%------------------------------------------------------------------------------
% File : Lash---1.13
% Problem : SEU875^5 : TPTP v9.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : lash -P picomus -M modes -p tstp -t %d %s
% Computer : n027.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 02:42:04 PM UTC 2025
% Result : Theorem 84.21s 84.59s
% Output : Proof 84.21s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
thf(ty_a,type,
a: $tType ).
thf(ty_t,type,
t: a ).
thf(ty_cA,type,
cA: ( a > $o ) > $o ).
thf(sP1,plain,
( sP1
<=> ! [X1: a] :
( ( t = X1 )
=> ( @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( t = X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) ) )
@ X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP1])]) ).
thf(sP2,plain,
( sP2
<=> ( @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) )
@ t ) ),
introduced(definition,[new_symbols(definition,[sP2])]) ).
thf(sP3,plain,
( sP3
<=> ( ~ ( ( ~ ( ( @+[X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( t = X2 ) ) )
@ ^ [X1: a] : $false )
=> ~ ! [X1: a > $o] :
( ( @+[X2: ( a > $o ) > $o] :
~ ( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( t = X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2
@ ^ [X3: a] : ( t = X3 ) ) )
@ X1 )
=> ! [X2: a] :
( ( t = X2 )
=> ( @+[X3: ( a > $o ) > $o] :
~ ( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( t = X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3
@ ^ [X4: a] : ( t = X4 ) ) )
@ ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) )
=> ( @+[X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( t = X2 ) ) )
@ ^ [X1: a] : ( t = X1 ) ) )
=> ~ ( ( t
= ( @+[X1: a] :
~ ( ( t = X1 )
=> ( @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ( X4 @ t ) ) ) ) )
@ X1 ) ) ) )
=> ( @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) )
@ @+[X1: a] :
~ ( ( t = X1 )
=> ( @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ( X4 @ t ) ) ) ) )
@ X1 ) ) ) ) )
=> ~ ( ~ ( ( cA
@ @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( t = X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) ) ) )
=> ~ sP1 )
=> ~ ( ( cA
@ @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( t = X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) ) ) )
=> ~ ( @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( t = X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) ) )
@ t ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP3])]) ).
thf(sP4,plain,
( sP4
<=> ( @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( t = X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) ) )
@ t ) ),
introduced(definition,[new_symbols(definition,[sP4])]) ).
thf(sP5,plain,
( sP5
<=> ( t
= ( @+[X1: a] :
~ ( ( t = X1 )
=> ( @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ( X4 @ t ) ) ) ) )
@ X1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP5])]) ).
thf(sP6,plain,
( sP6
<=> ( cA
@ @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ( cA @ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP6])]) ).
thf(sP7,plain,
( sP7
<=> ( ~ ( ( @+[X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( t = X2 ) ) )
@ ^ [X1: a] : $false )
=> ~ ! [X1: a > $o] :
( ( @+[X2: ( a > $o ) > $o] :
~ ( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( t = X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2
@ ^ [X3: a] : ( t = X3 ) ) )
@ X1 )
=> ! [X2: a] :
( ( t = X2 )
=> ( @+[X3: ( a > $o ) > $o] :
~ ( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( t = X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3
@ ^ [X4: a] : ( t = X4 ) ) )
@ ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) )
=> ( @+[X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( t = X2 ) ) )
@ ^ [X1: a] : ( t = X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP7])]) ).
thf(sP8,plain,
( sP8
<=> ( ( @+[X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( t = X2 ) ) )
@ ^ [X1: a] : $false )
=> ! [X1: a] :
( ( t = X1 )
=> ( @+[X2: ( a > $o ) > $o] :
~ ( ~ ( ( X2
@ ^ [X3: a] : $false )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( t = X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2
@ ^ [X3: a] : ( t = X3 ) ) )
@ ^ [X2: a] : ( X1 = X2 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP8])]) ).
thf(sP9,plain,
( sP9
<=> ( @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : $false )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) )
@ @+[X1: a] :
~ ( ( t = X1 )
=> ( @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : $false )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ( X4 @ t ) ) ) ) )
@ X1 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP9])]) ).
thf(sP10,plain,
( sP10
<=> ( @+[X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : $false )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( t = X2 ) ) )
@ ^ [X1: a] : $false ) ),
introduced(definition,[new_symbols(definition,[sP10])]) ).
thf(sP11,plain,
( sP11
<=> ( sP7
=> ~ ( sP5
=> sP9 ) ) ),
introduced(definition,[new_symbols(definition,[sP11])]) ).
thf(sP12,plain,
( sP12
<=> ( sP5
=> sP9 ) ),
introduced(definition,[new_symbols(definition,[sP12])]) ).
thf(sP13,plain,
( sP13
<=> ( cA
@ @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ! [X2: a] :
( ( t = X2 )
=> ( X1 @ X2 ) ) )
=> ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP13])]) ).
thf(sP14,plain,
( sP14
<=> $false ),
introduced(definition,[new_symbols(definition,[sP14])]) ).
thf(sP15,plain,
( sP15
<=> ! [X1: a > $o] :
( ~ ( ( ~ ( ( @+[X2: ( a > $o ) > $o] :
~ ( ~ ( ( X2
@ ^ [X3: a] : sP14 )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
@ ^ [X2: a] : sP14 )
=> ~ ! [X2: a > $o] :
( ( @+[X3: ( a > $o ) > $o] :
~ ( ~ ( ( X3
@ ^ [X4: a] : sP14 )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X1 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X1 ) )
@ X2 )
=> ! [X3: a] :
( ( X1 @ X3 )
=> ( @+[X4: ( a > $o ) > $o] :
~ ( ~ ( ( X4
@ ^ [X5: a] : sP14 )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X1 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X1 ) )
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( @+[X2: ( a > $o ) > $o] :
~ ( ~ ( ( X2
@ ^ [X3: a] : sP14 )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( X1 @ X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2 @ X1 ) )
@ X1 ) )
=> ~ ( ( X1
@ @+[X2: a] :
~ ( ( X1 @ X2 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: ( a > $o ) > $o] :
( ~ ( ( X5
@ ^ [X6: a] : sP14 )
=> ~ ! [X6: a > $o] :
( ( X5 @ X6 )
=> ! [X7: a] :
( ( X4 @ X7 )
=> ( X5
@ ^ [X8: a] :
( ~ ( X6 @ X8 )
=> ( X7 = X8 ) ) ) ) ) )
=> ( X5 @ X4 ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X3 @ X5 ) ) )
=> ~ ! [X5: a > $o] :
( ~ ( ( cA @ X5 )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X5 @ X6 ) ) )
=> ~ ( ( cA @ X5 )
=> ~ ( X5 @ t ) ) ) ) )
@ X2 ) ) )
=> ( @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) )
=> ~ ! [X3: a > $o] :
( ~ ( ! [X4: ( a > $o ) > $o] :
( ~ ( ( X4
@ ^ [X5: a] : sP14 )
=> ~ ! [X5: a > $o] :
( ( X4 @ X5 )
=> ! [X6: a] :
( ( X3 @ X6 )
=> ( X4
@ ^ [X7: a] :
( ~ ( X5 @ X7 )
=> ( X6 = X7 ) ) ) ) ) )
=> ( X4 @ X3 ) )
=> ~ ! [X4: a] :
( ( X3 @ X4 )
=> ( X2 @ X4 ) ) )
=> ~ ! [X4: a > $o] :
( ~ ( ( cA @ X4 )
=> ~ ! [X5: a] :
( ( X3 @ X5 )
=> ( X4 @ X5 ) ) )
=> ~ ( ( cA @ X4 )
=> ~ ( X4 @ t ) ) ) ) )
@ @+[X2: a] :
~ ( ( X1 @ X2 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) )
=> ~ ! [X4: a > $o] :
( ~ ( ! [X5: ( a > $o ) > $o] :
( ~ ( ( X5
@ ^ [X6: a] : sP14 )
=> ~ ! [X6: a > $o] :
( ( X5 @ X6 )
=> ! [X7: a] :
( ( X4 @ X7 )
=> ( X5
@ ^ [X8: a] :
( ~ ( X6 @ X8 )
=> ( X7 = X8 ) ) ) ) ) )
=> ( X5 @ X4 ) )
=> ~ ! [X5: a] :
( ( X4 @ X5 )
=> ( X3 @ X5 ) ) )
=> ~ ! [X5: a > $o] :
( ~ ( ( cA @ X5 )
=> ~ ! [X6: a] :
( ( X4 @ X6 )
=> ( X5 @ X6 ) ) )
=> ~ ( ( cA @ X5 )
=> ~ ( X5 @ t ) ) ) ) )
@ X2 ) ) ) ) )
=> ~ ( ~ ( ( cA
@ @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) ) ) )
=> ~ ! [X2: a] :
( ( X1 @ X2 )
=> ( @+[X3: a > $o] :
~ ( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) )
@ X2 ) ) )
=> ~ ( ( cA
@ @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) ) ) )
=> ~ ( @+[X2: a > $o] :
~ ( ~ ( ( cA @ X2 )
=> ~ ! [X3: a] :
( ( X1 @ X3 )
=> ( X2 @ X3 ) ) )
=> ~ ( ( cA @ X2 )
=> ~ ( X2 @ t ) ) )
@ t ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP15])]) ).
thf(sP16,plain,
( sP16
<=> ( sP13
=> ~ sP4 ) ),
introduced(definition,[new_symbols(definition,[sP16])]) ).
thf(sP17,plain,
( sP17
<=> ( sP13
=> ~ sP1 ) ),
introduced(definition,[new_symbols(definition,[sP17])]) ).
thf(sP18,plain,
( sP18
<=> ( ~ sP17
=> ~ sP16 ) ),
introduced(definition,[new_symbols(definition,[sP18])]) ).
thf(sP19,plain,
( sP19
<=> ! [X1: a > $o] :
( ( @+[X2: ( a > $o ) > $o] :
~ ( ~ ( ( X2
@ ^ [X3: a] : sP14 )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( t = X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2
@ ^ [X3: a] : ( t = X3 ) ) )
@ X1 )
=> ! [X2: a] :
( ( t = X2 )
=> ( @+[X3: ( a > $o ) > $o] :
~ ( ~ ( ( X3
@ ^ [X4: a] : sP14 )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( t = X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3
@ ^ [X4: a] : ( t = X4 ) ) )
@ ^ [X3: a] :
( ~ ( X1 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sP19])]) ).
thf(sP20,plain,
( sP20
<=> ! [X1: a] :
( ( t = X1 )
=> ( @+[X2: ( a > $o ) > $o] :
~ ( ~ ( ( X2
@ ^ [X3: a] : sP14 )
=> ~ ! [X3: a > $o] :
( ( X2 @ X3 )
=> ! [X4: a] :
( ( t = X4 )
=> ( X2
@ ^ [X5: a] :
( ~ ( X3 @ X5 )
=> ( X4 = X5 ) ) ) ) ) )
=> ( X2
@ ^ [X3: a] : ( t = X3 ) ) )
@ ^ [X2: a] : ( X1 = X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[sP20])]) ).
thf(sP21,plain,
( sP21
<=> ( sP10
=> ~ sP19 ) ),
introduced(definition,[new_symbols(definition,[sP21])]) ).
thf(sP22,plain,
( sP22
<=> ( @+[X1: ( a > $o ) > $o] :
~ ( ~ ( ( X1
@ ^ [X2: a] : sP14 )
=> ~ ! [X2: a > $o] :
( ( X1 @ X2 )
=> ! [X3: a] :
( ( t = X3 )
=> ( X1
@ ^ [X4: a] :
( ~ ( X2 @ X4 )
=> ( X3 = X4 ) ) ) ) ) )
=> ( X1
@ ^ [X2: a] : ( t = X2 ) ) )
@ ^ [X1: a] : ( t = X1 ) ) ),
introduced(definition,[new_symbols(definition,[sP22])]) ).
thf(cDOMLEMMA5_pme,conjecture,
~ ( ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : sP14 )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) ) ) ).
thf(h0,negated_conjecture,
( ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : sP14 )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) ) ),
inference(assume_negation,[status(cth)],[cDOMLEMMA5_pme]) ).
thf(h1,assumption,
~ ( ~ ( sP6
=> ~ ( @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ( cA @ X1 ) )
@ t ) )
=> sP6 ),
introduced(assumption,[]) ).
thf(h2,assumption,
~ ( ~ ( ( cA
@ @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : sP14 )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) ) )
=> ~ sP2 )
=> ~ sP15 ),
introduced(assumption,[]) ).
thf(h3,assumption,
~ ( sP6
=> ~ ( @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ( cA @ X1 ) )
@ t ) ),
introduced(assumption,[]) ).
thf(h4,assumption,
~ sP6,
introduced(assumption,[]) ).
thf(h5,assumption,
sP6,
introduced(assumption,[]) ).
thf(h6,assumption,
( @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ( cA @ X1 ) )
@ t ),
introduced(assumption,[]) ).
thf(1,plain,
$false,
inference(tab_conflict,[status(thm),assumptions([h5,h6,h3,h4,h1,h0,h0])],[h5,h4]) ).
thf(2,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h3,h4,h1,h0,h0]),tab_negimp(discharge,[h5,h6])],[h3,1,h5,h6]) ).
thf(3,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h1,h0,h0]),tab_negimp(discharge,[h3,h4])],[h1,2,h3,h4]) ).
thf(h7,assumption,
~ ( ( cA
@ @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : sP14 )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) ) )
=> ~ sP2 ),
introduced(assumption,[]) ).
thf(h8,assumption,
sP15,
introduced(assumption,[]) ).
thf(h9,assumption,
( cA
@ @+[X1: a > $o] :
~ ( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : sP14 )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) ) ),
introduced(assumption,[]) ).
thf(h10,assumption,
sP2,
introduced(assumption,[]) ).
thf(4,plain,
( ~ sP20
| sP22 ),
inference(all_rule,[status(thm)],[]) ).
thf(5,plain,
( ~ sP2
| sP9
| ~ sP5
| sP14 ),
inference(mating_rule,[status(thm)],[]) ).
thf(6,plain,
( ~ sP1
| sP4 ),
inference(all_rule,[status(thm)],[]) ).
thf(7,plain,
( ~ sP16
| ~ sP13
| ~ sP4 ),
inference(prop_rule,[status(thm)],[]) ).
thf(8,plain,
( sP17
| sP1 ),
inference(prop_rule,[status(thm)],[]) ).
thf(9,plain,
( sP17
| sP13 ),
inference(prop_rule,[status(thm)],[]) ).
thf(10,plain,
( ~ sP8
| ~ sP10
| sP20 ),
inference(prop_rule,[status(thm)],[]) ).
thf(11,plain,
( sP12
| ~ sP9 ),
inference(prop_rule,[status(thm)],[]) ).
thf(12,plain,
( sP12
| sP5 ),
inference(prop_rule,[status(thm)],[]) ).
thf(13,plain,
( sP18
| sP16 ),
inference(prop_rule,[status(thm)],[]) ).
thf(14,plain,
( sP18
| ~ sP17 ),
inference(prop_rule,[status(thm)],[]) ).
thf(15,plain,
( ~ sP19
| sP8 ),
inference(all_rule,[status(thm)],[]) ).
thf(16,plain,
( sP21
| sP19 ),
inference(prop_rule,[status(thm)],[]) ).
thf(17,plain,
( sP21
| sP10 ),
inference(prop_rule,[status(thm)],[]) ).
thf(18,plain,
( sP7
| ~ sP22 ),
inference(prop_rule,[status(thm)],[]) ).
thf(19,plain,
( sP7
| ~ sP21 ),
inference(prop_rule,[status(thm)],[]) ).
thf(20,plain,
( ~ sP11
| ~ sP7
| ~ sP12 ),
inference(prop_rule,[status(thm)],[]) ).
thf(21,plain,
( ~ sP3
| sP11
| ~ sP18 ),
inference(prop_rule,[status(thm)],[]) ).
thf(22,plain,
( ~ sP15
| sP3 ),
inference(all_rule,[status(thm)],[]) ).
thf(23,plain,
~ sP14,
inference(prop_rule,[status(thm)],[]) ).
thf(24,plain,
$false,
inference(prop_unsat,[status(thm),assumptions([h9,h10,h7,h8,h2,h0,h0])],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,h10,h8]) ).
thf(25,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h7,h8,h2,h0,h0]),tab_negimp(discharge,[h9,h10])],[h7,24,h9,h10]) ).
thf(26,plain,
$false,
inference(tab_negimp,[status(thm),assumptions([h2,h0,h0]),tab_negimp(discharge,[h7,h8])],[h2,25,h7,h8]) ).
thf(27,plain,
$false,
inference(tab_imp,[status(thm),assumptions([h0,h0]),tab_imp(discharge,[h1]),tab_imp(discharge,[h2])],[h0,3,26,h1,h2]) ).
thf(0,theorem,
~ ( ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ( cA @ X1 ) )
=> ~ ! [X1: a > $o] :
( ~ ( ( cA @ X1 )
=> ~ ( X1 @ t ) )
=> ~ ! [X2: a > $o] :
( ~ ( ! [X3: ( a > $o ) > $o] :
( ~ ( ( X3
@ ^ [X4: a] : sP14 )
=> ~ ! [X4: a > $o] :
( ( X3 @ X4 )
=> ! [X5: a] :
( ( X2 @ X5 )
=> ( X3
@ ^ [X6: a] :
( ~ ( X4 @ X6 )
=> ( X5 = X6 ) ) ) ) ) )
=> ( X3 @ X2 ) )
=> ~ ! [X3: a] :
( ( X2 @ X3 )
=> ( X1 @ X3 ) ) )
=> ~ ! [X3: a > $o] :
( ~ ( ( cA @ X3 )
=> ~ ! [X4: a] :
( ( X2 @ X4 )
=> ( X3 @ X4 ) ) )
=> ~ ( ( cA @ X3 )
=> ~ ( X3 @ t ) ) ) ) ) ),
inference(contra,[status(thm),contra(discharge,[h0])],[27,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU875^5 : TPTP v9.2.0. Released v4.0.0.
% 0.07/0.14 % Command : lash -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n027.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
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 21:23:38 EDT 2025
% 0.13/0.36 % CPUTime :
% 84.21/84.59 % SZS status Theorem
% 84.21/84.59 % Mode: cade22grackle2x4fb9
% 84.21/84.59 % Steps: 3047
% 84.21/84.59 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------