TSTP Solution File: ITP209^3 by Lash---1.13
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%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : ITP209^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n018.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 Aug 31 04:02:58 EDT 2023
% Result : Theorem 6.75s 6.97s
% Output : Proof 6.75s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_syntax_ac_operator_a,type,
syntax_ac_operator_a: ( a > a > a ) > $o ).
thf(ty_c,type,
c: a ).
thf(ty_f,type,
f: a > a > a ).
thf(ty_a2,type,
a2: a ).
thf(ty_b,type,
b: a ).
thf(sP1,plain,
( sP1
<=> ! [X1: a,X2: a] :
( ( f @ X1 @ X2 )
= ( f @ X2 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( ( f @ b @ ( f @ a2 @ c ) )
= ( f @ a2 @ ( f @ b @ c ) ) ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ! [X1: a > a > a,X2: a,X3: a,X4: a] :
( ( syntax_ac_operator_a @ X1 )
=> ( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ! [X1: a,X2: a,X3: a] :
( ( syntax_ac_operator_a @ f )
=> ( ( f @ X1 @ ( f @ X2 @ X3 ) )
= ( f @ ( f @ X1 @ X2 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ! [X1: a] :
( ( f @ b @ X1 )
= ( f @ X1 @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( ( f @ a2 @ ( f @ b @ c ) )
= ( f @ ( f @ a2 @ b ) @ c ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ! [X1: a,X2: a] :
( ( f @ b @ ( f @ X1 @ X2 ) )
= ( f @ X1 @ ( f @ b @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ! [X1: a,X2: a] :
( ( syntax_ac_operator_a @ f )
=> ( ( f @ a2 @ ( f @ X1 @ X2 ) )
= ( f @ ( f @ a2 @ X1 ) @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ! [X1: a] :
( ( syntax_ac_operator_a @ f )
=> ( ( f @ a2 @ ( f @ b @ X1 ) )
= ( f @ ( f @ a2 @ b ) @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( ( f @ ( f @ a2 @ b ) @ c )
= ( f @ ( f @ a2 @ c ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( ( syntax_ac_operator_a @ f )
=> sP6 ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ! [X1: a] :
( ( f @ b @ ( f @ a2 @ X1 ) )
= ( f @ a2 @ ( f @ b @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ! [X1: a,X2: a,X3: a] :
( ( f @ X1 @ ( f @ X2 @ X3 ) )
= ( f @ X2 @ ( f @ X1 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> ( syntax_ac_operator_a @ f ) ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ( ( f @ b @ ( f @ a2 @ c ) )
= ( f @ ( f @ a2 @ c ) @ b ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(conj_0,conjecture,
sP10 ).
thf(h0,negated_conjecture,
~ sP10,
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(1,plain,
( ~ sP2
| sP10
| ~ sP6
| ~ sP15 ),
inference(confrontation_rule,[status(thm)],]) ).
thf(2,plain,
( ~ sP5
| sP15 ),
inference(all_rule,[status(thm)],]) ).
thf(3,plain,
( ~ sP11
| ~ sP14
| sP6 ),
inference(prop_rule,[status(thm)],]) ).
thf(4,plain,
( ~ sP9
| sP11 ),
inference(all_rule,[status(thm)],]) ).
thf(5,plain,
( ~ sP8
| sP9 ),
inference(all_rule,[status(thm)],]) ).
thf(6,plain,
( ~ sP4
| sP8 ),
inference(all_rule,[status(thm)],]) ).
thf(7,plain,
( ~ sP3
| sP4 ),
inference(all_rule,[status(thm)],]) ).
thf(8,plain,
( ~ sP12
| sP2 ),
inference(all_rule,[status(thm)],]) ).
thf(9,plain,
( ~ sP7
| sP12 ),
inference(all_rule,[status(thm)],]) ).
thf(10,plain,
( ~ sP1
| sP5 ),
inference(all_rule,[status(thm)],]) ).
thf(11,plain,
( ~ sP13
| sP7 ),
inference(all_rule,[status(thm)],]) ).
thf(fact_6_ac__operator_Oleft__assoc,axiom,
sP3 ).
thf(fact_2_left__commute,axiom,
sP13 ).
thf(fact_1_commute,axiom,
sP1 ).
thf(fact_0_ac__operator__axioms,axiom,
sP14 ).
thf(12,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h0])],[1,2,3,4,5,6,7,8,9,10,11,h0,fact_6_ac__operator_Oleft__assoc,fact_2_left__commute,fact_1_commute,fact_0_ac__operator__axioms]) ).
thf(0,theorem,
sP10,
inference(contra,[status(thm),contra(discharge,[h0])],[12,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : ITP209^3 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n018.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.35 % CPULimit : 300
% 0.20/0.35 % WCLimit : 300
% 0.20/0.35 % DateTime : Sun Aug 27 16:37:16 EDT 2023
% 0.20/0.35 % CPUTime :
% 6.75/6.97 % SZS status Theorem
% 6.75/6.97 % Mode: cade22grackle2xfee4
% 6.75/6.97 % Steps: 314494
% 6.75/6.97 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------