TSTP Solution File: ITP209^1 by Satallax---3.5
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- Process Solution
%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP209^1 : TPTP v8.1.0. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n021.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 : 600s
% DateTime : Sun Jul 17 00:29:32 EDT 2022
% Result : Theorem 2.02s 2.28s
% Output : Proof 2.02s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_a2,type,
a2: a ).
thf(ty_b,type,
b: a ).
thf(ty_c,type,
c: a ).
thf(ty_f,type,
f: a > a > a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( f @ b @ ( f @ a2 @ X1 ) )
= ( f @ a2 @ ( f @ b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ a2 @ ( f @ b @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ( ( f @ a2 @ ( f @ b @ c ) )
!= ( f @ ( f @ a2 @ c ) @ b ) )
=> ! [X1: a] :
( ( X1
= ( f @ a2 @ ( f @ b @ c ) ) )
=> ( X1
!= ( f @ ( f @ a2 @ c ) @ b ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a] :
( ( f @ b @ X1 )
= ( f @ X1 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( f @ ( f @ a2 @ b ) @ X1 )
= ( f @ a2 @ ( f @ b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ! [X1: a,X2: a,X3: a] :
( ( f @ ( f @ X1 @ X2 ) @ X3 )
= ( f @ X1 @ ( f @ X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a,X2: a] :
( ( f @ ( f @ a2 @ X1 ) @ X2 )
= ( f @ a2 @ ( f @ X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( f @ a2 @ ( f @ b @ c ) )
= ( f @ ( f @ a2 @ c ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( ( f @ b @ ( f @ a2 @ c ) )
= ( f @ ( f @ a2 @ c ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ! [X1: a,X2: a > $o] :
( ( X2 @ X1 )
=> ! [X3: a] :
( ( X1 = X3 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( f @ b @ ( f @ a2 @ c ) )
= ( f @ a2 @ ( f @ b @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a > $o] :
( ( X1 @ ( f @ a2 @ ( f @ b @ c ) ) )
=> ! [X2: a] :
( ( X2
= ( f @ a2 @ ( f @ b @ c ) ) )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( sP11
=> ~ sP9 ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( sP2
=> ~ sP8 ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a] :
( ( X1
= ( f @ a2 @ ( f @ b @ c ) ) )
=> ( X1
!= ( f @ ( f @ a2 @ c ) @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ! [X1: a,X2: a > $o] :
( ( X2 @ X1 )
=> ! [X3: a] :
( ( X3 = X1 )
=> ( X2 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ! [X1: a] :
( ( ( f @ ( f @ a2 @ b ) @ c )
= X1 )
=> ( X1
!= ( f @ ( f @ a2 @ c ) @ b ) ) ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ! [X1: a,X2: a] :
( ( f @ b @ ( f @ X1 @ X2 ) )
= ( f @ X1 @ ( f @ b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a,X2: a] :
( ( f @ X1 @ X2 )
= ( f @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a > $o] :
( ( X1 @ ( f @ ( f @ a2 @ b ) @ c ) )
=> ! [X2: a] :
( ( ( f @ ( f @ a2 @ b ) @ c )
= X2 )
=> ( X1 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( ~ sP21
=> sP17 ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(sP23,plain,
( sP23
<=> ! [X1: a,X2: a,X3: a] :
( ( f @ X1 @ ( f @ X2 @ X3 ) )
= ( f @ X2 @ ( f @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP23])]) ).
thf(conj_0,conjecture,
sP21 ).
thf(h0,negated_conjecture,
~ sP21,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP19
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP4
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP13
| ~ sP11
| ~ sP9 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP15
| sP13 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP23
| sP18 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP18
| sP1 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP1
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP3
| sP8
| sP15 ),
inference(prop_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP12
| sP3 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP16
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
sP16,
inference(eq_ind_sym,[status(thm)],]) ).
thf(12,plain,
( ~ sP6
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(13,plain,
( ~ sP7
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(14,plain,
( ~ sP5
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(15,plain,
( ~ sP14
| ~ sP2
| ~ sP8 ),
inference(prop_rule,[status(thm)],]) ).
thf(16,plain,
( ~ sP17
| sP14 ),
inference(all_rule,[status(thm)],]) ).
thf(17,plain,
( ~ sP22
| sP21
| sP17 ),
inference(prop_rule,[status(thm)],]) ).
thf(18,plain,
( ~ sP20
| sP22 ),
inference(all_rule,[status(thm)],]) ).
thf(19,plain,
( ~ sP10
| sP20 ),
inference(all_rule,[status(thm)],]) ).
thf(20,plain,
sP10,
inference(eq_ind,[status(thm)],]) ).
thf(fact_3_right__assoc,axiom,
sP6 ).
thf(fact_2_left__commute,axiom,
sP23 ).
thf(fact_1_commute,axiom,
sP19 ).
thf(21,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,fact_3_right__assoc,fact_2_left__commute,fact_1_commute,h0]) ).
thf(0,theorem,
sP21,
inference(contra,[status(thm),contra(discharge,[h0])],[21,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : ITP209^1 : TPTP v8.1.0. Released v8.1.0.
% 0.08/0.14 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 2 20:09:02 EDT 2022
% 0.14/0.35 % CPUTime :
% 2.02/2.28 % SZS status Theorem
% 2.02/2.28 % Mode: mode506
% 2.02/2.28 % Inferences: 9290
% 2.02/2.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------