%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO041^1 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n014.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 : Unsatisfiable 1.63s 1.36s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 148 ( 8 unt; 0 typ; 15 def)
% Number of atoms : 1012 ( 156 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 786 ( 234 ~; 303 |; 3 &; 231 @)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 19 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_9,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f2533,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f33,f42,f51,f56,f61,f67,f349,f362,f406,f416,f428,f433,f495,f640,f667,f704,f2167,f2252,f2304,f2373,f2383,f2460,f2532]) ).
thf(f2532,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_9
| spl0_10
| spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f2531]) ).
thf(f2531,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_6
| ~ spl0_9
| spl0_10
| spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f2506,f55]) ).
thf(f55,plain,
( ( ( g @ y )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl0_9
<=> ( ( g @ y )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f2506,plain,
( ( ( g @ y )
!= $true )
| ~ spl0_1
| spl0_2
| ~ spl0_6
| spl0_10
| spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f2502]) ).
thf(f2502,plain,
( ( $false != $false )
| ( ( g @ y )
!= $true )
| ~ spl0_1
| spl0_2
| ~ spl0_6
| spl0_10
| spl0_13 ),
inference(constrained_superposition,[status(thm)],[f2466,f41]) ).
thf(f41,plain,
( ( $false
= ( g @ ( g @ y ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl0_6
<=> ( $false
= ( g @ ( g @ y ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f2466,plain,
( ( $false
!= ( g @ $true ) )
| ~ spl0_1
| spl0_2
| spl0_10
| spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f2465,f59]) ).
thf(f59,plain,
( ( ( g @ y )
!= $false )
| spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl0_10
<=> ( ( g @ y )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f2465,plain,
( ( ( g @ y )
= $false )
| ( $false
!= ( g @ $true ) )
| ~ spl0_1
| spl0_2
| spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f2404,f360]) ).
thf(f360,plain,
( ( ( f @ ( f @ ( g @ y ) ) )
!= $false )
| spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f359]) ).
thf(f359,definition,
( spl0_13
<=> ( ( f @ ( f @ ( g @ y ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f2404,plain,
( ( ( f @ ( f @ ( g @ y ) ) )
= $false )
| ( $false
!= ( g @ $true ) )
| ( ( g @ y )
= $false )
| ~ spl0_1
| spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f2391]) ).
thf(f2391,plain,
( ( $false
!= ( g @ $true ) )
| ( ( g @ y )
!= ( f @ ( f @ ( g @ y ) ) ) )
| ~ spl0_1
| spl0_2 ),
inference(constrained_superposition,[status(thm)],[f22,f19]) ).
thf(f19,plain,
( ( $true
= ( f @ ( f @ ( f @ ( g @ y ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl0_1
<=> ( $true
= ( f @ ( f @ ( f @ ( g @ y ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f22,plain,
( ( $false
!= ( g @ ( f @ ( g @ y ) ) ) )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl0_2
<=> ( $false
= ( g @ ( f @ ( g @ y ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f2460,plain,
( spl0_2
| spl0_7
| ~ spl0_10
| spl0_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f2459]) ).
thf(f2459,plain,
( $false
| spl0_2
| spl0_7
| ~ spl0_10
| spl0_11 ),
inference(subsumption_resolution,[status(thm)],[f2458,f352]) ).
thf(f352,plain,
( ( $false
!= ( f @ $false ) )
| spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f351]) ).
thf(f351,definition,
( spl0_11
<=> ( $false
= ( f @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f2458,plain,
( ( $false
= ( f @ $false ) )
| spl0_2
| spl0_7
| ~ spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f2455,f45]) ).
thf(f45,plain,
( ( y != $false )
| spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl0_7
<=> ( y = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f2455,plain,
( ( y = $false )
| ( $false
= ( f @ $false ) )
| spl0_2
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f2453]) ).
thf(f2453,plain,
( ( y
!= ( f @ $false ) )
| spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f2446]) ).
thf(f2446,plain,
( ( $false != $false )
| ( y
!= ( f @ $false ) )
| spl0_2
| ~ spl0_10 ),
inference(constrained_superposition,[status(thm)],[f2387,f60]) ).
thf(f60,plain,
( ( ( g @ y )
= $false )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f2387,plain,
( ( ( g @ ( f @ $false ) )
!= $false )
| spl0_2
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f22,f60]) ).
thf(f2383,plain,
( ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f2382]) ).
thf(f2382,plain,
( $false
| ~ spl0_1
| ~ spl0_11
| ~ spl0_12
| spl0_21 ),
inference(subsumption_resolution,[status(thm)],[f2381,f357]) ).
thf(f357,plain,
( ( $false
= ( f @ ( g @ y ) ) )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f355]) ).
thf(f355,definition,
( spl0_12
<=> ( $false
= ( f @ ( g @ y ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f2381,plain,
( ( $false
!= ( f @ ( g @ y ) ) )
| ~ spl0_1
| ~ spl0_11
| spl0_21 ),
inference(subsumption_resolution,[status(thm)],[f2339,f2211]) ).
thf(f2211,plain,
( ( $true
!= ( f @ $false ) )
| spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f2210]) ).
thf(f2210,definition,
( spl0_21
<=> ( $true
= ( f @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f2339,plain,
( ( $true
= ( f @ $false ) )
| ( $false
!= ( f @ ( g @ y ) ) )
| ~ spl0_1
| ~ spl0_11 ),
inference(constrained_superposition,[status(thm)],[f19,f353]) ).
thf(f353,plain,
( ( $false
= ( f @ $false ) )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f351]) ).
thf(f2373,plain,
( ~ spl0_11
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f2372]) ).
thf(f2372,plain,
( $false
| ~ spl0_11
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f2361]) ).
thf(f2361,plain,
( ( $true = $false )
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f2212,f353]) ).
thf(f2212,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f2210]) ).
thf(f2304,plain,
( spl0_21
| ~ spl0_1
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f1532,f359,f17,f2210]) ).
thf(f1532,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_1
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f19,f361]) ).
thf(f361,plain,
( ( ( f @ ( f @ ( g @ y ) ) )
= $false )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f359]) ).
thf(f2252,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f2251]) ).
thf(f2251,plain,
( $false
| spl0_11
| ~ spl0_12
| ~ spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f1143,f357]) ).
thf(f1143,plain,
( ( $false
!= ( f @ ( g @ y ) ) )
| spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f1123]) ).
thf(f1123,plain,
( ( $false
!= ( f @ ( g @ y ) ) )
| ( $false != $false )
| spl0_11
| ~ spl0_13 ),
inference(constrained_superposition,[status(thm)],[f352,f361]) ).
thf(f2167,plain,
( ~ spl0_3
| spl0_11
| ~ spl0_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f2166]) ).
thf(f2166,plain,
( $false
| ~ spl0_3
| spl0_11
| ~ spl0_13 ),
inference(subsumption_resolution,[status(thm)],[f2025,f361]) ).
thf(f2025,plain,
( ( ( f @ ( f @ ( g @ y ) ) )
!= $false )
| ~ spl0_3
| spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f1965]) ).
thf(f1965,plain,
( ( $false != $false )
| ( ( f @ ( f @ ( g @ y ) ) )
!= $false )
| ~ spl0_3
| spl0_11 ),
inference(constrained_superposition,[status(thm)],[f352,f28]) ).
thf(f28,plain,
( ( $false
= ( f @ ( f @ ( f @ ( g @ y ) ) ) ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl0_3
<=> ( $false
= ( f @ ( f @ ( f @ ( g @ y ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f704,plain,
( ~ spl0_2
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f703]) ).
thf(f703,plain,
( $false
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f676]) ).
thf(f676,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f32,f23]) ).
thf(f23,plain,
( ( $false
= ( g @ ( f @ ( g @ y ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f32,plain,
( ( $true
= ( g @ ( f @ ( g @ y ) ) ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl0_4
<=> ( $true
= ( g @ ( f @ ( g @ y ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f667,plain,
( ~ spl0_11
| ~ spl0_2
| spl0_7
| spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f666,f355,f44,f21,f351]) ).
thf(f666,plain,
( ( $false
!= ( f @ $false ) )
| ~ spl0_2
| spl0_7
| spl0_12 ),
inference(subsumption_resolution,[status(thm)],[f665,f45]) ).
thf(f665,plain,
( ( y = $false )
| ( $false
!= ( f @ $false ) )
| ~ spl0_2
| spl0_12 ),
inference(subsumption_resolution,[status(thm)],[f659,f356]) ).
thf(f356,plain,
( ( $false
!= ( f @ ( g @ y ) ) )
| spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f355]) ).
thf(f659,plain,
( ( $false
= ( f @ ( g @ y ) ) )
| ( y = $false )
| ( $false
!= ( f @ $false ) )
| ~ spl0_2
| spl0_12 ),
inference(binary_proxy_clausification,[status(thm)],[f650]) ).
thf(f650,plain,
( ( y
!= ( f @ ( g @ y ) ) )
| ( $false
!= ( f @ $false ) )
| ~ spl0_2
| spl0_12 ),
inference(constrained_superposition,[status(thm)],[f356,f23]) ).
thf(f640,plain,
( ~ spl0_12
| ~ spl0_2
| spl0_17 ),
inference(avatar_split_clause,[status(thm)],[f617,f413,f21,f355]) ).
thf(f413,definition,
( spl0_17
<=> ( $false
= ( g @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f617,plain,
( ( $false
!= ( f @ ( g @ y ) ) )
| ~ spl0_2
| spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f593]) ).
thf(f593,plain,
( ( $false
!= ( f @ ( g @ y ) ) )
| ( $false != $false )
| ~ spl0_2
| spl0_17 ),
inference(constrained_superposition,[status(thm)],[f414,f23]) ).
thf(f414,plain,
( ( $false
!= ( g @ $false ) )
| spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f413]) ).
thf(f495,plain,
( ~ spl0_8
| ~ spl0_10
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[status(thm)],[f494]) ).
thf(f494,plain,
( $false
| ~ spl0_8
| ~ spl0_10
| ~ spl0_17 ),
inference(subsumption_resolution,[status(thm)],[f479,f60]) ).
thf(f479,plain,
( ( ( g @ y )
!= $false )
| ~ spl0_8
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f465]) ).
thf(f465,plain,
( ( $true = $false )
| ( ( g @ y )
!= $false )
| ~ spl0_8
| ~ spl0_17 ),
inference(constrained_superposition,[status(thm)],[f415,f50]) ).
thf(f50,plain,
( ( $true
= ( g @ ( g @ y ) ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl0_8
<=> ( $true
= ( g @ ( g @ y ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f415,plain,
( ( $false
= ( g @ $false ) )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f413]) ).
thf(f433,plain,
( spl0_12
| spl0_2
| spl0_7
| ~ spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f432,f58,f44,f21,f355]) ).
thf(f432,plain,
( ( $false
= ( f @ ( g @ y ) ) )
| spl0_2
| spl0_7
| ~ spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f426,f45]) ).
thf(f426,plain,
( ( y = $false )
| ( $false
= ( f @ ( g @ y ) ) )
| spl0_2
| ~ spl0_10 ),
inference(binary_proxy_clausification,[status(thm)],[f424]) ).
thf(f424,plain,
( ( y
!= ( f @ ( g @ y ) ) )
| spl0_2
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f419]) ).
thf(f419,plain,
( ( $false != $false )
| ( y
!= ( f @ ( g @ y ) ) )
| spl0_2
| ~ spl0_10 ),
inference(constrained_superposition,[status(thm)],[f22,f60]) ).
thf(f428,plain,
( ~ spl0_9
| ~ spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f427]) ).
thf(f427,plain,
( $false
| ~ spl0_9
| ~ spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f417]) ).
thf(f417,plain,
( ( $true = $false )
| ~ spl0_9
| ~ spl0_10 ),
inference(superposition,[status(thm)],[f60,f55]) ).
thf(f416,plain,
( spl0_10
| spl0_17
| ~ spl0_6
| spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f411,f44,f39,f413,f58]) ).
thf(f411,plain,
( ( $false
= ( g @ $false ) )
| ( ( g @ y )
= $false )
| ~ spl0_6
| spl0_7 ),
inference(subsumption_resolution,[status(thm)],[f86,f45]) ).
thf(f86,plain,
( ( ( g @ y )
= $false )
| ( $false
= ( g @ $false ) )
| ( y = $false )
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( y
!= ( g @ y ) )
| ( $false
= ( g @ $false ) )
| ~ spl0_6 ),
inference(constrained_superposition,[status(thm)],[f41,f41]) ).
thf(f406,plain,
( spl0_12
| spl0_2
| ~ spl0_6
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f405,f58,f39,f21,f355]) ).
thf(f405,plain,
( ( $false
= ( f @ ( g @ y ) ) )
| spl0_2
| ~ spl0_6
| spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f394,f59]) ).
thf(f394,plain,
( ( ( g @ y )
= $false )
| ( $false
= ( f @ ( g @ y ) ) )
| spl0_2
| ~ spl0_6 ),
inference(binary_proxy_clausification,[status(thm)],[f392]) ).
thf(f392,plain,
( ( ( g @ y )
!= ( f @ ( g @ y ) ) )
| spl0_2
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f384]) ).
thf(f384,plain,
( ( ( g @ y )
!= ( f @ ( g @ y ) ) )
| ( $false != $false )
| spl0_2
| ~ spl0_6 ),
inference(constrained_superposition,[status(thm)],[f22,f41]) ).
thf(f362,plain,
( spl0_11
| spl0_12
| spl0_13
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f312,f26,f359,f355,f351]) ).
thf(f312,plain,
( ( ( f @ ( f @ ( g @ y ) ) )
= $false )
| ( $false
= ( f @ ( g @ y ) ) )
| ( $false
= ( f @ $false ) )
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f281]) ).
thf(f281,plain,
( ( ( f @ ( f @ ( g @ y ) ) )
!= ( f @ ( g @ y ) ) )
| ( $false
= ( f @ $false ) )
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f28,f28]) ).
thf(f349,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f348]) ).
thf(f348,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f347,f200]) ).
thf(f200,plain,
( ( ( f @ $true )
!= $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| spl0_10 ),
inference(trivial_inequality_removal,[status(thm)],[f184]) ).
thf(f184,plain,
( ( ( f @ $true )
!= $false )
| ( $false != $false )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9
| spl0_10 ),
inference(constrained_superposition,[status(thm)],[f91,f118]) ).
thf(f118,plain,
( ( $false
= ( g @ ( f @ $true ) ) )
| ~ spl0_2
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f23,f55]) ).
thf(f91,plain,
( ( $false
!= ( g @ $false ) )
| ~ spl0_7
| spl0_10 ),
inference(superposition,[status(thm)],[f59,f46]) ).
thf(f46,plain,
( ( y = $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f347,plain,
( ( ( f @ $true )
= $false )
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9
| spl0_10 ),
inference(subsumption_resolution,[status(thm)],[f346,f91]) ).
thf(f346,plain,
( ( $false
= ( g @ $false ) )
| ( ( f @ $true )
= $false )
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f302,f143]) ).
thf(f143,plain,
( ( $false
!= ( f @ ( g @ y ) ) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $true = $false )
| ( $false
!= ( f @ ( g @ y ) ) )
| ~ spl0_2
| ~ spl0_7
| ~ spl0_9 ),
inference(constrained_superposition,[status(thm)],[f23,f69]) ).
thf(f69,plain,
( ( $true
= ( g @ $false ) )
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f55,f46]) ).
thf(f302,plain,
( ( $false
= ( f @ ( g @ y ) ) )
| ( $false
= ( g @ $false ) )
| ( ( f @ $true )
= $false )
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f282]) ).
thf(f282,plain,
( ( ( f @ $true )
= $false )
| ( ( g @ $false )
!= ( f @ ( g @ y ) ) )
| ~ spl0_2
| ~ spl0_3
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(constrained_superposition,[status(thm)],[f28,f222]) ).
thf(f222,plain,
( ( ( f @ ( g @ $false ) )
= $true )
| ~ spl0_2
| spl0_5
| ~ spl0_7
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f144,f46]) ).
thf(f144,plain,
( ( $true
= ( f @ ( g @ y ) ) )
| ~ spl0_2
| spl0_5
| ~ spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f140,f36]) ).
thf(f36,plain,
( ( y != $true )
| spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl0_5
<=> ( y = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f140,plain,
( ( $true
= ( f @ ( g @ y ) ) )
| ( y = $true )
| ~ spl0_2
| ~ spl0_9 ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( ( y
!= ( f @ ( g @ y ) ) )
| ~ spl0_2
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f122]) ).
thf(f122,plain,
( ( y
!= ( f @ ( g @ y ) ) )
| ( $true = $false )
| ~ spl0_2
| ~ spl0_9 ),
inference(constrained_superposition,[status(thm)],[f55,f23]) ).
thf(f67,plain,
( ~ spl0_5
| ~ spl0_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f66]) ).
thf(f66,plain,
( $false
| ~ spl0_5
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true = $false )
| ~ spl0_5
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f37,f46]) ).
thf(f37,plain,
( ( y = $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f61,plain,
( spl0_7
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f11,f58,f44]) ).
thf(f11,plain,
( ( ( g @ y )
= $false )
| ( y = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( y
!= ( g @ y ) ),
inference(definition_unfolding,[status(thm)],[f4,f6]) ).
thf(f6,plain,
( x
= ( g @ y ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( x
= ( g @ y ) )
& ( y
= ( g @ x ) )
& ( x != y )
& ( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.WfkYqsXNeY/DTF2THF_19654.p',3) ).
thf(f4,plain,
x != y,
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f56,plain,
( spl0_5
| spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f10,f53,f35]) ).
thf(f10,plain,
( ( ( g @ y )
= $true )
| ( y = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f8]) ).
thf(f51,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f13,f48,f44]) ).
thf(f13,plain,
( ( y = $false )
| ( $true
= ( g @ ( g @ y ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f7,plain,
( y
= ( g @ ( g @ y ) ) ),
inference(definition_unfolding,[status(thm)],[f5,f6]) ).
thf(f5,plain,
( y
= ( g @ x ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f42,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f12,f39,f35]) ).
thf(f12,plain,
( ( y = $true )
| ( $false
= ( g @ ( g @ y ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f7]) ).
thf(f33,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f15,f30,f26]) ).
thf(f15,plain,
( ( $true
= ( g @ ( f @ ( g @ y ) ) ) )
| ( $false
= ( f @ ( f @ ( f @ ( g @ y ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
thf(f9,plain,
( ( f @ ( f @ ( f @ ( g @ y ) ) ) )
= ( g @ ( f @ ( g @ y ) ) ) ),
inference(definition_unfolding,[status(thm)],[f3,f6,f6]) ).
thf(f3,plain,
( ( f @ ( f @ ( f @ x ) ) )
= ( g @ ( f @ x ) ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f24,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f17]) ).
thf(f14,plain,
( ( $true
= ( f @ ( f @ ( f @ ( g @ y ) ) ) ) )
| ( $false
= ( g @ ( f @ ( g @ y ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO041^1 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.33 % Computer : n014.cluster.edu
% 0.18/0.33 % Model : x86_64 x86_64
% 0.18/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.33 % Memory : 8042.1875MB
% 0.18/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.33 % CPULimit : 300
% 0.18/0.33 % WCLimit : 300
% 0.18/0.33 % DateTime : Tue Feb 24 14:22:27 EST 2026
% 0.18/0.33 % CPUTime :
% 0.18/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SYO041^1 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Syntactic
% 0.19/0.45 % Problem : Unsatisfiable basic formula 3
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
% 0.19/0.45 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.19/0.45 % Source : [BS09a]
% 0.19/0.45 % Names :
% 0.19/0.45
% 0.19/0.45 % Status : Unsatisfiable
% 0.19/0.45 % Rating : 0.00 v5.4.0, 0.33 v5.3.0, 0.67 v4.1.0, 1.00 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.19/0.45 % Number of atoms : 19 ( 4 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 4 ( 19 avg)
% 0.19/0.45 % Number of connectives : 11 ( 1 ~; 0 |; 3 &; 7 @)
% 0.19/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 4 ( 4 avg)
% 0.19/0.45 % Number of types : 1 ( 0 usr)
% 0.19/0.45 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 6 ( 5 usr; 3 con; 0-2 aty)
% 0.19/0.45 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.19/0.45 % SPC : TH0_UNS_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : The fragment of simple type theory that restricts equations to
% 0.19/0.45 % base types and disallows lambda abstraction and quantification is
% 0.19/0.45 % decidable. This is an example.
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(a,type,
% 0.19/0.45 a: $o ).
% 0.19/0.45
% 0.19/0.45 thf(f,type,
% 0.19/0.45 f: $o > $o ).
% 0.19/0.45
% 0.19/0.45 thf(g,type,
% 0.19/0.45 g: $o > $o ).
% 0.19/0.45
% 0.19/0.45 thf(x,type,
% 0.19/0.45 x: $o ).
% 0.19/0.45
% 0.19/0.45 thf(y,type,
% 0.19/0.45 y: $o ).
% 0.19/0.45
% 0.19/0.45 thf(3,axiom,
% 0.19/0.45 ( ( x != y )
% 0.19/0.45 & ( ( g @ x )
% 0.19/0.45 = y )
% 0.19/0.45 & ( ( g @ y )
% 0.19/0.45 = x )
% 0.19/0.45 & ( ( f @ ( f @ ( f @ x ) ) )
% 0.19/0.45 = ( g @ ( f @ x ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.47/1.29 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 14:22:28 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.WfkYqsXNeY/DTF2DTF19654.p
% See solution above
% 1.47/1.29 ------------------------
% 1.63/1.30 ---- Cleaned THF ---
% 1.63/1.30 thf(a,type,
% 1.63/1.30 a: $o ).
% 1.63/1.30
% 1.63/1.30 thf(f,type,
% 1.63/1.30 f: $o > $o ).
% 1.63/1.30
% 1.63/1.30 thf(g,type,
% 1.63/1.30 g: $o > $o ).
% 1.63/1.30
% 1.63/1.30 thf(x,type,
% 1.63/1.30 x: $o ).
% 1.63/1.30
% 1.63/1.30 thf(y,type,
% 1.63/1.30 y: $o ).
% 1.63/1.30
% 1.63/1.30 thf(3,axiom,
% 1.63/1.30 ( ( x != y )
% 1.63/1.30 & ( ( g @ x )
% 1.63/1.30 = y )
% 1.63/1.30 & ( ( g @ y )
% 1.63/1.30 = x )
% 1.63/1.30 & ( ( f @ ( f @ ( f @ x ) ) )
% 1.63/1.30 = ( g @ ( f @ x ) ) ) ) ).
% 1.63/1.30 ------------------------
% 1.63/1.32 % (19859)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/183Mi)
% 1.63/1.32 % (19864)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_19654 for (2999ds/275Mi)
% 1.63/1.32 % (19864)Refutation not found, incomplete strategy
% 1.63/1.32 % (19864)------------------------------
% 1.63/1.32 % (19864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (19864)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.32
% 1.63/1.32
% 1.63/1.32 % (19864)Memory used [KB]: 5373
% 1.63/1.32 % (19864)Time elapsed: 0.001 s
% 1.63/1.32 % (19864)------------------------------
% 1.63/1.32 % (19864)------------------------------
% 1.63/1.32 % (19861)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_19654 for (2999ds/27Mi)
% 1.63/1.32 % (19862)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/2Mi)
% 1.63/1.32 % (19862)Instruction limit reached!
% 1.63/1.32 % (19862)------------------------------
% 1.63/1.32 % (19862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (19862)Termination reason: Unknown
% 1.63/1.32 % (19862)Termination phase: Saturation
% 1.63/1.32
% 1.63/1.32 % (19862)Memory used [KB]: 5500
% 1.63/1.32 % (19862)Time elapsed: 0.002 s
% 1.63/1.32 % (19862)Instructions burned: 2 (million)
% 1.63/1.32 % (19862)------------------------------
% 1.63/1.32 % (19862)------------------------------
% 1.63/1.32 % (19861)Refutation not found, incomplete strategy
% 1.63/1.32 % (19861)------------------------------
% 1.63/1.32 % (19861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.32 % (19861)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.32
% 1.63/1.32
% 1.63/1.32 % (19861)Memory used [KB]: 5500
% 1.63/1.32 % (19861)Time elapsed: 0.002 s
% 1.63/1.32 % (19861)Instructions burned: 2 (million)
% 1.63/1.32 % (19861)------------------------------
% 1.63/1.32 % (19861)------------------------------
% 1.63/1.33 % (19860)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_19654 for (2999ds/4Mi)
% 1.63/1.33 % (19863)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_19654 for (2999ds/2Mi)
% 1.63/1.33 % (19865)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/18Mi)
% 1.63/1.33 % (19863)Refutation not found, incomplete strategy
% 1.63/1.33 % (19863)------------------------------
% 1.63/1.33 % (19863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (19863)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.33
% 1.63/1.33
% 1.63/1.33 % (19863)Memory used [KB]: 5373
% 1.63/1.33 % (19863)Time elapsed: 0.003 s
% 1.63/1.33 % (19863)Instructions burned: 1 (million)
% 1.63/1.33 % (19863)------------------------------
% 1.63/1.33 % (19863)------------------------------
% 1.63/1.33 % (19860)Instruction limit reached!
% 1.63/1.33 % (19860)------------------------------
% 1.63/1.33 % (19860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (19860)Termination reason: Unknown
% 1.63/1.33 % (19860)Termination phase: Saturation
% 1.63/1.33
% 1.63/1.33 % (19860)Memory used [KB]: 5500
% 1.63/1.33 % (19860)Time elapsed: 0.005 s
% 1.63/1.33 % (19860)Instructions burned: 4 (million)
% 1.63/1.33 % (19860)------------------------------
% 1.63/1.33 % (19860)------------------------------
% 1.63/1.33 % (19866)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/3Mi)
% 1.63/1.33 % (19867)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_19654 for (2999ds/37Mi)
% 1.63/1.33 % (19866)Refutation not found, incomplete strategy
% 1.63/1.33 % (19866)------------------------------
% 1.63/1.33 % (19866)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (19866)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.33
% 1.63/1.33
% 1.63/1.33 % (19866)Memory used [KB]: 5500
% 1.63/1.33 % (19866)Time elapsed: 0.002 s
% 1.63/1.33 % (19866)Instructions burned: 2 (million)
% 1.63/1.33 % (19866)------------------------------
% 1.63/1.33 % (19866)------------------------------
% 1.63/1.33 % (19865)Refutation not found, incomplete strategy
% 1.63/1.33 % (19865)------------------------------
% 1.63/1.33 % (19865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.33 % (19865)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.33
% 1.63/1.33
% 1.63/1.33 % (19865)Memory used [KB]: 5500
% 1.63/1.33 % (19865)Time elapsed: 0.009 s
% 1.63/1.33 % (19865)Instructions burned: 10 (million)
% 1.63/1.33 % (19865)------------------------------
% 1.63/1.33 % (19865)------------------------------
% 1.63/1.34 % (19868)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_19654 for (2999ds/15Mi)
% 1.63/1.34 % (19868)Refutation not found, incomplete strategy
% 1.63/1.34 % (19868)------------------------------
% 1.63/1.34 % (19868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19868)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.34
% 1.63/1.34
% 1.63/1.34 % (19868)Memory used [KB]: 5373
% 1.63/1.34 % (19868)Time elapsed: 0.002 s
% 1.63/1.34 % (19868)Instructions burned: 1 (million)
% 1.63/1.34 % (19868)------------------------------
% 1.63/1.34 % (19868)------------------------------
% 1.63/1.34 % (19871)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/7Mi)
% 1.63/1.34 % (19871)Instruction limit reached!
% 1.63/1.34 % (19871)------------------------------
% 1.63/1.34 % (19871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19871)Termination reason: Unknown
% 1.63/1.34 % (19871)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (19871)Memory used [KB]: 1023
% 1.63/1.34 % (19871)Time elapsed: 0.004 s
% 1.63/1.34 % (19871)Instructions burned: 9 (million)
% 1.63/1.34 % (19871)------------------------------
% 1.63/1.34 % (19871)------------------------------
% 1.63/1.34 % (19867)Instruction limit reached!
% 1.63/1.34 % (19867)------------------------------
% 1.63/1.34 % (19867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (19867)Termination reason: Unknown
% 1.63/1.34 % (19867)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (19867)Memory used [KB]: 5628
% 1.63/1.34 % (19867)Time elapsed: 0.016 s
% 1.63/1.34 % (19867)Instructions burned: 38 (million)
% 1.63/1.34 % (19867)------------------------------
% 1.63/1.34 % (19867)------------------------------
% 1.63/1.35 % (19869)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_19654 for (2999ds/3Mi)
% 1.63/1.35 % (19870)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_19654 for (2999ds/1041Mi)
% 1.63/1.35 % (19869)Refutation not found, incomplete strategy
% 1.63/1.35 % (19869)------------------------------
% 1.63/1.35 % (19869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (19869)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (19869)Memory used [KB]: 5500
% 1.63/1.35 % (19869)Time elapsed: 0.003 s
% 1.63/1.35 % (19869)Instructions burned: 1 (million)
% 1.63/1.35 % (19869)------------------------------
% 1.63/1.35 % (19869)------------------------------
% 1.63/1.35 % (19872)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/16Mi)
% 1.63/1.35 % (19874)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/3Mi)
% 1.63/1.35 % (19870)Refutation not found, incomplete strategy
% 1.63/1.35 % (19870)------------------------------
% 1.63/1.35 % (19870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (19870)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (19870)Memory used [KB]: 5500
% 1.63/1.35 % (19870)Time elapsed: 0.008 s
% 1.63/1.35 % (19870)Instructions burned: 9 (million)
% 1.63/1.35 % (19870)------------------------------
% 1.63/1.35 % (19870)------------------------------
% 1.63/1.35 % (19874)Instruction limit reached!
% 1.63/1.35 % (19874)------------------------------
% 1.63/1.35 % (19874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (19874)Termination reason: Unknown
% 1.63/1.35 % (19874)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (19874)Memory used [KB]: 1023
% 1.63/1.35 % (19874)Time elapsed: 0.002 s
% 1.63/1.35 % (19874)Instructions burned: 3 (million)
% 1.63/1.35 % (19874)------------------------------
% 1.63/1.35 % (19874)------------------------------
% 1.63/1.35 % (19875)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/7Mi)
% 1.63/1.36 % (19873)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_19654 for (2999ds/3Mi)
% 1.63/1.36 % (19875)Instruction limit reached!
% 1.63/1.36 % (19875)------------------------------
% 1.63/1.36 % (19875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (19875)Termination reason: Unknown
% 1.63/1.36 % (19875)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (19875)Memory used [KB]: 5500
% 1.63/1.36 % (19875)Time elapsed: 0.004 s
% 1.63/1.36 % (19875)Instructions burned: 7 (million)
% 1.63/1.36 % (19875)------------------------------
% 1.63/1.36 % (19875)------------------------------
% 1.63/1.36 % (19873)Refutation not found, incomplete strategy
% 1.63/1.36 % (19873)------------------------------
% 1.63/1.36 % (19873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (19873)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.36
% 1.63/1.36
% 1.63/1.36 % (19873)Memory used [KB]: 5500
% 1.63/1.36 % (19873)Time elapsed: 0.003 s
% 1.63/1.36 % (19873)Instructions burned: 2 (million)
% 1.63/1.36 % (19873)------------------------------
% 1.63/1.36 % (19873)------------------------------
% 1.63/1.36 % (19859)First to succeed.
% 1.63/1.36 % (19872)Instruction limit reached!
% 1.63/1.36 % (19872)------------------------------
% 1.63/1.36 % (19872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (19872)Termination reason: Unknown
% 1.63/1.36 % (19872)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (19872)Memory used [KB]: 5500
% 1.63/1.36 % (19872)Time elapsed: 0.011 s
% 1.63/1.36 % (19872)Instructions burned: 17 (million)
% 1.63/1.36 % (19872)------------------------------
% 1.63/1.36 % (19872)------------------------------
% 1.63/1.36 % (19877)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19654 for (2999ds/4Mi)
% 1.63/1.36 % (19859)Refutation found. Thanks to Tanya!
% 1.63/1.36 % SZS status Unsatisfiable for DTF2THF_19654
% 1.63/1.36 % SZS output start Proof for DTF2THF_19654
% 1.63/1.36 thf(func_def_1, type, f: $o > $o).
% 1.63/1.36 thf(func_def_2, type, g: $o > $o).
% 1.63/1.36 thf(func_def_9, type, ph1: !>[X0: $tType]:(X0)).
% 1.63/1.36 thf(f2533,plain,(
% 1.63/1.36 $false),
% 1.63/1.36 inference(avatar_sat_refutation,[status(thm)],[f24,f33,f42,f51,f56,f61,f67,f349,f362,f406,f416,f428,f433,f495,f640,f667,f704,f2167,f2252,f2304,f2373,f2383,f2460,f2532])).
% 1.63/1.36 thf(f2532,plain,(
% 1.63/1.36 ~spl0_1 | spl0_2 | ~spl0_6 | ~spl0_9 | spl0_10 | spl0_13),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f2531])).
% 1.63/1.36 thf(f2531,plain,(
% 1.63/1.36 $false | (~spl0_1 | spl0_2 | ~spl0_6 | ~spl0_9 | spl0_10 | spl0_13)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f2506,f55])).
% 1.63/1.36 thf(f55,plain,(
% 1.63/1.36 ((g @ y) = $true) | ~spl0_9),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.63/1.36 thf(f53,definition,(
% 1.63/1.36 spl0_9 <=> ((g @ y) = $true)),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.63/1.36 thf(f2506,plain,(
% 1.63/1.36 ((g @ y) != $true) | (~spl0_1 | spl0_2 | ~spl0_6 | spl0_10 | spl0_13)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f2502])).
% 1.63/1.36 thf(f2502,plain,(
% 1.63/1.36 ($false != $false) | ((g @ y) != $true) | (~spl0_1 | spl0_2 | ~spl0_6 | spl0_10 | spl0_13)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f2466,f41])).
% 1.63/1.36 thf(f41,plain,(
% 1.63/1.36 ($false = (g @ (g @ y))) | ~spl0_6),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.63/1.36 thf(f39,definition,(
% 1.63/1.36 spl0_6 <=> ($false = (g @ (g @ y)))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.63/1.36 thf(f2466,plain,(
% 1.63/1.36 ($false != (g @ $true)) | (~spl0_1 | spl0_2 | spl0_10 | spl0_13)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f2465,f59])).
% 1.63/1.36 thf(f59,plain,(
% 1.63/1.36 ((g @ y) != $false) | spl0_10),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.63/1.36 thf(f58,definition,(
% 1.63/1.36 spl0_10 <=> ((g @ y) = $false)),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.63/1.36 thf(f2465,plain,(
% 1.63/1.36 ((g @ y) = $false) | ($false != (g @ $true)) | (~spl0_1 | spl0_2 | spl0_13)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f2404,f360])).
% 1.63/1.36 thf(f360,plain,(
% 1.63/1.36 ((f @ (f @ (g @ y))) != $false) | spl0_13),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f359])).
% 1.63/1.36 thf(f359,definition,(
% 1.63/1.36 spl0_13 <=> ((f @ (f @ (g @ y))) = $false)),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.63/1.36 thf(f2404,plain,(
% 1.63/1.36 ((f @ (f @ (g @ y))) = $false) | ($false != (g @ $true)) | ((g @ y) = $false) | (~spl0_1 | spl0_2)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f2391])).
% 1.63/1.36 thf(f2391,plain,(
% 1.63/1.36 ($false != (g @ $true)) | ((g @ y) != (f @ (f @ (g @ y)))) | (~spl0_1 | spl0_2)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f22,f19])).
% 1.63/1.36 thf(f19,plain,(
% 1.63/1.36 ($true = (f @ (f @ (f @ (g @ y))))) | ~spl0_1),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.63/1.36 thf(f17,definition,(
% 1.63/1.36 spl0_1 <=> ($true = (f @ (f @ (f @ (g @ y)))))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.63/1.36 thf(f22,plain,(
% 1.63/1.36 ($false != (g @ (f @ (g @ y)))) | spl0_2),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.63/1.36 thf(f21,definition,(
% 1.63/1.36 spl0_2 <=> ($false = (g @ (f @ (g @ y))))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.63/1.36 thf(f2460,plain,(
% 1.63/1.36 spl0_2 | spl0_7 | ~spl0_10 | spl0_11),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f2459])).
% 1.63/1.36 thf(f2459,plain,(
% 1.63/1.36 $false | (spl0_2 | spl0_7 | ~spl0_10 | spl0_11)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f2458,f352])).
% 1.63/1.36 thf(f352,plain,(
% 1.63/1.36 ($false != (f @ $false)) | spl0_11),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f351])).
% 1.63/1.36 thf(f351,definition,(
% 1.63/1.36 spl0_11 <=> ($false = (f @ $false))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.63/1.36 thf(f2458,plain,(
% 1.63/1.36 ($false = (f @ $false)) | (spl0_2 | spl0_7 | ~spl0_10)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f2455,f45])).
% 1.63/1.36 thf(f45,plain,(
% 1.63/1.36 (y != $false) | spl0_7),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.63/1.36 thf(f44,definition,(
% 1.63/1.36 spl0_7 <=> (y = $false)),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.63/1.36 thf(f2455,plain,(
% 1.63/1.36 (y = $false) | ($false = (f @ $false)) | (spl0_2 | ~spl0_10)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f2453])).
% 1.63/1.36 thf(f2453,plain,(
% 1.63/1.36 (y != (f @ $false)) | (spl0_2 | ~spl0_10)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f2446])).
% 1.63/1.36 thf(f2446,plain,(
% 1.63/1.36 ($false != $false) | (y != (f @ $false)) | (spl0_2 | ~spl0_10)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f2387,f60])).
% 1.63/1.36 thf(f60,plain,(
% 1.63/1.36 ((g @ y) = $false) | ~spl0_10),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.63/1.36 thf(f2387,plain,(
% 1.63/1.36 ((g @ (f @ $false)) != $false) | (spl0_2 | ~spl0_10)),
% 1.63/1.36 inference(superposition,[status(thm)],[f22,f60])).
% 1.63/1.36 thf(f2383,plain,(
% 1.63/1.36 ~spl0_1 | ~spl0_11 | ~spl0_12 | spl0_21),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f2382])).
% 1.63/1.36 thf(f2382,plain,(
% 1.63/1.36 $false | (~spl0_1 | ~spl0_11 | ~spl0_12 | spl0_21)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f2381,f357])).
% 1.63/1.36 thf(f357,plain,(
% 1.63/1.36 ($false = (f @ (g @ y))) | ~spl0_12),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f355])).
% 1.63/1.36 thf(f355,definition,(
% 1.63/1.36 spl0_12 <=> ($false = (f @ (g @ y)))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.63/1.36 thf(f2381,plain,(
% 1.63/1.36 ($false != (f @ (g @ y))) | (~spl0_1 | ~spl0_11 | spl0_21)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f2339,f2211])).
% 1.63/1.36 thf(f2211,plain,(
% 1.63/1.36 ($true != (f @ $false)) | spl0_21),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f2210])).
% 1.63/1.36 thf(f2210,definition,(
% 1.63/1.36 spl0_21 <=> ($true = (f @ $false))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 1.63/1.36 thf(f2339,plain,(
% 1.63/1.36 ($true = (f @ $false)) | ($false != (f @ (g @ y))) | (~spl0_1 | ~spl0_11)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f19,f353])).
% 1.63/1.36 thf(f353,plain,(
% 1.63/1.36 ($false = (f @ $false)) | ~spl0_11),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f351])).
% 1.63/1.36 thf(f2373,plain,(
% 1.63/1.36 ~spl0_11 | ~spl0_21),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f2372])).
% 1.63/1.36 thf(f2372,plain,(
% 1.63/1.36 $false | (~spl0_11 | ~spl0_21)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f2361])).
% 1.63/1.36 thf(f2361,plain,(
% 1.63/1.36 ($true = $false) | (~spl0_11 | ~spl0_21)),
% 1.63/1.36 inference(superposition,[status(thm)],[f2212,f353])).
% 1.63/1.36 thf(f2212,plain,(
% 1.63/1.36 ($true = (f @ $false)) | ~spl0_21),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f2210])).
% 1.63/1.36 thf(f2304,plain,(
% 1.63/1.36 spl0_21 | ~spl0_1 | ~spl0_13),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f1532,f359,f17,f2210])).
% 1.63/1.36 thf(f1532,plain,(
% 1.63/1.36 ($true = (f @ $false)) | (~spl0_1 | ~spl0_13)),
% 1.63/1.36 inference(superposition,[status(thm)],[f19,f361])).
% 1.63/1.36 thf(f361,plain,(
% 1.63/1.36 ((f @ (f @ (g @ y))) = $false) | ~spl0_13),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f359])).
% 1.63/1.36 thf(f2252,plain,(
% 1.63/1.36 spl0_11 | ~spl0_12 | ~spl0_13),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f2251])).
% 1.63/1.36 thf(f2251,plain,(
% 1.63/1.36 $false | (spl0_11 | ~spl0_12 | ~spl0_13)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f1143,f357])).
% 1.63/1.36 thf(f1143,plain,(
% 1.63/1.36 ($false != (f @ (g @ y))) | (spl0_11 | ~spl0_13)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f1123])).
% 1.63/1.36 thf(f1123,plain,(
% 1.63/1.36 ($false != (f @ (g @ y))) | ($false != $false) | (spl0_11 | ~spl0_13)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f352,f361])).
% 1.63/1.36 thf(f2167,plain,(
% 1.63/1.36 ~spl0_3 | spl0_11 | ~spl0_13),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f2166])).
% 1.63/1.36 thf(f2166,plain,(
% 1.63/1.36 $false | (~spl0_3 | spl0_11 | ~spl0_13)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f2025,f361])).
% 1.63/1.36 thf(f2025,plain,(
% 1.63/1.36 ((f @ (f @ (g @ y))) != $false) | (~spl0_3 | spl0_11)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f1965])).
% 1.63/1.36 thf(f1965,plain,(
% 1.63/1.36 ($false != $false) | ((f @ (f @ (g @ y))) != $false) | (~spl0_3 | spl0_11)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f352,f28])).
% 1.63/1.36 thf(f28,plain,(
% 1.63/1.36 ($false = (f @ (f @ (f @ (g @ y))))) | ~spl0_3),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.63/1.36 thf(f26,definition,(
% 1.63/1.36 spl0_3 <=> ($false = (f @ (f @ (f @ (g @ y)))))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.63/1.36 thf(f704,plain,(
% 1.63/1.36 ~spl0_2 | ~spl0_4),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f703])).
% 1.63/1.36 thf(f703,plain,(
% 1.63/1.36 $false | (~spl0_2 | ~spl0_4)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f676])).
% 1.63/1.36 thf(f676,plain,(
% 1.63/1.36 ($true = $false) | (~spl0_2 | ~spl0_4)),
% 1.63/1.36 inference(superposition,[status(thm)],[f32,f23])).
% 1.63/1.36 thf(f23,plain,(
% 1.63/1.36 ($false = (g @ (f @ (g @ y)))) | ~spl0_2),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.63/1.36 thf(f32,plain,(
% 1.63/1.36 ($true = (g @ (f @ (g @ y)))) | ~spl0_4),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.63/1.36 thf(f30,definition,(
% 1.63/1.36 spl0_4 <=> ($true = (g @ (f @ (g @ y))))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.63/1.36 thf(f667,plain,(
% 1.63/1.36 ~spl0_11 | ~spl0_2 | spl0_7 | spl0_12),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f666,f355,f44,f21,f351])).
% 1.63/1.36 thf(f666,plain,(
% 1.63/1.36 ($false != (f @ $false)) | (~spl0_2 | spl0_7 | spl0_12)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f665,f45])).
% 1.63/1.36 thf(f665,plain,(
% 1.63/1.36 (y = $false) | ($false != (f @ $false)) | (~spl0_2 | spl0_12)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f659,f356])).
% 1.63/1.36 thf(f356,plain,(
% 1.63/1.36 ($false != (f @ (g @ y))) | spl0_12),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f355])).
% 1.63/1.36 thf(f659,plain,(
% 1.63/1.36 ($false = (f @ (g @ y))) | (y = $false) | ($false != (f @ $false)) | (~spl0_2 | spl0_12)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f650])).
% 1.63/1.36 thf(f650,plain,(
% 1.63/1.36 (y != (f @ (g @ y))) | ($false != (f @ $false)) | (~spl0_2 | spl0_12)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f356,f23])).
% 1.63/1.36 thf(f640,plain,(
% 1.63/1.36 ~spl0_12 | ~spl0_2 | spl0_17),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f617,f413,f21,f355])).
% 1.63/1.36 thf(f413,definition,(
% 1.63/1.36 spl0_17 <=> ($false = (g @ $false))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.63/1.36 thf(f617,plain,(
% 1.63/1.36 ($false != (f @ (g @ y))) | (~spl0_2 | spl0_17)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f593])).
% 1.63/1.36 thf(f593,plain,(
% 1.63/1.36 ($false != (f @ (g @ y))) | ($false != $false) | (~spl0_2 | spl0_17)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f414,f23])).
% 1.63/1.36 thf(f414,plain,(
% 1.63/1.36 ($false != (g @ $false)) | spl0_17),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f413])).
% 1.63/1.36 thf(f495,plain,(
% 1.63/1.36 ~spl0_8 | ~spl0_10 | ~spl0_17),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f494])).
% 1.63/1.36 thf(f494,plain,(
% 1.63/1.36 $false | (~spl0_8 | ~spl0_10 | ~spl0_17)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f479,f60])).
% 1.63/1.36 thf(f479,plain,(
% 1.63/1.36 ((g @ y) != $false) | (~spl0_8 | ~spl0_17)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f465])).
% 1.63/1.36 thf(f465,plain,(
% 1.63/1.36 ($true = $false) | ((g @ y) != $false) | (~spl0_8 | ~spl0_17)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f415,f50])).
% 1.63/1.36 thf(f50,plain,(
% 1.63/1.36 ($true = (g @ (g @ y))) | ~spl0_8),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.63/1.36 thf(f48,definition,(
% 1.63/1.36 spl0_8 <=> ($true = (g @ (g @ y)))),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.63/1.36 thf(f415,plain,(
% 1.63/1.36 ($false = (g @ $false)) | ~spl0_17),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f413])).
% 1.63/1.36 thf(f433,plain,(
% 1.63/1.36 spl0_12 | spl0_2 | spl0_7 | ~spl0_10),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f432,f58,f44,f21,f355])).
% 1.63/1.36 thf(f432,plain,(
% 1.63/1.36 ($false = (f @ (g @ y))) | (spl0_2 | spl0_7 | ~spl0_10)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f426,f45])).
% 1.63/1.36 thf(f426,plain,(
% 1.63/1.36 (y = $false) | ($false = (f @ (g @ y))) | (spl0_2 | ~spl0_10)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f424])).
% 1.63/1.36 thf(f424,plain,(
% 1.63/1.36 (y != (f @ (g @ y))) | (spl0_2 | ~spl0_10)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f419])).
% 1.63/1.36 thf(f419,plain,(
% 1.63/1.36 ($false != $false) | (y != (f @ (g @ y))) | (spl0_2 | ~spl0_10)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f22,f60])).
% 1.63/1.36 thf(f428,plain,(
% 1.63/1.36 ~spl0_9 | ~spl0_10),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f427])).
% 1.63/1.36 thf(f427,plain,(
% 1.63/1.36 $false | (~spl0_9 | ~spl0_10)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f417])).
% 1.63/1.36 thf(f417,plain,(
% 1.63/1.36 ($true = $false) | (~spl0_9 | ~spl0_10)),
% 1.63/1.36 inference(superposition,[status(thm)],[f60,f55])).
% 1.63/1.36 thf(f416,plain,(
% 1.63/1.36 spl0_10 | spl0_17 | ~spl0_6 | spl0_7),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f411,f44,f39,f413,f58])).
% 1.63/1.36 thf(f411,plain,(
% 1.63/1.36 ($false = (g @ $false)) | ((g @ y) = $false) | (~spl0_6 | spl0_7)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f86,f45])).
% 1.63/1.36 thf(f86,plain,(
% 1.63/1.36 ((g @ y) = $false) | ($false = (g @ $false)) | (y = $false) | ~spl0_6),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f71])).
% 1.63/1.36 thf(f71,plain,(
% 1.63/1.36 (y != (g @ y)) | ($false = (g @ $false)) | ~spl0_6),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f41,f41])).
% 1.63/1.36 thf(f406,plain,(
% 1.63/1.36 spl0_12 | spl0_2 | ~spl0_6 | spl0_10),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f405,f58,f39,f21,f355])).
% 1.63/1.36 thf(f405,plain,(
% 1.63/1.36 ($false = (f @ (g @ y))) | (spl0_2 | ~spl0_6 | spl0_10)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f394,f59])).
% 1.63/1.36 thf(f394,plain,(
% 1.63/1.36 ((g @ y) = $false) | ($false = (f @ (g @ y))) | (spl0_2 | ~spl0_6)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f392])).
% 1.63/1.36 thf(f392,plain,(
% 1.63/1.36 ((g @ y) != (f @ (g @ y))) | (spl0_2 | ~spl0_6)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f384])).
% 1.63/1.36 thf(f384,plain,(
% 1.63/1.36 ((g @ y) != (f @ (g @ y))) | ($false != $false) | (spl0_2 | ~spl0_6)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f22,f41])).
% 1.63/1.36 thf(f362,plain,(
% 1.63/1.36 spl0_11 | spl0_12 | spl0_13 | ~spl0_3),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f312,f26,f359,f355,f351])).
% 1.63/1.36 thf(f312,plain,(
% 1.63/1.36 ((f @ (f @ (g @ y))) = $false) | ($false = (f @ (g @ y))) | ($false = (f @ $false)) | ~spl0_3),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f281])).
% 1.63/1.36 thf(f281,plain,(
% 1.63/1.36 ((f @ (f @ (g @ y))) != (f @ (g @ y))) | ($false = (f @ $false)) | ~spl0_3),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f28,f28])).
% 1.63/1.36 thf(f349,plain,(
% 1.63/1.36 ~spl0_2 | ~spl0_3 | spl0_5 | ~spl0_7 | ~spl0_9 | spl0_10),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f348])).
% 1.63/1.36 thf(f348,plain,(
% 1.63/1.36 $false | (~spl0_2 | ~spl0_3 | spl0_5 | ~spl0_7 | ~spl0_9 | spl0_10)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f347,f200])).
% 1.63/1.36 thf(f200,plain,(
% 1.63/1.36 ((f @ $true) != $false) | (~spl0_2 | ~spl0_7 | ~spl0_9 | spl0_10)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f184])).
% 1.63/1.36 thf(f184,plain,(
% 1.63/1.36 ((f @ $true) != $false) | ($false != $false) | (~spl0_2 | ~spl0_7 | ~spl0_9 | spl0_10)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f91,f118])).
% 1.63/1.36 thf(f118,plain,(
% 1.63/1.36 ($false = (g @ (f @ $true))) | (~spl0_2 | ~spl0_9)),
% 1.63/1.36 inference(superposition,[status(thm)],[f23,f55])).
% 1.63/1.36 thf(f91,plain,(
% 1.63/1.36 ($false != (g @ $false)) | (~spl0_7 | spl0_10)),
% 1.63/1.36 inference(superposition,[status(thm)],[f59,f46])).
% 1.63/1.36 thf(f46,plain,(
% 1.63/1.36 (y = $false) | ~spl0_7),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.63/1.36 thf(f347,plain,(
% 1.63/1.36 ((f @ $true) = $false) | (~spl0_2 | ~spl0_3 | spl0_5 | ~spl0_7 | ~spl0_9 | spl0_10)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f346,f91])).
% 1.63/1.36 thf(f346,plain,(
% 1.63/1.36 ($false = (g @ $false)) | ((f @ $true) = $false) | (~spl0_2 | ~spl0_3 | spl0_5 | ~spl0_7 | ~spl0_9)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f302,f143])).
% 1.63/1.36 thf(f143,plain,(
% 1.63/1.36 ($false != (f @ (g @ y))) | (~spl0_2 | ~spl0_7 | ~spl0_9)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.63/1.36 thf(f119,plain,(
% 1.63/1.36 ($true = $false) | ($false != (f @ (g @ y))) | (~spl0_2 | ~spl0_7 | ~spl0_9)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f23,f69])).
% 1.63/1.36 thf(f69,plain,(
% 1.63/1.36 ($true = (g @ $false)) | (~spl0_7 | ~spl0_9)),
% 1.63/1.36 inference(superposition,[status(thm)],[f55,f46])).
% 1.63/1.36 thf(f302,plain,(
% 1.63/1.36 ($false = (f @ (g @ y))) | ($false = (g @ $false)) | ((f @ $true) = $false) | (~spl0_2 | ~spl0_3 | spl0_5 | ~spl0_7 | ~spl0_9)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f282])).
% 1.63/1.36 thf(f282,plain,(
% 1.63/1.36 ((f @ $true) = $false) | ((g @ $false) != (f @ (g @ y))) | (~spl0_2 | ~spl0_3 | spl0_5 | ~spl0_7 | ~spl0_9)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f28,f222])).
% 1.63/1.36 thf(f222,plain,(
% 1.63/1.36 ((f @ (g @ $false)) = $true) | (~spl0_2 | spl0_5 | ~spl0_7 | ~spl0_9)),
% 1.63/1.36 inference(superposition,[status(thm)],[f144,f46])).
% 1.63/1.36 thf(f144,plain,(
% 1.63/1.36 ($true = (f @ (g @ y))) | (~spl0_2 | spl0_5 | ~spl0_9)),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f140,f36])).
% 1.63/1.36 thf(f36,plain,(
% 1.63/1.36 (y != $true) | spl0_5),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.63/1.36 thf(f35,definition,(
% 1.63/1.36 spl0_5 <=> (y = $true)),
% 1.63/1.36 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.63/1.36 thf(f140,plain,(
% 1.63/1.36 ($true = (f @ (g @ y))) | (y = $true) | (~spl0_2 | ~spl0_9)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 1.63/1.36 thf(f139,plain,(
% 1.63/1.36 (y != (f @ (g @ y))) | (~spl0_2 | ~spl0_9)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f122])).
% 1.63/1.36 thf(f122,plain,(
% 1.63/1.36 (y != (f @ (g @ y))) | ($true = $false) | (~spl0_2 | ~spl0_9)),
% 1.63/1.36 inference(constrained_superposition,[status(thm)],[f55,f23])).
% 1.63/1.36 thf(f67,plain,(
% 1.63/1.36 ~spl0_5 | ~spl0_7),
% 1.63/1.36 inference(avatar_contradiction_clause,[status(thm)],[f66])).
% 1.63/1.36 thf(f66,plain,(
% 1.63/1.36 $false | (~spl0_5 | ~spl0_7)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.63/1.36 thf(f63,plain,(
% 1.63/1.36 ($true = $false) | (~spl0_5 | ~spl0_7)),
% 1.63/1.36 inference(superposition,[status(thm)],[f37,f46])).
% 1.63/1.36 thf(f37,plain,(
% 1.63/1.36 (y = $true) | ~spl0_5),
% 1.63/1.36 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.63/1.36 thf(f61,plain,(
% 1.63/1.36 spl0_7 | spl0_10),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f11,f58,f44])).
% 1.63/1.36 thf(f11,plain,(
% 1.63/1.36 ((g @ y) = $false) | (y = $false)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.63/1.36 thf(f8,plain,(
% 1.63/1.36 (y != (g @ y))),
% 1.63/1.36 inference(definition_unfolding,[status(thm)],[f4,f6])).
% 1.63/1.36 thf(f6,plain,(
% 1.63/1.36 (x = (g @ y))),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f1])).
% 1.63/1.36 thf(f1,axiom,(
% 1.63/1.36 (x = (g @ y)) & (y = (g @ x)) & (x != y) & ((f @ (f @ (f @ x))) = (g @ (f @ x)))),
% 1.63/1.36 file('/export/starexec/sandbox/tmp/tmp.WfkYqsXNeY/DTF2THF_19654.p',3)).
% 1.63/1.36 thf(f4,plain,(
% 1.63/1.36 (x != y)),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f1])).
% 1.63/1.36 thf(f56,plain,(
% 1.63/1.36 spl0_5 | spl0_9),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f10,f53,f35])).
% 1.63/1.36 thf(f10,plain,(
% 1.63/1.36 ((g @ y) = $true) | (y = $true)),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f8])).
% 1.63/1.36 thf(f51,plain,(
% 1.63/1.36 spl0_7 | spl0_8),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f13,f48,f44])).
% 1.63/1.36 thf(f13,plain,(
% 1.63/1.36 (y = $false) | ($true = (g @ (g @ y)))),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.63/1.36 thf(f7,plain,(
% 1.63/1.36 (y = (g @ (g @ y)))),
% 1.63/1.36 inference(definition_unfolding,[status(thm)],[f5,f6])).
% 1.63/1.36 thf(f5,plain,(
% 1.63/1.36 (y = (g @ x))),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f1])).
% 1.63/1.36 thf(f42,plain,(
% 1.63/1.36 spl0_5 | spl0_6),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f12,f39,f35])).
% 1.63/1.36 thf(f12,plain,(
% 1.63/1.36 (y = $true) | ($false = (g @ (g @ y)))),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f7])).
% 1.63/1.36 thf(f33,plain,(
% 1.63/1.36 spl0_3 | spl0_4),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f15,f30,f26])).
% 1.63/1.36 thf(f15,plain,(
% 1.63/1.36 ($true = (g @ (f @ (g @ y)))) | ($false = (f @ (f @ (f @ (g @ y)))))),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.63/1.36 thf(f9,plain,(
% 1.63/1.36 ((f @ (f @ (f @ (g @ y)))) = (g @ (f @ (g @ y))))),
% 1.63/1.36 inference(definition_unfolding,[status(thm)],[f3,f6,f6])).
% 1.63/1.36 thf(f3,plain,(
% 1.63/1.36 ((f @ (f @ (f @ x))) = (g @ (f @ x)))),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f1])).
% 1.63/1.36 thf(f24,plain,(
% 1.63/1.36 spl0_1 | spl0_2),
% 1.63/1.36 inference(avatar_split_clause,[status(thm)],[f14,f21,f17])).
% 1.63/1.36 thf(f14,plain,(
% 1.63/1.36 ($true = (f @ (f @ (f @ (g @ y))))) | ($false = (g @ (f @ (g @ y))))),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f9])).
% 1.63/1.36 % SZS output end Proof for DTF2THF_19654
% 1.63/1.36 % (19859)------------------------------
% 1.63/1.36 % (19859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (19859)Termination reason: Refutation
% 1.63/1.36
% 1.63/1.36 % (19859)Memory used [KB]: 6524
% 1.63/1.36 % (19859)Time elapsed: 0.046 s
% 1.63/1.36 % (19859)Instructions burned: 124 (million)
% 1.63/1.36 % (19859)------------------------------
% 1.63/1.36 % (19859)------------------------------
% 1.63/1.36 % (19858)Success in time 0.045 s
%------------------------------------------------------------------------------