TSTP Solution File: SYO041^2 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SYO041^2 : TPTP v8.2.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.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 : Theorem 0.20s 0.39s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 46
% Syntax : Number of formulae : 378 ( 8 unt; 13 typ; 0 def)
% Number of atoms : 2848 ( 352 equ; 0 cnn)
% Maximal formula atoms : 9 ( 7 avg)
% Number of connectives : 1850 ( 847 ~; 964 |; 9 &; 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(f885,plain,
$false,
inference(avatar_sat_refutation,[],[f22,f31,f35,f70,f81,f86,f89,f98,f101,f114,f123,f138,f144,f149,f198,f205,f225,f232,f239,f248,f254,f269,f270,f276,f283,f301,f310,f315,f319,f327,f341,f347,f357,f359,f365,f376,f389,f407,f408,f424,f439,f479,f520,f538,f552,f561,f569,f587,f599,f616,f620,f633,f635,f646,f648,f670,f675,f682,f688,f694,f704,f709,f714,f723,f747,f750,f752,f774,f845,f851,f861,f881,f884]) ).
thf(f884,plain,
( spl0_19
| ~ spl0_22
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f846,f842,f362,f266]) ).
thf(f266,plain,
( spl0_19
<=> ( $false = vAPP($o,$o,f,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
thf(f362,plain,
( spl0_22
<=> ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
thf(f842,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(f846,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_22
| ~ spl0_29 ),
inference(forward_demodulation,[],[f844,f364]) ).
thf(f364,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f844,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f842]) ).
thf(f881,plain,
( ~ spl0_16
| spl0_15
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f820,f229,f222,f229]) ).
thf(f222,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(f229,plain,
( spl0_16
<=> ( $true = vAPP($o,$o,f,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
thf(f820,plain,
( ( $true != vAPP($o,$o,f,$true) )
| spl0_15
| ~ spl0_16 ),
inference(forward_demodulation,[],[f800,f230]) ).
thf(f230,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f800,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| spl0_15
| ~ spl0_16 ),
inference(superposition,[],[f224,f230]) ).
thf(f224,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| spl0_15 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f861,plain,
( spl0_24
| ~ spl0_4
| spl0_27 ),
inference(avatar_split_clause,[],[f759,f630,f33,f404]) ).
thf(f404,plain,
( spl0_24
<=> ( $false = vAPP($o,$o,f,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
thf(f33,plain,
( spl0_4
<=> ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
thf(f630,plain,
( spl0_27
<=> ( $true = vAPP($o,$o,f,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
thf(f759,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_4
| spl0_27 ),
inference(trivial_inequality_removal,[],[f758]) ).
thf(f758,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_4
| spl0_27 ),
inference(superposition,[],[f632,f34]) ).
thf(f34,plain,
( ! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f33]) ).
thf(f632,plain,
( ( $true != vAPP($o,$o,f,$false) )
| spl0_27 ),
inference(avatar_component_clause,[],[f630]) ).
thf(f851,plain,
( ~ spl0_30
| ~ spl0_7
| spl0_13 ),
inference(avatar_split_clause,[],[f733,f195,f78,f848]) ).
thf(f848,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(f78,plain,
( spl0_7
<=> ( x = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
thf(f195,plain,
( spl0_13
<=> ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
thf(f733,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| spl0_13 ),
inference(forward_demodulation,[],[f196,f80]) ).
thf(f80,plain,
( ( x = $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f78]) ).
thf(f196,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) != $true )
| spl0_13 ),
inference(avatar_component_clause,[],[f195]) ).
thf(f845,plain,
( spl0_29
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f594,f245,f78,f842]) ).
thf(f245,plain,
( spl0_18
<=> ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
thf(f594,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[],[f247,f80]) ).
thf(f247,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $false )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f774,plain,
( ~ spl0_10
| ~ spl0_16
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[],[f773]) ).
thf(f773,plain,
( $false
| ~ spl0_10
| ~ spl0_16
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f772]) ).
thf(f772,plain,
( ( $true = $false )
| ~ spl0_10
| ~ spl0_16
| ~ spl0_21 ),
inference(forward_demodulation,[],[f762,f143]) ).
thf(f143,plain,
( ( $false = vAPP($o,$o,g,$true) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f141,plain,
( spl0_10
<=> ( $false = vAPP($o,$o,g,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
thf(f762,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ~ spl0_16
| ~ spl0_21 ),
inference(superposition,[],[f356,f230]) ).
thf(f356,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f354]) ).
thf(f354,plain,
( spl0_21
<=> ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
thf(f752,plain,
( ~ spl0_20
| ~ spl0_4
| spl0_5
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f418,f78,f67,f33,f344]) ).
thf(f344,plain,
( spl0_20
<=> ( $false = vAPP($o,$o,g,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
thf(f67,plain,
( spl0_5
<=> ( vAPP($o,$o,g,x) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
thf(f418,plain,
( ( $false != vAPP($o,$o,g,$false) )
| ~ spl0_4
| spl0_5
| ~ spl0_7 ),
inference(forward_demodulation,[],[f68,f115]) ).
thf(f115,plain,
( ( x = $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f95]) ).
thf(f95,plain,
( ( $true = $false )
| ( x = $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(superposition,[],[f80,f34]) ).
thf(f68,plain,
( ( vAPP($o,$o,g,x) != $false )
| spl0_5 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f750,plain,
( ~ spl0_11
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f749]) ).
thf(f749,plain,
( $false
| ~ spl0_11
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f743]) ).
thf(f743,plain,
( ( $true = $false )
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f345,f148]) ).
thf(f148,plain,
( ( $true = vAPP($o,$o,g,$false) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f146]) ).
thf(f146,plain,
( spl0_11
<=> ( $true = vAPP($o,$o,g,$false) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
thf(f345,plain,
( ( $false = vAPP($o,$o,g,$false) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f344]) ).
thf(f747,plain,
( ~ spl0_11
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[],[f746]) ).
thf(f746,plain,
( $false
| ~ spl0_11
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f745]) ).
thf(f745,plain,
( ( $true = $false )
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f148,f345]) ).
thf(f723,plain,
( ~ spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f722]) ).
thf(f722,plain,
( $false
| ~ spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f721]) ).
thf(f721,plain,
( ( $true = $false )
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f720,f405]) ).
thf(f405,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f404]) ).
thf(f720,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f364,f405]) ).
thf(f714,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f713]) ).
thf(f713,plain,
( $false
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f712]) ).
thf(f712,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f711,f405]) ).
thf(f711,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f710,f405]) ).
thf(f710,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f581,f405]) ).
thf(f581,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| ~ spl0_13 ),
inference(superposition,[],[f197,f80]) ).
thf(f197,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f195]) ).
thf(f709,plain,
( ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f708]) ).
thf(f708,plain,
( $false
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f707]) ).
thf(f707,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f706,f405]) ).
thf(f706,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f705,f405]) ).
thf(f705,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_7
| ~ spl0_13
| ~ spl0_24 ),
inference(forward_demodulation,[],[f700,f405]) ).
thf(f700,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| ~ spl0_13 ),
inference(forward_demodulation,[],[f197,f80]) ).
thf(f704,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f703]) ).
thf(f703,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f702]) ).
thf(f702,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f701,f405]) ).
thf(f701,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f700,f473]) ).
thf(f473,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_4
| spl0_22 ),
inference(trivial_inequality_removal,[],[f472]) ).
thf(f472,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_4
| spl0_22 ),
inference(superposition,[],[f363,f34]) ).
thf(f363,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| spl0_22 ),
inference(avatar_component_clause,[],[f362]) ).
thf(f694,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f693]) ).
thf(f693,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f692]) ).
thf(f692,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f691,f405]) ).
thf(f691,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f690]) ).
thf(f690,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f689,f473]) ).
thf(f689,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,f80]) ).
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,[],[f653]) ).
thf(f653,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f493]) ).
thf(f493,plain,
( ( $true != $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(constrained_superposition,[],[f363,f197]) ).
thf(f688,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f687]) ).
thf(f687,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f686]) ).
thf(f686,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f685,f405]) ).
thf(f685,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f684]) ).
thf(f684,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f683,f473]) ).
thf(f683,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,[],[f656,f80]) ).
thf(f656,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,[],[f494]) ).
thf(f494,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) != vAPP($o,$o,f,$false) )
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f493]) ).
thf(f682,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f681]) ).
thf(f681,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f680]) ).
thf(f680,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f679,f405]) ).
thf(f679,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f678]) ).
thf(f678,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f677,f473]) ).
thf(f677,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,[],[f495,f80]) ).
thf(f495,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,[],[f494]) ).
thf(f675,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f674]) ).
thf(f674,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f673]) ).
thf(f673,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f672,f405]) ).
thf(f672,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f671]) ).
thf(f671,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f564,f473]) ).
thf(f564,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f495,f115]) ).
thf(f670,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f669]) ).
thf(f669,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(trivial_inequality_removal,[],[f668]) ).
thf(f668,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22
| ~ spl0_24 ),
inference(forward_demodulation,[],[f667,f405]) ).
thf(f667,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f581,f473]) ).
thf(f648,plain,
( spl0_20
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f647,f643,f404,f344]) ).
thf(f643,plain,
( spl0_28
<=> ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
thf(f647,plain,
( ( $false = vAPP($o,$o,g,$false) )
| ~ spl0_24
| ~ spl0_28 ),
inference(forward_demodulation,[],[f645,f405]) ).
thf(f645,plain,
( ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$false)) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f643]) ).
thf(f646,plain,
( spl0_28
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f578,f191,f78,f33,f643]) ).
thf(f191,plain,
( spl0_12
<=> ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
thf(f578,plain,
( ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12 ),
inference(forward_demodulation,[],[f193,f115]) ).
thf(f193,plain,
( ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $false )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f635,plain,
( spl0_24
| ~ spl0_4
| ~ spl0_7
| ~ spl0_18
| spl0_22 ),
inference(avatar_split_clause,[],[f623,f362,f245,f78,f33,f404]) ).
thf(f623,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_18
| spl0_22 ),
inference(forward_demodulation,[],[f594,f473]) ).
thf(f633,plain,
( ~ spl0_27
| ~ spl0_4
| ~ spl0_7
| spl0_13
| spl0_22 ),
inference(avatar_split_clause,[],[f622,f362,f195,f78,f33,f630]) ).
thf(f622,plain,
( ( $true != vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f621,f473]) ).
thf(f621,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$false))) )
| ~ spl0_7
| spl0_13 ),
inference(forward_demodulation,[],[f196,f80]) ).
thf(f620,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f619]) ).
thf(f619,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f618]) ).
thf(f618,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f617,f578]) ).
thf(f617,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$false)) )
| ~ spl0_7
| ~ spl0_17 ),
inference(forward_demodulation,[],[f243,f80]) ).
thf(f243,plain,
( ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f241]) ).
thf(f241,plain,
( spl0_17
<=> ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
thf(f616,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f615]) ).
thf(f615,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f614]) ).
thf(f614,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_12
| ~ spl0_17 ),
inference(forward_demodulation,[],[f582,f578]) ).
thf(f582,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$false)) )
| ~ spl0_7
| ~ spl0_17 ),
inference(superposition,[],[f243,f80]) ).
thf(f599,plain,
( spl0_24
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f595,f266,f245,f195,f78,f33,f404]) ).
thf(f595,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_18
| ~ spl0_19 ),
inference(forward_demodulation,[],[f594,f541]) ).
thf(f541,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f540,f115]) ).
thf(f540,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f539]) ).
thf(f539,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_4
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f487,f268]) ).
thf(f268,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f266]) ).
thf(f487,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $false )
| ~ spl0_4
| ~ spl0_13 ),
inference(superposition,[],[f197,f34]) ).
thf(f587,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f586]) ).
thf(f586,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f585]) ).
thf(f585,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17
| ~ spl0_19 ),
inference(forward_demodulation,[],[f584,f268]) ).
thf(f584,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f581,f548]) ).
thf(f548,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f547,f115]) ).
thf(f547,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f546]) ).
thf(f546,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f545,f115]) ).
thf(f545,plain,
( ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f544]) ).
thf(f544,plain,
( ( $true = $false )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f500,f143]) ).
thf(f500,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,[],[f489]) ).
thf(f489,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ( x != vAPP($o,$o,f,vAPP($o,$o,f,x)) )
| ~ spl0_13
| ~ spl0_17 ),
inference(constrained_superposition,[],[f243,f197]) ).
thf(f569,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(avatar_contradiction_clause,[],[f568]) ).
thf(f568,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(trivial_inequality_removal,[],[f567]) ).
thf(f567,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f566,f450]) ).
thf(f450,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12 ),
inference(forward_demodulation,[],[f449,f115]) ).
thf(f449,plain,
( ( vAPP($o,$o,f,x) = $false )
| ~ spl0_4
| ~ spl0_10
| spl0_12 ),
inference(trivial_inequality_removal,[],[f448]) ).
thf(f448,plain,
( ( $false != $false )
| ( vAPP($o,$o,f,x) = $false )
| ~ spl0_4
| ~ spl0_10
| spl0_12 ),
inference(forward_demodulation,[],[f443,f143]) ).
thf(f443,plain,
( ( $false != vAPP($o,$o,g,$true) )
| ( vAPP($o,$o,f,x) = $false )
| ~ spl0_4
| spl0_12 ),
inference(superposition,[],[f192,f34]) ).
thf(f192,plain,
( ( vAPP($o,$o,g,vAPP($o,$o,f,x)) != $false )
| spl0_12 ),
inference(avatar_component_clause,[],[f191]) ).
thf(f566,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(duplicate_literal_removal,[],[f565]) ).
thf(f565,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| spl0_22 ),
inference(forward_demodulation,[],[f564,f450]) ).
thf(f561,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[],[f560]) ).
thf(f560,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f559]) ).
thf(f559,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f558,f450]) ).
thf(f558,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f557,f450]) ).
thf(f557,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f556,f115]) ).
thf(f556,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f555]) ).
thf(f555,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f554,f115]) ).
thf(f554,plain,
( ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f553]) ).
thf(f553,plain,
( ( $false != $false )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_10
| spl0_12
| ~ spl0_13 ),
inference(forward_demodulation,[],[f498,f143]) ).
thf(f498,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,[],[f490]) ).
thf(f490,plain,
( ( $false != vAPP($o,$o,g,$true) )
| ( x != vAPP($o,$o,f,vAPP($o,$o,f,x)) )
| spl0_12
| ~ spl0_13 ),
inference(constrained_superposition,[],[f192,f197]) ).
thf(f552,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f551]) ).
thf(f551,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f550]) ).
thf(f550,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f549,f450]) ).
thf(f549,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_17 ),
inference(forward_demodulation,[],[f548,f450]) ).
thf(f538,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f537]) ).
thf(f537,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f536]) ).
thf(f536,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f535,f450]) ).
thf(f535,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f534,f450]) ).
thf(f534,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f533,f115]) ).
thf(f533,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f532]) ).
thf(f532,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f531,f450]) ).
thf(f531,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f530,f115]) ).
thf(f530,plain,
( ( vAPP($o,$o,f,x) = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f529]) ).
thf(f529,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,[],[f503,f268]) ).
thf(f503,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,[],[f486]) ).
thf(f486,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,[],[f197,f197]) ).
thf(f520,plain,
( ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f519]) ).
thf(f519,plain,
( $false
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f518,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f517,f450]) ).
thf(f517,plain,
( ( $true = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f516,f450]) ).
thf(f516,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f515,f115]) ).
thf(f515,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f514]) ).
thf(f514,plain,
( ( $true = $false )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f513,f115]) ).
thf(f513,plain,
( ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f512]) ).
thf(f512,plain,
( ( $true = $false )
| ( x = $true )
| ( vAPP($o,$o,f,vAPP($o,$o,f,x)) = $true )
| ~ spl0_4
| ~ spl0_7
| ~ spl0_10
| spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_demodulation,[],[f511,f450]) ).
thf(f511,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,[],[f505,f268]) ).
thf(f505,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,[],[f483]) ).
thf(f483,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,[],[f197,f197]) ).
thf(f479,plain,
( ~ spl0_26
| ~ spl0_19
| spl0_23 ),
inference(avatar_split_clause,[],[f377,f373,f266,f476]) ).
thf(f476,plain,
( spl0_26
<=> ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$false)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
thf(f373,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(f377,plain,
( ( $false != vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_19
| spl0_23 ),
inference(forward_demodulation,[],[f375,f268]) ).
thf(f375,plain,
( ( $false != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| spl0_23 ),
inference(avatar_component_clause,[],[f373]) ).
thf(f439,plain,
( spl0_25
| spl0_3 ),
inference(avatar_split_clause,[],[f14,f28,f436]) ).
thf(f436,plain,
( spl0_25
<=> ( vAPP($o,$o,g,y) = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
thf(f28,plain,
( spl0_3
<=> ( x = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
thf(f14,plain,
( ( x = $true )
| ( vAPP($o,$o,g,y) = $false ) ),
inference(binary_proxy_clausification,[],[f8]) ).
thf(f8,plain,
x = vAPP($o,$o,g,y),
inference(cnf_transformation,[],[f5]) ).
thf(f5,plain,
( ( vAPP($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,$o,g,x) )
& ( x != y ) ),
inference(flattening,[],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ( vAPP($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,$o,g,x) )
& ( x != y ) ),
inference(negated_conjecture,[],[f1]) ).
thf(f1,conjecture,
~ ( ( vAPP($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(f424,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[],[f423]) ).
thf(f423,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f422]) ).
thf(f422,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f26,f414]) ).
thf(f414,plain,
( ( y = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(trivial_inequality_removal,[],[f413]) ).
thf(f413,plain,
( ( $true = $false )
| ( y = $false )
| ~ spl0_4
| ~ spl0_8
| ~ spl0_10 ),
inference(forward_demodulation,[],[f165,f143]) ).
thf(f165,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ( y = $false )
| ~ spl0_4
| ~ spl0_8 ),
inference(superposition,[],[f113,f34]) ).
thf(f113,plain,
( ( vAPP($o,$o,g,y) = $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f111,plain,
( spl0_8
<=> ( vAPP($o,$o,g,y) = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
thf(f26,plain,
( ( y = $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f24,plain,
( spl0_2
<=> ( y = $true ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
thf(f408,plain,
( spl0_24
| ~ spl0_4
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f371,f362,f266,f33,f404]) ).
thf(f371,plain,
( ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_19
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f370]) ).
thf(f370,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_demodulation,[],[f367,f268]) ).
thf(f367,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( $false = vAPP($o,$o,f,$false) )
| ~ spl0_4
| ~ spl0_22 ),
inference(superposition,[],[f364,f34]) ).
thf(f407,plain,
( ~ spl0_24
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f369,f362,f266,f404]) ).
thf(f369,plain,
( ( $false != vAPP($o,$o,f,$false) )
| ~ spl0_19
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f368]) ).
thf(f368,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f,$false) )
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_demodulation,[],[f366,f268]) ).
thf(f366,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ( $false != vAPP($o,$o,f,$false) )
| ~ spl0_22 ),
inference(constrained_superposition,[],[f364,f364]) ).
thf(f389,plain,
( spl0_10
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(avatar_split_clause,[],[f317,f67,f33,f28,f141]) ).
thf(f317,plain,
( ( $false = vAPP($o,$o,g,$true) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f316]) ).
thf(f316,plain,
( ( $true = $false )
| ( $false = vAPP($o,$o,g,$true) )
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5 ),
inference(forward_demodulation,[],[f159,f30]) ).
thf(f30,plain,
( ( x = $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f159,plain,
( ( $false = vAPP($o,$o,g,$true) )
| ( x = $false )
| ~ spl0_4
| ~ spl0_5 ),
inference(superposition,[],[f69,f34]) ).
thf(f69,plain,
( ( vAPP($o,$o,g,x) = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f67]) ).
thf(f376,plain,
( ~ spl0_23
| ~ spl0_3
| spl0_18 ),
inference(avatar_split_clause,[],[f304,f245,f28,f373]) ).
thf(f304,plain,
( ( $false != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_3
| spl0_18 ),
inference(forward_demodulation,[],[f246,f30]) ).
thf(f246,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) != $false )
| spl0_18 ),
inference(avatar_component_clause,[],[f245]) ).
thf(f365,plain,
( spl0_22
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f360,f266,f222,f362]) ).
thf(f360,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,$false)) )
| ~ spl0_15
| ~ spl0_19 ),
inference(forward_demodulation,[],[f223,f268]) ).
thf(f223,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f222]) ).
thf(f359,plain,
( spl0_15
| ~ spl0_3
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f273,f195,f28,f222]) ).
thf(f273,plain,
( ( $true = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_3
| ~ spl0_13 ),
inference(forward_demodulation,[],[f197,f30]) ).
thf(f357,plain,
( spl0_21
| ~ spl0_3
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f311,f241,f28,f354]) ).
thf(f311,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f243,f30]) ).
thf(f347,plain,
( ~ spl0_20
| spl0_14
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f342,f266,f202,f344]) ).
thf(f202,plain,
( spl0_14
<=> ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$true)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
thf(f342,plain,
( ( $false != vAPP($o,$o,g,$false) )
| spl0_14
| ~ spl0_19 ),
inference(forward_demodulation,[],[f203,f268]) ).
thf(f203,plain,
( ( $false != vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| spl0_14 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f341,plain,
( ~ spl0_14
| ~ spl0_3
| spl0_12 ),
inference(avatar_split_clause,[],[f295,f191,f28,f202]) ).
thf(f295,plain,
( ( $false != vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_3
| spl0_12 ),
inference(forward_demodulation,[],[f192,f30]) ).
thf(f327,plain,
( ~ spl0_3
| ~ spl0_5
| spl0_10 ),
inference(avatar_split_clause,[],[f326,f141,f67,f28]) ).
thf(f326,plain,
( ( x != $true )
| ~ spl0_5
| spl0_10 ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f321,plain,
( ( $false != $false )
| ( x != $true )
| ~ spl0_5
| spl0_10 ),
inference(constrained_superposition,[],[f142,f69]) ).
thf(f142,plain,
( ( $false != vAPP($o,$o,g,$true) )
| spl0_10 ),
inference(avatar_component_clause,[],[f141]) ).
thf(f319,plain,
( ~ spl0_10
| spl0_14
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f294,f229,f202,f141]) ).
thf(f294,plain,
( ( $false != vAPP($o,$o,g,$true) )
| spl0_14
| ~ spl0_16 ),
inference(forward_demodulation,[],[f203,f230]) ).
thf(f315,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f314]) ).
thf(f314,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f313]) ).
thf(f313,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f312,f143]) ).
thf(f312,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f311,f230]) ).
thf(f310,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f309]) ).
thf(f309,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f308]) ).
thf(f308,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_10
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f307,f143]) ).
thf(f307,plain,
( ( $true = vAPP($o,$o,g,$true) )
| ~ spl0_3
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[],[f280,f230]) ).
thf(f280,plain,
( ( $true = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_3
| ~ spl0_17 ),
inference(forward_demodulation,[],[f243,f30]) ).
thf(f301,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f285,f245,f229,f28,f266]) ).
thf(f285,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f284,f230]) ).
thf(f284,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| ~ spl0_3
| ~ spl0_16
| ~ spl0_18 ),
inference(forward_demodulation,[],[f249,f230]) ).
thf(f249,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_3
| ~ spl0_18 ),
inference(forward_demodulation,[],[f247,f30]) ).
thf(f283,plain,
( ~ spl0_3
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f282]) ).
thf(f282,plain,
( $false
| ~ spl0_3
| ~ spl0_14
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f281]) ).
thf(f281,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_14
| ~ spl0_17 ),
inference(forward_demodulation,[],[f280,f204]) ).
thf(f204,plain,
( ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f276,plain,
( spl0_19
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(avatar_split_clause,[],[f251,f245,f202,f111,f74,f28,f266]) ).
thf(f74,plain,
( spl0_6
<=> ( y = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
thf(f251,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f250,f220]) ).
thf(f220,plain,
( ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f219]) ).
thf(f219,plain,
( ( $true = $false )
| ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[],[f217,f76]) ).
thf(f76,plain,
( ( y = $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f217,plain,
( ( y = $true )
| ( $true = vAPP($o,$o,f,$true) )
| ~ spl0_8
| ~ spl0_14 ),
inference(binary_proxy_clausification,[],[f216]) ).
thf(f216,plain,
( ( y != vAPP($o,$o,f,$true) )
| ~ spl0_8
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f208]) ).
thf(f208,plain,
( ( $true = $false )
| ( y != vAPP($o,$o,f,$true) )
| ~ spl0_8
| ~ spl0_14 ),
inference(constrained_superposition,[],[f204,f113]) ).
thf(f250,plain,
( ( $false = vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| ~ spl0_18 ),
inference(forward_demodulation,[],[f249,f220]) ).
thf(f270,plain,
( ~ spl0_19
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f263,f202,f146,f266]) ).
thf(f263,plain,
( ( $false != vAPP($o,$o,f,$true) )
| ~ spl0_11
| ~ spl0_14 ),
inference(trivial_inequality_removal,[],[f257]) ).
thf(f257,plain,
( ( $true = $false )
| ( $false != vAPP($o,$o,f,$true) )
| ~ spl0_11
| ~ spl0_14 ),
inference(constrained_superposition,[],[f148,f204]) ).
thf(f269,plain,
( spl0_19
| ~ spl0_4
| spl0_16 ),
inference(avatar_split_clause,[],[f235,f229,f33,f266]) ).
thf(f235,plain,
( ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_4
| spl0_16 ),
inference(trivial_inequality_removal,[],[f234]) ).
thf(f234,plain,
( ( $true != $true )
| ( $false = vAPP($o,$o,f,$true) )
| ~ spl0_4
| spl0_16 ),
inference(superposition,[],[f231,f34]) ).
thf(f231,plain,
( ( $true != vAPP($o,$o,f,$true) )
| spl0_16 ),
inference(avatar_component_clause,[],[f229]) ).
thf(f254,plain,
( spl0_11
| ~ spl0_6
| ~ spl0_8 ),
inference(avatar_split_clause,[],[f164,f111,f74,f146]) ).
thf(f164,plain,
( ( $true = vAPP($o,$o,g,$false) )
| ~ spl0_6
| ~ spl0_8 ),
inference(superposition,[],[f113,f76]) ).
thf(f248,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f17,f245,f241]) ).
thf(f17,plain,
( ( vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = $false )
| ( vAPP($o,$o,g,vAPP($o,$o,f,x)) = $true ) ),
inference(binary_proxy_clausification,[],[f9]) ).
thf(f9,plain,
vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,x))) = vAPP($o,$o,g,vAPP($o,$o,f,x)),
inference(cnf_transformation,[],[f5]) ).
thf(f239,plain,
( ~ spl0_6
| ~ spl0_8
| spl0_11 ),
inference(avatar_split_clause,[],[f189,f146,f111,f74]) ).
thf(f189,plain,
( ( y != $false )
| ~ spl0_8
| spl0_11 ),
inference(trivial_inequality_removal,[],[f184]) ).
thf(f184,plain,
( ( $true != $true )
| ( y != $false )
| ~ spl0_8
| spl0_11 ),
inference(constrained_superposition,[],[f147,f113]) ).
thf(f147,plain,
( ( $true != vAPP($o,$o,g,$false) )
| spl0_11 ),
inference(avatar_component_clause,[],[f146]) ).
thf(f232,plain,
( ~ spl0_16
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| spl0_15 ),
inference(avatar_split_clause,[],[f227,f222,f202,f111,f74,f229]) ).
thf(f227,plain,
( ( $true != vAPP($o,$o,f,$true) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f226,f220]) ).
thf(f226,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,$true)) )
| ~ spl0_6
| ~ spl0_8
| ~ spl0_14
| spl0_15 ),
inference(forward_demodulation,[],[f224,f220]) ).
thf(f225,plain,
( ~ spl0_15
| ~ spl0_3
| spl0_13 ),
inference(avatar_split_clause,[],[f199,f195,f28,f222]) ).
thf(f199,plain,
( ( $true != vAPP($o,$o,f,vAPP($o,$o,f,vAPP($o,$o,f,$true))) )
| ~ spl0_3
| spl0_13 ),
inference(forward_demodulation,[],[f196,f30]) ).
thf(f205,plain,
( spl0_14
| ~ spl0_3
| ~ spl0_12 ),
inference(avatar_split_clause,[],[f200,f191,f28,f202]) ).
thf(f200,plain,
( ( $false = vAPP($o,$o,g,vAPP($o,$o,f,$true)) )
| ~ spl0_3
| ~ spl0_12 ),
inference(forward_demodulation,[],[f193,f30]) ).
thf(f198,plain,
( spl0_12
| spl0_13 ),
inference(avatar_split_clause,[],[f16,f195,f191]) ).
thf(f16,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,[],[f9]) ).
thf(f149,plain,
( spl0_11
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f130,f78,f33,f24,f146]) ).
thf(f130,plain,
( ( $true = vAPP($o,$o,g,$false) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f129,f115]) ).
thf(f129,plain,
( ( vAPP($o,$o,g,x) = $true )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f128]) ).
thf(f128,plain,
( ( $true = $false )
| ( vAPP($o,$o,g,x) = $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f13,f26]) ).
thf(f13,plain,
( ( y = $false )
| ( vAPP($o,$o,g,x) = $true ) ),
inference(binary_proxy_clausification,[],[f7]) ).
thf(f7,plain,
y = vAPP($o,$o,g,x),
inference(cnf_transformation,[],[f5]) ).
thf(f144,plain,
( spl0_10
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f127,f78,f33,f24,f141]) ).
thf(f127,plain,
( ( $false = vAPP($o,$o,g,$true) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f126,f26]) ).
thf(f126,plain,
( ( vAPP($o,$o,g,y) = $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f125]) ).
thf(f125,plain,
( ( $true = $false )
| ( vAPP($o,$o,g,y) = $false )
| ~ spl0_4
| ~ spl0_7 ),
inference(forward_demodulation,[],[f14,f115]) ).
thf(f138,plain,
( ~ spl0_9
| ~ spl0_2
| spl0_8 ),
inference(avatar_split_clause,[],[f124,f111,f24,f135]) ).
thf(f135,plain,
( spl0_9
<=> ( $true = vAPP($o,$o,g,$true) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
thf(f124,plain,
( ( $true != vAPP($o,$o,g,$true) )
| ~ spl0_2
| spl0_8 ),
inference(forward_demodulation,[],[f112,f26]) ).
thf(f112,plain,
( ( vAPP($o,$o,g,y) != $true )
| spl0_8 ),
inference(avatar_component_clause,[],[f111]) ).
thf(f123,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f122]) ).
thf(f122,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f121]) ).
thf(f121,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[],[f26,f117]) ).
thf(f117,plain,
( ( y = $false )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f116]) ).
thf(f116,plain,
( ( $true = $false )
| ( y = $false )
| ~ spl0_5 ),
inference(forward_demodulation,[],[f13,f69]) ).
thf(f114,plain,
( spl0_8
| ~ spl0_3 ),
inference(avatar_split_clause,[],[f105,f28,f111]) ).
thf(f105,plain,
( ( vAPP($o,$o,g,y) = $true )
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f104]) ).
thf(f104,plain,
( ( $true = $false )
| ( vAPP($o,$o,g,y) = $true )
| ~ spl0_3 ),
inference(forward_demodulation,[],[f15,f30]) ).
thf(f15,plain,
( ( x = $false )
| ( vAPP($o,$o,g,y) = $true ) ),
inference(binary_proxy_clausification,[],[f8]) ).
thf(f101,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f100]) ).
thf(f100,plain,
( $false
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f94]) ).
thf(f94,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f80,f30]) ).
thf(f98,plain,
( ~ spl0_3
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[],[f97]) ).
thf(f97,plain,
( $false
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f96]) ).
thf(f96,plain,
( ( $true = $false )
| ~ spl0_3
| ~ spl0_7 ),
inference(superposition,[],[f30,f80]) ).
thf(f89,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f88]) ).
thf(f88,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f82]) ).
thf(f82,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f76,f26]) ).
thf(f86,plain,
( ~ spl0_2
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f85]) ).
thf(f85,plain,
( $false
| ~ spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f84]) ).
thf(f84,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_6 ),
inference(superposition,[],[f26,f76]) ).
thf(f81,plain,
( spl0_6
| spl0_7 ),
inference(avatar_split_clause,[],[f11,f78,f74]) ).
thf(f11,plain,
( ( x = $false )
| ( y = $false ) ),
inference(binary_proxy_clausification,[],[f6]) ).
thf(f6,plain,
x != y,
inference(cnf_transformation,[],[f5]) ).
thf(f70,plain,
( spl0_5
| spl0_2 ),
inference(avatar_split_clause,[],[f12,f24,f67]) ).
thf(f12,plain,
( ( y = $true )
| ( vAPP($o,$o,g,x) = $false ) ),
inference(binary_proxy_clausification,[],[f7]) ).
thf(f35,plain,
spl0_4,
inference(avatar_split_clause,[],[f4,f33]) ).
thf(f4,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = X0 ) ),
introduced(fool_axiom,[]) ).
thf(f31,plain,
( spl0_2
| spl0_3 ),
inference(avatar_split_clause,[],[f10,f28,f24]) ).
thf(f10,plain,
( ( x = $true )
| ( y = $true ) ),
inference(binary_proxy_clausification,[],[f6]) ).
thf(f22,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f3,f19]) ).
thf(f19,plain,
( spl0_1
<=> ( $true = $false ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
thf(f3,plain,
$true != $false,
introduced(fool_axiom,[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SYO041^2 : TPTP v8.2.0. Released v4.1.0.
% 0.03/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n002.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 : 300
% 0.14/0.35 % DateTime : Mon May 20 09:45:08 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (21159)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37 % (21162)WARNING: value z3 for option sas not known
% 0.20/0.37 % (21163)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37 % (21161)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37 % (21160)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37 % (21164)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)
% 0.20/0.37 % Exception at run slice level% Exception at run slice level
% 0.20/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.37
% 0.20/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.37 % Exception at run slice level
% 0.20/0.37 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.37 % (21166)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)
% 0.20/0.37 % (21166)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.37 % (21165)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)
% 0.20/0.37 % (21162)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)
% 0.20/0.39 % (21164)First to succeed.
% 0.20/0.39 % (21169)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 % (21168)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 % (21167)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.20/0.39 % (21168)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.20/0.39 % (21167)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 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.39 % (21164)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-21159"
% 0.20/0.39 % (21164)Refutation found. Thanks to Tanya!
% 0.20/0.39 % SZS status Theorem for theBenchmark
% 0.20/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39 % (21164)------------------------------
% 0.20/0.39 % (21164)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.39 % (21164)Termination reason: Refutation
% 0.20/0.39
% 0.20/0.39 % (21164)Memory used [KB]: 1009
% 0.20/0.39 % (21164)Time elapsed: 0.021 s
% 0.20/0.39 % (21164)Instructions burned: 34 (million)
% 0.20/0.39 % (21159)Success in time 0.033 s
%------------------------------------------------------------------------------