%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP132^1 : 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 : n009.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 01:47:03 PM UTC 2025
% Result : Theorem 11.43s 11.57s
% Output : Proof 11.43s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_set_nat,type,
set_nat: $tType ).
thf(ty_nat,type,
nat: $tType ).
thf(ty_p,type,
p: nat > nat ).
thf(ty_set_ord_atMost_nat,type,
set_ord_atMost_nat: nat > set_nat ).
thf(ty_n,type,
n: nat ).
thf(ty_minus_minus_nat,type,
minus_minus_nat: nat > nat > nat ).
thf(ty_times_times_nat,type,
times_times_nat: nat > nat > nat ).
thf(ty_k,type,
k: nat ).
thf(ty_zero_zero_nat,type,
zero_zero_nat: nat ).
thf(ty_number1551313001itions,type,
number1551313001itions: ( nat > nat ) > nat > $o ).
thf(ty_groups1842438620at_nat,type,
groups1842438620at_nat: ( nat > nat ) > set_nat > nat ).
thf(ty_one_one_nat,type,
one_one_nat: nat ).
thf(ty_ord_less_eq_nat,type,
ord_less_eq_nat: nat > nat > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: nat > nat,X2: nat] :
( ( number1551313001itions @ X1 @ X2 )
=> ~ ( ! [X3: nat] :
( ( ( X1 @ X3 )
!= zero_zero_nat )
=> ~ ( ( ord_less_eq_nat @ one_one_nat @ X3 )
=> ~ ( ord_less_eq_nat @ X3 @ X2 ) ) )
=> ( ( groups1842438620at_nat
@ ^ [X3: nat] : ( times_times_nat @ ( X1 @ X3 ) @ X3 )
@ ( set_ord_atMost_nat @ X2 ) )
!= X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ! [X1: nat,X2: nat] :
( ( ( minus_minus_nat @ X1 @ X2 )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ X2 @ X1 )
= zero_zero_nat )
=> ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( minus_minus_nat @ k @ k )
= zero_zero_nat )
=> ( k = k ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( ( ( minus_minus_nat @ k @ k )
= zero_zero_nat )
=> sP3 ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( ( number1551313001itions @ p @ n )
=> ~ ( ! [X1: nat] :
( ( ( p @ X1 )
!= zero_zero_nat )
=> ~ ( ( ord_less_eq_nat @ one_one_nat @ X1 )
=> ~ ( ord_less_eq_nat @ X1 @ n ) ) )
=> ( ( groups1842438620at_nat
@ ^ [X1: nat] : ( times_times_nat @ ( p @ X1 ) @ X1 )
@ ( set_ord_atMost_nat @ n ) )
!= n ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( groups1842438620at_nat
@ ^ [X1: nat] : ( times_times_nat @ ( p @ X1 ) @ X1 )
@ ( set_ord_atMost_nat @ n ) )
= n ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ( minus_minus_nat
@ ( groups1842438620at_nat
@ ^ [X1: nat] : ( times_times_nat @ ( p @ X1 ) @ X1 )
@ ( set_ord_atMost_nat @ n ) )
@ k )
= ( minus_minus_nat @ n @ k ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: nat] :
( ( number1551313001itions @ p @ X1 )
=> ~ ( ! [X2: nat] :
( ( ( p @ X2 )
!= zero_zero_nat )
=> ~ ( ( ord_less_eq_nat @ one_one_nat @ X2 )
=> ~ ( ord_less_eq_nat @ X2 @ X1 ) ) )
=> ( ( groups1842438620at_nat
@ ^ [X2: nat] : ( times_times_nat @ ( p @ X2 ) @ X2 )
@ ( set_ord_atMost_nat @ X1 ) )
!= X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: nat] :
( ( minus_minus_nat @ X1 @ X1 )
= zero_zero_nat ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ! [X1: nat] :
( ( ( p @ X1 )
!= zero_zero_nat )
=> ~ ( ( ord_less_eq_nat @ one_one_nat @ X1 )
=> ~ ( ord_less_eq_nat @ X1 @ n ) ) )
=> ~ sP6 ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( k = k ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( number1551313001itions @ p @ n ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( ( minus_minus_nat @ k @ k )
= zero_zero_nat ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ! [X1: nat] :
( ( ( minus_minus_nat @ k @ X1 )
= zero_zero_nat )
=> ( ( ( minus_minus_nat @ X1 @ k )
= zero_zero_nat )
=> ( k = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(conj_0,conjecture,
sP7 ).
thf(h0,negated_conjecture,
~ sP7,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP14
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(2,plain,
( ~ sP4
| ~ sP13
| sP3 ),
inference(prop_rule,[status(thm)],[]) ).
thf(3,plain,
( ~ sP3
| ~ sP13
| sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(4,plain,
( sP10
| sP6 ),
inference(prop_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP8
| sP5 ),
inference(all_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP5
| ~ sP12
| ~ sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP1
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(8,plain,
( ~ sP9
| sP13 ),
inference(all_rule,[status(thm)],[]) ).
thf(9,plain,
( ~ sP2
| sP14 ),
inference(all_rule,[status(thm)],[]) ).
thf(10,plain,
( sP7
| ~ sP6
| ~ sP11 ),
inference(prop_rule,[status(thm)],[]) ).
thf(fact_100_diffs0__imp__equal,axiom,
sP2 ).
thf(fact_72_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
sP9 ).
thf(fact_63_partitionsE,axiom,
sP1 ).
thf(fact_0_partitions,axiom,
sP12 ).
thf(11,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,h0,fact_100_diffs0__imp__equal,fact_72_cancel__comm__monoid__add__class_Odiff__cancel,fact_63_partitionsE,fact_0_partitions]) ).
thf(0,theorem,
sP7,
inference(contra,[status(thm),contra(discharge,[h0])],[11,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ITP132^1 : TPTP v9.2.0. Released v7.5.0.
% 0.11/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Oct 8 18:05:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 11.43/11.57 % SZS status Theorem
% 11.43/11.57 % Mode: mode507:USE_SINE=true:SINE_TOLERANCE=3.0:SINE_GENERALITY_THRESHOLD=0:SINE_RANK_LIMIT=1.:SINE_DEPTH=1
% 11.43/11.57 % Inferences: 512
% 11.43/11.57 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------