%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO315^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 1.47s 1.26s
% Output : Refutation 1.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 7 unt; 0 typ; 2 def)
% Number of atoms : 226 ( 74 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 241 ( 62 ~; 29 |; 48 &; 94 @)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 38 ( 38 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 76 ( 0 ^; 24 !; 52 ?; 76 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_5,type,
sK0: $i > $o ).
thf(func_def_8,type,
sK3: $i > $o ).
thf(func_def_10,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f52,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f35,f40,f51]) ).
thf(f51,plain,
~ spl4_4,
inference(avatar_contradiction_clause,[status(thm)],[f50]) ).
thf(f50,plain,
( $false
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f46]) ).
thf(f46,plain,
( ( $true != $true )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f14,f44]) ).
thf(f44,plain,
( ( $true
= ( sK3 @ sK2 ) )
| ~ spl4_4 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $true != $true )
| ( $true
= ( sK3 @ sK2 ) )
| ~ spl4_4 ),
inference(superposition,[status(thm)],[f34,f15]) ).
thf(f15,plain,
( $true
= ( sK3 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( $true
= ( sK3 @ sK1 ) )
& ( $true
!= ( sK3 @ sK2 ) )
& ( $true
!= ( sK0 @ z ) )
& ( $true
= ( sK0 @ sK2 ) )
& ! [X4: $i,X5: $i > $o,X6: $i > $o,X7: $i] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( X5 @ X7 ) )
| ( $true
!= ( X5 @ X4 ) )
| ( $true
= ( X6 @ z ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9]) ).
thf(f9,plain,
( ? [X0: $i > $o,X1: $i,X2: $i,X3: $i > $o] :
( ( $true
= ( X3 @ X1 ) )
& ( $true
!= ( X3 @ X2 ) )
& ( ( X0 @ z )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
=> ( ( $true
= ( sK3 @ sK1 ) )
& ( $true
!= ( sK3 @ sK2 ) )
& ( $true
!= ( sK0 @ z ) )
& ( $true
= ( sK0 @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ? [X0: $i > $o,X1: $i,X2: $i,X3: $i > $o] :
( ( $true
= ( X3 @ X1 ) )
& ( $true
!= ( X3 @ X2 ) )
& ( ( X0 @ z )
!= $true )
& ( ( X0 @ X2 )
= $true ) )
& ! [X4: $i,X5: $i > $o,X6: $i > $o,X7: $i] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( X5 @ X7 ) )
| ( $true
!= ( X5 @ X4 ) )
| ( $true
= ( X6 @ z ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X2: $i > $o,X0: $i,X1: $i,X3: $i > $o] :
( ( $true
= ( X3 @ X0 ) )
& ( $true
!= ( X3 @ X1 ) )
& ( $true
!= ( X2 @ z ) )
& ( $true
= ( X2 @ X1 ) ) )
& ! [X7: $i,X6: $i > $o,X5: $i > $o,X4: $i] :
( ( $true
!= ( X5 @ X4 ) )
| ( $true
= ( X6 @ X4 ) )
| ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( X5 @ z ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ? [X2: $i > $o,X0: $i,X1: $i,X3: $i > $o] :
( ( $true
= ( X3 @ X0 ) )
& ( $true
!= ( X3 @ X1 ) )
& ( $true
!= ( X2 @ z ) )
& ( $true
= ( X2 @ X1 ) ) )
=> ? [X4: $i,X5: $i > $o,X6: $i > $o,X7: $i] :
( ( $true
!= ( X5 @ z ) )
& ( $true
= ( X5 @ X4 ) )
& ( $true
= ( X6 @ X7 ) )
& ( $true
!= ( X6 @ X4 ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ? [X0: $i,X1: $i,X2: $i > $o,X3: $i > $o] :
( ( $true
= ( X3 @ X0 ) )
& ( $true
!= ( X3 @ X1 ) )
& ( $true
!= ( X2 @ z ) )
& ( $true
= ( X2 @ X1 ) ) )
=> ? [X4: $i,X5: $i > $o,X6: $i > $o,X7: $i] :
( ( $true
!= ( X6 @ X4 ) )
& ( $true
!= ( X5 @ z ) )
& ( $true
= ( X5 @ X4 ) )
& ( $true
= ( X6 @ X7 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ? [X0: $i,X1: $i,X2: $i > $o,X3: $i > $o] :
( ( X3 @ X0 )
& ~ ( X3 @ X1 )
& ~ ( X2 @ z )
& ( X2 @ X1 ) )
=> ? [X4: $i,X5: $i > $o,X6: $i > $o,X7: $i] :
( ~ ( X6 @ X4 )
& ~ ( X5 @ z )
& ( X5 @ X4 )
& ( X6 @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ? [X2: $i,X3: $i,X1: $i > $o,X0: $i > $o] :
( ( X0 @ X2 )
& ~ ( X0 @ X3 )
& ~ ( X1 @ z )
& ( X1 @ X3 ) )
=> ? [X3: $i,X1: $i > $o,X0: $i > $o,X2: $i] :
( ~ ( X0 @ X3 )
& ~ ( X1 @ z )
& ( X1 @ X3 )
& ( X0 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ? [X2: $i,X3: $i,X1: $i > $o,X0: $i > $o] :
( ( X0 @ X2 )
& ~ ( X0 @ X3 )
& ~ ( X1 @ z )
& ( X1 @ X3 ) )
=> ? [X3: $i,X1: $i > $o,X0: $i > $o,X2: $i] :
( ~ ( X0 @ X3 )
& ~ ( X1 @ z )
& ( X1 @ X3 )
& ( X0 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.MFnmrStzB6/DTF2THF_25790.p',cSILLYWFF) ).
thf(f34,plain,
( ! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( X0 @ sK2 ) ) )
| ~ spl4_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl4_4
<=> ! [X0: $i > $o,X1: $i] :
( ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( X0 @ sK2 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f14,plain,
( $true
!= ( sK3 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f40,plain,
~ spl4_3,
inference(avatar_contradiction_clause,[status(thm)],[f39]) ).
thf(f39,plain,
( $false
| ~ spl4_3 ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true != $true )
| ~ spl4_3 ),
inference(superposition,[status(thm)],[f13,f31]) ).
thf(f31,plain,
( ( $true
= ( sK0 @ z ) )
| ~ spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl4_3
<=> ( $true
= ( sK0 @ z ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f13,plain,
( $true
!= ( sK0 @ z ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f35,plain,
( spl4_3
| spl4_4 ),
inference(avatar_split_clause,[status(thm)],[f18,f33,f29]) ).
thf(f18,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( sK0 @ z ) )
| ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( X0 @ sK2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i > $o,X1: $i] :
( ( $true
= ( X0 @ sK2 ) )
| ( $true != $true )
| ( $true
!= ( X0 @ X1 ) )
| ( $true
= ( sK0 @ z ) ) ),
inference(superposition,[status(thm)],[f11,f12]) ).
thf(f12,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f11,plain,
! [X6: $i > $o,X7: $i,X4: $i,X5: $i > $o] :
( ( $true
!= ( X6 @ X7 ) )
| ( $true
= ( X6 @ z ) )
| ( $true
!= ( X5 @ X4 ) )
| ( $true
= ( X5 @ X7 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO315^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n026.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 14:28:10 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.44 ---- Original DTF file ---
% 0.17/0.44 thf(spec,logic,$$dhol).
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 % File : SYO315^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.44 % Domain : Syntactic
% 0.17/0.44 % Problem : TPS problem from BASIC-HO-THMS
% 0.17/0.44 % Version : Especial.
% 0.17/0.44 % English :
% 0.17/0.44
% 0.17/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.44 % Source : [Bro09]
% 0.17/0.44 % Names : tps_0909 [Bro09]
% 0.17/0.44
% 0.17/0.44 % Status : Theorem
% 0.17/0.44 % 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 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.1, 0.33 v4.0.0
% 0.17/0.44 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.17/0.44 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.17/0.44 % Maximal formula atoms : 0 ( 0 avg)
% 0.17/0.44 % Number of connectives : 19 ( 4 ~; 0 |; 6 &; 8 @)
% 0.17/0.44 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.17/0.44 % Maximal formula depth : 11 ( 11 avg)
% 0.17/0.44 % Number of types : 2 ( 0 usr)
% 0.17/0.44 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.17/0.44 % Number of symbols : 1 ( 1 usr; 1 con; 0-0 aty)
% 0.17/0.44 % Number of variables : 8 ( 0 ^; 0 !; 8 ?; 8 :)
% 0.17/0.44 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.44
% 0.17/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 thf(z,type,
% 0.17/0.44 z: $i ).
% 0.17/0.44
% 0.17/0.44 thf(cSILLYWFF,conjecture,
% 0.17/0.44 ( ? [Xp: $i > $o,Xq: $i > $o,Xx: $i,Xy: $i] :
% 0.17/0.44 ( ( Xp @ Xx )
% 0.17/0.44 & ~ ( Xp @ Xy )
% 0.17/0.44 & ( Xq @ Xy )
% 0.17/0.44 & ~ ( Xq @ z ) )
% 0.17/0.44 => ? [Xp: $i > $o,Xq: $i > $o,Xx: $i,Xy: $i] :
% 0.17/0.44 ( ~ ( Xq @ z )
% 0.17/0.44 & ( Xq @ Xy )
% 0.17/0.44 & ( Xp @ Xx )
% 0.17/0.44 & ~ ( Xp @ Xy ) ) ) ).
% 0.17/0.44
% 0.17/0.44 %------------------------------------------------------------------------------
% 0.17/0.44 ------------------------
% 1.47/1.23 ---- Embedded in THF ---
% 1.47/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.23 %%% Generated on Tue Feb 24 14:28:11 EST 2026
% 1.47/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.23 %%% Logic specification used:
% 1.47/1.23 %%% thf(spec, logic, $$dhol).
% 1.47/1.23
% 1.47/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MFnmrStzB6/DTF2DTF25790.p
% See solution above
% 1.47/1.23 ------------------------
% 1.47/1.24 ---- Cleaned THF ---
% 1.47/1.24 thf(z,type,
% 1.47/1.24 z: $i ).
% 1.47/1.24
% 1.47/1.24 thf(cSILLYWFF,conjecture,
% 1.47/1.24 ( ? [Xp: $i > $o,Xq: $i > $o,Xx: $i,Xy: $i] :
% 1.47/1.24 ( ( Xp @ Xx )
% 1.47/1.24 & ~ ( Xp @ Xy )
% 1.47/1.24 & ( Xq @ Xy )
% 1.47/1.24 & ~ ( Xq @ z ) )
% 1.47/1.24 => ? [Xp: $i > $o,Xq: $i > $o,Xx: $i,Xy: $i] :
% 1.47/1.24 ( ~ ( Xq @ z )
% 1.47/1.24 & ( Xq @ Xy )
% 1.47/1.24 & ( Xp @ Xx )
% 1.47/1.24 & ~ ( Xp @ Xy ) ) ) ).
% 1.47/1.24 ------------------------
% 1.47/1.25 % (25953)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_25790 for (2999ds/27Mi)
% 1.47/1.25 % (25954)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25790 for (2999ds/2Mi)
% 1.47/1.26 % (25954)Instruction limit reached!
% 1.47/1.26 % (25954)------------------------------
% 1.47/1.26 % (25954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.26 % (25954)Termination reason: Unknown
% 1.47/1.26 % (25954)Termination phase: Saturation
% 1.47/1.26
% 1.47/1.26 % (25954)Memory used [KB]: 5500
% 1.47/1.26 % (25954)Time elapsed: 0.002 s
% 1.47/1.26 % (25954)Instructions burned: 2 (million)
% 1.47/1.26 % (25954)------------------------------
% 1.47/1.26 % (25954)------------------------------
% 1.47/1.26 % (25953)First to succeed.
% 1.47/1.26 % (25953)Refutation found. Thanks to Tanya!
% 1.47/1.26 % SZS status Theorem for DTF2THF_25790
% 1.47/1.26 % SZS output start Proof for DTF2THF_25790
% 1.47/1.26 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.47/1.26 thf(func_def_5, type, sK0: $i > $o).
% 1.47/1.26 thf(func_def_8, type, sK3: $i > $o).
% 1.47/1.26 thf(func_def_10, type, ph5: !>[X0: $tType]:(X0)).
% 1.47/1.26 thf(f52,plain,(
% 1.47/1.26 $false),
% 1.47/1.26 inference(avatar_sat_refutation,[status(thm)],[f35,f40,f51])).
% 1.47/1.26 thf(f51,plain,(
% 1.47/1.26 ~spl4_4),
% 1.47/1.26 inference(avatar_contradiction_clause,[status(thm)],[f50])).
% 1.47/1.26 thf(f50,plain,(
% 1.47/1.26 $false | ~spl4_4),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f46])).
% 1.47/1.26 thf(f46,plain,(
% 1.47/1.26 ($true != $true) | ~spl4_4),
% 1.47/1.26 inference(superposition,[status(thm)],[f14,f44])).
% 1.47/1.26 thf(f44,plain,(
% 1.47/1.26 ($true = (sK3 @ sK2)) | ~spl4_4),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.47/1.26 thf(f42,plain,(
% 1.47/1.26 ($true != $true) | ($true = (sK3 @ sK2)) | ~spl4_4),
% 1.47/1.26 inference(superposition,[status(thm)],[f34,f15])).
% 1.47/1.26 thf(f15,plain,(
% 1.47/1.26 ($true = (sK3 @ sK1))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.26 thf(f10,plain,(
% 1.47/1.26 (($true = (sK3 @ sK1)) & ($true != (sK3 @ sK2)) & ($true != (sK0 @ z)) & ($true = (sK0 @ sK2))) & ! [X4 : $i,X5 : $i > $o,X6 : $i > $o,X7 : $i] : (($true != (X6 @ X7)) | ($true = (X5 @ X7)) | ($true != (X5 @ X4)) | ($true = (X6 @ z)))),
% 1.47/1.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f8,f9])).
% 1.47/1.26 thf(f9,plain,(
% 1.47/1.26 ? [X0 : $i > $o,X1 : $i,X2 : $i,X3 : $i > $o] : (($true = (X3 @ X1)) & ($true != (X3 @ X2)) & ((X0 @ z) != $true) & ((X0 @ X2) = $true)) => (($true = (sK3 @ sK1)) & ($true != (sK3 @ sK2)) & ($true != (sK0 @ z)) & ($true = (sK0 @ sK2)))),
% 1.47/1.26 introduced(definition,[],[choice_axiom])).
% 1.47/1.26 thf(f8,plain,(
% 1.47/1.26 ? [X0 : $i > $o,X1 : $i,X2 : $i,X3 : $i > $o] : (($true = (X3 @ X1)) & ($true != (X3 @ X2)) & ((X0 @ z) != $true) & ((X0 @ X2) = $true)) & ! [X4 : $i,X5 : $i > $o,X6 : $i > $o,X7 : $i] : (($true != (X6 @ X7)) | ($true = (X5 @ X7)) | ($true != (X5 @ X4)) | ($true = (X6 @ z)))),
% 1.47/1.26 inference(rectify,[status(thm)],[f7])).
% 1.47/1.26 thf(f7,plain,(
% 1.47/1.26 ? [X2 : $i > $o,X0 : $i,X1 : $i,X3 : $i > $o] : (($true = (X3 @ X0)) & ($true != (X3 @ X1)) & ($true != (X2 @ z)) & ($true = (X2 @ X1))) & ! [X7 : $i,X6 : $i > $o,X5 : $i > $o,X4 : $i] : (($true != (X5 @ X4)) | ($true = (X6 @ X4)) | ($true != (X6 @ X7)) | ($true = (X5 @ z)))),
% 1.47/1.26 inference(ennf_transformation,[status(thm)],[f6])).
% 1.47/1.26 thf(f6,plain,(
% 1.47/1.26 ~(? [X2 : $i > $o,X0 : $i,X1 : $i,X3 : $i > $o] : (($true = (X3 @ X0)) & ($true != (X3 @ X1)) & ($true != (X2 @ z)) & ($true = (X2 @ X1))) => ? [X4 : $i,X5 : $i > $o,X6 : $i > $o,X7 : $i] : (($true != (X5 @ z)) & ($true = (X5 @ X4)) & ($true = (X6 @ X7)) & ($true != (X6 @ X4))))),
% 1.47/1.26 inference(flattening,[status(thm)],[f5])).
% 1.47/1.26 thf(f5,plain,(
% 1.47/1.26 ~(? [X0 : $i,X1 : $i,X2 : $i > $o,X3 : $i > $o] : (($true = (X3 @ X0)) & ~($true = (X3 @ X1)) & ~($true = (X2 @ z)) & ($true = (X2 @ X1))) => ? [X4 : $i,X5 : $i > $o,X6 : $i > $o,X7 : $i] : (~($true = (X6 @ X4)) & ~($true = (X5 @ z)) & ($true = (X5 @ X4)) & ($true = (X6 @ X7))))),
% 1.47/1.26 inference(fool_elimination,[status(thm)],[f4])).
% 1.47/1.26 thf(f4,plain,(
% 1.47/1.26 ~(? [X0 : $i,X1 : $i,X2 : $i > $o,X3 : $i > $o] : ((X3 @ X0) & ~(X3 @ X1) & ~(X2 @ z) & (X2 @ X1)) => ? [X4 : $i,X5 : $i > $o,X6 : $i > $o,X7 : $i] : (~(X6 @ X4) & ~(X5 @ z) & (X5 @ X4) & (X6 @ X7)))),
% 1.47/1.26 inference(rectify,[status(thm)],[f2])).
% 1.47/1.26 thf(f2,negated_conjecture,(
% 1.47/1.26 ~(? [X2 : $i,X3 : $i,X1 : $i > $o,X0 : $i > $o] : ((X0 @ X2) & ~(X0 @ X3) & ~(X1 @ z) & (X1 @ X3)) => ? [X3 : $i,X1 : $i > $o,X0 : $i > $o,X2 : $i] : (~(X0 @ X3) & ~(X1 @ z) & (X1 @ X3) & (X0 @ X2)))),
% 1.47/1.26 inference(negated_conjecture,[status(cth)],[f1])).
% 1.47/1.26 thf(f1,conjecture,(
% 1.47/1.26 ? [X2 : $i,X3 : $i,X1 : $i > $o,X0 : $i > $o] : ((X0 @ X2) & ~(X0 @ X3) & ~(X1 @ z) & (X1 @ X3)) => ? [X3 : $i,X1 : $i > $o,X0 : $i > $o,X2 : $i] : (~(X0 @ X3) & ~(X1 @ z) & (X1 @ X3) & (X0 @ X2))),
% 1.47/1.26 file('/export/starexec/sandbox2/tmp/tmp.MFnmrStzB6/DTF2THF_25790.p',cSILLYWFF)).
% 1.47/1.26 thf(f34,plain,(
% 1.47/1.26 ( ! [X0 : $i > $o,X1 : $i] : (($true != (X0 @ X1)) | ($true = (X0 @ sK2))) ) | ~spl4_4),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.47/1.26 thf(f33,definition,(
% 1.47/1.26 spl4_4 <=> ! [X0 : $i > $o,X1 : $i] : (($true != (X0 @ X1)) | ($true = (X0 @ sK2)))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 1.47/1.26 thf(f14,plain,(
% 1.47/1.26 ($true != (sK3 @ sK2))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.26 thf(f40,plain,(
% 1.47/1.26 ~spl4_3),
% 1.47/1.26 inference(avatar_contradiction_clause,[status(thm)],[f39])).
% 1.47/1.26 thf(f39,plain,(
% 1.47/1.26 $false | ~spl4_3),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.47/1.26 thf(f37,plain,(
% 1.47/1.26 ($true != $true) | ~spl4_3),
% 1.47/1.26 inference(superposition,[status(thm)],[f13,f31])).
% 1.47/1.26 thf(f31,plain,(
% 1.47/1.26 ($true = (sK0 @ z)) | ~spl4_3),
% 1.47/1.26 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.47/1.26 thf(f29,definition,(
% 1.47/1.26 spl4_3 <=> ($true = (sK0 @ z))),
% 1.47/1.26 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.47/1.26 thf(f13,plain,(
% 1.47/1.26 ($true != (sK0 @ z))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.26 thf(f35,plain,(
% 1.47/1.26 spl4_3 | spl4_4),
% 1.47/1.26 inference(avatar_split_clause,[status(thm)],[f18,f33,f29])).
% 1.47/1.26 thf(f18,plain,(
% 1.47/1.26 ( ! [X0 : $i > $o,X1 : $i] : (($true = (sK0 @ z)) | ($true != (X0 @ X1)) | ($true = (X0 @ sK2))) )),
% 1.47/1.26 inference(trivial_inequality_removal,[status(thm)],[f16])).
% 1.47/1.26 thf(f16,plain,(
% 1.47/1.26 ( ! [X0 : $i > $o,X1 : $i] : (($true = (X0 @ sK2)) | ($true != $true) | ($true != (X0 @ X1)) | ($true = (sK0 @ z))) )),
% 1.47/1.26 inference(superposition,[status(thm)],[f11,f12])).
% 1.47/1.26 thf(f12,plain,(
% 1.47/1.26 ($true = (sK0 @ sK2))),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.26 thf(f11,plain,(
% 1.47/1.26 ( ! [X6 : $i > $o,X7 : $i,X4 : $i,X5 : $i > $o] : (($true != (X6 @ X7)) | ($true = (X6 @ z)) | ($true != (X5 @ X4)) | ($true = (X5 @ X7))) )),
% 1.47/1.26 inference(cnf_transformation,[status(thm)],[f10])).
% 1.47/1.26 % SZS output end Proof for DTF2THF_25790
% 1.47/1.26 % (25953)------------------------------
% 1.47/1.26 % (25953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.47/1.26 % (25953)Termination reason: Refutation
% 1.47/1.26
% 1.47/1.26 % (25953)Memory used [KB]: 5500
% 1.47/1.26 % (25953)Time elapsed: 0.005 s
% 1.47/1.26 % (25953)Instructions burned: 3 (million)
% 1.47/1.26 % (25953)------------------------------
% 1.47/1.26 % (25953)------------------------------
% 1.47/1.26 % (25950)Success in time 0.014 s
%------------------------------------------------------------------------------