=2634766927: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)
% 5.95/1.84 % (1097197)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 5.95/1.84 % (1097197)Instruction limit reached!
% 5.95/1.84 % (1097197)------------------------------
% 5.95/1.84 % (1097197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.84 % (1097197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.84 % (1097197)CaDiCaL version: 2.1.3
% 5.95/1.84 % (1097197)Termination reason: Instruction limit
% 5.95/1.84 % (1097197)Termination phase: Saturation
% 5.95/1.84 % (1097197)Time elapsed: 0.059 s
% 5.95/1.84 % (1097197)Peak memory usage: 88 MB
% 5.95/1.84 % (1097197)Instructions burned: 110 (million)
% 5.95/1.84 % (1097198)Instruction limit reached!
% 5.95/1.84 % (1097198)------------------------------
% 5.95/1.84 % (1097198)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.84 % (1097198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.84 % (1097198)CaDiCaL version: 2.1.3
% 5.95/1.84 % (1097198)Termination reason: Instruction limit
% 5.95/1.84 % (1097198)Termination phase: Saturation
% 5.95/1.84 % (1097198)Time elapsed: 0.062 s
% 5.95/1.84 % (1097198)Peak memory usage: 88 MB
% 5.95/1.84 % (1097198)Instructions burned: 120 (million)
% 5.95/1.84 % (1097200)Instruction limit reached!
% 5.95/1.84 % (1097200)------------------------------
% 5.95/1.84 % (1097200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.84 % (1097200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.84 % (1097200)CaDiCaL version: 2.1.3
% 5.95/1.84 % (1097200)Termination reason: Instruction limit
% 5.95/1.84 % (1097200)Termination phase: Saturation
% 5.95/1.84 % (1097200)Time elapsed: 0.067 s
% 5.95/1.84 % (1097200)Peak memory usage: 89 MB
% 5.95/1.84 % (1097200)Instructions burned: 130 (million)
% 5.95/1.84 % (1097199)Instruction limit reached!
% 5.95/1.84 % (1097199)------------------------------
% 5.95/1.84 % (1097199)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.95/1.84 % (1097199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.95/1.84 % (1097199)CaDiCaL version: 2.1.3
% 5.95/1.84 % (1097199)Termination reason: Instruction limit
% 5.95/1.84 % (1097199)Termination phase: Saturation
% 5.95/1.84 % (1097199)Time elapsed: 0.092 s
% 5.95/1.84 % (1097199)Peak memory usage: 90 MB
% 5.95/1.84 % (1097199)Instructions burned: 140 (million)
% 5.95/1.84 % Exception at run slice level
% 5.95/1.84 User error: GNN currently only supports monomorphic FOL.
% 5.95/1.84 % (1097208)lrs+10_1_sil=8000:sp=occurrence:random_seed=96689627:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.95/1.84 % (1097209)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3633409791:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.95/1.84 % (1097210)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4219589649:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.69/1.95 % (1097211)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=2569211248:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.69/1.95 % (1097212)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3516776730:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 6.69/1.95 % (1097209)Instruction limit reached!
% 6.69/1.95 % (1097209)------------------------------
% 6.69/1.95 % (1097209)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097209)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097209)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097209)Termination reason: Instruction limit
% 6.69/1.95 % (1097209)Termination phase: Saturation
% 6.69/1.95 % (1097209)Time elapsed: 0.076 s
% 6.69/1.95 % (1097209)Peak memory usage: 89 MB
% 6.69/1.95 % (1097209)Instructions burned: 157 (million)
% 6.69/1.95 % (1097208)Instruction limit reached!
% 6.69/1.95 % (1097208)------------------------------
% 6.69/1.95 % (1097208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097208)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097208)Termination reason: Instruction limit
% 6.69/1.95 % (1097208)Termination phase: Saturation
% 6.69/1.95 % (1097208)Time elapsed: 0.138 s
% 6.69/1.95 % (1097208)Peak memory usage: 89 MB
% 6.69/1.95 % (1097208)Instructions burned: 287 (million)
% 6.69/1.95 % (1097212)Instruction limit reached!
% 6.69/1.95 % (1097212)------------------------------
% 6.69/1.95 % (1097212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097212)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097212)Termination reason: Instruction limit
% 6.69/1.95 % (1097212)Termination phase: Saturation
% 6.69/1.95 % (1097212)Time elapsed: 0.082 s
% 6.69/1.95 % (1097212)Peak memory usage: 89 MB
% 6.69/1.95 % (1097212)Instructions burned: 295 (million)
% 6.69/1.95 % Exception at run slice level
% 6.69/1.95 User error: GNN currently only supports monomorphic FOL.
% 6.69/1.95 % Exception at run slice level
% 6.69/1.95 User error: GNN currently only supports monomorphic FOL.
% 6.69/1.95 % (1097211)Instruction limit reached!
% 6.69/1.95 % (1097211)------------------------------
% 6.69/1.95 % (1097211)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097211)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097211)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097211)Termination reason: Instruction limit
% 6.69/1.95 % (1097211)Termination phase: Saturation
% 6.69/1.95 % (1097211)Time elapsed: 0.150 s
% 6.69/1.95 % (1097211)Peak memory usage: 90 MB
% 6.69/1.95 % (1097211)Instructions burned: 249 (million)
% 6.69/1.95 % (1097210)Instruction limit reached!
% 6.69/1.95 % (1097210)------------------------------
% 6.69/1.95 % (1097210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097210)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097210)Termination reason: Instruction limit
% 6.69/1.95 % (1097210)Termination phase: Saturation
% 6.69/1.95 % (1097210)Time elapsed: 0.190 s
% 6.69/1.95 % (1097210)Peak memory usage: 90 MB
% 6.69/1.95 % (1097210)Instructions burned: 326 (million)
% 6.69/1.95 % (1097218)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3459689478:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 6.69/1.95 % (1097220)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3730076249:i=127:av=off:fsr=off:sup=off_2995 on theBenchmark for (2995ds/127Mi)
% 6.69/1.95 % (1097220)Refutation not found, incomplete strategy
% 6.69/1.95 % (1097220)------------------------------
% 6.69/1.95 % (1097220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097220)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097220)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.95 % (1097220)Time elapsed: 0.002 s
% 6.69/1.95 % (1097220)Peak memory usage: 88 MB
% 6.69/1.95 % (1097220)Instructions burned: 7 (million)
% 6.69/1.95 % (1097219)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3723935987:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 6.69/1.95 % (1097219)Refutation not found, incomplete strategy
% 6.69/1.95 % (1097219)------------------------------
% 6.69/1.95 % (1097219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097219)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097219)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.95 % (1097219)Time elapsed: 0.007 s
% 6.69/1.95 % (1097219)Peak memory usage: 89 MB
% 6.69/1.95 % (1097219)Instructions burned: 9 (million)
% 6.69/1.95 % (1097221)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=1680341900:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2994 on theBenchmark for (2994ds/114Mi)
% 6.69/1.95 % (1097222)lrs+10_1_sil=8000:sp=occurrence:random_seed=3535588394:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2994 on theBenchmark for (2994ds/907Mi)
% 6.69/1.95 % (1097223)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3043747787:i=437:sd=1:aac=none:ss=included_2994 on theBenchmark for (2994ds/437Mi)
% 6.69/1.95 % (1097223)Refutation not found, incomplete strategy
% 6.69/1.95 % (1097223)------------------------------
% 6.69/1.95 % (1097223)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097223)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097223)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097223)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.95 % (1097223)Time elapsed: 0.006 s
% 6.69/1.95 % (1097223)Peak memory usage: 88 MB
% 6.69/1.95 % (1097223)Instructions burned: 8 (million)
% 6.69/1.95 % (1097225)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=68550527:i=5202:ss=axioms:sgt=16_2994 on theBenchmark for (2994ds/5202Mi)
% 6.69/1.95 % (1097221)Instruction limit reached!
% 6.69/1.95 % (1097221)------------------------------
% 6.69/1.95 % (1097221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097221)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097221)Termination reason: Instruction limit
% 6.69/1.95 % (1097221)Termination phase: Saturation
% 6.69/1.95 % (1097221)Time elapsed: 0.059 s
% 6.69/1.95 % (1097221)Peak memory usage: 88 MB
% 6.69/1.95 % (1097221)Instructions burned: 114 (million)
% 6.69/1.95 % (1097220)------------------------------
% 6.69/1.95 % (1097220)------------------------------
% 6.69/1.95 % (1097222)First to succeed.
% 6.69/1.95 % (1097222)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1097189"
% 6.69/1.95 % (1097233)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=1380775801:st=8:i=592:sd=3:ep=RST:ss=axioms_2992 on theBenchmark for (2992ds/592Mi)
% 6.69/1.95 % (1097232)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2139788409:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2992 on theBenchmark for (2992ds/134Mi)
% 6.69/1.95 % (1097219)------------------------------
% 6.69/1.95 % (1097219)------------------------------
% 6.69/1.95 % (1097223)------------------------------
% 6.69/1.95 % (1097223)------------------------------
% 6.69/1.95 % Exception at run slice level
% 6.69/1.95 User error: GNN currently only supports monomorphic FOL.
% 6.69/1.95 % (1097232)Instruction limit reached!
% 6.69/1.95 % (1097232)------------------------------
% 6.69/1.95 % (1097232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097232)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097232)Termination reason: Instruction limit
% 6.69/1.95 % (1097232)Termination phase: Saturation
% 6.69/1.95 % (1097232)Time elapsed: 0.073 s
% 6.69/1.95 % (1097232)Peak memory usage: 90 MB
% 6.69/1.95 % (1097232)Instructions burned: 135 (million)
% 6.69/1.95 % (1097233)Instruction limit reached!
% 6.69/1.95 % (1097233)------------------------------
% 6.69/1.95 % (1097233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097233)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097233)Termination reason: Instruction limit
% 6.69/1.95 % (1097233)Termination phase: Saturation
% 6.69/1.95 % (1097233)Time elapsed: 0.150 s
% 6.69/1.95 % (1097233)Peak memory usage: 89 MB
% 6.69/1.95 % (1097233)Instructions burned: 594 (million)
% 6.69/1.95 % (1097236)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2498005315:st=3:i=13193:sd=3:ss=axioms_2991 on theBenchmark for (2991ds/13193Mi)
% 6.69/1.95 % (1097237)lrs+1666_7_slsqr=4,1:sil=8000:plsq=on:plsqc=1:sos=on:urr=on:plsql=on:rp=on:alpa=false:sac=on:slsq=on:random_seed=2038921545:i=125:slsql=off:bs=unit_only:gtg=position:fdi=2:gsp=on:ss=axioms:sgt=8_2990 on theBenchmark for (2990ds/125Mi)
% 6.69/1.95 % (1097237)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.69/1.95 % Exception at run slice level
% 6.69/1.95 User error: GNN currently only supports monomorphic FOL.
% 6.69/1.95 % (1097238)lrs+10_1024_to=lpo:sil=8000:tgt=full:sp=arity:slsq=on:random_seed=2982339737:i=134:gtgl=5:slsql=off:gtg=exists_sym_2990 on theBenchmark for (2990ds/134Mi)
% 6.69/1.95 % Exception at run slice level
% 6.69/1.95 User error: Immediate (shared) subterms of term/literal app_2E2(X1,X0,sF10(X0,X1,X2),X3) = sF11(X1,X0,X2,X3) have different types/not well-typed!
% 6.69/1.95 % (1097239)lrs+10_1_sil=16000:plsq=on:plsqc=1:plsqr=32,1:sos=on:lcm=reverse:fd=off:newcnf=on:random_seed=1298553935:i=141:sd=1:gsp=on:sup=off:ss=axioms:sgt=8_2990 on theBenchmark for (2990ds/141Mi)
% 6.69/1.95 % (1097239)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 6.69/1.95 % (1097239)Refutation not found, incomplete strategy
% 6.69/1.95 % (1097239)------------------------------
% 6.69/1.95 % (1097239)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.69/1.95 % (1097239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.69/1.95 % (1097239)CaDiCaL version: 2.1.3
% 6.69/1.95 % (1097239)Termination reason: Refutation not found, incomplete strategy
% 6.69/1.95 % (1097239)Time elapsed: 0.003 s
% 6.69/1.95 % (1097239)Peak memory usage: 88 MB
% 6.69/1.95 % (1097239)Instructions burned: 3 (million)
% 6.69/1.95 % (1097241)lrs+1011_1_sil=8000:plsq=on:sp=occurrence:fs=off:random_seed=2161479315:i=431:sd=1:fsr=off:sup=off:ss=axioms:sgt=64_2990 on theBenchmark for (2990ds/431Mi)
% 6.69/1.95 % (1097222)Refutation found. Thanks to Tanya!
% 6.69/1.95 % SZS status Theorem for theBenchmark
% 6.69/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/2.14 % (1097222)------------------------------
% 0.18/2.14 % (1097222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.18/2.14 % (1097222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/2.14 % (1097222)CaDiCaL version: 2.1.3
% 0.18/2.14 % (1097222)Termination reason: Refutation
% 0.18/2.14 % (1097222)Time elapsed: 0.175 s
% 0.18/2.14 % (1097222)Peak memory usage: 90 MB
% 0.18/2.14 % (1097222)Instructions burned: 353 (million)
% 0.18/2.14 % (1097222)------------------------------
% 0.18/2.14 % (1097222)------------------------------
% 0.18/2.14 % (1097189)Success in time 1.083 s
% 0.18/2.14 % Vampire exiting
%------------------------------------------------------------------------------