%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO041^2 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n001.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 : Wed Feb 25 09:53:13 AM UTC 2026
% Result : Theorem 1.65s 1.42s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 183 ( 13 unt; 0 typ; 21 def)
% Number of atoms : 1110 ( 179 equ; 0 cnn)
% Maximal formula atoms : 5 ( 6 avg)
% Number of connectives : 850 ( 281 ~; 299 |; 18 &; 231 @)
% ( 21 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 25 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
f: $o > $o ).
thf(func_def_2,type,
g: $o > $o ).
thf(func_def_12,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f521,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f35,f37,f40,f54,f63,f86,f100,f134,f147,f154,f158,f195,f197,f231,f236,f255,f277,f302,f309,f312,f321,f332,f338,f345,f348,f353,f356,f376,f391,f414,f433,f471,f506]) ).
thf(f506,plain,
( ~ spl0_2
| spl0_9
| spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f505]) ).
thf(f505,plain,
( $false
| ~ spl0_2
| spl0_9
| spl0_16
| ~ spl0_17 ),
inference(subsumption_resolution,[status(thm)],[f504,f434]) ).
thf(f434,plain,
( ( $true
!= ( f @ $true ) )
| spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f124,f129]) ).
thf(f129,plain,
( ( x = $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f127]) ).
thf(f127,definition,
( spl0_17
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f124,plain,
( ( ( f @ x )
!= $true )
| spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f122,definition,
( spl0_16
<=> ( ( f @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f504,plain,
( ( $true
= ( f @ $true ) )
| ~ spl0_2
| spl0_9
| spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f487,f468]) ).
thf(f468,plain,
( ( $true
= ( f @ ( f @ $true ) ) )
| spl0_9
| spl0_16
| ~ spl0_17 ),
inference(subsumption_resolution,[status(thm)],[f456,f434]) ).
thf(f456,plain,
( ( $true
= ( f @ $true ) )
| ( $true
= ( f @ ( f @ $true ) ) )
| spl0_9
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f440]) ).
thf(f440,plain,
( ( ( f @ $true )
!= ( f @ ( f @ $true ) ) )
| spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f81,f129]) ).
thf(f81,plain,
( ( ( f @ x )
!= ( f @ ( f @ x ) ) )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f79]) ).
thf(f79,definition,
( spl0_9
<=> ( ( f @ x )
= ( f @ ( f @ x ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f487,plain,
( ( $true
= ( f @ ( f @ ( f @ $true ) ) ) )
| ~ spl0_2
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f408,f476]) ).
thf(f476,plain,
( ( $true
= ( g @ ( f @ $true ) ) )
| ~ spl0_2
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f25,f129]) ).
thf(f25,plain,
( ( ( g @ ( f @ x ) )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl0_2
<=> ( ( g @ ( f @ x ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f408,plain,
( ( ( f @ ( f @ ( f @ $true ) ) )
= ( g @ ( f @ $true ) ) )
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f9,f129]) ).
thf(f9,plain,
( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( $true
= ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( $true
= ( ( x
= ( g @ y ) )
& ( x != y )
& ( y
= ( g @ x ) )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ~ ( ( x
= ( g @ y ) )
& ( x != y )
& ( y
= ( g @ x ) )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ~ ~ ( ( x
= ( g @ y ) )
& ( x != y )
& ( y
= ( g @ x ) )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ( ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) )
& ( y
= ( g @ x ) )
& ( x != y )
& ( x
= ( g @ y ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ( ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) )
& ( y
= ( g @ x ) )
& ( x != y )
& ( x
= ( g @ y ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yFqzB6dDSE/DTF2THF_29953.p',3) ).
thf(f471,plain,
( spl0_9
| spl0_16
| ~ spl0_17
| spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f470]) ).
thf(f470,plain,
( $false
| spl0_9
| spl0_16
| ~ spl0_17
| spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f469]) ).
thf(f469,plain,
( ( $true = $false )
| spl0_9
| spl0_16
| ~ spl0_17
| spl0_21 ),
inference(forward_demodulation,[status(thm)],[f468,f464]) ).
thf(f464,plain,
( ( $false
= ( f @ ( f @ $true ) ) )
| spl0_9
| ~ spl0_17
| spl0_21 ),
inference(subsumption_resolution,[status(thm)],[f457,f404]) ).
thf(f404,plain,
( ( $false
!= ( f @ $true ) )
| ~ spl0_17
| spl0_21 ),
inference(forward_demodulation,[status(thm)],[f230,f129]) ).
thf(f230,plain,
( ( ( f @ x )
!= $false )
| spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f228]) ).
thf(f228,definition,
( spl0_21
<=> ( ( f @ x )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f457,plain,
( ( $false
= ( f @ ( f @ $true ) ) )
| ( $false
= ( f @ $true ) )
| spl0_9
| ~ spl0_17 ),
inference(binary_proxy_clausification,[status(thm)],[f440]) ).
thf(f433,plain,
( ~ spl0_1
| ~ spl0_9
| ~ spl0_17
| spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f432]) ).
thf(f432,plain,
( $false
| ~ spl0_1
| ~ spl0_9
| ~ spl0_17
| spl0_21 ),
inference(subsumption_resolution,[status(thm)],[f431,f404]) ).
thf(f431,plain,
( ( $false
= ( f @ $true ) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f365,f429]) ).
thf(f429,plain,
( ( $false
= ( f @ ( f @ $true ) ) )
| ~ spl0_1
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f419,f365]) ).
thf(f419,plain,
( ( ( f @ ( f @ ( f @ $true ) ) )
= $false )
| ~ spl0_1
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f21,f129]) ).
thf(f21,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl0_1
<=> ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f365,plain,
( ( ( f @ $true )
= ( f @ ( f @ $true ) ) )
| ~ spl0_9
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f80,f129]) ).
thf(f80,plain,
( ( ( f @ x )
= ( f @ ( f @ x ) ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f79]) ).
thf(f414,plain,
( ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[status(thm)],[f413]) ).
thf(f413,plain,
( $false
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f412]) ).
thf(f412,plain,
( ( $true = $false )
| ~ spl0_16
| ~ spl0_17
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f411,f133]) ).
thf(f133,plain,
( ( $false
= ( g @ $true ) )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f131]) ).
thf(f131,definition,
( spl0_18
<=> ( $false
= ( g @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f411,plain,
( ( $true
= ( g @ $true ) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f410,f387]) ).
thf(f387,plain,
( ( $true
= ( f @ $true ) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f123,f129]) ).
thf(f123,plain,
( ( ( f @ x )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f410,plain,
( ( ( g @ $true )
= ( f @ $true ) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f409,f387]) ).
thf(f409,plain,
( ( ( g @ $true )
= ( f @ ( f @ $true ) ) )
| ~ spl0_16
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f408,f387]) ).
thf(f391,plain,
( spl0_18
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[status(thm)],[f373,f127,f60,f131]) ).
thf(f60,definition,
( spl0_8
<=> ( ( g @ x )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f373,plain,
( ( $false
= ( g @ $true ) )
| ~ spl0_8
| ~ spl0_17 ),
inference(forward_demodulation,[status(thm)],[f62,f129]) ).
thf(f62,plain,
( ( ( g @ x )
= $false )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f376,plain,
( ~ spl0_4
| ~ spl0_9
| spl0_16
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f375]) ).
thf(f375,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| spl0_16
| ~ spl0_17 ),
inference(subsumption_resolution,[status(thm)],[f374,f362]) ).
thf(f362,plain,
( ( $true
!= ( f @ $true ) )
| spl0_16
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f124,f129]) ).
thf(f374,plain,
( ( $true
= ( f @ $true ) )
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f365,f367]) ).
thf(f367,plain,
( ( $true
= ( f @ ( f @ $true ) ) )
| ~ spl0_4
| ~ spl0_9
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f359,f365]) ).
thf(f359,plain,
( ( $true
= ( f @ ( f @ ( f @ $true ) ) ) )
| ~ spl0_4
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f34,f129]) ).
thf(f34,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl0_4
<=> ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f356,plain,
( spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f355,f32,f23]) ).
thf(f355,plain,
( ( ( g @ ( f @ x ) )
= $true )
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f9,f34]) ).
thf(f353,plain,
( spl0_17
| ~ spl0_5
| ~ spl0_22 ),
inference(avatar_split_clause,[status(thm)],[f352,f233,f47,f127]) ).
thf(f47,definition,
( spl0_5
<=> ( y = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f233,definition,
( spl0_22
<=> ( $true
= ( g @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition]) ).
thf(f352,plain,
( ( x = $true )
| ~ spl0_5
| ~ spl0_22 ),
inference(forward_demodulation,[status(thm)],[f350,f235]) ).
thf(f235,plain,
( ( $true
= ( g @ $false ) )
| ~ spl0_22 ),
inference(avatar_component_clause,[status(thm)],[f233]) ).
thf(f350,plain,
( ( x
= ( g @ $false ) )
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f15,f49]) ).
thf(f49,plain,
( ( y = $false )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f15,plain,
( x
= ( g @ y ) ),
inference(equality_proxy_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( $true
= ( x
= ( g @ y ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f11,plain,
( $true
= ( ( x
= ( g @ y ) )
& ( x != y ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( $true
= ( ( x
= ( g @ y ) )
& ( x != y )
& ( y
= ( g @ x ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f6]) ).
thf(f348,plain,
( ~ spl0_9
| ~ spl0_14
| spl0_19
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f347]) ).
thf(f347,plain,
( $false
| ~ spl0_9
| ~ spl0_14
| spl0_19
| ~ spl0_20 ),
inference(subsumption_resolution,[status(thm)],[f346,f186]) ).
thf(f186,plain,
( ( $true
!= ( f @ $false ) )
| spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f185]) ).
thf(f185,definition,
( spl0_19
<=> ( $true
= ( f @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f346,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_9
| ~ spl0_14
| ~ spl0_20 ),
inference(backward_demodulation,[status(thm)],[f339,f191]) ).
thf(f191,plain,
( ( $true
= ( f @ ( f @ $false ) ) )
| ~ spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f189]) ).
thf(f189,definition,
( spl0_20
<=> ( $true
= ( f @ ( f @ $false ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition]) ).
thf(f339,plain,
( ( ( f @ ( f @ $false ) )
= ( f @ $false ) )
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f80,f115]) ).
thf(f115,plain,
( ( x = $false )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f113,definition,
( spl0_14
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f345,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_14
| spl0_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f344]) ).
thf(f344,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_14
| spl0_20 ),
inference(subsumption_resolution,[status(thm)],[f343,f190]) ).
thf(f190,plain,
( ( $true
!= ( f @ ( f @ $false ) ) )
| spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f189]) ).
thf(f343,plain,
( ( $true
= ( f @ ( f @ $false ) ) )
| ~ spl0_4
| ~ spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f297,f339]) ).
thf(f297,plain,
( ( $true
= ( f @ ( f @ ( f @ $false ) ) ) )
| ~ spl0_4
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f34,f115]) ).
thf(f338,plain,
( ~ spl0_11
| spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f337,f113,f92,f88]) ).
thf(f88,definition,
( spl0_11
<=> ( ( f @ ( f @ $false ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f92,definition,
( spl0_12
<=> ( x
= ( f @ ( f @ x ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f337,plain,
( ( ( f @ ( f @ $false ) )
!= $false )
| spl0_12
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f94,f115]) ).
thf(f94,plain,
( ( x
!= ( f @ ( f @ x ) ) )
| spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f332,plain,
( spl0_3
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f331]) ).
thf(f331,plain,
( $false
| spl0_3
| ~ spl0_14
| ~ spl0_18
| ~ spl0_19 ),
inference(subsumption_resolution,[status(thm)],[f328,f133]) ).
thf(f328,plain,
( ( $false
!= ( g @ $true ) )
| spl0_3
| ~ spl0_14
| ~ spl0_19 ),
inference(backward_demodulation,[status(thm)],[f273,f187]) ).
thf(f187,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f185]) ).
thf(f273,plain,
( ( ( g @ ( f @ $false ) )
!= $false )
| spl0_3
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f29,f115]) ).
thf(f29,plain,
( ( ( g @ ( f @ x ) )
!= $false )
| spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl0_3
<=> ( ( g @ ( f @ x ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f321,plain,
( spl0_19
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f319,f113,f88,f32,f185]) ).
thf(f319,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_4
| ~ spl0_11
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f297,f90]) ).
thf(f90,plain,
( ( ( f @ ( f @ $false ) )
= $false )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f312,plain,
( spl0_22
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f290,f113,f51,f233]) ).
thf(f51,definition,
( spl0_6
<=> ( ( g @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f290,plain,
( ( $true
= ( g @ $false ) )
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f53,f115]) ).
thf(f53,plain,
( ( ( g @ x )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f309,plain,
( ~ spl0_13
| spl0_8
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f308,f113,f60,f97]) ).
thf(f97,definition,
( spl0_13
<=> ( $false
= ( g @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f308,plain,
( ( $false
!= ( g @ $false ) )
| spl0_8
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f61,f115]) ).
thf(f61,plain,
( ( ( g @ x )
!= $false )
| spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f302,plain,
( ~ spl0_4
| ~ spl0_10
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f301]) ).
thf(f301,plain,
( $false
| ~ spl0_4
| ~ spl0_10
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f300]) ).
thf(f300,plain,
( ( $true = $false )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f299,f85]) ).
thf(f85,plain,
( ( $false
= ( f @ $false ) )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f83,definition,
( spl0_10
<=> ( $false
= ( f @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f299,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f298,f85]) ).
thf(f298,plain,
( ( $true
= ( f @ ( f @ $false ) ) )
| ~ spl0_4
| ~ spl0_10
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f297,f85]) ).
thf(f277,plain,
( spl0_5
| ~ spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f204,f60,f47]) ).
thf(f204,plain,
( ( y = $false )
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f12,f62]) ).
thf(f12,plain,
( y
= ( g @ x ) ),
inference(equality_proxy_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
( $true
= ( y
= ( g @ x ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f255,plain,
( ~ spl0_5
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f254]) ).
thf(f254,plain,
( $false
| ~ spl0_5
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f253]) ).
thf(f253,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f252]) ).
thf(f252,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_5
| ~ spl0_14 ),
inference(boolean_simplification,[status(thm)],[f250]) ).
thf(f250,plain,
( ( $true
= ( $false != $false ) )
| ~ spl0_5
| ~ spl0_14 ),
inference(backward_demodulation,[status(thm)],[f205,f115]) ).
thf(f205,plain,
( ( $true
= ( x != $false ) )
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f13,f49]) ).
thf(f13,plain,
( ( x != y )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f11]) ).
thf(f236,plain,
( spl0_14
| spl0_22
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f215,f47,f233,f113]) ).
thf(f215,plain,
( ( x = $false )
| ( $true
= ( g @ $false ) )
| ~ spl0_5 ),
inference(binary_proxy_clausification,[status(thm)],[f201]) ).
thf(f201,plain,
( ( x
= ( g @ $false ) )
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f15,f49]) ).
thf(f231,plain,
( ~ spl0_21
| spl0_14
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f219,f47,f28,f113,f228]) ).
thf(f219,plain,
( ( x = $false )
| ( ( f @ x )
!= $false )
| ~ spl0_3
| ~ spl0_5 ),
inference(constrained_superposition,[status(thm)],[f30,f201]) ).
thf(f30,plain,
( ( ( g @ ( f @ x ) )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f197,plain,
( spl0_14
| ~ spl0_7
| ~ spl0_18 ),
inference(avatar_split_clause,[status(thm)],[f196,f131,f56,f113]) ).
thf(f56,definition,
( spl0_7
<=> ( y = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f196,plain,
( ( x = $false )
| ~ spl0_7
| ~ spl0_18 ),
inference(forward_demodulation,[status(thm)],[f74,f133]) ).
thf(f74,plain,
( ( x
= ( g @ $true ) )
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f15,f58]) ).
thf(f58,plain,
( ( y = $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f195,plain,
( spl0_9
| spl0_10
| spl0_11
| ~ spl0_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f194]) ).
thf(f194,plain,
( $false
| spl0_9
| spl0_10
| spl0_11
| ~ spl0_14 ),
inference(subsumption_resolution,[status(thm)],[f193,f84]) ).
thf(f84,plain,
( ( $false
!= ( f @ $false ) )
| spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f83]) ).
thf(f193,plain,
( ( $false
= ( f @ $false ) )
| spl0_9
| spl0_11
| ~ spl0_14 ),
inference(subsumption_resolution,[status(thm)],[f180,f89]) ).
thf(f89,plain,
( ( ( f @ ( f @ $false ) )
!= $false )
| spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f180,plain,
( ( ( f @ ( f @ $false ) )
= $false )
| ( $false
= ( f @ $false ) )
| spl0_9
| ~ spl0_14 ),
inference(binary_proxy_clausification,[status(thm)],[f156]) ).
thf(f156,plain,
( ( ( f @ ( f @ $false ) )
!= ( f @ $false ) )
| spl0_9
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f81,f115]) ).
thf(f158,plain,
( ~ spl0_10
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f157,f113,f51,f28,f83]) ).
thf(f157,plain,
( ( $false
!= ( f @ $false ) )
| ~ spl0_3
| ~ spl0_6
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f105,f115]) ).
thf(f105,plain,
( ( x
!= ( f @ x ) )
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ( x
!= ( f @ x ) )
| ( $true = $false )
| ~ spl0_3
| ~ spl0_6 ),
inference(constrained_superposition,[status(thm)],[f53,f30]) ).
thf(f154,plain,
( spl0_18
| ~ spl0_7
| ~ spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f153,f113,f56,f131]) ).
thf(f153,plain,
( ( $false
= ( g @ $true ) )
| ~ spl0_7
| ~ spl0_14 ),
inference(forward_demodulation,[status(thm)],[f74,f115]) ).
thf(f147,plain,
( ~ spl0_7
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f146]) ).
thf(f146,plain,
( $false
| ~ spl0_7
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f145]) ).
thf(f145,plain,
( ( $true = $false )
| ~ spl0_7
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f144]) ).
thf(f144,plain,
( ( $true = ( ~ $true ) )
| ~ spl0_7
| ~ spl0_17 ),
inference(boolean_simplification,[status(thm)],[f139]) ).
thf(f139,plain,
( ( $true
= ( $true != $true ) )
| ~ spl0_7
| ~ spl0_17 ),
inference(backward_demodulation,[status(thm)],[f73,f129]) ).
thf(f73,plain,
( ( $true
= ( x != $true ) )
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f13,f58]) ).
thf(f134,plain,
( spl0_17
| spl0_18
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f106,f56,f131,f127]) ).
thf(f106,plain,
( ( x = $true )
| ( $false
= ( g @ $true ) )
| ~ spl0_7 ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f100,plain,
( ~ spl0_12
| spl0_13
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f77,f28,f19,f97,f92]) ).
thf(f77,plain,
( ( x
!= ( f @ ( f @ x ) ) )
| ( $false
= ( g @ $false ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f30,f21]) ).
thf(f86,plain,
( ~ spl0_9
| spl0_10
| ~ spl0_1 ),
inference(avatar_split_clause,[status(thm)],[f76,f19,f83,f79]) ).
thf(f76,plain,
( ( ( f @ x )
!= ( f @ ( f @ x ) ) )
| ( $false
= ( f @ $false ) )
| ~ spl0_1 ),
inference(constrained_superposition,[status(thm)],[f21,f21]) ).
thf(f63,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f44,f60,f56]) ).
thf(f44,plain,
( ( y = $true )
| ( ( g @ x )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f54,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f45,f51,f47]) ).
thf(f45,plain,
( ( y = $false )
| ( ( g @ x )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f40,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f39]) ).
thf(f39,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f25,f30]) ).
thf(f37,plain,
( spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f36,f23,f32]) ).
thf(f36,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ~ spl0_2 ),
inference(backward_demodulation,[status(thm)],[f9,f25]) ).
thf(f35,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f16,f32,f28]) ).
thf(f16,plain,
( ( ( g @ ( f @ x ) )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f26,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f17,f23,f19]) ).
thf(f17,plain,
( ( ( g @ ( f @ x ) )
= $true )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO041^2 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n001.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 14:23:20 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.44 ---- Original DTF file ---
% 0.20/0.44 thf(spec,logic,$$dhol).
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 % File : SYO041^2 : TPTP v9.2.1. Released v4.1.0.
% 0.20/0.44 % Domain : Syntactic
% 0.20/0.44 % Problem : Unsatisfiable basic formula 3
% 0.20/0.44 % Version : Especial.
% 0.20/0.44 % Theorem formulation : As a conjecture rather than UNS set.
% 0.20/0.44 % English : Variant of the Kaminski equation.
% 0.20/0.44
% 0.20/0.44 % Refs : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
% 0.20/0.44 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.20/0.44 % : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.20/0.44 % Source : [BS09a]
% 0.20/0.44 % Names : basic3 [Bro09]
% 0.20/0.44
% 0.20/0.44 % Status : Theorem
% 0.20/0.44 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0
% 0.20/0.44 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.20/0.44 % Number of atoms : 19 ( 4 equ; 0 cnn)
% 0.20/0.44 % Maximal formula atoms : 4 ( 19 avg)
% 0.20/0.44 % Number of connectives : 12 ( 2 ~; 0 |; 3 &; 7 @)
% 0.20/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.44 % Maximal formula depth : 5 ( 5 avg)
% 0.20/0.44 % Number of types : 1 ( 0 usr)
% 0.20/0.44 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.44 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.20/0.44 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.20/0.44 % SPC : TH0_THM_EQU_NAR
% 0.20/0.44
% 0.20/0.44 % Comments : The fragment of simple type theory that restricts equations to
% 0.20/0.44 % base types and disallows lambda abstraction and quantification is
% 0.20/0.44 % decidable. This is an example.
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 thf(a,type,
% 0.20/0.44 a: $o ).
% 0.20/0.44
% 0.20/0.44 thf(f,type,
% 0.20/0.44 f: $o > $o ).
% 0.20/0.44
% 0.20/0.44 thf(g,type,
% 0.20/0.44 g: $o > $o ).
% 0.20/0.44
% 0.20/0.44 thf(x,type,
% 0.20/0.44 x: $o ).
% 0.20/0.44
% 0.20/0.44 thf(y,type,
% 0.20/0.44 y: $o ).
% 0.20/0.44
% 0.20/0.44 thf(3,conjecture,
% 0.20/0.44 ~ ( ( x != y )
% 0.20/0.44 & ( ( g @ x )
% 0.20/0.44 = y )
% 0.20/0.44 & ( ( g @ y )
% 0.20/0.44 = x )
% 0.20/0.44 & ( ( f @ ( f @ ( f @ x ) ) )
% 0.20/0.44 = ( g @ ( f @ x ) ) ) ) ).
% 0.20/0.44
% 0.20/0.44 %------------------------------------------------------------------------------
% 0.20/0.44 ------------------------
% 1.52/1.35 ---- Embedded in THF ---
% 1.52/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.35 %%% Generated on Tue Feb 24 14:23:21 EST 2026
% 1.52/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.35 %%% Logic specification used:
% 1.52/1.35 %%% thf(spec, logic, $$dhol).
% 1.52/1.35
% 1.52/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yFqzB6dDSE/DTF2DTF29953.p
% See solution above
% 1.52/1.35 ------------------------
% 1.52/1.36 ---- Cleaned THF ---
% 1.52/1.36 thf(a,type,
% 1.52/1.36 a: $o ).
% 1.52/1.36
% 1.52/1.36 thf(f,type,
% 1.52/1.36 f: $o > $o ).
% 1.52/1.36
% 1.52/1.36 thf(g,type,
% 1.52/1.36 g: $o > $o ).
% 1.52/1.36
% 1.52/1.36 thf(x,type,
% 1.52/1.36 x: $o ).
% 1.52/1.36
% 1.52/1.36 thf(y,type,
% 1.52/1.36 y: $o ).
% 1.52/1.36
% 1.52/1.36 thf(3,conjecture,
% 1.52/1.36 ~ ( ( x != y )
% 1.52/1.36 & ( ( g @ x )
% 1.52/1.36 = y )
% 1.52/1.36 & ( ( g @ y )
% 1.52/1.36 = x )
% 1.52/1.36 & ( ( f @ ( f @ ( f @ x ) ) )
% 1.52/1.36 = ( g @ ( f @ x ) ) ) ) ).
% 1.52/1.36 ------------------------
% 1.52/1.38 % (30051)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29953 for (3000ds/183Mi)
% 1.52/1.38 % (30055)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_29953 for (3000ds/2Mi)
% 1.52/1.38 % (30053)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_29953 for (3000ds/27Mi)
% 1.52/1.38 % (30056)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_29953 for (3000ds/275Mi)
% 1.52/1.38 % (30052)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_29953 for (3000ds/4Mi)
% 1.52/1.38 % (30054)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29953 for (3000ds/2Mi)
% 1.52/1.38 % (30057)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29953 for (3000ds/18Mi)
% 1.52/1.38 % (30054)Instruction limit reached!
% 1.52/1.38 % (30054)------------------------------
% 1.52/1.38 % (30054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.38 % (30054)Termination reason: Unknown
% 1.52/1.38 % (30054)Termination phase: Saturation
% 1.52/1.38 % (30055)Instruction limit reached!
% 1.52/1.38 % (30055)------------------------------
% 1.52/1.38 % (30055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.38 % (30055)Termination reason: Unknown
% 1.52/1.38 % (30055)Termination phase: Saturation
% 1.52/1.38
% 1.52/1.38 % (30055)Memory used [KB]: 5373
% 1.52/1.38 % (30055)Time elapsed: 0.003 s
% 1.52/1.38 % (30055)Instructions burned: 2 (million)
% 1.52/1.38 % (30055)------------------------------
% 1.52/1.38 % (30055)------------------------------
% 1.52/1.38
% 1.52/1.38 % (30054)Memory used [KB]: 5500
% 1.52/1.38 % (30054)Time elapsed: 0.003 s
% 1.52/1.38 % (30054)Instructions burned: 2 (million)
% 1.52/1.38 % (30054)------------------------------
% 1.52/1.38 % (30054)------------------------------
% 1.52/1.38 % (30056)Refutation not found, incomplete strategy
% 1.52/1.38 % (30056)------------------------------
% 1.52/1.38 % (30056)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.38 % (30056)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.38
% 1.52/1.38
% 1.52/1.39 % (30056)Memory used [KB]: 5500
% 1.52/1.39 % (30056)Time elapsed: 0.004 s
% 1.52/1.39 % (30056)Instructions burned: 3 (million)
% 1.52/1.39 % (30056)------------------------------
% 1.52/1.39 % (30056)------------------------------
% 1.52/1.39 % (30052)Instruction limit reached!
% 1.52/1.39 % (30052)------------------------------
% 1.52/1.39 % (30052)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.39 % (30052)Termination reason: Unknown
% 1.52/1.39 % (30052)Termination phase: Saturation
% 1.52/1.39
% 1.52/1.39 % (30052)Memory used [KB]: 5500
% 1.52/1.39 % (30052)Time elapsed: 0.005 s
% 1.52/1.39 % (30052)Instructions burned: 5 (million)
% 1.52/1.39 % (30052)------------------------------
% 1.52/1.39 % (30052)------------------------------
% 1.52/1.39 % (30053)Refutation not found, incomplete strategy
% 1.52/1.39 % (30053)------------------------------
% 1.52/1.39 % (30053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.39 % (30053)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.39
% 1.52/1.39
% 1.52/1.39 % (30053)Memory used [KB]: 5500
% 1.52/1.39 % (30053)Time elapsed: 0.006 s
% 1.52/1.39 % (30053)Instructions burned: 6 (million)
% 1.52/1.39 % (30053)------------------------------
% 1.52/1.39 % (30053)------------------------------
% 1.52/1.39 % (30057)Instruction limit reached!
% 1.52/1.39 % (30057)------------------------------
% 1.52/1.39 % (30057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.39 % (30057)Termination reason: Unknown
% 1.52/1.39 % (30057)Termination phase: Saturation
% 1.52/1.39
% 1.52/1.39 % (30057)Memory used [KB]: 5628
% 1.52/1.39 % (30057)Time elapsed: 0.012 s
% 1.52/1.39 % (30057)Instructions burned: 18 (million)
% 1.52/1.39 % (30057)------------------------------
% 1.52/1.39 % (30057)------------------------------
% 1.65/1.40 % (30059)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_29953 for (2999ds/37Mi)
% 1.65/1.40 % (30058)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29953 for (2999ds/3Mi)
% 1.65/1.40 % (30061)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29953 for (2999ds/3Mi)
% 1.65/1.40 % (30060)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_29953 for (2999ds/15Mi)
% 1.65/1.40 % (30058)Refutation not found, incomplete strategy
% 1.65/1.40 % (30058)------------------------------
% 1.65/1.40 % (30058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (30058)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.40
% 1.65/1.40
% 1.65/1.40 % (30058)Memory used [KB]: 5500
% 1.65/1.40 % (30058)Time elapsed: 0.003 s
% 1.65/1.40 % (30058)Instructions burned: 2 (million)
% 1.65/1.40 % (30058)------------------------------
% 1.65/1.40 % (30058)------------------------------
% 1.65/1.40 % (30061)Refutation not found, incomplete strategy
% 1.65/1.40 % (30061)------------------------------
% 1.65/1.40 % (30061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (30061)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.40
% 1.65/1.40
% 1.65/1.40 % (30061)Memory used [KB]: 5500
% 1.65/1.40 % (30061)Time elapsed: 0.002 s
% 1.65/1.40 % (30061)Instructions burned: 1 (million)
% 1.65/1.40 % (30061)------------------------------
% 1.65/1.40 % (30061)------------------------------
% 1.65/1.40 % (30062)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_29953 for (2999ds/1041Mi)
% 1.65/1.41 % (30062)Refutation not found, incomplete strategy
% 1.65/1.41 % (30062)------------------------------
% 1.65/1.41 % (30062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (30062)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.41
% 1.65/1.41
% 1.65/1.41 % (30062)Memory used [KB]: 5500
% 1.65/1.41 % (30062)Time elapsed: 0.006 s
% 1.65/1.41 % (30062)Instructions burned: 8 (million)
% 1.65/1.41 % (30062)------------------------------
% 1.65/1.41 % (30062)------------------------------
% 1.65/1.41 % (30063)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29953 for (2999ds/7Mi)
% 1.65/1.41 % (30060)Instruction limit reached!
% 1.65/1.41 % (30060)------------------------------
% 1.65/1.41 % (30060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (30060)Termination reason: Unknown
% 1.65/1.41 % (30060)Termination phase: Saturation
% 1.65/1.41
% 1.65/1.41 % (30060)Memory used [KB]: 5628
% 1.65/1.41 % (30060)Time elapsed: 0.010 s
% 1.65/1.41 % (30060)Instructions burned: 15 (million)
% 1.65/1.41 % (30060)------------------------------
% 1.65/1.41 % (30060)------------------------------
% 1.65/1.41 % (30063)Instruction limit reached!
% 1.65/1.41 % (30063)------------------------------
% 1.65/1.41 % (30063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (30063)Termination reason: Unknown
% 1.65/1.41 % (30063)Termination phase: Saturation
% 1.65/1.41
% 1.65/1.41 % (30063)Memory used [KB]: 1023
% 1.65/1.41 % (30063)Time elapsed: 0.006 s
% 1.65/1.41 % (30063)Instructions burned: 8 (million)
% 1.65/1.41 % (30063)------------------------------
% 1.65/1.41 % (30063)------------------------------
% 1.65/1.42 % (30064)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29953 for (2999ds/16Mi)
% 1.65/1.42 % (30065)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_29953 for (2999ds/3Mi)
% 1.65/1.42 % (30059)First to succeed.
% 1.65/1.42 % (30065)Refutation not found, incomplete strategy
% 1.65/1.42 % (30065)------------------------------
% 1.65/1.42 % (30065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (30065)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.42
% 1.65/1.42
% 1.65/1.42 % (30065)Memory used [KB]: 5500
% 1.65/1.42 % (30065)Time elapsed: 0.003 s
% 1.65/1.42 % (30065)Instructions burned: 1 (million)
% 1.65/1.42 % (30065)------------------------------
% 1.65/1.42 % (30065)------------------------------
% 1.65/1.42 % (30064)Also succeeded, but the first one will report.
% 1.65/1.42 % (30059)Refutation found. Thanks to Tanya!
% 1.65/1.42 % SZS status Theorem for DTF2THF_29953
% 1.65/1.42 % SZS output start Proof for DTF2THF_29953
% 1.65/1.42 thf(func_def_1, type, f: $o > $o).
% 1.65/1.42 thf(func_def_2, type, g: $o > $o).
% 1.65/1.42 thf(func_def_12, type, ph1: !>[X0: $tType]:(X0)).
% 1.65/1.42 thf(f521,plain,(
% 1.65/1.42 $false),
% 1.65/1.42 inference(avatar_sat_refutation,[status(thm)],[f26,f35,f37,f40,f54,f63,f86,f100,f134,f147,f154,f158,f195,f197,f231,f236,f255,f277,f302,f309,f312,f321,f332,f338,f345,f348,f353,f356,f376,f391,f414,f433,f471,f506])).
% 1.65/1.42 thf(f506,plain,(
% 1.65/1.42 ~spl0_2 | spl0_9 | spl0_16 | ~spl0_17),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f505])).
% 1.65/1.42 thf(f505,plain,(
% 1.65/1.42 $false | (~spl0_2 | spl0_9 | spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f504,f434])).
% 1.65/1.42 thf(f434,plain,(
% 1.65/1.42 ($true != (f @ $true)) | (spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f124,f129])).
% 1.65/1.42 thf(f129,plain,(
% 1.65/1.42 (x = $true) | ~spl0_17),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f127])).
% 1.65/1.42 thf(f127,definition,(
% 1.65/1.42 spl0_17 <=> (x = $true)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.65/1.42 thf(f124,plain,(
% 1.65/1.42 ((f @ x) != $true) | spl0_16),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f122])).
% 1.65/1.42 thf(f122,definition,(
% 1.65/1.42 spl0_16 <=> ((f @ x) = $true)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.65/1.42 thf(f504,plain,(
% 1.65/1.42 ($true = (f @ $true)) | (~spl0_2 | spl0_9 | spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f487,f468])).
% 1.65/1.42 thf(f468,plain,(
% 1.65/1.42 ($true = (f @ (f @ $true))) | (spl0_9 | spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f456,f434])).
% 1.65/1.42 thf(f456,plain,(
% 1.65/1.42 ($true = (f @ $true)) | ($true = (f @ (f @ $true))) | (spl0_9 | ~spl0_17)),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f440])).
% 1.65/1.42 thf(f440,plain,(
% 1.65/1.42 ((f @ $true) != (f @ (f @ $true))) | (spl0_9 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f81,f129])).
% 1.65/1.42 thf(f81,plain,(
% 1.65/1.42 ((f @ x) != (f @ (f @ x))) | spl0_9),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f79])).
% 1.65/1.42 thf(f79,definition,(
% 1.65/1.42 spl0_9 <=> ((f @ x) = (f @ (f @ x)))),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.65/1.42 thf(f487,plain,(
% 1.65/1.42 ($true = (f @ (f @ (f @ $true)))) | (~spl0_2 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f408,f476])).
% 1.65/1.42 thf(f476,plain,(
% 1.65/1.42 ($true = (g @ (f @ $true))) | (~spl0_2 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f25,f129])).
% 1.65/1.42 thf(f25,plain,(
% 1.65/1.42 ((g @ (f @ x)) = $true) | ~spl0_2),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.65/1.42 thf(f23,definition,(
% 1.65/1.42 spl0_2 <=> ((g @ (f @ x)) = $true)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.65/1.42 thf(f408,plain,(
% 1.65/1.42 ((f @ (f @ (f @ $true))) = (g @ (f @ $true))) | ~spl0_17),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f9,f129])).
% 1.65/1.42 thf(f9,plain,(
% 1.65/1.42 ((f @ (f @ (f @ x))) = (g @ (f @ x)))),
% 1.65/1.42 inference(equality_proxy_clausification,[status(thm)],[f7])).
% 1.65/1.42 thf(f7,plain,(
% 1.65/1.42 ($true = ((f @ (f @ (f @ x))) = (g @ (f @ x))))),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f6])).
% 1.65/1.42 thf(f6,plain,(
% 1.65/1.42 ($true = ((((x = (g @ y)) & (~ (x = y))) & (y = (g @ x))) & ((f @ (f @ (f @ x))) = (g @ (f @ x)))))),
% 1.65/1.42 inference(boolean_simplification,[status(thm)],[f5])).
% 1.65/1.42 thf(f5,plain,(
% 1.65/1.42 ((~ (~ ((((x = (g @ y)) & (~ (x = y))) & (y = (g @ x))) & ((f @ (f @ (f @ x))) = (g @ (f @ x)))))) = $true)),
% 1.65/1.42 inference(cnf_transformation,[status(thm)],[f4])).
% 1.65/1.42 thf(f4,plain,(
% 1.65/1.42 ((~ (~ ((((x = (g @ y)) & (~ (x = y))) & (y = (g @ x))) & ((f @ (f @ (f @ x))) = (g @ (f @ x)))))) = $true)),
% 1.65/1.42 inference(fool_elimination,[status(thm)],[f2])).
% 1.65/1.42 thf(f2,negated_conjecture,(
% 1.65/1.42 ~~(((f @ (f @ (f @ x))) = (g @ (f @ x))) & (y = (g @ x)) & (x != y) & (x = (g @ y)))),
% 1.65/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.65/1.42 thf(f1,conjecture,(
% 1.65/1.42 ~(((f @ (f @ (f @ x))) = (g @ (f @ x))) & (y = (g @ x)) & (x != y) & (x = (g @ y)))),
% 1.65/1.42 file('/export/starexec/sandbox2/tmp/tmp.yFqzB6dDSE/DTF2THF_29953.p',3)).
% 1.65/1.42 thf(f471,plain,(
% 1.65/1.42 spl0_9 | spl0_16 | ~spl0_17 | spl0_21),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f470])).
% 1.65/1.42 thf(f470,plain,(
% 1.65/1.42 $false | (spl0_9 | spl0_16 | ~spl0_17 | spl0_21)),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f469])).
% 1.65/1.42 thf(f469,plain,(
% 1.65/1.42 ($true = $false) | (spl0_9 | spl0_16 | ~spl0_17 | spl0_21)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f468,f464])).
% 1.65/1.42 thf(f464,plain,(
% 1.65/1.42 ($false = (f @ (f @ $true))) | (spl0_9 | ~spl0_17 | spl0_21)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f457,f404])).
% 1.65/1.42 thf(f404,plain,(
% 1.65/1.42 ($false != (f @ $true)) | (~spl0_17 | spl0_21)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f230,f129])).
% 1.65/1.42 thf(f230,plain,(
% 1.65/1.42 ((f @ x) != $false) | spl0_21),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f228])).
% 1.65/1.42 thf(f228,definition,(
% 1.65/1.42 spl0_21 <=> ((f @ x) = $false)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 1.65/1.42 thf(f457,plain,(
% 1.65/1.42 ($false = (f @ (f @ $true))) | ($false = (f @ $true)) | (spl0_9 | ~spl0_17)),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f440])).
% 1.65/1.42 thf(f433,plain,(
% 1.65/1.42 ~spl0_1 | ~spl0_9 | ~spl0_17 | spl0_21),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f432])).
% 1.65/1.42 thf(f432,plain,(
% 1.65/1.42 $false | (~spl0_1 | ~spl0_9 | ~spl0_17 | spl0_21)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f431,f404])).
% 1.65/1.42 thf(f431,plain,(
% 1.65/1.42 ($false = (f @ $true)) | (~spl0_1 | ~spl0_9 | ~spl0_17)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f365,f429])).
% 1.65/1.42 thf(f429,plain,(
% 1.65/1.42 ($false = (f @ (f @ $true))) | (~spl0_1 | ~spl0_9 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f419,f365])).
% 1.65/1.42 thf(f419,plain,(
% 1.65/1.42 ((f @ (f @ (f @ $true))) = $false) | (~spl0_1 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f21,f129])).
% 1.65/1.42 thf(f21,plain,(
% 1.65/1.42 ((f @ (f @ (f @ x))) = $false) | ~spl0_1),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.65/1.42 thf(f19,definition,(
% 1.65/1.42 spl0_1 <=> ((f @ (f @ (f @ x))) = $false)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.65/1.42 thf(f365,plain,(
% 1.65/1.42 ((f @ $true) = (f @ (f @ $true))) | (~spl0_9 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f80,f129])).
% 1.65/1.42 thf(f80,plain,(
% 1.65/1.42 ((f @ x) = (f @ (f @ x))) | ~spl0_9),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f79])).
% 1.65/1.42 thf(f414,plain,(
% 1.65/1.42 ~spl0_16 | ~spl0_17 | ~spl0_18),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f413])).
% 1.65/1.42 thf(f413,plain,(
% 1.65/1.42 $false | (~spl0_16 | ~spl0_17 | ~spl0_18)),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f412])).
% 1.65/1.42 thf(f412,plain,(
% 1.65/1.42 ($true = $false) | (~spl0_16 | ~spl0_17 | ~spl0_18)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f411,f133])).
% 1.65/1.42 thf(f133,plain,(
% 1.65/1.42 ($false = (g @ $true)) | ~spl0_18),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f131])).
% 1.65/1.42 thf(f131,definition,(
% 1.65/1.42 spl0_18 <=> ($false = (g @ $true))),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.65/1.42 thf(f411,plain,(
% 1.65/1.42 ($true = (g @ $true)) | (~spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f410,f387])).
% 1.65/1.42 thf(f387,plain,(
% 1.65/1.42 ($true = (f @ $true)) | (~spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f123,f129])).
% 1.65/1.42 thf(f123,plain,(
% 1.65/1.42 ((f @ x) = $true) | ~spl0_16),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f122])).
% 1.65/1.42 thf(f410,plain,(
% 1.65/1.42 ((g @ $true) = (f @ $true)) | (~spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f409,f387])).
% 1.65/1.42 thf(f409,plain,(
% 1.65/1.42 ((g @ $true) = (f @ (f @ $true))) | (~spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f408,f387])).
% 1.65/1.42 thf(f391,plain,(
% 1.65/1.42 spl0_18 | ~spl0_8 | ~spl0_17),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f373,f127,f60,f131])).
% 1.65/1.42 thf(f60,definition,(
% 1.65/1.42 spl0_8 <=> ((g @ x) = $false)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.65/1.42 thf(f373,plain,(
% 1.65/1.42 ($false = (g @ $true)) | (~spl0_8 | ~spl0_17)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f62,f129])).
% 1.65/1.42 thf(f62,plain,(
% 1.65/1.42 ((g @ x) = $false) | ~spl0_8),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.65/1.42 thf(f376,plain,(
% 1.65/1.42 ~spl0_4 | ~spl0_9 | spl0_16 | ~spl0_17),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f375])).
% 1.65/1.42 thf(f375,plain,(
% 1.65/1.42 $false | (~spl0_4 | ~spl0_9 | spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f374,f362])).
% 1.65/1.42 thf(f362,plain,(
% 1.65/1.42 ($true != (f @ $true)) | (spl0_16 | ~spl0_17)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f124,f129])).
% 1.65/1.42 thf(f374,plain,(
% 1.65/1.42 ($true = (f @ $true)) | (~spl0_4 | ~spl0_9 | ~spl0_17)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f365,f367])).
% 1.65/1.42 thf(f367,plain,(
% 1.65/1.42 ($true = (f @ (f @ $true))) | (~spl0_4 | ~spl0_9 | ~spl0_17)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f359,f365])).
% 1.65/1.42 thf(f359,plain,(
% 1.65/1.42 ($true = (f @ (f @ (f @ $true)))) | (~spl0_4 | ~spl0_17)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f34,f129])).
% 1.65/1.42 thf(f34,plain,(
% 1.65/1.42 ((f @ (f @ (f @ x))) = $true) | ~spl0_4),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.65/1.42 thf(f32,definition,(
% 1.65/1.42 spl0_4 <=> ((f @ (f @ (f @ x))) = $true)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.65/1.42 thf(f356,plain,(
% 1.65/1.42 spl0_2 | ~spl0_4),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f355,f32,f23])).
% 1.65/1.42 thf(f355,plain,(
% 1.65/1.42 ((g @ (f @ x)) = $true) | ~spl0_4),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f9,f34])).
% 1.65/1.42 thf(f353,plain,(
% 1.65/1.42 spl0_17 | ~spl0_5 | ~spl0_22),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f352,f233,f47,f127])).
% 1.65/1.42 thf(f47,definition,(
% 1.65/1.42 spl0_5 <=> (y = $false)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.65/1.42 thf(f233,definition,(
% 1.65/1.42 spl0_22 <=> ($true = (g @ $false))),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition])).
% 1.65/1.42 thf(f352,plain,(
% 1.65/1.42 (x = $true) | (~spl0_5 | ~spl0_22)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f350,f235])).
% 1.65/1.42 thf(f235,plain,(
% 1.65/1.42 ($true = (g @ $false)) | ~spl0_22),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f233])).
% 1.65/1.42 thf(f350,plain,(
% 1.65/1.42 (x = (g @ $false)) | ~spl0_5),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f15,f49])).
% 1.65/1.42 thf(f49,plain,(
% 1.65/1.42 (y = $false) | ~spl0_5),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.65/1.42 thf(f15,plain,(
% 1.65/1.42 (x = (g @ y))),
% 1.65/1.42 inference(equality_proxy_clausification,[status(thm)],[f14])).
% 1.65/1.42 thf(f14,plain,(
% 1.65/1.42 ($true = (x = (g @ y)))),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.65/1.42 thf(f11,plain,(
% 1.65/1.42 ($true = ((x = (g @ y)) & (~ (x = y))))),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.65/1.42 thf(f8,plain,(
% 1.65/1.42 ($true = (((x = (g @ y)) & (~ (x = y))) & (y = (g @ x))))),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f6])).
% 1.65/1.42 thf(f348,plain,(
% 1.65/1.42 ~spl0_9 | ~spl0_14 | spl0_19 | ~spl0_20),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f347])).
% 1.65/1.42 thf(f347,plain,(
% 1.65/1.42 $false | (~spl0_9 | ~spl0_14 | spl0_19 | ~spl0_20)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f346,f186])).
% 1.65/1.42 thf(f186,plain,(
% 1.65/1.42 ($true != (f @ $false)) | spl0_19),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f185])).
% 1.65/1.42 thf(f185,definition,(
% 1.65/1.42 spl0_19 <=> ($true = (f @ $false))),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 1.65/1.42 thf(f346,plain,(
% 1.65/1.42 ($true = (f @ $false)) | (~spl0_9 | ~spl0_14 | ~spl0_20)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f339,f191])).
% 1.65/1.42 thf(f191,plain,(
% 1.65/1.42 ($true = (f @ (f @ $false))) | ~spl0_20),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f189])).
% 1.65/1.42 thf(f189,definition,(
% 1.65/1.42 spl0_20 <=> ($true = (f @ (f @ $false)))),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
% 1.65/1.42 thf(f339,plain,(
% 1.65/1.42 ((f @ (f @ $false)) = (f @ $false)) | (~spl0_9 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f80,f115])).
% 1.65/1.42 thf(f115,plain,(
% 1.65/1.42 (x = $false) | ~spl0_14),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f113])).
% 1.65/1.42 thf(f113,definition,(
% 1.65/1.42 spl0_14 <=> (x = $false)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.65/1.42 thf(f345,plain,(
% 1.65/1.42 ~spl0_4 | ~spl0_9 | ~spl0_14 | spl0_20),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f344])).
% 1.65/1.42 thf(f344,plain,(
% 1.65/1.42 $false | (~spl0_4 | ~spl0_9 | ~spl0_14 | spl0_20)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f343,f190])).
% 1.65/1.42 thf(f190,plain,(
% 1.65/1.42 ($true != (f @ (f @ $false))) | spl0_20),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f189])).
% 1.65/1.42 thf(f343,plain,(
% 1.65/1.42 ($true = (f @ (f @ $false))) | (~spl0_4 | ~spl0_9 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f297,f339])).
% 1.65/1.42 thf(f297,plain,(
% 1.65/1.42 ($true = (f @ (f @ (f @ $false)))) | (~spl0_4 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f34,f115])).
% 1.65/1.42 thf(f338,plain,(
% 1.65/1.42 ~spl0_11 | spl0_12 | ~spl0_14),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f337,f113,f92,f88])).
% 1.65/1.42 thf(f88,definition,(
% 1.65/1.42 spl0_11 <=> ((f @ (f @ $false)) = $false)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.65/1.42 thf(f92,definition,(
% 1.65/1.42 spl0_12 <=> (x = (f @ (f @ x)))),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.65/1.42 thf(f337,plain,(
% 1.65/1.42 ((f @ (f @ $false)) != $false) | (spl0_12 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f94,f115])).
% 1.65/1.42 thf(f94,plain,(
% 1.65/1.42 (x != (f @ (f @ x))) | spl0_12),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.65/1.42 thf(f332,plain,(
% 1.65/1.42 spl0_3 | ~spl0_14 | ~spl0_18 | ~spl0_19),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f331])).
% 1.65/1.42 thf(f331,plain,(
% 1.65/1.42 $false | (spl0_3 | ~spl0_14 | ~spl0_18 | ~spl0_19)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f328,f133])).
% 1.65/1.42 thf(f328,plain,(
% 1.65/1.42 ($false != (g @ $true)) | (spl0_3 | ~spl0_14 | ~spl0_19)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f273,f187])).
% 1.65/1.42 thf(f187,plain,(
% 1.65/1.42 ($true = (f @ $false)) | ~spl0_19),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f185])).
% 1.65/1.42 thf(f273,plain,(
% 1.65/1.42 ((g @ (f @ $false)) != $false) | (spl0_3 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f29,f115])).
% 1.65/1.42 thf(f29,plain,(
% 1.65/1.42 ((g @ (f @ x)) != $false) | spl0_3),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.65/1.42 thf(f28,definition,(
% 1.65/1.42 spl0_3 <=> ((g @ (f @ x)) = $false)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.65/1.42 thf(f321,plain,(
% 1.65/1.42 spl0_19 | ~spl0_4 | ~spl0_11 | ~spl0_14),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f319,f113,f88,f32,f185])).
% 1.65/1.42 thf(f319,plain,(
% 1.65/1.42 ($true = (f @ $false)) | (~spl0_4 | ~spl0_11 | ~spl0_14)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f297,f90])).
% 1.65/1.42 thf(f90,plain,(
% 1.65/1.42 ((f @ (f @ $false)) = $false) | ~spl0_11),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.65/1.42 thf(f312,plain,(
% 1.65/1.42 spl0_22 | ~spl0_6 | ~spl0_14),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f290,f113,f51,f233])).
% 1.65/1.42 thf(f51,definition,(
% 1.65/1.42 spl0_6 <=> ((g @ x) = $true)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.65/1.42 thf(f290,plain,(
% 1.65/1.42 ($true = (g @ $false)) | (~spl0_6 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f53,f115])).
% 1.65/1.42 thf(f53,plain,(
% 1.65/1.42 ((g @ x) = $true) | ~spl0_6),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.65/1.42 thf(f309,plain,(
% 1.65/1.42 ~spl0_13 | spl0_8 | ~spl0_14),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f308,f113,f60,f97])).
% 1.65/1.42 thf(f97,definition,(
% 1.65/1.42 spl0_13 <=> ($false = (g @ $false))),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.65/1.42 thf(f308,plain,(
% 1.65/1.42 ($false != (g @ $false)) | (spl0_8 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f61,f115])).
% 1.65/1.42 thf(f61,plain,(
% 1.65/1.42 ((g @ x) != $false) | spl0_8),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.65/1.42 thf(f302,plain,(
% 1.65/1.42 ~spl0_4 | ~spl0_10 | ~spl0_14),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f301])).
% 1.65/1.42 thf(f301,plain,(
% 1.65/1.42 $false | (~spl0_4 | ~spl0_10 | ~spl0_14)),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f300])).
% 1.65/1.42 thf(f300,plain,(
% 1.65/1.42 ($true = $false) | (~spl0_4 | ~spl0_10 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f299,f85])).
% 1.65/1.42 thf(f85,plain,(
% 1.65/1.42 ($false = (f @ $false)) | ~spl0_10),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.65/1.42 thf(f83,definition,(
% 1.65/1.42 spl0_10 <=> ($false = (f @ $false))),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.65/1.42 thf(f299,plain,(
% 1.65/1.42 ($true = (f @ $false)) | (~spl0_4 | ~spl0_10 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f298,f85])).
% 1.65/1.42 thf(f298,plain,(
% 1.65/1.42 ($true = (f @ (f @ $false))) | (~spl0_4 | ~spl0_10 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f297,f85])).
% 1.65/1.42 thf(f277,plain,(
% 1.65/1.42 spl0_5 | ~spl0_8),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f204,f60,f47])).
% 1.65/1.42 thf(f204,plain,(
% 1.65/1.42 (y = $false) | ~spl0_8),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f12,f62])).
% 1.65/1.42 thf(f12,plain,(
% 1.65/1.42 (y = (g @ x))),
% 1.65/1.42 inference(equality_proxy_clausification,[status(thm)],[f10])).
% 1.65/1.42 thf(f10,plain,(
% 1.65/1.42 ($true = (y = (g @ x)))),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.65/1.42 thf(f255,plain,(
% 1.65/1.42 ~spl0_5 | ~spl0_14),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f254])).
% 1.65/1.42 thf(f254,plain,(
% 1.65/1.42 $false | (~spl0_5 | ~spl0_14)),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f253])).
% 1.65/1.42 thf(f253,plain,(
% 1.65/1.42 ($true = $false) | (~spl0_5 | ~spl0_14)),
% 1.65/1.42 inference(boolean_simplification,[status(thm)],[f252])).
% 1.65/1.42 thf(f252,plain,(
% 1.65/1.42 ($true = (~ $true)) | (~spl0_5 | ~spl0_14)),
% 1.65/1.42 inference(boolean_simplification,[status(thm)],[f250])).
% 1.65/1.42 thf(f250,plain,(
% 1.65/1.42 ($true = (~ ($false = $false))) | (~spl0_5 | ~spl0_14)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f205,f115])).
% 1.65/1.42 thf(f205,plain,(
% 1.65/1.42 ($true = (~ (x = $false))) | ~spl0_5),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f13,f49])).
% 1.65/1.42 thf(f13,plain,(
% 1.65/1.42 ((~ (x = y)) = $true)),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f11])).
% 1.65/1.42 thf(f236,plain,(
% 1.65/1.42 spl0_14 | spl0_22 | ~spl0_5),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f215,f47,f233,f113])).
% 1.65/1.42 thf(f215,plain,(
% 1.65/1.42 (x = $false) | ($true = (g @ $false)) | ~spl0_5),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f201])).
% 1.65/1.42 thf(f201,plain,(
% 1.65/1.42 (x = (g @ $false)) | ~spl0_5),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f15,f49])).
% 1.65/1.42 thf(f231,plain,(
% 1.65/1.42 ~spl0_21 | spl0_14 | ~spl0_3 | ~spl0_5),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f219,f47,f28,f113,f228])).
% 1.65/1.42 thf(f219,plain,(
% 1.65/1.42 (x = $false) | ((f @ x) != $false) | (~spl0_3 | ~spl0_5)),
% 1.65/1.42 inference(constrained_superposition,[status(thm)],[f30,f201])).
% 1.65/1.42 thf(f30,plain,(
% 1.65/1.42 ((g @ (f @ x)) = $false) | ~spl0_3),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.65/1.42 thf(f197,plain,(
% 1.65/1.42 spl0_14 | ~spl0_7 | ~spl0_18),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f196,f131,f56,f113])).
% 1.65/1.42 thf(f56,definition,(
% 1.65/1.42 spl0_7 <=> (y = $true)),
% 1.65/1.42 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.65/1.42 thf(f196,plain,(
% 1.65/1.42 (x = $false) | (~spl0_7 | ~spl0_18)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f74,f133])).
% 1.65/1.42 thf(f74,plain,(
% 1.65/1.42 (x = (g @ $true)) | ~spl0_7),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f15,f58])).
% 1.65/1.42 thf(f58,plain,(
% 1.65/1.42 (y = $true) | ~spl0_7),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.65/1.42 thf(f195,plain,(
% 1.65/1.42 spl0_9 | spl0_10 | spl0_11 | ~spl0_14),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f194])).
% 1.65/1.42 thf(f194,plain,(
% 1.65/1.42 $false | (spl0_9 | spl0_10 | spl0_11 | ~spl0_14)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f193,f84])).
% 1.65/1.42 thf(f84,plain,(
% 1.65/1.42 ($false != (f @ $false)) | spl0_10),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f83])).
% 1.65/1.42 thf(f193,plain,(
% 1.65/1.42 ($false = (f @ $false)) | (spl0_9 | spl0_11 | ~spl0_14)),
% 1.65/1.42 inference(subsumption_resolution,[status(thm)],[f180,f89])).
% 1.65/1.42 thf(f89,plain,(
% 1.65/1.42 ((f @ (f @ $false)) != $false) | spl0_11),
% 1.65/1.42 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.65/1.42 thf(f180,plain,(
% 1.65/1.42 ((f @ (f @ $false)) = $false) | ($false = (f @ $false)) | (spl0_9 | ~spl0_14)),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f156])).
% 1.65/1.42 thf(f156,plain,(
% 1.65/1.42 ((f @ (f @ $false)) != (f @ $false)) | (spl0_9 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f81,f115])).
% 1.65/1.42 thf(f158,plain,(
% 1.65/1.42 ~spl0_10 | ~spl0_3 | ~spl0_6 | ~spl0_14),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f157,f113,f51,f28,f83])).
% 1.65/1.42 thf(f157,plain,(
% 1.65/1.42 ($false != (f @ $false)) | (~spl0_3 | ~spl0_6 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f105,f115])).
% 1.65/1.42 thf(f105,plain,(
% 1.65/1.42 (x != (f @ x)) | (~spl0_3 | ~spl0_6)),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.65/1.42 thf(f102,plain,(
% 1.65/1.42 (x != (f @ x)) | ($true = $false) | (~spl0_3 | ~spl0_6)),
% 1.65/1.42 inference(constrained_superposition,[status(thm)],[f53,f30])).
% 1.65/1.42 thf(f154,plain,(
% 1.65/1.42 spl0_18 | ~spl0_7 | ~spl0_14),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f153,f113,f56,f131])).
% 1.65/1.42 thf(f153,plain,(
% 1.65/1.42 ($false = (g @ $true)) | (~spl0_7 | ~spl0_14)),
% 1.65/1.42 inference(forward_demodulation,[status(thm)],[f74,f115])).
% 1.65/1.42 thf(f147,plain,(
% 1.65/1.42 ~spl0_7 | ~spl0_17),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f146])).
% 1.65/1.42 thf(f146,plain,(
% 1.65/1.42 $false | (~spl0_7 | ~spl0_17)),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f145])).
% 1.65/1.42 thf(f145,plain,(
% 1.65/1.42 ($true = $false) | (~spl0_7 | ~spl0_17)),
% 1.65/1.42 inference(boolean_simplification,[status(thm)],[f144])).
% 1.65/1.42 thf(f144,plain,(
% 1.65/1.42 ($true = (~ $true)) | (~spl0_7 | ~spl0_17)),
% 1.65/1.42 inference(boolean_simplification,[status(thm)],[f139])).
% 1.65/1.42 thf(f139,plain,(
% 1.65/1.42 ($true = (~ ($true = $true))) | (~spl0_7 | ~spl0_17)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f73,f129])).
% 1.65/1.42 thf(f73,plain,(
% 1.65/1.42 ($true = (~ (x = $true))) | ~spl0_7),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f13,f58])).
% 1.65/1.42 thf(f134,plain,(
% 1.65/1.42 spl0_17 | spl0_18 | ~spl0_7),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f106,f56,f131,f127])).
% 1.65/1.42 thf(f106,plain,(
% 1.65/1.42 (x = $true) | ($false = (g @ $true)) | ~spl0_7),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.65/1.42 thf(f100,plain,(
% 1.65/1.42 ~spl0_12 | spl0_13 | ~spl0_1 | ~spl0_3),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f77,f28,f19,f97,f92])).
% 1.65/1.42 thf(f77,plain,(
% 1.65/1.42 (x != (f @ (f @ x))) | ($false = (g @ $false)) | (~spl0_1 | ~spl0_3)),
% 1.65/1.42 inference(constrained_superposition,[status(thm)],[f30,f21])).
% 1.65/1.42 thf(f86,plain,(
% 1.65/1.42 ~spl0_9 | spl0_10 | ~spl0_1),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f76,f19,f83,f79])).
% 1.65/1.42 thf(f76,plain,(
% 1.65/1.42 ((f @ x) != (f @ (f @ x))) | ($false = (f @ $false)) | ~spl0_1),
% 1.65/1.42 inference(constrained_superposition,[status(thm)],[f21,f21])).
% 1.65/1.42 thf(f63,plain,(
% 1.65/1.42 spl0_7 | spl0_8),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f44,f60,f56])).
% 1.65/1.42 thf(f44,plain,(
% 1.65/1.42 (y = $true) | ((g @ x) = $false)),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.65/1.42 thf(f54,plain,(
% 1.65/1.42 spl0_5 | spl0_6),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f45,f51,f47])).
% 1.65/1.42 thf(f45,plain,(
% 1.65/1.42 (y = $false) | ((g @ x) = $true)),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.65/1.42 thf(f40,plain,(
% 1.65/1.42 ~spl0_2 | ~spl0_3),
% 1.65/1.42 inference(avatar_contradiction_clause,[status(thm)],[f39])).
% 1.65/1.42 thf(f39,plain,(
% 1.65/1.42 $false | (~spl0_2 | ~spl0_3)),
% 1.65/1.42 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.65/1.42 thf(f38,plain,(
% 1.65/1.42 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f25,f30])).
% 1.65/1.42 thf(f37,plain,(
% 1.65/1.42 spl0_4 | ~spl0_2),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f36,f23,f32])).
% 1.65/1.42 thf(f36,plain,(
% 1.65/1.42 ((f @ (f @ (f @ x))) = $true) | ~spl0_2),
% 1.65/1.42 inference(backward_demodulation,[status(thm)],[f9,f25])).
% 1.65/1.42 thf(f35,plain,(
% 1.65/1.42 spl0_3 | spl0_4),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f16,f32,f28])).
% 1.65/1.42 thf(f16,plain,(
% 1.65/1.42 ((g @ (f @ x)) = $false) | ((f @ (f @ (f @ x))) = $true)),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.65/1.42 thf(f26,plain,(
% 1.65/1.42 spl0_1 | spl0_2),
% 1.65/1.42 inference(avatar_split_clause,[status(thm)],[f17,f23,f19])).
% 1.65/1.42 thf(f17,plain,(
% 1.65/1.42 ((g @ (f @ x)) = $true) | ((f @ (f @ (f @ x))) = $false)),
% 1.65/1.42 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.65/1.42 % SZS output end Proof for DTF2THF_29953
% 1.65/1.42 % (30059)------------------------------
% 1.65/1.42 % (30059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.42 % (30059)Termination reason: Refutation
% 1.65/1.42
% 1.65/1.42 % (30059)Memory used [KB]: 5756
% 1.65/1.42 % (30059)Time elapsed: 0.023 s
% 1.65/1.42 % (30059)Instructions burned: 33 (million)
% 1.65/1.42 % (30059)------------------------------
% 1.65/1.42 % (30059)------------------------------
% 1.65/1.42 % (30050)Success in time 0.046 s
%------------------------------------------------------------------------------