%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO017^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 09:53:08 AM UTC 2026
% Result : Theorem 1.54s 1.33s
% Output : Refutation 1.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 6 unt; 0 typ; 5 def)
% Number of atoms : 290 ( 56 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 205 ( 73 ~; 67 |; 0 &; 60 @)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 7 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
h: $o > $o ).
thf(func_def_6,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f124,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f17,f26,f29,f52,f57,f65,f120,f123]) ).
thf(f123,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f122]) ).
thf(f122,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f112,f48]) ).
thf(f48,plain,
( ( ( h @ $true )
= $false )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl0_6
<=> ( ( h @ $true )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f112,plain,
( ( $true
= ( h @ $true ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(equality_proxy_clausification,[status(thm)],[f111]) ).
thf(f111,plain,
( ( ( $true
= ( h @ $true ) )
!= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f84]) ).
thf(f84,plain,
( ( $true = $false )
| ( ( $true
= ( h @ $true ) )
!= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f16,f67]) ).
thf(f67,plain,
( ( ( h
@ ( $true
= ( h @ $true ) ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f25,f16]) ).
thf(f25,plain,
( ( ( h
@ ( ( h @ $false )
= ( h @ $true ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl0_4
<=> ( ( h
@ ( ( h @ $false )
= ( h @ $true ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f16,plain,
( ( $true
= ( h @ $false ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f14]) ).
thf(f14,definition,
( spl0_2
<=> ( $true
= ( h @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f120,plain,
( spl0_6
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f114,f23,f14,f47]) ).
thf(f114,plain,
( ( ( h @ $true )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[status(thm)],[f113]) ).
thf(f113,plain,
( ( ( h @ ( $true = $true ) )
= $false )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f67,f112]) ).
thf(f65,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f12,f25]) ).
thf(f12,plain,
( ( $true
= ( h
@ ( ( h @ $false )
= ( h @ $true ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f10]) ).
thf(f10,definition,
( spl0_1
<=> ( $true
= ( h
@ ( ( h @ $false )
= ( h @ $true ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f57,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( $true = $false )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f54,f48]) ).
thf(f54,plain,
( ( $true
= ( h @ $true ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(boolean_simplification,[status(thm)],[f53]) ).
thf(f53,plain,
( ( ( h @ ( $false = $false ) )
= $true )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f31,f48]) ).
thf(f31,plain,
( ( $true
= ( h
@ ( $false
= ( h @ $true ) ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f12,f21]) ).
thf(f21,plain,
( ( ( h @ $false )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl0_3
<=> ( ( h @ $false )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f52,plain,
( spl0_6
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f38,f19,f10,f47]) ).
thf(f38,plain,
( ( ( h @ $true )
= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( $false
= ( h @ $true ) )
!= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( $true = $false )
| ( ( $false
= ( h @ $true ) )
!= $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f31,f21]) ).
thf(f29,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f28]) ).
thf(f28,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $true = $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f16,f21]) ).
thf(f26,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f8,f23,f19]) ).
thf(f8,plain,
( ( ( h @ $false )
= $false )
| ( ( h
@ ( ( h @ $false )
= ( h @ $true ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ $false )
= ( h @ $true ) ) ) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ $false )
= ( h @ $true ) ) ) ),
inference(flattening,[status(thm)],[f4]) ).
thf(f4,plain,
( ( h @ $false )
!= ( h
@ ( ( h @ $false )
= ( h @ $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( h @ $false )
!= ( h
@ ( ( h @ $false )
= ( h @ $true ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( h @ $false )
= ( h
@ ( ( h @ $false )
= ( h @ $true ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.lxsDoh8N5K/DTF2THF_31930.p',conj) ).
thf(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f7,f14,f10]) ).
thf(f7,plain,
( ( $true
= ( h @ $false ) )
| ( $true
= ( h
@ ( ( h @ $false )
= ( h @ $true ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO017^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n004.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Tue Feb 24 14:21:11 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO017^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : Formula valid in MBb, but not in model classes not requiring b
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.16/0.39 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Ben09]
% 0.16/0.39 % Names : Example 18b [BB05]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % : Without Boolean extensionality : CounterSatisfiable
% 0.16/0.39 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.0, 0.33 v3.7.0
% 0.16/0.39 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.16/0.39 % Number of atoms : 9 ( 2 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 1 ( 9 avg)
% 0.16/0.39 % Number of connectives : 4 ( 0 ~; 0 |; 0 &; 4 @)
% 0.16/0.39 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 1 ( 1 avg)
% 0.16/0.39 % Number of types : 1 ( 0 usr)
% 0.16/0.39 % Number of type conns : 1 ( 1 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 4 ( 1 usr; 2 con; 0-2 aty)
% 0.16/0.39 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments :
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(h,type,
% 0.16/0.39 h: $o > $o ).
% 0.16/0.39
% 0.16/0.39 thf(conj,conjecture,
% 0.16/0.39 ( ( h
% 0.16/0.39 @ ( ( h @ $true )
% 0.16/0.39 = ( h @ $false ) ) )
% 0.16/0.39 = ( h @ $false ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.36/1.29 ---- Embedded in THF ---
% 1.36/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.36/1.29 %%% Generated on Tue Feb 24 14:21:12 EST 2026
% 1.36/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.36/1.29 %%% Logic specification used:
% 1.36/1.29 %%% thf(spec, logic, $$dhol).
% 1.36/1.29
% 1.36/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.lxsDoh8N5K/DTF2DTF31930.p
% See solution above
% 1.36/1.29 ------------------------
% 1.54/1.30 ---- Cleaned THF ---
% 1.54/1.30 thf(h,type,
% 1.54/1.30 h: $o > $o ).
% 1.54/1.30
% 1.54/1.30 thf(conj,conjecture,
% 1.54/1.30 ( ( h
% 1.54/1.30 @ ( ( h @ $true )
% 1.54/1.30 = ( h @ $false ) ) )
% 1.54/1.30 = ( h @ $false ) ) ).
% 1.54/1.30 ------------------------
% 1.54/1.32 % (32033)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31930 for (3000ds/18Mi)
% 1.54/1.32 % (32030)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31930 for (3000ds/2Mi)
% 1.54/1.32 % (32031)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_31930 for (3000ds/2Mi)
% 1.54/1.32 % (32028)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_31930 for (3000ds/4Mi)
% 1.54/1.32 % (32029)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_31930 for (3000ds/27Mi)
% 1.54/1.32 % (32027)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31930 for (3000ds/183Mi)
% 1.54/1.32 % (32032)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_31930 for (3000ds/275Mi)
% 1.54/1.32 % (32031)Refutation not found, incomplete strategy
% 1.54/1.32 % (32031)------------------------------
% 1.54/1.32 % (32031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.32 % (32031)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.32
% 1.54/1.32
% 1.54/1.32 % (32031)Memory used [KB]: 5500
% 1.54/1.32 % (32031)Time elapsed: 0.003 s
% 1.54/1.32 % (32031)Instructions burned: 1 (million)
% 1.54/1.32 % (32031)------------------------------
% 1.54/1.32 % (32031)------------------------------
% 1.54/1.32 % (32030)Refutation not found, incomplete strategy
% 1.54/1.32 % (32030)------------------------------
% 1.54/1.32 % (32030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.32 % (32030)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.32
% 1.54/1.32
% 1.54/1.32 % (32030)Memory used [KB]: 5500
% 1.54/1.32 % (32030)Time elapsed: 0.003 s
% 1.54/1.32 % (32030)Instructions burned: 1 (million)
% 1.54/1.32 % (32030)------------------------------
% 1.54/1.32 % (32030)------------------------------
% 1.54/1.32 % (32032)Refutation not found, incomplete strategy
% 1.54/1.32 % (32032)------------------------------
% 1.54/1.32 % (32032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.32 % (32032)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.32
% 1.54/1.32
% 1.54/1.32 % (32032)Memory used [KB]: 5500
% 1.54/1.32 % (32032)Time elapsed: 0.003 s
% 1.54/1.32 % (32032)Instructions burned: 1 (million)
% 1.54/1.32 % (32032)------------------------------
% 1.54/1.32 % (32032)------------------------------
% 1.54/1.32 % (32029)Refutation not found, incomplete strategy
% 1.54/1.32 % (32029)------------------------------
% 1.54/1.32 % (32029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.32 % (32029)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.32
% 1.54/1.32
% 1.54/1.32 % (32029)Memory used [KB]: 5500
% 1.54/1.32 % (32029)Time elapsed: 0.003 s
% 1.54/1.32 % (32029)Instructions burned: 1 (million)
% 1.54/1.32 % (32029)------------------------------
% 1.54/1.32 % (32029)------------------------------
% 1.54/1.32 % (32028)Instruction limit reached!
% 1.54/1.32 % (32028)------------------------------
% 1.54/1.32 % (32028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.32 % (32028)Termination reason: Unknown
% 1.54/1.32 % (32028)Termination phase: Saturation
% 1.54/1.32
% 1.54/1.32 % (32028)Memory used [KB]: 5500
% 1.54/1.32 % (32028)Time elapsed: 0.005 s
% 1.54/1.32 % (32028)Instructions burned: 4 (million)
% 1.54/1.32 % (32028)------------------------------
% 1.54/1.32 % (32028)------------------------------
% 1.54/1.32 % (32033)First to succeed.
% 1.54/1.33 % (32033)Refutation found. Thanks to Tanya!
% 1.54/1.33 % SZS status Theorem for DTF2THF_31930
% 1.54/1.33 % SZS output start Proof for DTF2THF_31930
% 1.54/1.33 thf(func_def_0, type, h: $o > $o).
% 1.54/1.33 thf(func_def_6, type, ph1: !>[X0: $tType]:(X0)).
% 1.54/1.33 thf(f124,plain,(
% 1.54/1.33 $false),
% 1.54/1.33 inference(avatar_sat_refutation,[status(thm)],[f17,f26,f29,f52,f57,f65,f120,f123])).
% 1.54/1.33 thf(f123,plain,(
% 1.54/1.33 ~spl0_2 | ~spl0_4 | ~spl0_6),
% 1.54/1.33 inference(avatar_contradiction_clause,[status(thm)],[f122])).
% 1.54/1.33 thf(f122,plain,(
% 1.54/1.33 $false | (~spl0_2 | ~spl0_4 | ~spl0_6)),
% 1.54/1.33 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.54/1.33 thf(f121,plain,(
% 1.54/1.33 ($true = $false) | (~spl0_2 | ~spl0_4 | ~spl0_6)),
% 1.54/1.33 inference(backward_demodulation,[status(thm)],[f112,f48])).
% 1.54/1.33 thf(f48,plain,(
% 1.54/1.33 ((h @ $true) = $false) | ~spl0_6),
% 1.54/1.33 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.54/1.33 thf(f47,definition,(
% 1.54/1.33 spl0_6 <=> ((h @ $true) = $false)),
% 1.54/1.33 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.54/1.33 thf(f112,plain,(
% 1.54/1.33 ($true = (h @ $true)) | (~spl0_2 | ~spl0_4)),
% 1.54/1.33 inference(equality_proxy_clausification,[status(thm)],[f111])).
% 1.54/1.33 thf(f111,plain,(
% 1.54/1.33 (($true = (h @ $true)) != $false) | (~spl0_2 | ~spl0_4)),
% 1.54/1.33 inference(trivial_inequality_removal,[status(thm)],[f84])).
% 1.54/1.33 thf(f84,plain,(
% 1.54/1.33 ($true = $false) | (($true = (h @ $true)) != $false) | (~spl0_2 | ~spl0_4)),
% 1.54/1.33 inference(constrained_superposition,[status(thm)],[f16,f67])).
% 1.54/1.33 thf(f67,plain,(
% 1.54/1.33 ((h @ ($true = (h @ $true))) = $false) | (~spl0_2 | ~spl0_4)),
% 1.54/1.33 inference(backward_demodulation,[status(thm)],[f25,f16])).
% 1.54/1.33 thf(f25,plain,(
% 1.54/1.33 ((h @ ((h @ $false) = (h @ $true))) = $false) | ~spl0_4),
% 1.54/1.33 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.54/1.33 thf(f23,definition,(
% 1.54/1.33 spl0_4 <=> ((h @ ((h @ $false) = (h @ $true))) = $false)),
% 1.54/1.33 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.54/1.33 thf(f16,plain,(
% 1.54/1.33 ($true = (h @ $false)) | ~spl0_2),
% 1.54/1.33 inference(avatar_component_clause,[status(thm)],[f14])).
% 1.54/1.33 thf(f14,definition,(
% 1.54/1.33 spl0_2 <=> ($true = (h @ $false))),
% 1.54/1.33 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.54/1.33 thf(f120,plain,(
% 1.54/1.33 spl0_6 | ~spl0_2 | ~spl0_4),
% 1.54/1.33 inference(avatar_split_clause,[status(thm)],[f114,f23,f14,f47])).
% 1.54/1.33 thf(f114,plain,(
% 1.54/1.33 ((h @ $true) = $false) | (~spl0_2 | ~spl0_4)),
% 1.54/1.33 inference(boolean_simplification,[status(thm)],[f113])).
% 1.54/1.33 thf(f113,plain,(
% 1.54/1.33 ((h @ ($true = $true)) = $false) | (~spl0_2 | ~spl0_4)),
% 1.54/1.33 inference(backward_demodulation,[status(thm)],[f67,f112])).
% 1.54/1.33 thf(f65,plain,(
% 1.54/1.33 ~spl0_1 | ~spl0_4),
% 1.54/1.33 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.54/1.33 thf(f64,plain,(
% 1.54/1.33 $false | (~spl0_1 | ~spl0_4)),
% 1.54/1.33 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.54/1.33 thf(f63,plain,(
% 1.54/1.33 ($true = $false) | (~spl0_1 | ~spl0_4)),
% 1.54/1.33 inference(forward_demodulation,[status(thm)],[f12,f25])).
% 1.54/1.33 thf(f12,plain,(
% 1.54/1.33 ($true = (h @ ((h @ $false) = (h @ $true)))) | ~spl0_1),
% 1.54/1.33 inference(avatar_component_clause,[status(thm)],[f10])).
% 1.54/1.33 thf(f10,definition,(
% 1.54/1.33 spl0_1 <=> ($true = (h @ ((h @ $false) = (h @ $true))))),
% 1.54/1.33 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.54/1.33 thf(f57,plain,(
% 1.54/1.33 ~spl0_1 | ~spl0_3 | ~spl0_6),
% 1.54/1.33 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.54/1.33 thf(f56,plain,(
% 1.54/1.33 $false | (~spl0_1 | ~spl0_3 | ~spl0_6)),
% 1.54/1.33 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.54/1.33 thf(f55,plain,(
% 1.54/1.33 ($true = $false) | (~spl0_1 | ~spl0_3 | ~spl0_6)),
% 1.54/1.33 inference(forward_demodulation,[status(thm)],[f54,f48])).
% 1.54/1.33 thf(f54,plain,(
% 1.54/1.33 ($true = (h @ $true)) | (~spl0_1 | ~spl0_3 | ~spl0_6)),
% 1.54/1.33 inference(boolean_simplification,[status(thm)],[f53])).
% 1.54/1.33 thf(f53,plain,(
% 1.54/1.33 ((h @ ($false = $false)) = $true) | (~spl0_1 | ~spl0_3 | ~spl0_6)),
% 1.54/1.33 inference(backward_demodulation,[status(thm)],[f31,f48])).
% 1.54/1.33 thf(f31,plain,(
% 1.54/1.33 ($true = (h @ ($false = (h @ $true)))) | (~spl0_1 | ~spl0_3)),
% 1.54/1.33 inference(forward_demodulation,[status(thm)],[f12,f21])).
% 1.54/1.33 thf(f21,plain,(
% 1.54/1.33 ((h @ $false) = $false) | ~spl0_3),
% 1.54/1.33 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.54/1.33 thf(f19,definition,(
% 1.54/1.33 spl0_3 <=> ((h @ $false) = $false)),
% 1.54/1.33 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.54/1.33 thf(f52,plain,(
% 1.54/1.33 spl0_6 | ~spl0_1 | ~spl0_3),
% 1.54/1.33 inference(avatar_split_clause,[status(thm)],[f38,f19,f10,f47])).
% 1.54/1.33 thf(f38,plain,(
% 1.54/1.33 ((h @ $true) = $false) | (~spl0_1 | ~spl0_3)),
% 1.54/1.33 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.54/1.33 thf(f37,plain,(
% 1.54/1.33 (($false = (h @ $true)) != $false) | (~spl0_1 | ~spl0_3)),
% 1.54/1.33 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.54/1.33 thf(f34,plain,(
% 1.54/1.33 ($true = $false) | (($false = (h @ $true)) != $false) | (~spl0_1 | ~spl0_3)),
% 1.54/1.33 inference(constrained_superposition,[status(thm)],[f31,f21])).
% 1.54/1.33 thf(f29,plain,(
% 1.54/1.33 ~spl0_2 | ~spl0_3),
% 1.54/1.33 inference(avatar_contradiction_clause,[status(thm)],[f28])).
% 1.54/1.33 thf(f28,plain,(
% 1.54/1.33 $false | (~spl0_2 | ~spl0_3)),
% 1.54/1.33 inference(trivial_inequality_removal,[status(thm)],[f27])).
% 1.54/1.33 thf(f27,plain,(
% 1.54/1.33 ($true = $false) | (~spl0_2 | ~spl0_3)),
% 1.54/1.33 inference(forward_demodulation,[status(thm)],[f16,f21])).
% 1.54/1.33 thf(f26,plain,(
% 1.54/1.33 spl0_3 | spl0_4),
% 1.54/1.33 inference(avatar_split_clause,[status(thm)],[f8,f23,f19])).
% 1.54/1.33 thf(f8,plain,(
% 1.54/1.33 ((h @ $false) = $false) | ((h @ ((h @ $false) = (h @ $true))) = $false)),
% 1.54/1.33 inference(binary_proxy_clausification,[status(thm)],[f6])).
% 1.54/1.33 thf(f6,plain,(
% 1.54/1.33 ((h @ $false) != (h @ ((h @ $false) = (h @ $true))))),
% 1.54/1.33 inference(cnf_transformation,[status(thm)],[f5])).
% 1.54/1.33 thf(f5,plain,(
% 1.54/1.33 ((h @ $false) != (h @ ((h @ $false) = (h @ $true))))),
% 1.54/1.33 inference(flattening,[status(thm)],[f4])).
% 1.54/1.33 thf(f4,plain,(
% 1.54/1.33 ~((h @ $false) = (h @ ((h @ $false) = (h @ $true))))),
% 1.54/1.33 inference(fool_elimination,[status(thm)],[f2])).
% 1.54/1.33 thf(f2,negated_conjecture,(
% 1.54/1.33 ~((h @ $false) = (h @ ((h @ $false) = (h @ $true))))),
% 1.54/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 1.54/1.33 thf(f1,conjecture,(
% 1.54/1.33 ((h @ $false) = (h @ ((h @ $false) = (h @ $true))))),
% 1.54/1.33 file('/export/starexec/sandbox/tmp/tmp.lxsDoh8N5K/DTF2THF_31930.p',conj)).
% 1.54/1.33 thf(f17,plain,(
% 1.54/1.33 spl0_1 | spl0_2),
% 1.54/1.33 inference(avatar_split_clause,[status(thm)],[f7,f14,f10])).
% 1.54/1.33 thf(f7,plain,(
% 1.54/1.33 ($true = (h @ $false)) | ($true = (h @ ((h @ $false) = (h @ $true))))),
% 1.54/1.33 inference(binary_proxy_clausification,[status(thm)],[f6])).
% 1.54/1.33 % SZS output end Proof for DTF2THF_31930
% 1.54/1.33 % (32033)------------------------------
% 1.54/1.33 % (32033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.33 % (32033)Termination reason: Refutation
% 1.54/1.33
% 1.54/1.33 % (32033)Memory used [KB]: 5500
% 1.54/1.33 % (32033)Time elapsed: 0.007 s
% 1.54/1.33 % (32033)Instructions burned: 6 (million)
% 1.54/1.33 % (32033)------------------------------
% 1.54/1.33 % (32033)------------------------------
% 1.54/1.33 % (32026)Success in time 0.02 s
%------------------------------------------------------------------------------