%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP059^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n025.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 01:46:50 PM UTC 2025
% Result : Theorem 91.58s 91.28s
% Output : Proof 91.58s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_list_message_p_v,type,
list_message_p_v: $tType ).
thf(ty_message_p_v,type,
message_p_v: $tType ).
thf(ty_list_c1059388851t_unit,type,
list_c1059388851t_unit: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_msg,type,
msg: message_p_v ).
thf(ty_firstO1414030372_p_v_s,type,
firstO1414030372_p_v_s: list_c1059388851t_unit > list_message_p_v > message_p_v > nat > $o ).
thf(ty_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(ty_suc,type,
suc: nat > nat ).
thf(ty_ft,type,
ft: nat > list_message_p_v ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(ty_ord_less_nat,type,
ord_less_nat: nat > nat > $o ).
thf(ty_fe,type,
fe: nat > list_c1059388851t_unit ).
thf(ty_index,type,
index: nat ).
thf(ty_nMsg,type,
nMsg: nat ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(ty_size_s1406904903t_unit,type,
size_s1406904903t_unit: list_c1059388851t_unit > nat ).
thf(sP1,plain,
( sP1
<=> ( ord_less_nat @ zero_zero_nat @ nMsg ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ nMsg )
=> ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ord_less_nat @ nMsg @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( sP1
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ nMsg ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ nMsg ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: nat,X2: nat] :
( ( ord_less_nat @ X1 @ X2 )
=> ( ord_less_eq_nat @ ( suc @ X1 ) @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( sP3
=> sP2 ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] :
( sP3
=> ( ( ord_less_eq_nat @ X1 @ nMsg )
=> ( ord_less_nat @ ( minus_minus_nat @ nMsg @ X1 ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat] :
( ( ord_less_nat @ zero_zero_nat @ X1 )
=> ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: nat,X2: nat] :
( ( ord_less_nat @ nMsg @ X1 )
=> ( ( ord_less_eq_nat @ X2 @ nMsg )
=> ( ord_less_nat @ ( minus_minus_nat @ nMsg @ X2 ) @ ( minus_minus_nat @ X1 @ X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ord_less_nat @ ( minus_minus_nat @ nMsg @ ( suc @ zero_zero_nat ) ) @ ( minus_minus_nat @ ( size_s1406904903t_unit @ ( fe @ index ) ) @ ( suc @ zero_zero_nat ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: nat] :
( ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ X1 )
=> ( ord_less_nat @ X1 @ ( size_s1406904903t_unit @ ( fe @ index ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( firstO1414030372_p_v_s @ ( fe @ ( suc @ index ) ) @ ( ft @ ( suc @ index ) ) @ msg @ nMsg ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: nat,X2: nat,X3: nat] :
( ( ord_less_nat @ X1 @ X2 )
=> ( ( ord_less_eq_nat @ X3 @ X1 )
=> ( ord_less_nat @ ( minus_minus_nat @ X1 @ X3 ) @ ( minus_minus_nat @ X2 @ X3 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(conj_0,conjecture,
sP11 ).
thf(h0,negated_conjecture,
~ sP11,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP9
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| ~ sP1
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP13
| sP12 ),
inference(all_rule,[status(thm)],[]) ).
thf(4,plain,
( ~ sP12
| ~ sP14
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP6
| sP9 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP15
| sP10 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP10
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP8
| sP7 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP7
| ~ sP3
| sP2 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP2
| ~ sP5
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_0_AssumpOcc6_I1_J,axiom,
sP1 ).
thf(fact_3_AssumptionSubset_I3_J,axiom,
sP14 ).
thf(fact_4_SmallIndex,axiom,
sP13 ).
thf(fact_180_Suc__leI,axiom,
sP6 ).
thf(fact_192_diff__less__mono,axiom,
sP15 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,fact_0_AssumpOcc6_I1_J,fact_3_AssumptionSubset_I3_J,fact_4_SmallIndex,fact_180_Suc__leI,fact_192_diff__less__mono,h0]) ).
thf(0,theorem,
sP11,
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : ITP059^1 : TPTP v9.2.0. Released v7.5.0.
% 0.03/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.15/0.36 % Computer : n025.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Wed Oct 8 18:42:23 EDT 2025
% 0.15/0.36 % CPUTime :
% 91.58/91.28 % SZS status Theorem
% 91.58/91.28 % Mode: mode454:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=4:SINE_RANK_LIMIT=3.:SINE_DEPTH=0
% 91.58/91.28 % Inferences: 234
% 91.58/91.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------