%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO314^5 : 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 : n026.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 09:53:55 AM UTC 2026
% Result : Theorem 1.51s 1.21s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 16
% Syntax : Number of formulae : 92 ( 1 unt; 0 typ; 13 def)
% Number of atoms : 679 ( 186 equ; 0 cnn)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 604 ( 169 ~; 141 |; 69 &; 204 @)
% ( 18 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 64 ( 64 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 20 con; 0-2 aty)
% Number of variables : 128 ( 0 ^; 56 !; 72 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_4,type,
sK0: $i > $o ).
thf(func_def_7,type,
sK3: $i > $o ).
thf(func_def_10,type,
sK6: $i > $o ).
thf(func_def_11,type,
sK7: $i > $o ).
thf(func_def_14,type,
ph9:
!>[X0: $tType] : X0 ).
thf(f171,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f43,f48,f53,f58,f67,f68,f69,f70,f71,f72,f73,f74,f78,f79,f80,f81,f112,f117,f124,f125,f143,f170]) ).
thf(f170,plain,
( spl8_1
| ~ spl8_8
| ~ spl8_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f169]) ).
thf(f169,plain,
( $false
| spl8_1
| ~ spl8_8
| ~ spl8_13 ),
inference(subsumption_resolution,[status(thm)],[f160,f66]) ).
thf(f66,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl8_8 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl8_8
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition]) ).
thf(f160,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| spl8_1
| ~ spl8_13 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true != $true )
| spl8_1
| ~ spl8_13 ),
inference(superposition,[status(thm)],[f33,f111]) ).
thf(f111,plain,
( ! [X1: $i > $o] :
( ( ( X1 @ z )
= $true )
| ( $true
!= ( X1 @ sK1 ) ) )
| ~ spl8_13 ),
inference(avatar_component_clause,[status(thm)],[f110]) ).
thf(f110,definition,
( spl8_13
<=> ! [X1: $i > $o] :
( ( ( X1 @ z )
= $true )
| ( $true
!= ( X1 @ sK1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl8_13])],[avatar_definition]) ).
thf(f33,plain,
( ( $true
!= ( sK0 @ z ) )
| spl8_1 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl8_1
<=> ( $true
= ( sK0 @ z ) ) ),
introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition]) ).
thf(f143,plain,
( ~ spl8_2
| spl8_7
| ~ spl8_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f142]) ).
thf(f142,plain,
( $false
| ~ spl8_2
| spl8_7
| ~ spl8_11 ),
inference(subsumption_resolution,[status(thm)],[f141,f37]) ).
thf(f37,plain,
( ( $true
= ( sK6 @ sK5 ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl8_2
<=> ( $true
= ( sK6 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition]) ).
thf(f141,plain,
( ( $true
!= ( sK6 @ sK5 ) )
| spl8_7
| ~ spl8_11 ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $true
!= ( sK6 @ sK5 ) )
| ( $true != $true )
| spl8_7
| ~ spl8_11 ),
inference(superposition,[status(thm)],[f62,f104]) ).
thf(f104,plain,
( ! [X1: $i > $o] :
( ( ( X1 @ z )
= $true )
| ( ( X1 @ sK5 )
!= $true ) )
| ~ spl8_11 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f103,definition,
( spl8_11
<=> ! [X1: $i > $o] :
( ( ( X1 @ z )
= $true )
| ( ( X1 @ sK5 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl8_11])],[avatar_definition]) ).
thf(f62,plain,
( ( $true
!= ( sK6 @ z ) )
| spl8_7 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl8_7
<=> ( $true
= ( sK6 @ z ) ) ),
introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition]) ).
thf(f125,plain,
( spl8_11
| spl8_10
| spl8_3
| ~ spl8_9 ),
inference(avatar_split_clause,[status(thm)],[f119,f76,f40,f100,f103]) ).
thf(f100,definition,
( spl8_10
<=> ! [X0: $i] :
( ( sK7 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl8_10])],[avatar_definition]) ).
thf(f40,definition,
( spl8_3
<=> ( $true
= ( sK7 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition]) ).
thf(f76,definition,
( spl8_9
<=> ! [X0: $i > $o,X3: $i > $o,X2: $i,X1: $i] :
( ( $true
!= ( X0 @ X1 ) )
| ( ( X0 @ z )
= $true )
| ( $true
!= ( X3 @ X2 ) )
| ( ( X3 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition]) ).
thf(f119,plain,
( ! [X0: $i,X1: $i > $o] :
( ( ( sK7 @ X0 )
!= $true )
| ( ( X1 @ z )
= $true )
| ( ( X1 @ sK5 )
!= $true ) )
| spl8_3
| ~ spl8_9 ),
inference(trivial_inequality_removal,[status(thm)],[f118]) ).
thf(f118,plain,
( ! [X0: $i,X1: $i > $o] :
( ( $true != $true )
| ( ( sK7 @ X0 )
!= $true )
| ( ( X1 @ sK5 )
!= $true )
| ( ( X1 @ z )
= $true ) )
| spl8_3
| ~ spl8_9 ),
inference(superposition,[status(thm)],[f42,f77]) ).
thf(f77,plain,
( ! [X2: $i,X3: $i > $o,X0: $i > $o,X1: $i] :
( ( ( X3 @ X1 )
= $true )
| ( $true
!= ( X3 @ X2 ) )
| ( ( X0 @ z )
= $true )
| ( $true
!= ( X0 @ X1 ) ) )
| ~ spl8_9 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f42,plain,
( ( $true
!= ( sK7 @ sK5 ) )
| spl8_3 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f124,plain,
( ~ spl8_6
| ~ spl8_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f123]) ).
thf(f123,plain,
( $false
| ~ spl8_6
| ~ spl8_10 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $true != $true )
| ~ spl8_6
| ~ spl8_10 ),
inference(superposition,[status(thm)],[f101,f57]) ).
thf(f57,plain,
( ( $true
= ( sK7 @ sK4 ) )
| ~ spl8_6 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl8_6
<=> ( $true
= ( sK7 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition]) ).
thf(f101,plain,
( ! [X0: $i] :
( ( sK7 @ X0 )
!= $true )
| ~ spl8_10 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f117,plain,
( ~ spl8_5
| ~ spl8_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f116]) ).
thf(f116,plain,
( $false
| ~ spl8_5
| ~ spl8_12 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $true != $true )
| ~ spl8_5
| ~ spl8_12 ),
inference(superposition,[status(thm)],[f108,f52]) ).
thf(f52,plain,
( ( $true
= ( sK3 @ sK2 ) )
| ~ spl8_5 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl8_5
<=> ( $true
= ( sK3 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition]) ).
thf(f108,plain,
( ! [X0: $i] :
( $true
!= ( sK3 @ X0 ) )
| ~ spl8_12 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl8_12
<=> ! [X0: $i] :
( $true
!= ( sK3 @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_12])],[avatar_definition]) ).
thf(f112,plain,
( spl8_12
| spl8_13
| spl8_4
| ~ spl8_9 ),
inference(avatar_split_clause,[status(thm)],[f92,f76,f45,f110,f107]) ).
thf(f45,definition,
( spl8_4
<=> ( $true
= ( sK3 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition]) ).
thf(f92,plain,
( ! [X0: $i,X1: $i > $o] :
( ( ( X1 @ z )
= $true )
| ( $true
!= ( sK3 @ X0 ) )
| ( $true
!= ( X1 @ sK1 ) ) )
| spl8_4
| ~ spl8_9 ),
inference(trivial_inequality_removal,[status(thm)],[f88]) ).
thf(f88,plain,
( ! [X0: $i,X1: $i > $o] :
( ( $true
!= ( sK3 @ X0 ) )
| ( $true != $true )
| ( ( X1 @ z )
= $true )
| ( $true
!= ( X1 @ sK1 ) ) )
| spl8_4
| ~ spl8_9 ),
inference(superposition,[status(thm)],[f47,f77]) ).
thf(f47,plain,
( ( $true
!= ( sK3 @ sK1 ) )
| spl8_4 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f81,plain,
( ~ spl8_3
| spl8_8 ),
inference(avatar_split_clause,[status(thm)],[f17,f64,f40]) ).
thf(f17,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
!= ( sK7 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i,X3: $i > $o] :
( ( ( X3 @ X1 )
= $true )
| ( ( X0 @ z )
= $true )
| ( $true
!= ( X0 @ X1 ) )
| ( $true
!= ( X3 @ X2 ) ) )
| ! [X4: $i,X5: $i,X6: $i > $o,X7: $i > $o] :
( ( $true
!= ( X6 @ X5 ) )
| ( ( X6 @ z )
= $true )
| ( $true
!= ( X7 @ X4 ) )
| ( $true
= ( X7 @ X5 ) ) ) )
& ( ( ( $true
!= ( sK3 @ sK1 ) )
& ( $true
!= ( sK0 @ z ) )
& ( $true
= ( sK0 @ sK1 ) )
& ( $true
= ( sK3 @ sK2 ) ) )
| ( ( $true
= ( sK6 @ sK5 ) )
& ( $true
!= ( sK6 @ z ) )
& ( $true
= ( sK7 @ sK4 ) )
& ( $true
!= ( sK7 @ sK5 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f9,f11,f10]) ).
thf(f10,plain,
( ? [X8: $i > $o,X9: $i,X10: $i,X11: $i > $o] :
( ( $true
!= ( X11 @ X9 ) )
& ( $true
!= ( X8 @ z ) )
& ( $true
= ( X8 @ X9 ) )
& ( ( X11 @ X10 )
= $true ) )
=> ( ( $true
!= ( sK3 @ sK1 ) )
& ( $true
!= ( sK0 @ z ) )
& ( $true
= ( sK0 @ sK1 ) )
& ( $true
= ( sK3 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X12: $i,X13: $i,X14: $i > $o,X15: $i > $o] :
( ( $true
= ( X14 @ X13 ) )
& ( $true
!= ( X14 @ z ) )
& ( $true
= ( X15 @ X12 ) )
& ( $true
!= ( X15 @ X13 ) ) )
=> ( ( $true
= ( sK6 @ sK5 ) )
& ( $true
!= ( sK6 @ z ) )
& ( $true
= ( sK7 @ sK4 ) )
& ( $true
!= ( sK7 @ sK5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( ! [X0: $i > $o,X1: $i,X2: $i,X3: $i > $o] :
( ( ( X3 @ X1 )
= $true )
| ( ( X0 @ z )
= $true )
| ( $true
!= ( X0 @ X1 ) )
| ( $true
!= ( X3 @ X2 ) ) )
| ! [X4: $i,X5: $i,X6: $i > $o,X7: $i > $o] :
( ( $true
!= ( X6 @ X5 ) )
| ( ( X6 @ z )
= $true )
| ( $true
!= ( X7 @ X4 ) )
| ( $true
= ( X7 @ X5 ) ) ) )
& ( ? [X8: $i > $o,X9: $i,X10: $i,X11: $i > $o] :
( ( $true
!= ( X11 @ X9 ) )
& ( $true
!= ( X8 @ z ) )
& ( $true
= ( X8 @ X9 ) )
& ( ( X11 @ X10 )
= $true ) )
| ? [X12: $i,X13: $i,X14: $i > $o,X15: $i > $o] :
( ( $true
= ( X14 @ X13 ) )
& ( $true
!= ( X14 @ z ) )
& ( $true
= ( X15 @ X12 ) )
& ( $true
!= ( X15 @ X13 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ! [X4: $i > $o,X7: $i,X6: $i,X5: $i > $o] :
( ( ( X5 @ X7 )
= $true )
| ( $true
= ( X4 @ z ) )
| ( ( X4 @ X7 )
!= $true )
| ( $true
!= ( X5 @ X6 ) ) )
| ! [X3: $i,X2: $i,X0: $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X0 @ z )
= $true )
| ( ( X1 @ X3 )
!= $true )
| ( $true
= ( X1 @ X2 ) ) ) )
& ( ? [X4: $i > $o,X7: $i,X6: $i,X5: $i > $o] :
( ( ( X5 @ X7 )
!= $true )
& ( $true
!= ( X4 @ z ) )
& ( ( X4 @ X7 )
= $true )
& ( $true
= ( X5 @ X6 ) ) )
| ? [X3: $i,X2: $i,X0: $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ z )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( $true
!= ( X1 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X3: $i,X2: $i,X0: $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ z )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( $true
!= ( X1 @ X2 ) ) )
<~> ? [X4: $i > $o,X7: $i,X6: $i,X5: $i > $o] :
( ( ( X5 @ X7 )
!= $true )
& ( $true
!= ( X4 @ z ) )
& ( ( X4 @ X7 )
= $true )
& ( $true
= ( X5 @ X6 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ? [X3: $i,X2: $i,X0: $i > $o,X1: $i > $o] :
( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ z )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( $true
!= ( X1 @ X2 ) ) )
<=> ? [X4: $i > $o,X7: $i,X6: $i,X5: $i > $o] :
( ( ( X5 @ X7 )
!= $true )
& ( $true
!= ( X4 @ z ) )
& ( ( X4 @ X7 )
= $true )
& ( $true
= ( X5 @ X6 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ( ( X0 @ z )
!= $true )
& ( $true
!= ( X1 @ X2 ) )
& ( ( X1 @ X3 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
<=> ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ( $true
!= ( X4 @ z ) )
& ( ( X5 @ X7 )
!= $true )
& ( $true
= ( X5 @ X6 ) )
& ( ( X4 @ X7 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: $i > $o,X1: $i > $o,X2: $i,X3: $i] :
( ~ ( X0 @ z )
& ~ ( X1 @ X2 )
& ( X1 @ X3 )
& ( X0 @ X2 ) )
<=> ? [X4: $i > $o,X5: $i > $o,X6: $i,X7: $i] :
( ~ ( X4 @ z )
& ~ ( X5 @ X7 )
& ( X5 @ X6 )
& ( X4 @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X1: $i > $o,X0: $i > $o,X3: $i,X2: $i] :
( ~ ( X1 @ z )
& ~ ( X0 @ X3 )
& ( X0 @ X2 )
& ( X1 @ X3 ) )
<=> ? [X1: $i > $o,X0: $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ z )
& ~ ( X0 @ X3 )
& ( X0 @ X2 )
& ( X1 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X1: $i > $o,X0: $i > $o,X3: $i,X2: $i] :
( ~ ( X1 @ z )
& ~ ( X0 @ X3 )
& ( X0 @ X2 )
& ( X1 @ X3 ) )
<=> ? [X1: $i > $o,X0: $i > $o,X2: $i,X3: $i] :
( ~ ( X1 @ z )
& ~ ( X0 @ X3 )
& ( X0 @ X2 )
& ( X1 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VpTuNNhuQJ/DTF2THF_25748.p',cSILLYWFF2) ).
thf(f80,plain,
( ~ spl8_4
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f35,f45]) ).
thf(f28,plain,
( ( $true
= ( sK6 @ sK5 ) )
| ( $true
!= ( sK3 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f79,plain,
( ~ spl8_7
| ~ spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f27,f45,f60]) ).
thf(f27,plain,
( ( $true
!= ( sK6 @ z ) )
| ( $true
!= ( sK3 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f78,plain,
( spl8_9
| spl8_9 ),
inference(avatar_split_clause,[status(thm)],[f29,f76,f76]) ).
thf(f29,plain,
! [X2: $i,X3: $i > $o,X0: $i > $o,X1: $i,X6: $i > $o,X7: $i > $o,X4: $i,X5: $i] :
( ( $true
!= ( X0 @ X1 ) )
| ( ( X3 @ X1 )
= $true )
| ( $true
!= ( X6 @ X5 ) )
| ( $true
!= ( X3 @ X2 ) )
| ( $true
!= ( X7 @ X4 ) )
| ( ( X0 @ z )
= $true )
| ( ( X6 @ z )
= $true )
| ( $true
= ( X7 @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f74,plain,
( spl8_5
| spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f14,f55,f50]) ).
thf(f14,plain,
( ( $true
= ( sK3 @ sK2 ) )
| ( $true
= ( sK7 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f73,plain,
( ~ spl8_7
| spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f15,f50,f60]) ).
thf(f15,plain,
( ( $true
!= ( sK6 @ z ) )
| ( $true
= ( sK3 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f72,plain,
( spl8_8
| spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f18,f55,f64]) ).
thf(f18,plain,
( ( $true
= ( sK7 @ sK4 ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f71,plain,
( spl8_8
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f20,f35,f64]) ).
thf(f20,plain,
( ( $true
= ( sK6 @ sK5 ) )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f70,plain,
( ~ spl8_7
| ~ spl8_1 ),
inference(avatar_split_clause,[status(thm)],[f23,f31,f60]) ).
thf(f23,plain,
( ( $true
!= ( sK0 @ z ) )
| ( $true
!= ( sK6 @ z ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f69,plain,
( spl8_5
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f13,f40,f50]) ).
thf(f13,plain,
( ( $true
= ( sK3 @ sK2 ) )
| ( $true
!= ( sK7 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f68,plain,
( spl8_6
| ~ spl8_4 ),
inference(avatar_split_clause,[status(thm)],[f26,f45,f55]) ).
thf(f26,plain,
( ( $true
!= ( sK3 @ sK1 ) )
| ( $true
= ( sK7 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f67,plain,
( ~ spl8_7
| spl8_8 ),
inference(avatar_split_clause,[status(thm)],[f19,f64,f60]) ).
thf(f19,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
!= ( sK6 @ z ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f58,plain,
( ~ spl8_1
| spl8_6 ),
inference(avatar_split_clause,[status(thm)],[f22,f55,f31]) ).
thf(f22,plain,
( ( $true
= ( sK7 @ sK4 ) )
| ( $true
!= ( sK0 @ z ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f53,plain,
( spl8_2
| spl8_5 ),
inference(avatar_split_clause,[status(thm)],[f16,f50,f35]) ).
thf(f16,plain,
( ( $true
= ( sK3 @ sK2 ) )
| ( $true
= ( sK6 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f48,plain,
( ~ spl8_4
| ~ spl8_3 ),
inference(avatar_split_clause,[status(thm)],[f25,f40,f45]) ).
thf(f25,plain,
( ( $true
!= ( sK3 @ sK1 ) )
| ( $true
!= ( sK7 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f43,plain,
( ~ spl8_3
| ~ spl8_1 ),
inference(avatar_split_clause,[status(thm)],[f21,f31,f40]) ).
thf(f21,plain,
( ( $true
!= ( sK0 @ z ) )
| ( $true
!= ( sK7 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f38,plain,
( ~ spl8_1
| spl8_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f35,f31]) ).
thf(f24,plain,
( ( $true
!= ( sK0 @ z ) )
| ( $true
= ( sK6 @ sK5 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO314^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:28:10 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SYO314^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Syntactic
% 0.18/0.45 % Problem : TPS problem from BASIC-HO-THMS
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0908 [Bro09]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v4.1.0, 0.33 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.18/0.45 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 0 ( 0 avg)
% 0.18/0.45 % Number of connectives : 19 ( 4 ~; 0 |; 6 &; 8 @)
% 0.18/0.45 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 1 ( 1 usr; 1 con; 0-0 aty)
% 0.18/0.45 % Number of variables : 8 ( 0 ^; 0 !; 8 ?; 8 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(z,type,
% 0.18/0.45 z: $i ).
% 0.18/0.45
% 0.18/0.45 thf(cSILLYWFF2,conjecture,
% 0.18/0.45 ( ? [Xp: $i > $o,Xq: $i > $o,Xx: $i,Xy: $i] :
% 0.18/0.45 ( ( Xp @ Xx )
% 0.18/0.45 & ~ ( Xp @ Xy )
% 0.18/0.45 & ( Xq @ Xy )
% 0.18/0.45 & ~ ( Xq @ z ) )
% 0.18/0.45 <=> ? [Xp: $i > $o,Xq: $i > $o,Xx: $i,Xy: $i] :
% 0.18/0.45 ( ~ ( Xq @ z )
% 0.18/0.45 & ( Xq @ Xy )
% 0.18/0.45 & ( Xp @ Xx )
% 0.18/0.45 & ~ ( Xp @ Xy ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.38/1.18 ---- Embedded in THF ---
% 1.38/1.18 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.18 %%% Generated on Tue Feb 24 14:28:11 EST 2026
% 1.38/1.18 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.18 %%% Logic specification used:
% 1.38/1.18 %%% thf(spec, logic, $$dhol).
% 1.38/1.18
% 1.38/1.18 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VpTuNNhuQJ/DTF2DTF25748.p
% See solution above
% 1.38/1.18 ------------------------
% 1.38/1.19 ---- Cleaned THF ---
% 1.38/1.20 thf(z,type,
% 1.38/1.20 z: $i ).
% 1.38/1.20
% 1.38/1.20 thf(cSILLYWFF2,conjecture,
% 1.38/1.20 ( ? [Xp: $i > $o,Xq: $i > $o,Xx: $i,Xy: $i] :
% 1.38/1.20 ( ( Xp @ Xx )
% 1.38/1.20 & ~ ( Xp @ Xy )
% 1.38/1.20 & ( Xq @ Xy )
% 1.38/1.20 & ~ ( Xq @ z ) )
% 1.38/1.20 <=> ? [Xp: $i > $o,Xq: $i > $o,Xx: $i,Xy: $i] :
% 1.38/1.20 ( ~ ( Xq @ z )
% 1.38/1.20 & ( Xq @ Xy )
% 1.38/1.20 & ( Xp @ Xx )
% 1.38/1.20 & ~ ( Xp @ Xy ) ) ) ).
% 1.38/1.20 ------------------------
% 1.51/1.21 % (25941)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_25748 for (3000ds/275Mi)
% 1.51/1.21 % (25938)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_25748 for (3000ds/27Mi)
% 1.51/1.21 % (25941)First to succeed.
% 1.51/1.21 % (25938)Also succeeded, but the first one will report.
% 1.51/1.21 % (25941)Refutation found. Thanks to Tanya!
% 1.51/1.21 % SZS status Theorem for DTF2THF_25748
% 1.51/1.21 % SZS output start Proof for DTF2THF_25748
% 1.51/1.21 thf(func_def_4, type, sK0: $i > $o).
% 1.51/1.21 thf(func_def_7, type, sK3: $i > $o).
% 1.51/1.21 thf(func_def_10, type, sK6: $i > $o).
% 1.51/1.21 thf(func_def_11, type, sK7: $i > $o).
% 1.51/1.21 thf(func_def_14, type, ph9: !>[X0: $tType]:(X0)).
% 1.51/1.21 thf(f171,plain,(
% 1.51/1.21 $false),
% 1.51/1.21 inference(avatar_sat_refutation,[status(thm)],[f38,f43,f48,f53,f58,f67,f68,f69,f70,f71,f72,f73,f74,f78,f79,f80,f81,f112,f117,f124,f125,f143,f170])).
% 1.51/1.21 thf(f170,plain,(
% 1.51/1.21 spl8_1 | ~spl8_8 | ~spl8_13),
% 1.51/1.21 inference(avatar_contradiction_clause,[status(thm)],[f169])).
% 1.51/1.21 thf(f169,plain,(
% 1.51/1.21 $false | (spl8_1 | ~spl8_8 | ~spl8_13)),
% 1.51/1.21 inference(subsumption_resolution,[status(thm)],[f160,f66])).
% 1.51/1.21 thf(f66,plain,(
% 1.51/1.21 ($true = (sK0 @ sK1)) | ~spl8_8),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.51/1.21 thf(f64,definition,(
% 1.51/1.21 spl8_8 <=> ($true = (sK0 @ sK1))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_8])],[avatar_definition])).
% 1.51/1.21 thf(f160,plain,(
% 1.51/1.21 ($true != (sK0 @ sK1)) | (spl8_1 | ~spl8_13)),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.51/1.21 thf(f157,plain,(
% 1.51/1.21 ($true != (sK0 @ sK1)) | ($true != $true) | (spl8_1 | ~spl8_13)),
% 1.51/1.21 inference(superposition,[status(thm)],[f33,f111])).
% 1.51/1.21 thf(f111,plain,(
% 1.51/1.21 ( ! [X1 : $i > $o] : (((X1 @ z) = $true) | ($true != (X1 @ sK1))) ) | ~spl8_13),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f110])).
% 1.51/1.21 thf(f110,definition,(
% 1.51/1.21 spl8_13 <=> ! [X1 : $i > $o] : (((X1 @ z) = $true) | ($true != (X1 @ sK1)))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_13])],[avatar_definition])).
% 1.51/1.21 thf(f33,plain,(
% 1.51/1.21 ($true != (sK0 @ z)) | spl8_1),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.51/1.21 thf(f31,definition,(
% 1.51/1.21 spl8_1 <=> ($true = (sK0 @ z))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_1])],[avatar_definition])).
% 1.51/1.21 thf(f143,plain,(
% 1.51/1.21 ~spl8_2 | spl8_7 | ~spl8_11),
% 1.51/1.21 inference(avatar_contradiction_clause,[status(thm)],[f142])).
% 1.51/1.21 thf(f142,plain,(
% 1.51/1.21 $false | (~spl8_2 | spl8_7 | ~spl8_11)),
% 1.51/1.21 inference(subsumption_resolution,[status(thm)],[f141,f37])).
% 1.51/1.21 thf(f37,plain,(
% 1.51/1.21 ($true = (sK6 @ sK5)) | ~spl8_2),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.51/1.21 thf(f35,definition,(
% 1.51/1.21 spl8_2 <=> ($true = (sK6 @ sK5))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_2])],[avatar_definition])).
% 1.51/1.21 thf(f141,plain,(
% 1.51/1.21 ($true != (sK6 @ sK5)) | (spl8_7 | ~spl8_11)),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.51/1.21 thf(f133,plain,(
% 1.51/1.21 ($true != (sK6 @ sK5)) | ($true != $true) | (spl8_7 | ~spl8_11)),
% 1.51/1.21 inference(superposition,[status(thm)],[f62,f104])).
% 1.51/1.21 thf(f104,plain,(
% 1.51/1.21 ( ! [X1 : $i > $o] : (((X1 @ z) = $true) | ((X1 @ sK5) != $true)) ) | ~spl8_11),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.51/1.21 thf(f103,definition,(
% 1.51/1.21 spl8_11 <=> ! [X1 : $i > $o] : (((X1 @ z) = $true) | ((X1 @ sK5) != $true))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_11])],[avatar_definition])).
% 1.51/1.21 thf(f62,plain,(
% 1.51/1.21 ($true != (sK6 @ z)) | spl8_7),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.51/1.21 thf(f60,definition,(
% 1.51/1.21 spl8_7 <=> ($true = (sK6 @ z))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_7])],[avatar_definition])).
% 1.51/1.21 thf(f125,plain,(
% 1.51/1.21 spl8_11 | spl8_10 | spl8_3 | ~spl8_9),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f119,f76,f40,f100,f103])).
% 1.51/1.21 thf(f100,definition,(
% 1.51/1.21 spl8_10 <=> ! [X0 : $i] : ((sK7 @ X0) != $true)),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_10])],[avatar_definition])).
% 1.51/1.21 thf(f40,definition,(
% 1.51/1.21 spl8_3 <=> ($true = (sK7 @ sK5))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_3])],[avatar_definition])).
% 1.51/1.21 thf(f76,definition,(
% 1.51/1.21 spl8_9 <=> ! [X0 : $i > $o,X3 : $i > $o,X2 : $i,X1 : $i] : (($true != (X0 @ X1)) | ((X0 @ z) = $true) | ($true != (X3 @ X2)) | ((X3 @ X1) = $true))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_9])],[avatar_definition])).
% 1.51/1.21 thf(f119,plain,(
% 1.51/1.21 ( ! [X0 : $i,X1 : $i > $o] : (((sK7 @ X0) != $true) | ((X1 @ z) = $true) | ((X1 @ sK5) != $true)) ) | (spl8_3 | ~spl8_9)),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f118])).
% 1.51/1.21 thf(f118,plain,(
% 1.51/1.21 ( ! [X0 : $i,X1 : $i > $o] : (($true != $true) | ((sK7 @ X0) != $true) | ((X1 @ sK5) != $true) | ((X1 @ z) = $true)) ) | (spl8_3 | ~spl8_9)),
% 1.51/1.21 inference(superposition,[status(thm)],[f42,f77])).
% 1.51/1.21 thf(f77,plain,(
% 1.51/1.21 ( ! [X2 : $i,X3 : $i > $o,X0 : $i > $o,X1 : $i] : (((X3 @ X1) = $true) | ($true != (X3 @ X2)) | ((X0 @ z) = $true) | ($true != (X0 @ X1))) ) | ~spl8_9),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.51/1.21 thf(f42,plain,(
% 1.51/1.21 ($true != (sK7 @ sK5)) | spl8_3),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.51/1.21 thf(f124,plain,(
% 1.51/1.21 ~spl8_6 | ~spl8_10),
% 1.51/1.21 inference(avatar_contradiction_clause,[status(thm)],[f123])).
% 1.51/1.21 thf(f123,plain,(
% 1.51/1.21 $false | (~spl8_6 | ~spl8_10)),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 1.51/1.21 thf(f120,plain,(
% 1.51/1.21 ($true != $true) | (~spl8_6 | ~spl8_10)),
% 1.51/1.21 inference(superposition,[status(thm)],[f101,f57])).
% 1.51/1.21 thf(f57,plain,(
% 1.51/1.21 ($true = (sK7 @ sK4)) | ~spl8_6),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.51/1.21 thf(f55,definition,(
% 1.51/1.21 spl8_6 <=> ($true = (sK7 @ sK4))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_6])],[avatar_definition])).
% 1.51/1.21 thf(f101,plain,(
% 1.51/1.21 ( ! [X0 : $i] : (((sK7 @ X0) != $true)) ) | ~spl8_10),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.51/1.21 thf(f117,plain,(
% 1.51/1.21 ~spl8_5 | ~spl8_12),
% 1.51/1.21 inference(avatar_contradiction_clause,[status(thm)],[f116])).
% 1.51/1.21 thf(f116,plain,(
% 1.51/1.21 $false | (~spl8_5 | ~spl8_12)),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.51/1.21 thf(f113,plain,(
% 1.51/1.21 ($true != $true) | (~spl8_5 | ~spl8_12)),
% 1.51/1.21 inference(superposition,[status(thm)],[f108,f52])).
% 1.51/1.21 thf(f52,plain,(
% 1.51/1.21 ($true = (sK3 @ sK2)) | ~spl8_5),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.51/1.21 thf(f50,definition,(
% 1.51/1.21 spl8_5 <=> ($true = (sK3 @ sK2))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_5])],[avatar_definition])).
% 1.51/1.21 thf(f108,plain,(
% 1.51/1.21 ( ! [X0 : $i] : (($true != (sK3 @ X0))) ) | ~spl8_12),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.51/1.21 thf(f107,definition,(
% 1.51/1.21 spl8_12 <=> ! [X0 : $i] : ($true != (sK3 @ X0))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_12])],[avatar_definition])).
% 1.51/1.21 thf(f112,plain,(
% 1.51/1.21 spl8_12 | spl8_13 | spl8_4 | ~spl8_9),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f92,f76,f45,f110,f107])).
% 1.51/1.21 thf(f45,definition,(
% 1.51/1.21 spl8_4 <=> ($true = (sK3 @ sK1))),
% 1.51/1.21 introduced(definition,[new_symbols(naming,[spl8_4])],[avatar_definition])).
% 1.51/1.21 thf(f92,plain,(
% 1.51/1.21 ( ! [X0 : $i,X1 : $i > $o] : (((X1 @ z) = $true) | ($true != (sK3 @ X0)) | ($true != (X1 @ sK1))) ) | (spl8_4 | ~spl8_9)),
% 1.51/1.21 inference(trivial_inequality_removal,[status(thm)],[f88])).
% 1.51/1.21 thf(f88,plain,(
% 1.51/1.21 ( ! [X0 : $i,X1 : $i > $o] : (($true != (sK3 @ X0)) | ($true != $true) | ((X1 @ z) = $true) | ($true != (X1 @ sK1))) ) | (spl8_4 | ~spl8_9)),
% 1.51/1.21 inference(superposition,[status(thm)],[f47,f77])).
% 1.51/1.21 thf(f47,plain,(
% 1.51/1.21 ($true != (sK3 @ sK1)) | spl8_4),
% 1.51/1.21 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.51/1.21 thf(f81,plain,(
% 1.51/1.21 ~spl8_3 | spl8_8),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f17,f64,f40])).
% 1.51/1.21 thf(f17,plain,(
% 1.51/1.21 ($true = (sK0 @ sK1)) | ($true != (sK7 @ sK5))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f12,plain,(
% 1.51/1.21 (! [X0 : $i > $o,X1 : $i,X2 : $i,X3 : $i > $o] : (((X3 @ X1) = $true) | ((X0 @ z) = $true) | ($true != (X0 @ X1)) | ($true != (X3 @ X2))) | ! [X4 : $i,X5 : $i,X6 : $i > $o,X7 : $i > $o] : (($true != (X6 @ X5)) | ((X6 @ z) = $true) | ($true != (X7 @ X4)) | ($true = (X7 @ X5)))) & ((($true != (sK3 @ sK1)) & ($true != (sK0 @ z)) & ($true = (sK0 @ sK1)) & ($true = (sK3 @ sK2))) | (($true = (sK6 @ sK5)) & ($true != (sK6 @ z)) & ($true = (sK7 @ sK4)) & ($true != (sK7 @ sK5))))),
% 1.51/1.21 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f9,f11,f10])).
% 1.51/1.21 thf(f10,plain,(
% 1.51/1.21 ? [X8 : $i > $o,X9 : $i,X10 : $i,X11 : $i > $o] : (($true != (X11 @ X9)) & ($true != (X8 @ z)) & ($true = (X8 @ X9)) & ((X11 @ X10) = $true)) => (($true != (sK3 @ sK1)) & ($true != (sK0 @ z)) & ($true = (sK0 @ sK1)) & ($true = (sK3 @ sK2)))),
% 1.51/1.21 introduced(definition,[],[choice_axiom])).
% 1.51/1.21 thf(f11,plain,(
% 1.51/1.21 ? [X12 : $i,X13 : $i,X14 : $i > $o,X15 : $i > $o] : (($true = (X14 @ X13)) & ($true != (X14 @ z)) & ($true = (X15 @ X12)) & ($true != (X15 @ X13))) => (($true = (sK6 @ sK5)) & ($true != (sK6 @ z)) & ($true = (sK7 @ sK4)) & ($true != (sK7 @ sK5)))),
% 1.51/1.21 introduced(definition,[],[choice_axiom])).
% 1.51/1.21 thf(f9,plain,(
% 1.51/1.21 (! [X0 : $i > $o,X1 : $i,X2 : $i,X3 : $i > $o] : (((X3 @ X1) = $true) | ((X0 @ z) = $true) | ($true != (X0 @ X1)) | ($true != (X3 @ X2))) | ! [X4 : $i,X5 : $i,X6 : $i > $o,X7 : $i > $o] : (($true != (X6 @ X5)) | ((X6 @ z) = $true) | ($true != (X7 @ X4)) | ($true = (X7 @ X5)))) & (? [X8 : $i > $o,X9 : $i,X10 : $i,X11 : $i > $o] : (($true != (X11 @ X9)) & ($true != (X8 @ z)) & ($true = (X8 @ X9)) & ((X11 @ X10) = $true)) | ? [X12 : $i,X13 : $i,X14 : $i > $o,X15 : $i > $o] : (($true = (X14 @ X13)) & ($true != (X14 @ z)) & ($true = (X15 @ X12)) & ($true != (X15 @ X13))))),
% 1.51/1.21 inference(rectify,[status(thm)],[f8])).
% 1.51/1.21 thf(f8,plain,(
% 1.51/1.21 (! [X4 : $i > $o,X7 : $i,X6 : $i,X5 : $i > $o] : (((X5 @ X7) = $true) | ($true = (X4 @ z)) | ((X4 @ X7) != $true) | ($true != (X5 @ X6))) | ! [X3 : $i,X2 : $i,X0 : $i > $o,X1 : $i > $o] : (((X0 @ X2) != $true) | ((X0 @ z) = $true) | ((X1 @ X3) != $true) | ($true = (X1 @ X2)))) & (? [X4 : $i > $o,X7 : $i,X6 : $i,X5 : $i > $o] : (((X5 @ X7) != $true) & ($true != (X4 @ z)) & ((X4 @ X7) = $true) & ($true = (X5 @ X6))) | ? [X3 : $i,X2 : $i,X0 : $i > $o,X1 : $i > $o] : (((X0 @ X2) = $true) & ((X0 @ z) != $true) & ((X1 @ X3) = $true) & ($true != (X1 @ X2))))),
% 1.51/1.21 inference(nnf_transformation,[status(thm)],[f7])).
% 1.51/1.21 thf(f7,plain,(
% 1.51/1.21 ? [X3 : $i,X2 : $i,X0 : $i > $o,X1 : $i > $o] : (((X0 @ X2) = $true) & ((X0 @ z) != $true) & ((X1 @ X3) = $true) & ($true != (X1 @ X2))) <~> ? [X4 : $i > $o,X7 : $i,X6 : $i,X5 : $i > $o] : (((X5 @ X7) != $true) & ($true != (X4 @ z)) & ((X4 @ X7) = $true) & ($true = (X5 @ X6)))),
% 1.51/1.21 inference(ennf_transformation,[status(thm)],[f6])).
% 1.51/1.21 thf(f6,plain,(
% 1.51/1.21 ~(? [X3 : $i,X2 : $i,X0 : $i > $o,X1 : $i > $o] : (((X0 @ X2) = $true) & ((X0 @ z) != $true) & ((X1 @ X3) = $true) & ($true != (X1 @ X2))) <=> ? [X4 : $i > $o,X7 : $i,X6 : $i,X5 : $i > $o] : (((X5 @ X7) != $true) & ($true != (X4 @ z)) & ((X4 @ X7) = $true) & ($true = (X5 @ X6))))),
% 1.51/1.21 inference(flattening,[status(thm)],[f5])).
% 1.51/1.21 thf(f5,plain,(
% 1.51/1.21 ~(? [X0 : $i > $o,X1 : $i > $o,X2 : $i,X3 : $i] : (~((X0 @ z) = $true) & ~($true = (X1 @ X2)) & ((X1 @ X3) = $true) & ((X0 @ X2) = $true)) <=> ? [X4 : $i > $o,X5 : $i > $o,X6 : $i,X7 : $i] : (~($true = (X4 @ z)) & ~((X5 @ X7) = $true) & ($true = (X5 @ X6)) & ((X4 @ X7) = $true)))),
% 1.51/1.21 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.21 thf(f4,plain,(
% 1.51/1.21 ~(? [X0 : $i > $o,X1 : $i > $o,X2 : $i,X3 : $i] : (~(X0 @ z) & ~(X1 @ X2) & (X1 @ X3) & (X0 @ X2)) <=> ? [X4 : $i > $o,X5 : $i > $o,X6 : $i,X7 : $i] : (~(X4 @ z) & ~(X5 @ X7) & (X5 @ X6) & (X4 @ X7)))),
% 1.51/1.21 inference(rectify,[status(thm)],[f2])).
% 1.51/1.21 thf(f2,negated_conjecture,(
% 1.51/1.21 ~(? [X1 : $i > $o,X0 : $i > $o,X3 : $i,X2 : $i] : (~(X1 @ z) & ~(X0 @ X3) & (X0 @ X2) & (X1 @ X3)) <=> ? [X1 : $i > $o,X0 : $i > $o,X2 : $i,X3 : $i] : (~(X1 @ z) & ~(X0 @ X3) & (X0 @ X2) & (X1 @ X3)))),
% 1.51/1.21 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.21 thf(f1,conjecture,(
% 1.51/1.21 ? [X1 : $i > $o,X0 : $i > $o,X3 : $i,X2 : $i] : (~(X1 @ z) & ~(X0 @ X3) & (X0 @ X2) & (X1 @ X3)) <=> ? [X1 : $i > $o,X0 : $i > $o,X2 : $i,X3 : $i] : (~(X1 @ z) & ~(X0 @ X3) & (X0 @ X2) & (X1 @ X3))),
% 1.51/1.21 file('/export/starexec/sandbox/tmp/tmp.VpTuNNhuQJ/DTF2THF_25748.p',cSILLYWFF2)).
% 1.51/1.21 thf(f80,plain,(
% 1.51/1.21 ~spl8_4 | spl8_2),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f28,f35,f45])).
% 1.51/1.21 thf(f28,plain,(
% 1.51/1.21 ($true = (sK6 @ sK5)) | ($true != (sK3 @ sK1))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f79,plain,(
% 1.51/1.21 ~spl8_7 | ~spl8_4),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f27,f45,f60])).
% 1.51/1.21 thf(f27,plain,(
% 1.51/1.21 ($true != (sK6 @ z)) | ($true != (sK3 @ sK1))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f78,plain,(
% 1.51/1.21 spl8_9 | spl8_9),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f29,f76,f76])).
% 1.51/1.21 thf(f29,plain,(
% 1.51/1.21 ( ! [X2 : $i,X3 : $i > $o,X0 : $i > $o,X1 : $i,X6 : $i > $o,X7 : $i > $o,X4 : $i,X5 : $i] : (($true != (X0 @ X1)) | ((X3 @ X1) = $true) | ($true != (X6 @ X5)) | ($true != (X3 @ X2)) | ($true != (X7 @ X4)) | ((X0 @ z) = $true) | ((X6 @ z) = $true) | ($true = (X7 @ X5))) )),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f74,plain,(
% 1.51/1.21 spl8_5 | spl8_6),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f14,f55,f50])).
% 1.51/1.21 thf(f14,plain,(
% 1.51/1.21 ($true = (sK3 @ sK2)) | ($true = (sK7 @ sK4))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f73,plain,(
% 1.51/1.21 ~spl8_7 | spl8_5),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f15,f50,f60])).
% 1.51/1.21 thf(f15,plain,(
% 1.51/1.21 ($true != (sK6 @ z)) | ($true = (sK3 @ sK2))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f72,plain,(
% 1.51/1.21 spl8_8 | spl8_6),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f18,f55,f64])).
% 1.51/1.21 thf(f18,plain,(
% 1.51/1.21 ($true = (sK7 @ sK4)) | ($true = (sK0 @ sK1))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f71,plain,(
% 1.51/1.21 spl8_8 | spl8_2),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f20,f35,f64])).
% 1.51/1.21 thf(f20,plain,(
% 1.51/1.21 ($true = (sK6 @ sK5)) | ($true = (sK0 @ sK1))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f70,plain,(
% 1.51/1.21 ~spl8_7 | ~spl8_1),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f23,f31,f60])).
% 1.51/1.21 thf(f23,plain,(
% 1.51/1.21 ($true != (sK0 @ z)) | ($true != (sK6 @ z))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f69,plain,(
% 1.51/1.21 spl8_5 | ~spl8_3),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f13,f40,f50])).
% 1.51/1.21 thf(f13,plain,(
% 1.51/1.21 ($true = (sK3 @ sK2)) | ($true != (sK7 @ sK5))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f68,plain,(
% 1.51/1.21 spl8_6 | ~spl8_4),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f26,f45,f55])).
% 1.51/1.21 thf(f26,plain,(
% 1.51/1.21 ($true != (sK3 @ sK1)) | ($true = (sK7 @ sK4))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f67,plain,(
% 1.51/1.21 ~spl8_7 | spl8_8),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f19,f64,f60])).
% 1.51/1.21 thf(f19,plain,(
% 1.51/1.21 ($true = (sK0 @ sK1)) | ($true != (sK6 @ z))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f58,plain,(
% 1.51/1.21 ~spl8_1 | spl8_6),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f22,f55,f31])).
% 1.51/1.21 thf(f22,plain,(
% 1.51/1.21 ($true = (sK7 @ sK4)) | ($true != (sK0 @ z))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f53,plain,(
% 1.51/1.21 spl8_2 | spl8_5),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f16,f50,f35])).
% 1.51/1.21 thf(f16,plain,(
% 1.51/1.21 ($true = (sK3 @ sK2)) | ($true = (sK6 @ sK5))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f48,plain,(
% 1.51/1.21 ~spl8_4 | ~spl8_3),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f25,f40,f45])).
% 1.51/1.21 thf(f25,plain,(
% 1.51/1.21 ($true != (sK3 @ sK1)) | ($true != (sK7 @ sK5))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f43,plain,(
% 1.51/1.21 ~spl8_3 | ~spl8_1),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f21,f31,f40])).
% 1.51/1.21 thf(f21,plain,(
% 1.51/1.21 ($true != (sK0 @ z)) | ($true != (sK7 @ sK5))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 thf(f38,plain,(
% 1.51/1.21 ~spl8_1 | spl8_2),
% 1.51/1.21 inference(avatar_split_clause,[status(thm)],[f24,f35,f31])).
% 1.51/1.21 thf(f24,plain,(
% 1.51/1.21 ($true != (sK0 @ z)) | ($true = (sK6 @ sK5))),
% 1.51/1.21 inference(cnf_transformation,[status(thm)],[f12])).
% 1.51/1.21 % SZS output end Proof for DTF2THF_25748
% 1.51/1.21 % (25941)------------------------------
% 1.51/1.21 % (25941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.21 % (25941)Termination reason: Refutation
% 1.51/1.21
% 1.51/1.21 % (25941)Memory used [KB]: 5628
% 1.51/1.21 % (25941)Time elapsed: 0.006 s
% 1.51/1.21 % (25941)Instructions burned: 9 (million)
% 1.51/1.21 % (25941)------------------------------
% 1.51/1.21 % (25941)------------------------------
% 1.51/1.21 % (25935)Success in time 0.004 s
%------------------------------------------------------------------------------