%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP203^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 01:45:25 PM UTC 2025
% Result : Theorem 42.18s 42.71s
% Output : Proof 42.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 72
% Syntax : Number of formulae : 100 ( 46 unt; 0 typ; 1 def)
% Number of atoms : 197 ( 65 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 690 ( 86 ~; 26 |; 0 &; 514 @)
% ( 26 <=>; 38 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 3 avg)
% Number of types : 11 ( 10 usr)
% Number of type conns : 141 ( 141 >; 0 *; 0 +; 0 <<)
% Number of symbols : 52 ( 50 usr; 37 con; 0-3 aty)
% Number of variables : 166 ( 147 ^; 19 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(ty_trm,type,
trm: $tType ).
thf(ty_option_fml,type,
option_fml: $tType ).
thf(ty_fml,type,
fml: $tType ).
thf(ty_produc1418842292n_game,type,
produc1418842292n_game: $tType ).
thf(ty_produc62062515n_game,type,
produc62062515n_game: $tType ).
thf(ty_set_variable,type,
set_variable: $tType ).
thf(ty_option_trm,type,
option_trm: $tType ).
thf(ty_produc799602994n_game,type,
produc799602994n_game: $tType ).
thf(ty_char,type,
char: $tType ).
thf(ty_option_game,type,
option_game: $tType ).
thf(ty_none_fml,type,
none_fml: option_fml ).
thf(ty_eigen__5,type,
eigen__5: fml ).
thf(ty_inf_inf_set_variable,type,
inf_inf_set_variable: set_variable > set_variable > set_variable ).
thf(ty_produc1420172399on_fml,type,
produc1420172399on_fml: ( ( char > option_fml ) > ( char > option_game ) > char > option_fml ) > produc799602994n_game > char > option_fml ).
thf(ty_none_trm,type,
none_trm: option_trm ).
thf(ty_if_option_fml,type,
if_option_fml: $o > option_fml > option_fml > option_fml ).
thf(ty_ua,type,
ua: set_variable ).
thf(ty_uSubst1408967625substt,type,
uSubst1408967625substt: trm > produc1418842292n_game ).
thf(ty_pred,type,
pred: char > trm > fml ).
thf(ty_theta,type,
theta: trm ).
thf(ty_p,type,
p: char ).
thf(ty_case_o209804997ml_fml,type,
case_o209804997ml_fml: option_fml > ( fml > option_fml ) > option_fml > option_fml ).
thf(ty_bot_bot_set_variable,type,
bot_bot_set_variable: set_variable ).
thf(ty_static_FVF,type,
static_FVF: fml > set_variable ).
thf(ty_va,type,
va: set_variable ).
thf(ty_some_fml,type,
some_fml: fml > option_fml ).
thf(ty_the_fml,type,
the_fml: option_fml > fml ).
thf(ty_produc1615133358on_fml,type,
produc1615133358on_fml: ( ( char > option_trm ) > produc799602994n_game > char > option_fml ) > produc62062515n_game > char > option_fml ).
thf(ty_produc1250175341on_fml,type,
produc1250175341on_fml: ( ( char > option_trm ) > produc62062515n_game > char > option_fml ) > produc1418842292n_game > char > option_fml ).
thf(ty_sigma,type,
sigma: produc1418842292n_game ).
thf(ty_the_trm,type,
the_trm: option_trm > trm ).
thf(ty_uSubst516392818stappt,type,
uSubst516392818stappt: produc1418842292n_game > set_variable > trm > option_trm ).
thf(ty_uSubst516392804stappf,type,
uSubst516392804stappf: produc1418842292n_game > set_variable > fml > option_fml ).
thf(h0,assumption,
! [X1: fml > $o,X2: fml] :
( ( X1 @ X2 )
=> ( X1 @ ( eps__0 @ X1 ) ) ),
introduced(assumption,[]) ).
thf(eigendef_eigen__5,definition,
( eigen__5
= ( eps__0
@ ^ [X1: fml] :
~ ( ( ( produc1250175341on_fml
@ ^ [X2: char > option_trm] :
( produc1615133358on_fml
@ ^ [X3: char > option_trm] :
( produc1420172399on_fml
@ ^ [X4: char > option_fml,X5: char > option_game] : X4 ) )
@ sigma
@ p )
= ( some_fml @ X1 ) )
=> ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
!= bot_bot_set_variable ) ) ) ),
introduced(definition,[new_symbols(definition,[eigen__5])]) ).
thf(sP1,plain,
( sP1
<=> ( bot_bot_set_variable
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
@ va ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p )
= ( some_fml @ eigen__5 ) )
=> ( ( inf_inf_set_variable @ ( static_FVF @ eigen__5 ) @ va )
!= bot_bot_set_variable ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p )
= ( some_fml @ eigen__5 ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( the_fml @ ( some_fml @ eigen__5 ) )
= ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
@ va )
= bot_bot_set_variable ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ theta ) )
= none_fml ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( inf_inf_set_variable @ ( static_FVF @ eigen__5 ) @ va )
= bot_bot_set_variable ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ~ sP7
=> ~ ( ( ( uSubst516392818stappt @ sigma @ va @ theta )
!= none_trm )
=> ~ ( ( ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p )
!= none_fml )
=> ~ ! [X1: fml] :
( ( ( produc1250175341on_fml
@ ^ [X2: char > option_trm] :
( produc1615133358on_fml
@ ^ [X3: char > option_trm] :
( produc1420172399on_fml
@ ^ [X4: char > option_fml,X5: char > option_game] : X4 ) )
@ sigma
@ p )
= ( some_fml @ X1 ) )
=> ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
!= bot_bot_set_variable ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> $false ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ! [X1: char,X2: trm] :
( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ X1 @ X2 ) )
!= none_fml )
=> ~ ( ( ( uSubst516392818stappt @ sigma @ va @ X2 )
!= none_trm )
=> ~ ( ( ( produc1250175341on_fml
@ ^ [X3: char > option_trm] :
( produc1615133358on_fml
@ ^ [X4: char > option_trm] :
( produc1420172399on_fml
@ ^ [X5: char > option_fml,X6: char > option_game] : X5 ) )
@ sigma
@ X1 )
!= none_fml )
=> ~ ! [X3: fml] :
( ( ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ X1 )
= ( some_fml @ X3 ) )
=> ( ( inf_inf_set_variable @ ( static_FVF @ X3 ) @ va )
!= bot_bot_set_variable ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p )
!= none_fml )
=> ~ ! [X1: fml] :
( ( ( produc1250175341on_fml
@ ^ [X2: char > option_trm] :
( produc1615133358on_fml
@ ^ [X3: char > option_trm] :
( produc1420172399on_fml
@ ^ [X4: char > option_fml,X5: char > option_game] : X4 ) )
@ sigma
@ p )
= ( some_fml @ X1 ) )
=> ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
!= bot_bot_set_variable ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: trm] :
( ( ( uSubst516392804stappf @ sigma @ va @ ( pred @ p @ X1 ) )
!= none_fml )
=> ~ ( ( ( uSubst516392818stappt @ sigma @ va @ X1 )
!= none_trm )
=> ~ sP12 ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) )
= eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: fml] :
( ( ( produc1250175341on_fml
@ ^ [X2: char > option_trm] :
( produc1615133358on_fml
@ ^ [X3: char > option_trm] :
( produc1420172399on_fml
@ ^ [X4: char > option_fml,X5: char > option_game] : X4 ) )
@ sigma
@ p )
= ( some_fml @ X1 ) )
=> ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
!= bot_bot_set_variable ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( ( the_fml @ ( some_fml @ eigen__5 ) )
= eigen__5 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: fml] :
( ( the_fml @ ( some_fml @ X1 ) )
= X1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p )
= none_fml ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ( eigen__5
= ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ( ( some_fml @ eigen__5 )
= ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( ( uSubst516392818stappt @ sigma @ va @ theta )
!= none_trm )
=> ~ sP12 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ! [X1: set_variable,X2: char,X3: trm] :
( ( ( uSubst516392804stappf @ sigma @ X1 @ ( pred @ X2 @ X3 ) )
!= none_fml )
=> ~ ( ( ( uSubst516392818stappt @ sigma @ X1 @ X3 )
!= none_trm )
=> ~ ( ( ( produc1250175341on_fml
@ ^ [X4: char > option_trm] :
( produc1615133358on_fml
@ ^ [X5: char > option_trm] :
( produc1420172399on_fml
@ ^ [X6: char > option_fml,X7: char > option_game] : X6 ) )
@ sigma
@ X2 )
!= none_fml )
=> ~ ! [X4: fml] :
( ( ( produc1250175341on_fml
@ ^ [X5: char > option_trm] :
( produc1615133358on_fml
@ ^ [X6: char > option_trm] :
( produc1420172399on_fml
@ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
@ sigma
@ X2 )
= ( some_fml @ X4 ) )
=> ( ( inf_inf_set_variable @ ( static_FVF @ X4 ) @ X1 )
!= bot_bot_set_variable ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(sP24,plain,
( sP24
<=> ! [X1: produc1418842292n_game,X2: set_variable,X3: char,X4: trm] :
( ( ( uSubst516392804stappf @ X1 @ X2 @ ( pred @ X3 @ X4 ) )
!= none_fml )
=> ~ ( ( ( uSubst516392818stappt @ X1 @ X2 @ X4 )
!= none_trm )
=> ~ ( ( ( produc1250175341on_fml
@ ^ [X5: char > option_trm] :
( produc1615133358on_fml
@ ^ [X6: char > option_trm] :
( produc1420172399on_fml
@ ^ [X7: char > option_fml,X8: char > option_game] : X7 ) )
@ X1
@ X3 )
!= none_fml )
=> ~ ! [X5: fml] :
( ( ( produc1250175341on_fml
@ ^ [X6: char > option_trm] :
( produc1615133358on_fml
@ ^ [X7: char > option_trm] :
( produc1420172399on_fml
@ ^ [X8: char > option_fml,X9: char > option_game] : X8 ) )
@ X1
@ X3 )
= ( some_fml @ X5 ) )
=> ( ( inf_inf_set_variable @ ( static_FVF @ X5 ) @ X2 )
!= bot_bot_set_variable ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP24])]) ).
thf(sP25,plain,
( sP25
<=> ( ( static_FVF @ eigen__5 )
= ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP25])]) ).
thf(sP26,plain,
( sP26
<=> ( ( inf_inf_set_variable @ ( static_FVF @ eigen__5 ) @ va )
= ( inf_inf_set_variable
@ ( static_FVF
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) )
@ va ) ) ),
introduced(definition,[new_symbols(definition,[sP26])]) ).
thf(conj_0,conjecture,
sP18 ).
thf(h1,negated_conjecture,
~ sP18,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(h2,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h3,assumption,
( none_fml
!= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP18,
introduced(assumption,[]) ).
thf(h5,assumption,
sP2,
introduced(assumption,[]) ).
thf(1,plain,
( sP5
| ~ sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP16
| sP14
| ~ sP5
| ~ sP16 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP17
| sP16 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP8
| sP1
| sP10
| ~ sP26 ),
inference(confrontation_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP14
| sP19 ),
inference(symeq,[status(thm)],[]) ).
thf(6,plain,
( sP25
| ~ sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( sP26
| sP10
| ~ sP25 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP4
| sP20 ),
inference(symeq,[status(thm)],[]) ).
thf(9,plain,
( sP3
| sP8 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( sP3
| sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP15
| ~ sP3 ),
inference(eigen_choice_rule,[status(thm),assumptions([h0])],[h0,eigendef_eigen__5]) ).
thf(12,plain,
( ~ sP12
| sP18
| ~ sP15 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP21
| sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( ~ sP9
| sP7
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP13
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( ~ sP11
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(17,plain,
( ~ sP22
| sP11 ),
inference(all_rule,[status(thm)],[]) ).
thf(18,plain,
( ~ sP24
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(19,plain,
( ~ sP1
| sP6 ),
inference(symeq,[status(thm)],[]) ).
thf(20,plain,
~ sP10,
inference(prop_rule,[status(thm)],[]) ).
thf(fact_1_Pred_Oprems_I2_J,axiom,
~ sP7 ).
thf(fact_139_usubstappf__pred__conv,axiom,
sP24 ).
thf(fact_130_option_Osel,axiom,
sP17 ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h4,h2,h3,h1,h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,fact_1_Pred_Oprems_I2_J,h2,fact_139_usubstappf__pred__conv,fact_130_option_Osel,h4]) ).
thf(h6,assumption,
~ ( sP6
=> ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_fml )
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ) ),
introduced(assumption,[]) ).
thf(h7,assumption,
~ ( ~ sP6
=> ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_fml )
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) )
= none_fml ) ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP6,
introduced(assumption,[]) ).
thf(h9,assumption,
( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_fml )
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) )
!= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
~ ( sP6
=> sP23 ),
introduced(assumption,[]) ).
thf(h11,assumption,
~ ( ~ sP6
=> ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= none_fml ) ),
introduced(assumption,[]) ).
thf(h12,assumption,
~ sP23,
introduced(assumption,[]) ).
thf(h13,assumption,
sP23,
introduced(assumption,[]) ).
thf(h14,assumption,
sP18,
introduced(assumption,[]) ).
thf(22,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h8,h12,h10,h8,h9,h6,h5,h2,h3,h1,h0])],[h13,h12]) ).
thf(23,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h8,h12,h10,h8,h9,h6,h5,h2,h3,h1,h0])],[h14,h1]) ).
thf(fact_29_calculation_I2_J,axiom,
( ~ sP23
=> sP18 ) ).
thf(24,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h12,h10,h8,h9,h6,h5,h2,h3,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[fact_29_calculation_I2_J,22,23,h13,h14]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h8,h9,h6,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h12])],[h10,24,h8,h12]) ).
thf(h15,assumption,
( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
!= none_fml ),
introduced(assumption,[]) ).
thf(26,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h2,h15,h11,h8,h9,h6,h5,h2,h3,h1,h0])],[h8,h2]) ).
thf(27,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h2,h15,h11,h8,h9,h6,h5,h2,h3,h1,h0])],[h14,h1]) ).
thf(28,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h15,h11,h8,h9,h6,h5,h2,h3,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[fact_29_calculation_I2_J,26,27,h13,h14]) ).
thf(29,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h8,h9,h6,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h2,h15])],[h11,28,h2,h15]) ).
thf(fact_28_calculation_I1_J,axiom,
( ( sP6
=> sP23 )
=> ~ ( ~ sP6
=> ( ( uSubst516392804stappf @ sigma @ ua @ ( pred @ p @ theta ) )
= none_fml ) ) ) ).
thf(30,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h9,h6,h5,h2,h3,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_28_calculation_I1_J,25,29,h10,h11]) ).
thf(31,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h6,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h9])],[h6,30,h8,h9]) ).
thf(h16,assumption,
( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_fml )
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) )
!= none_fml ),
introduced(assumption,[]) ).
thf(32,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h8,h12,h10,h2,h16,h7,h5,h2,h3,h1,h0])],[h13,h12]) ).
thf(33,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h8,h12,h10,h2,h16,h7,h5,h2,h3,h1,h0])],[h14,h1]) ).
thf(34,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h8,h12,h10,h2,h16,h7,h5,h2,h3,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[fact_29_calculation_I2_J,32,33,h13,h14]) ).
thf(35,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h10,h2,h16,h7,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h8,h12])],[h10,34,h8,h12]) ).
thf(fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062,axiom,
~ sP2 ).
thf(36,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h13,h2,h15,h11,h2,h16,h7,h5,h2,h3,h1,h0])],[h5,fact_26__092_060open_062usubstappf_A_092_060sigma_062_AU_A_IPred_Ap_A_092_060theta_062_J_A_092_060noteq_062_Ausubstappf_A_092_060sigma_062_AV_A_IPred_Ap_A_092_060theta_062_J_092_060close_062]) ).
thf(37,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h14,h2,h15,h11,h2,h16,h7,h5,h2,h3,h1,h0])],[h14,h1]) ).
thf(38,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h15,h11,h2,h16,h7,h5,h2,h3,h1,h0]),tab_imp(discharge,[h13]),tab_imp(discharge,[h14])],[fact_29_calculation_I2_J,36,37,h13,h14]) ).
thf(39,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h11,h2,h16,h7,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h2,h15])],[h11,38,h2,h15]) ).
thf(40,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h16,h7,h5,h2,h3,h1,h0]),tab_imp(discharge,[h10]),tab_imp(discharge,[h11])],[fact_28_calculation_I1_J,35,39,h10,h11]) ).
thf(41,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h5,h2,h3,h1,h0]),tab_negimp(discharge,[h2,h16])],[h7,40,h2,h16]) ).
thf(fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_092_060close_062,axiom,
( ( sP6
=> ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_fml )
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) )
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ) )
=> ~ ( ~ sP6
=> ( ( case_o209804997ml_fml @ ( some_fml @ ( pred @ p @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) )
@ ^ [X1: fml] :
( if_option_fml
@ ( ( inf_inf_set_variable @ ( static_FVF @ X1 ) @ va )
= bot_bot_set_variable )
@ ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable @ X1 )
@ none_fml )
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) )
= none_fml ) ) ) ).
thf(42,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h5,h2,h3,h1,h0]),tab_imp(discharge,[h6]),tab_imp(discharge,[h7])],[fact_10__092_060open_062_Icase_ASPreds_A_092_060sigma_062_Ap_Aof_ANone_A_092_060Rightarrow_062_AAfml_A_IPred_Ap_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_124_ASome_Af_A_092_060Rightarrow_062_Aif_AFVF_Af_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_Af_Aelse_Aundeff_J_A_092_060noteq_062_A_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_092_060close_062,31,41,h6,h7]) ).
thf(fact_9_f9,axiom,
( sP18
=> sP2 ) ).
thf(43,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h2,h3,h1,h0]),tab_imp(discharge,[h4]),tab_imp(discharge,[h5])],[fact_9_f9,21,42,h4,h5]) ).
thf(fact_8__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062,axiom,
~ ( ~ sP6
=> ( none_fml
= ( uSubst516392804stappf @ ( uSubst1408967625substt @ ( the_trm @ ( uSubst516392818stappt @ sigma @ va @ theta ) ) ) @ bot_bot_set_variable
@ ( the_fml
@ ( produc1250175341on_fml
@ ^ [X1: char > option_trm] :
( produc1615133358on_fml
@ ^ [X2: char > option_trm] :
( produc1420172399on_fml
@ ^ [X3: char > option_fml,X4: char > option_game] : X3 ) )
@ sigma
@ p ) ) ) ) ) ).
thf(44,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0]),tab_negimp(discharge,[h2,h3])],[fact_8__092_060open_062_Iif_AFVF_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_A_092_060inter_062_AV_A_061_A_123_125_Athen_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_Aelse_Aundeff_J_A_092_060noteq_062_Ausubstappf_A_Idotsubstt_A_Ithe_A_Iusubstappt_A_092_060sigma_062_AV_A_092_060theta_062_J_J_J_A_123_125_A_Ithe_A_ISPreds_A_092_060sigma_062_Ap_J_J_092_060close_062,43,h2,h3]) ).
thf(45,plain,
$false,
inference(eigenvar_choice,[status(thm),assumptions([h1]),eigenvar_choice(discharge,[h0])],[44,h0]) ).
thf(0,theorem,
sP18,
inference(contra,[status(thm),contra(discharge,[h1])],[44,h1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP203^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.13 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.14/0.34 % Computer : n011.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Oct 8 17:52:53 EDT 2025
% 0.14/0.35 % CPUTime :
% 42.18/42.71 % SZS status Theorem
% 42.18/42.71 % Mode: cade22sinegrackle2x26c3
% 42.18/42.71 % Steps: 5506
% 42.18/42.71 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------