TSTP Solution File: SYO041^1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO041^1 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n011.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 : Tue May 21 09:10:04 EDT 2024
% Result : Unsatisfiable 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 46
% Syntax : Number of formulae : 376 ( 8 unt; 13 typ; 0 def)
% Number of atoms : 2796 ( 344 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1839 ( 842 ~; 964 |; 3 &; 0 @)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 20 ( 19 >; 1 *; 0 +; 0 <<)
% Number of symbols : 47 ( 44 usr; 35 con; 0-6 aty)
% Number of variables : 9 ( 0 ^ 3 !; 0 ?; 9 :)
% ( 6 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $o ).
thf(func_def_1,type,
f: $o > $o ).
thf(func_def_2,type,
g: $o > $o ).
thf(func_def_3,type,
x: $o ).
thf(func_def_4,type,
y: $o ).
thf(func_def_9,type,
kCOMB:
!>[X0: $tType,X1: $tType] : ( X0 > X1 > X0 ) ).
thf(func_def_10,type,
bCOMB:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X1 > X2 ) > ( X0 > X1 ) > X0 > X2 ) ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
vOR: $o > $o > $o ).
thf(func_def_13,type,
vIMP: $o > $o > $o ).
thf(func_def_14,type,
vNOT: $o > $o ).
thf(func_def_15,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f883,plain,
$false,
inference(avatar_sat_refutation,[],[f20,f24,f61,f68,f79,f84,f87,f96,f99,f112,f121,f136,f142,f147,f196,f203,f223,f230,f237,f246,f252,f267,f268,f274,f281,f299,f308,f313,f317,f325,f339,f345,f355,f357,f363,f374,f387,f405,f406,f422,f437,f477,f518,f536,f550,f559,f567,f585,f597,f614,f618,f631,f633,f644,f646,f668,f673,f680,f686,f692,f702,f707,f712,f721,f745,f748,f750,f772,f843,f849,f859,f879,f882]) ).
thf(f882,plain,
( spl0_19
| ~ spl0_22
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f844,f840,f360,f264]) ).
thf(f264,plain,
( spl0_19
<=> ( $false = vAPP($o,$o,f,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f360,plain,
( spl0_22
<=> ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f840,plain,
( spl0_29
<=> ( $false = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
thf(f844,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_22
| ~ spl0_29 ),
inference(forward_demodulation,[],[f842,f362]) ).
thf(f362,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f360]) ).
thf(f842,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f840]) ).
thf(f879,plain,
( ~ spl0_16
| spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f818,f227,f220,f227]) ).
thf(f220,plain,
( spl0_15
<=> ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
thf(f227,plain,
( spl0_16
<=> ( $true = vAPP($o,$o,f,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f818,plain,
( ( $true != vAPP($o,$o,f,$true) )
| spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f798,f228]) ).
thf(f228,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f798,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f222,f228]) ).
thf(f222,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| spl0_15 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f859,plain,
( spl0_24
| ~ spl0_2
| spl0_27 ),
inference(avatar_split_clause,[],[f757,f628,f22,f402]) ).
thf(f402,plain,
( spl0_24
<=> ( $false = vAPP($o,$o,f,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f22,plain,
( spl0_2
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f628,plain,
( spl0_27
<=> ( $true = vAPP($o,$o,f,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f757,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_2
| spl0_27 ),
inference(trivial_inequality_removal,[],[f756]) ).
thf(f756,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_2
| spl0_27 ),
inference(superposition,[],[f630,f23]) ).
thf(f23,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f22]) ).
thf(f630,plain,
( ( $true != vAPP($o,$o,f,$false) )
| spl0_27 ),
inference(avatar_component_clause,[],[f628]) ).
thf(f849,plain,
( ~ spl0_30
| ~ spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f731,f193,f76,f846]) ).
thf(f846,plain,
( spl0_30
<=> ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
thf(f76,plain,
( spl0_7
<=> ( x = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f193,plain,
( spl0_13
<=> ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f731,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| spl0_13 ),
inference(forward_demodulation,[],[f194,f78]) ).
thf(f78,plain,
( ( x = $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f76]) ).
thf(f194,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) != $true )
| spl0_13 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f843,plain,
( spl0_29
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f592,f243,f76,f840]) ).
thf(f243,plain,
( spl0_18
<=> ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f592,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f245,f78]) ).
thf(f245,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $false )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f772,plain,
( ~ spl0_10
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f771]) ).
thf(f771,plain,
( $false
| ~ spl0_10
| ~ spl0_16
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f770]) ).
thf(f770,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f760,f141]) ).
thf(f141,plain,
( ( $false = vAPP($o,$o,g,$true) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f139]) ).
thf(f139,plain,
( spl0_10
<=> ( $false = vAPP($o,$o,g,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f760,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f354,f228]) ).
thf(f354,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f352]) ).
thf(f352,plain,
( spl0_21
<=> ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f750,plain,
( ~ spl0_20
| ~ spl0_2
| spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f416,f76,f65,f22,f342]) ).
thf(f342,plain,
( spl0_20
<=> ( $false = vAPP($o,$o,g,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f65,plain,
( spl0_5
<=> ( vAPP($o,$o,g,x) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f416,plain,
( ( $false != vAPP($o,$o,g,$false) )
| ~ spl0_2
| spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f66,f113]) ).
thf(f113,plain,
( ( x = $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f93]) ).
thf(f93,plain,
( ( $true = $false )
| ( x = $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(superposition,[],[f78,f23]) ).
thf(f66,plain,
( ( vAPP($o,$o,g,x) != $false )
| spl0_5 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f748,plain,
( ~ spl0_11
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f747]) ).
thf(f747,plain,
( $false
| ~ spl0_11
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f741]) ).
thf(f741,plain,
( ( $true = $false )
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f343,f146]) ).
thf(f146,plain,
( ( $true = vAPP($o,$o,g,$false) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f144]) ).
thf(f144,plain,
( spl0_11
<=> ( $true = vAPP($o,$o,g,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f343,plain,
( ( $false = vAPP($o,$o,g,$false) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f342]) ).
thf(f745,plain,
( ~ spl0_11
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f744]) ).
thf(f744,plain,
( $false
| ~ spl0_11
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f743]) ).
thf(f743,plain,
( ( $true = $false )
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f146,f343]) ).
thf(f721,plain,
( ~ spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f720]) ).
thf(f720,plain,
( $false
| ~ spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f719]) ).
thf(f719,plain,
( ( $true = $false )
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f718,f403]) ).
thf(f403,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f402]) ).
thf(f718,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f362,f403]) ).
thf(f712,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f711]) ).
thf(f711,plain,
( $false
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f710]) ).
thf(f710,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f709,f403]) ).
thf(f709,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f708,f403]) ).
thf(f708,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f579,f403]) ).
thf(f579,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| ~ spl0_13 ),
inference(superposition,[],[f195,f78]) ).
thf(f195,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f707,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f706]) ).
thf(f706,plain,
( $false
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f705]) ).
thf(f705,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f704,f403]) ).
thf(f704,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f703,f403]) ).
thf(f703,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f698,f403]) ).
thf(f698,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f195,f78]) ).
thf(f702,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f701]) ).
thf(f701,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f700]) ).
thf(f700,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f699,f403]) ).
thf(f699,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f698,f471]) ).
thf(f471,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_2
| spl0_22 ),
inference(trivial_inequality_removal,[],[f470]) ).
thf(f470,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_2
| spl0_22 ),
inference(superposition,[],[f361,f23]) ).
thf(f361,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| spl0_22 ),
inference(avatar_component_clause,[],[f360]) ).
thf(f692,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f691]) ).
thf(f691,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f690]) ).
thf(f690,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f689,f403]) ).
thf(f689,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f688]) ).
thf(f688,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f687,f471]) ).
thf(f687,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f652,f78]) ).
thf(f652,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(binary_proxy_clausification,[],[f651]) ).
thf(f651,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f491]) ).
thf(f491,plain,
( ( $true != $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(constrained_superposition,[],[f361,f195]) ).
thf(f686,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f685]) ).
thf(f685,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f684]) ).
thf(f684,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f683,f403]) ).
thf(f683,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f682]) ).
thf(f682,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f681,f471]) ).
thf(f681,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f654,f78]) ).
thf(f654,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(binary_proxy_clausification,[],[f492]) ).
thf(f492,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f491]) ).
thf(f680,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f679]) ).
thf(f679,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f678]) ).
thf(f678,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f677,f403]) ).
thf(f677,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f676]) ).
thf(f676,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f675,f471]) ).
thf(f675,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f493,f78]) ).
thf(f493,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(binary_proxy_clausification,[],[f492]) ).
thf(f673,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f672]) ).
thf(f672,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f671]) ).
thf(f671,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f670,f403]) ).
thf(f670,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f669]) ).
thf(f669,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f562,f471]) ).
thf(f562,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f493,f113]) ).
thf(f668,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f667]) ).
thf(f667,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f666]) ).
thf(f666,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f665,f403]) ).
thf(f665,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f579,f471]) ).
thf(f646,plain,
( spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f645,f641,f402,f342]) ).
thf(f641,plain,
( spl0_28
<=> ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
thf(f645,plain,
( ( $false = vAPP($o,$o,g,$false) )
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f643,f403]) ).
thf(f643,plain,
( ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$false)) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f641]) ).
thf(f644,plain,
( spl0_28
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f576,f189,f76,f22,f641]) ).
thf(f189,plain,
( spl0_12
<=> ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f576,plain,
( ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$false)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f191,f113]) ).
thf(f191,plain,
( ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f633,plain,
( spl0_24
| ~ spl0_2
| ~ spl0_7
| ~ spl0_18
| spl0_22 ),
inference(avatar_split_clause,[],[f621,f360,f243,f76,f22,f402]) ).
thf(f621,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_18
| spl0_22 ),
inference(forward_demodulation,[],[f592,f471]) ).
thf(f631,plain,
( ~ spl0_27
| ~ spl0_2
| ~ spl0_7
| spl0_13
| spl0_22 ),
inference(avatar_split_clause,[],[f620,f360,f193,f76,f22,f628]) ).
thf(f620,plain,
( ( $true != vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f619,f471]) ).
thf(f619,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| spl0_13 ),
inference(forward_demodulation,[],[f194,f78]) ).
thf(f618,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f617]) ).
thf(f617,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f616]) ).
thf(f616,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f615,f576]) ).
thf(f615,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$false)) )
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f241,f78]) ).
thf(f241,plain,
( ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f239,plain,
( spl0_17
<=> ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f614,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f613]) ).
thf(f613,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f612]) ).
thf(f612,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f580,f576]) ).
thf(f580,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$false)) )
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f241,f78]) ).
thf(f597,plain,
( spl0_24
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f593,f264,f243,f193,f76,f22,f402]) ).
thf(f593,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f592,f539]) ).
thf(f539,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f538,f113]) ).
thf(f538,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f537]) ).
thf(f537,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_2
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f485,f266]) ).
thf(f266,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f264]) ).
thf(f485,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_2
| ~ spl0_13 ),
inference(superposition,[],[f195,f23]) ).
thf(f585,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f584]) ).
thf(f584,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f583]) ).
thf(f583,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f582,f266]) ).
thf(f582,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f579,f546]) ).
thf(f546,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f545,f113]) ).
thf(f545,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f544]) ).
thf(f544,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f543,f113]) ).
thf(f543,plain,
( ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f542]) ).
thf(f542,plain,
( ( $true = $false )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f498,f141]) ).
thf(f498,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_13
| ~ spl0_17 ),
inference(binary_proxy_clausification,[],[f487]) ).
thf(f487,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ( x != vAPP($o,$o,f,vAPP($o,$o,f,x)) )
| ~ spl0_13
| ~ spl0_17 ),
inference(constrained_superposition,[],[f241,f195]) ).
thf(f567,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f566]) ).
thf(f566,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f565]) ).
thf(f565,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f564,f448]) ).
thf(f448,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12 ),
inference(forward_demodulation,[],[f447,f113]) ).
thf(f447,plain,
( ( vAPP($o,$o,f,x) = $false )
| ~ spl0_2
| ~ spl0_10
| spl0_12 ),
inference(trivial_inequality_removal,[],[f446]) ).
thf(f446,plain,
( ( $false != $false )
| ( vAPP($o,$o,f,x) = $false )
| ~ spl0_2
| ~ spl0_10
| spl0_12 ),
inference(forward_demodulation,[],[f441,f141]) ).
thf(f441,plain,
( ( $false != vAPP($o,$o,g,$true) )
| ( vAPP($o,$o,f,x) = $false )
| ~ spl0_2
| spl0_12 ),
inference(superposition,[],[f190,f23]) ).
thf(f190,plain,
( ( vAPP($o,$o,g,vAPP($o,$o,f,x)) != $false )
| spl0_12 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f564,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(duplicate_literal_removal,[],[f563]) ).
thf(f563,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f562,f448]) ).
thf(f559,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f558]) ).
thf(f558,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f557]) ).
thf(f557,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f556,f448]) ).
thf(f556,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f555,f448]) ).
thf(f555,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f554,f113]) ).
thf(f554,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f553]) ).
thf(f553,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f552,f113]) ).
thf(f552,plain,
( ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f551]) ).
thf(f551,plain,
( ( $false != $false )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f496,f141]) ).
thf(f496,plain,
( ( $false != vAPP($o,$o,g,$true) )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| spl0_12
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f488]) ).
thf(f488,plain,
( ( $false != vAPP($o,$o,g,$true) )
| ( x != vAPP($o,$o,f,vAPP($o,$o,f,x)) )
| spl0_12
| ~ spl0_13 ),
inference(constrained_superposition,[],[f190,f195]) ).
thf(f550,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f549]) ).
thf(f549,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f548]) ).
thf(f548,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f547,f448]) ).
thf(f547,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f546,f448]) ).
thf(f536,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f535]) ).
thf(f535,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f534]) ).
thf(f534,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f533,f448]) ).
thf(f533,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f532,f448]) ).
thf(f532,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f531,f113]) ).
thf(f531,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f530]) ).
thf(f530,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f529,f448]) ).
thf(f529,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f528,f113]) ).
thf(f528,plain,
( ( vAPP($o,$o,f,x) = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f527]) ).
thf(f527,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,x) = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f501,f266]) ).
thf(f501,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( vAPP($o,$o,f,x) = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f484]) ).
thf(f484,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( vAPP($o,$o,f,x) != vAPP($o,$o,f,vAPP($o,$o,f,x)) )
| ~ spl0_13 ),
inference(constrained_superposition,[],[f195,f195]) ).
thf(f518,plain,
( ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f517]) ).
thf(f517,plain,
( $false
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f516]) ).
thf(f516,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f515,f448]) ).
thf(f515,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f514,f448]) ).
thf(f514,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f513,f113]) ).
thf(f513,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f512,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f511,f113]) ).
thf(f511,plain,
( ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f510]) ).
thf(f510,plain,
( ( $true = $false )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f509,f448]) ).
thf(f509,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f503,f266]) ).
thf(f503,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_13 ),
inference(binary_proxy_clausification,[],[f481]) ).
thf(f481,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| ( x != vAPP($o,$o,f,vAPP($o,$o,f,x)) )
| ~ spl0_13 ),
inference(constrained_superposition,[],[f195,f195]) ).
thf(f477,plain,
( ~ spl0_26
| ~ spl0_19
| spl0_23 ),
inference(avatar_split_clause,[],[f375,f371,f264,f474]) ).
thf(f474,plain,
( spl0_26
<=> ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f371,plain,
( spl0_23
<=> ( $false = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
thf(f375,plain,
( ( $false != vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_19
| spl0_23 ),
inference(forward_demodulation,[],[f373,f266]) ).
thf(f373,plain,
( ( $false != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| spl0_23 ),
inference(avatar_component_clause,[],[f371]) ).
thf(f437,plain,
( spl0_25
| spl0_4 ),
inference(avatar_split_clause,[],[f12,f58,f434]) ).
thf(f434,plain,
( spl0_25
<=> ( vAPP($o,$o,g,y) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f58,plain,
( spl0_4
<=> ( x = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f12,plain,
( ( x = $true )
| ( vAPP($o,$o,g,y) = $false ) ),
inference(binary_proxy_clausification,[],[f6]) ).
thf(f6,plain,
x = vAPP($o,$o,g,y),
inference(cnf_transformation,[],[f1]) ).
thf(f1,axiom,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = vAPP($o,$o,g,vAPP($o,$o,f,x)) )
& ( x = vAPP($o,$o,g,y) )
& ( y = vAPP($o,$o,g,x) )
& ( x != y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',3) ).
thf(f422,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f421]) ).
thf(f421,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f420]) ).
thf(f420,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f56,f412]) ).
thf(f412,plain,
( ( y = $false )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f411]) ).
thf(f411,plain,
( ( $true = $false )
| ( y = $false )
| ~ spl0_2
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f163,f141]) ).
thf(f163,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ( y = $false )
| ~ spl0_2
| ~ spl0_8 ),
inference(superposition,[],[f111,f23]) ).
thf(f111,plain,
( ( vAPP($o,$o,g,y) = $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f109,plain,
( spl0_8
<=> ( vAPP($o,$o,g,y) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f56,plain,
( ( y = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f54]) ).
thf(f54,plain,
( spl0_3
<=> ( y = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f406,plain,
( spl0_24
| ~ spl0_2
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f369,f360,f264,f22,f402]) ).
thf(f369,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f368]) ).
thf(f368,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_demodulation,[],[f365,f266]) ).
thf(f365,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_2
| ~ spl0_22 ),
inference(superposition,[],[f362,f23]) ).
thf(f405,plain,
( ~ spl0_24
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f367,f360,f264,f402]) ).
thf(f367,plain,
( ( $false != vAPP($o,$o,f,$false) )
| ~ spl0_19
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f366]) ).
thf(f366,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f,$false) )
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_demodulation,[],[f364,f266]) ).
thf(f364,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( $false != vAPP($o,$o,f,$false) )
| ~ spl0_22 ),
inference(constrained_superposition,[],[f362,f362]) ).
thf(f387,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f315,f65,f58,f22,f139]) ).
thf(f315,plain,
( ( $false = vAPP($o,$o,g,$true) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f314,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,g,$true) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f157,f60]) ).
thf(f60,plain,
( ( x = $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f58]) ).
thf(f157,plain,
( ( $false = vAPP($o,$o,g,$true) )
| ( x = $false )
| ~ spl0_2
| ~ spl0_5 ),
inference(superposition,[],[f67,f23]) ).
thf(f67,plain,
( ( vAPP($o,$o,g,x) = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f374,plain,
( ~ spl0_23
| ~ spl0_4
| spl0_18 ),
inference(avatar_split_clause,[],[f302,f243,f58,f371]) ).
thf(f302,plain,
( ( $false != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_4
| spl0_18 ),
inference(forward_demodulation,[],[f244,f60]) ).
thf(f244,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) != $false )
| spl0_18 ),
inference(avatar_component_clause,[],[f243]) ).
thf(f363,plain,
( spl0_22
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f358,f264,f220,f360]) ).
thf(f358,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f221,f266]) ).
thf(f221,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f220]) ).
thf(f357,plain,
( spl0_15
| ~ spl0_4
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f271,f193,f58,f220]) ).
thf(f271,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_4
| ~ spl0_13 ),
inference(forward_demodulation,[],[f195,f60]) ).
thf(f355,plain,
( spl0_21
| ~ spl0_4
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f309,f239,f58,f352]) ).
thf(f309,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f241,f60]) ).
thf(f345,plain,
( ~ spl0_20
| spl0_14
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f340,f264,f200,f342]) ).
thf(f200,plain,
( spl0_14
<=> ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f340,plain,
( ( $false != vAPP($o,$o,g,$false) )
| spl0_14
| ~ spl0_19 ),
inference(forward_demodulation,[],[f201,f266]) ).
thf(f201,plain,
( ( $false != vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| spl0_14 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f339,plain,
( ~ spl0_14
| ~ spl0_4
| spl0_12 ),
inference(avatar_split_clause,[],[f293,f189,f58,f200]) ).
thf(f293,plain,
( ( $false != vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_4
| spl0_12 ),
inference(forward_demodulation,[],[f190,f60]) ).
thf(f325,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_10 ),
inference(avatar_split_clause,[],[f324,f139,f65,f58]) ).
thf(f324,plain,
( ( x != $true )
| ~ spl0_5
| spl0_10 ),
inference(trivial_inequality_removal,[],[f319]) ).
thf(f319,plain,
( ( $false != $false )
| ( x != $true )
| ~ spl0_5
| spl0_10 ),
inference(constrained_superposition,[],[f140,f67]) ).
thf(f140,plain,
( ( $false != vAPP($o,$o,g,$true) )
| spl0_10 ),
inference(avatar_component_clause,[],[f139]) ).
thf(f317,plain,
( ~ spl0_10
| spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f292,f227,f200,f139]) ).
thf(f292,plain,
( ( $false != vAPP($o,$o,g,$true) )
| spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f201,f228]) ).
thf(f313,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f312]) ).
thf(f312,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f311]) ).
thf(f311,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f310,f141]) ).
thf(f310,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f309,f228]) ).
thf(f308,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f307]) ).
thf(f307,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f306]) ).
thf(f306,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f305,f141]) ).
thf(f305,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f278,f228]) ).
thf(f278,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_4
| ~ spl0_17 ),
inference(forward_demodulation,[],[f241,f60]) ).
thf(f299,plain,
( spl0_19
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f283,f243,f227,f58,f264]) ).
thf(f283,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f282,f228]) ).
thf(f282,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| ~ spl0_4
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f247,f228]) ).
thf(f247,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_4
| ~ spl0_18 ),
inference(forward_demodulation,[],[f245,f60]) ).
thf(f281,plain,
( ~ spl0_4
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f280]) ).
thf(f280,plain,
( $false
| ~ spl0_4
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f279,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f278,f202]) ).
thf(f202,plain,
( ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f200]) ).
thf(f274,plain,
( spl0_19
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f249,f243,f200,f109,f72,f58,f264]) ).
thf(f72,plain,
( spl0_6
<=> ( y = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f249,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f248,f218]) ).
thf(f218,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f217,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f215,f74]) ).
thf(f74,plain,
( ( y = $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f72]) ).
thf(f215,plain,
( ( y = $true )
| ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_8
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f214]) ).
thf(f214,plain,
( ( y != vAPP($o,$o,f,$true) )
| ~ spl0_8
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f206]) ).
thf(f206,plain,
( ( $true = $false )
| ( y != vAPP($o,$o,f,$true) )
| ~ spl0_8
| ~ spl0_14 ),
inference(constrained_superposition,[],[f202,f111]) ).
thf(f248,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| ~ spl0_4
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f247,f218]) ).
thf(f268,plain,
( ~ spl0_19
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f261,f200,f144,f264]) ).
thf(f261,plain,
( ( $false != vAPP($o,$o,f,$true) )
| ~ spl0_11
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f255]) ).
thf(f255,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f,$true) )
| ~ spl0_11
| ~ spl0_14 ),
inference(constrained_superposition,[],[f146,f202]) ).
thf(f267,plain,
( spl0_19
| ~ spl0_2
| spl0_16 ),
inference(avatar_split_clause,[],[f233,f227,f22,f264]) ).
thf(f233,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_2
| spl0_16 ),
inference(trivial_inequality_removal,[],[f232]) ).
thf(f232,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_2
| spl0_16 ),
inference(superposition,[],[f229,f23]) ).
thf(f229,plain,
( ( $true != vAPP($o,$o,f,$true) )
| spl0_16 ),
inference(avatar_component_clause,[],[f227]) ).
thf(f252,plain,
( spl0_11
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f162,f109,f72,f144]) ).
thf(f162,plain,
( ( $true = vAPP($o,$o,g,$false) )
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f111,f74]) ).
thf(f246,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f15,f243,f239]) ).
thf(f15,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $false )
| ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $true ) ),
inference(binary_proxy_clausification,[],[f7]) ).
thf(f7,plain,
vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = vAPP($o,$o,g,vAPP($o,$o,f,x)),
inference(cnf_transformation,[],[f1]) ).
thf(f237,plain,
( ~ spl0_6
| ~ spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f187,f144,f109,f72]) ).
thf(f187,plain,
( ( y != $false )
| ~ spl0_8
| spl0_11 ),
inference(trivial_inequality_removal,[],[f182]) ).
thf(f182,plain,
( ( $true != $true )
| ( y != $false )
| ~ spl0_8
| spl0_11 ),
inference(constrained_superposition,[],[f145,f111]) ).
thf(f145,plain,
( ( $true != vAPP($o,$o,g,$false) )
| spl0_11 ),
inference(avatar_component_clause,[],[f144]) ).
thf(f230,plain,
( ~ spl0_16
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f225,f220,f200,f109,f72,f227]) ).
thf(f225,plain,
( ( $true != vAPP($o,$o,f,$true) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f224,f218]) ).
thf(f224,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f222,f218]) ).
thf(f223,plain,
( ~ spl0_15
| ~ spl0_4
| spl0_13 ),
inference(avatar_split_clause,[],[f197,f193,f58,f220]) ).
thf(f197,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_4
| spl0_13 ),
inference(forward_demodulation,[],[f194,f60]) ).
thf(f203,plain,
( spl0_14
| ~ spl0_4
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f198,f189,f58,f200]) ).
thf(f198,plain,
( ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_4
| ~ spl0_12 ),
inference(forward_demodulation,[],[f191,f60]) ).
thf(f196,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f14,f193,f189]) ).
thf(f14,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $true )
| ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $false ) ),
inference(binary_proxy_clausification,[],[f7]) ).
thf(f147,plain,
( spl0_11
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f128,f76,f54,f22,f144]) ).
thf(f128,plain,
( ( $true = vAPP($o,$o,g,$false) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f127,f113]) ).
thf(f127,plain,
( ( vAPP($o,$o,g,x) = $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f126]) ).
thf(f126,plain,
( ( $true = $false )
| ( vAPP($o,$o,g,x) = $true )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f11,f56]) ).
thf(f11,plain,
( ( y = $false )
| ( vAPP($o,$o,g,x) = $true ) ),
inference(binary_proxy_clausification,[],[f5]) ).
thf(f5,plain,
y = vAPP($o,$o,g,x),
inference(cnf_transformation,[],[f1]) ).
thf(f142,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f125,f76,f54,f22,f139]) ).
thf(f125,plain,
( ( $false = vAPP($o,$o,g,$true) )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_7 ),
inference(forward_demodulation,[],[f124,f56]) ).
thf(f124,plain,
( ( vAPP($o,$o,g,y) = $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f123,plain,
( ( $true = $false )
| ( vAPP($o,$o,g,y) = $false )
| ~ spl0_2
| ~ spl0_7 ),
inference(forward_demodulation,[],[f12,f113]) ).
thf(f136,plain,
( ~ spl0_9
| ~ spl0_3
| spl0_8 ),
inference(avatar_split_clause,[],[f122,f109,f54,f133]) ).
thf(f133,plain,
( spl0_9
<=> ( $true = vAPP($o,$o,g,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f122,plain,
( ( $true != vAPP($o,$o,g,$true) )
| ~ spl0_3
| spl0_8 ),
inference(forward_demodulation,[],[f110,f56]) ).
thf(f110,plain,
( ( vAPP($o,$o,g,y) != $true )
| spl0_8 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f121,plain,
( ~ spl0_3
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f120]) ).
thf(f120,plain,
( $false
| ~ spl0_3
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f119]) ).
thf(f119,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(forward_demodulation,[],[f56,f115]) ).
thf(f115,plain,
( ( y = $false )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f114]) ).
thf(f114,plain,
( ( $true = $false )
| ( y = $false )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f11,f67]) ).
thf(f112,plain,
( spl0_8
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f103,f58,f109]) ).
thf(f103,plain,
( ( vAPP($o,$o,g,y) = $true )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f102,plain,
( ( $true = $false )
| ( vAPP($o,$o,g,y) = $true )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f13,f60]) ).
thf(f13,plain,
( ( x = $false )
| ( vAPP($o,$o,g,y) = $true ) ),
inference(binary_proxy_clausification,[],[f6]) ).
thf(f99,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f98]) ).
thf(f98,plain,
( $false
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f92]) ).
thf(f92,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f78,f60]) ).
thf(f96,plain,
( ~ spl0_4
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f95]) ).
thf(f95,plain,
( $false
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f94,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f60,f78]) ).
thf(f87,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f86]) ).
thf(f86,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f80,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f74,f56]) ).
thf(f84,plain,
( ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f83]) ).
thf(f83,plain,
( $false
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f82,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(superposition,[],[f56,f74]) ).
thf(f79,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f9,f76,f72]) ).
thf(f9,plain,
( ( x = $false )
| ( y = $false ) ),
inference(binary_proxy_clausification,[],[f4]) ).
thf(f4,plain,
x != y,
inference(cnf_transformation,[],[f1]) ).
thf(f68,plain,
( spl0_5
| spl0_3 ),
inference(avatar_split_clause,[],[f10,f54,f65]) ).
thf(f10,plain,
( ( y = $true )
| ( vAPP($o,$o,g,x) = $false ) ),
inference(binary_proxy_clausification,[],[f5]) ).
thf(f61,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f8,f58,f54]) ).
thf(f8,plain,
( ( x = $true )
| ( y = $true ) ),
inference(binary_proxy_clausification,[],[f4]) ).
thf(f24,plain,
spl0_2,
inference(avatar_split_clause,[],[f3,f22]) ).
thf(f3,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f20,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2,f17]) ).
thf(f17,plain,
( spl0_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f2,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYO041^1 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.35 % Computer : n011.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 : Mon May 20 10:05:23 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % (27859)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.37 % (27862)WARNING: value z3 for option sas not known
% 0.13/0.37 % (27863)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.13/0.37 % (27860)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.13/0.37 % (27861)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.13/0.37 % (27864)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.13/0.37 % (27862)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.37 % (27865)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.13/0.37 % (27866)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.13/0.37 % Exception at run slice level% Exception at run slice level
% 0.13/0.37 % Exception at run slice level
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.13/0.37 % (27866)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.13/0.37
% 0.13/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.39 % (27864)First to succeed.
% 0.20/0.39 % (27867)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.39 % (27868)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.20/0.39 % (27867)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 % (27868)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 % Exception at run slice level
% 0.20/0.39 % (27869)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.20/0.39 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.39 % (27862)Also succeeded, but the first one will report.
% 0.20/0.39 % (27864)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-27859"
% 0.20/0.39 % (27864)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Unsatisfiable for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.40 % (27864)------------------------------
% 0.20/0.40 % (27864)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.40 % (27864)Termination reason: Refutation
% 0.20/0.40
% 0.20/0.40 % (27864)Memory used [KB]: 1009
% 0.20/0.40 % (27864)Time elapsed: 0.021 s
% 0.20/0.40 % (27864)Instructions burned: 34 (million)
% 0.20/0.40 % (27859)Success in time 0.022 s
%------------------------------------------------------------------------------