%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO040^2 : TPTP v9.2.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 : Theorem 1.51s 1.23s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 73 ( 6 unt; 0 typ; 9 def)
% Number of atoms : 395 ( 61 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 335 ( 121 ~; 120 |; 0 &; 85 @)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $o > $o ).
thf(func_def_1,type,
h: $o > $i ).
thf(func_def_7,type,
ph1:
!>[X0: $tType] : X0 ).
thf(f174,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f17,f26,f30,f64,f65,f66,f71,f73,f75,f78,f103,f113,f130,f134,f162]) ).
thf(f162,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_6
| spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f161]) ).
thf(f161,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| spl0_6
| spl0_9 ),
inference(subsumption_resolution,[status(thm)],[f160,f69]) ).
thf(f69,plain,
( ( $true
!= ( f @ $true ) )
| spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f68,definition,
( spl0_9
<=> ( $true
= ( f @ $true ) ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f160,plain,
( ( $true
= ( f @ $true ) )
| ~ spl0_2
| ~ spl0_4
| spl0_6 ),
inference(subsumption_resolution,[status(thm)],[f158,f52]) ).
thf(f52,plain,
( ( x != $true )
| spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl0_6
<=> ( x = $true ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f158,plain,
( ( x = $true )
| ( $true
= ( f @ $true ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(binary_proxy_clausification,[status(thm)],[f157]) ).
thf(f157,plain,
( ( x
!= ( f @ $true ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( $false = $true )
| ( x
!= ( f @ $true ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(constrained_superposition,[status(thm)],[f16,f126]) ).
thf(f126,plain,
( ( $false
= ( f @ ( f @ $true ) ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f25,f16]) ).
thf(f25,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $false )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl0_4
<=> ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f16,plain,
( ( ( f @ x )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f14]) ).
thf(f14,definition,
( spl0_2
<=> ( ( f @ x )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f134,plain,
( ~ spl0_6
| ~ spl0_2
| spl0_9 ),
inference(avatar_split_clause,[status(thm)],[f133,f68,f14,f51]) ).
thf(f133,plain,
( ( x != $true )
| ~ spl0_2
| spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( x != $true )
| ( $true != $true )
| ~ spl0_2
| spl0_9 ),
inference(constrained_superposition,[status(thm)],[f69,f16]) ).
thf(f130,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f129]) ).
thf(f129,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(backward_demodulation,[status(thm)],[f70,f127]) ).
thf(f127,plain,
( ( $false
= ( f @ $true ) )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f126,f70]) ).
thf(f70,plain,
( ( $true
= ( f @ $true ) )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f68]) ).
thf(f113,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
( ( ( h @ $true )
!= ( h @ $true ) )
| ~ spl0_1
| ~ spl0_6
| ~ spl0_9 ),
inference(forward_demodulation,[status(thm)],[f106,f70]) ).
thf(f106,plain,
( ( ( h @ ( f @ $true ) )
!= ( h @ $true ) )
| ~ spl0_1
| ~ spl0_6 ),
inference(backward_demodulation,[status(thm)],[f100,f53]) ).
thf(f53,plain,
( ( x = $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f100,plain,
( ( ( h @ ( f @ x ) )
!= ( h @ $true ) )
| ~ spl0_1 ),
inference(backward_demodulation,[status(thm)],[f5,f12]) ).
thf(f12,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f10]) ).
thf(f10,definition,
( spl0_1
<=> ( ( f @ ( f @ ( f @ x ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f5,plain,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
inference(flattening,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
!= ( h @ ( f @ x ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
= ( h @ ( f @ x ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KDrLZYz61F/DTF2THF_19699.p',2) ).
thf(f103,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(backward_demodulation,[status(thm)],[f12,f25]) ).
thf(f78,plain,
( ~ spl0_5
| ~ spl0_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl0_5
| ~ spl0_8 ),
inference(trivial_inequality_removal,[status(thm)],[f76]) ).
thf(f76,plain,
( ( $false = $true )
| ~ spl0_5
| ~ spl0_8 ),
inference(backward_demodulation,[status(thm)],[f49,f62]) ).
thf(f62,plain,
( ( $false
= ( f @ $false ) )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f60,definition,
( spl0_8
<=> ( $false
= ( f @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f49,plain,
( ( $true
= ( f @ $false ) )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl0_5
<=> ( $true
= ( f @ $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f75,plain,
( spl0_9
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(avatar_split_clause,[status(thm)],[f74,f47,f19,f10,f68]) ).
thf(f19,definition,
( spl0_3
<=> ( ( f @ x )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f74,plain,
( ( $true
= ( f @ $true ) )
| ~ spl0_1
| ~ spl0_3
| ~ spl0_5 ),
inference(backward_demodulation,[status(thm)],[f31,f49]) ).
thf(f31,plain,
( ( $true
= ( f @ ( f @ $false ) ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f12,f21]) ).
thf(f21,plain,
( ( ( f @ x )
= $false )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f73,plain,
( spl0_8
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[status(thm)],[f72,f56,f19,f60]) ).
thf(f56,definition,
( spl0_7
<=> ( x = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f72,plain,
( ( $false
= ( f @ $false ) )
| ~ spl0_3
| ~ spl0_7 ),
inference(backward_demodulation,[status(thm)],[f21,f58]) ).
thf(f58,plain,
( ( x = $false )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f71,plain,
( spl0_9
| ~ spl0_8
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f36,f19,f10,f60,f68]) ).
thf(f36,plain,
( ( $true
= ( f @ $true ) )
| ( $false
!= ( f @ $false ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f31,f31]) ).
thf(f66,plain,
( spl0_7
| spl0_8
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f42,f19,f10,f60,f56]) ).
thf(f42,plain,
( ( $false
= ( f @ $false ) )
| ( x = $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
( ( x
!= ( f @ $false ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( x
!= ( f @ $false ) )
| ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f21,f31]) ).
thf(f65,plain,
( spl0_6
| spl0_5
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f41,f19,f10,f47,f51]) ).
thf(f41,plain,
( ( x = $true )
| ( $true
= ( f @ $false ) )
| ~ spl0_1
| ~ spl0_3 ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f64,plain,
( ~ spl0_7
| spl0_5
| ~ spl0_1
| ~ spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f37,f19,f10,f47,f56]) ).
thf(f37,plain,
( ( $true
= ( f @ $false ) )
| ( x != $false )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[status(thm)],[f31,f21]) ).
thf(f30,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f29]) ).
thf(f29,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(backward_demodulation,[status(thm)],[f16,f21]) ).
thf(f26,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f8,f23,f19]) ).
thf(f8,plain,
( ( ( f @ x )
= $false )
| ( ( f @ ( f @ ( f @ x ) ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( f @ x )
!= ( f @ ( f @ ( f @ x ) ) ) ),
inference(equality_resolution,[status(thm)],[f5]) ).
thf(f17,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f7,f14,f10]) ).
thf(f7,plain,
( ( ( f @ ( f @ ( f @ x ) ) )
= $true )
| ( ( f @ x )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO040^2 : TPTP v9.2.1. Released v4.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n014.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 14:22:27 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : SYO040^2 : TPTP v9.2.1. Released v4.1.0.
% 0.19/0.44 % Domain : Syntactic
% 0.19/0.44 % Problem : Unsatisfiable basic formula 2
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % Theorem formulation : As a conjecture rather than UNS set.
% 0.19/0.44 % English : Variant of the Kaminski equation.
% 0.19/0.44
% 0.19/0.44 % Refs : [BS09a] Brown E. & Smolka (2009), Terminating Tableaux for the
% 0.19/0.44 % : [BS09b] Brown E. & Smolka (2009), Extended First-Order Logic
% 0.19/0.44 % : [Bro09] Brown E. (2009), Email to Geoff Sutcliffe
% 0.19/0.44 % Source : [BS09a]
% 0.19/0.44 % Names : basic2 [Bro09]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v6.0.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0
% 0.19/0.44 % Syntax : Number of formulae : 4 ( 1 unt; 3 typ; 0 def)
% 0.19/0.44 % Number of atoms : 7 ( 1 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 1 ( 7 avg)
% 0.19/0.44 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 6 @)
% 0.19/0.44 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 1 ( 1 avg)
% 0.19/0.44 % Number of types : 2 ( 0 usr)
% 0.19/0.44 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 4 ( 3 usr; 1 con; 0-2 aty)
% 0.19/0.44 % Number of variables : 0 ( 0 ^; 0 !; 0 ?; 0 :)
% 0.19/0.44 % SPC : TH0_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : The fragment of simple type theory that restricts equations to
% 0.19/0.44 % base types and disallows lambda abstraction and quantification is
% 0.19/0.44 % decidable. This is an example.
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(f,type,
% 0.19/0.44 f: $o > $o ).
% 0.19/0.44
% 0.19/0.44 thf(h,type,
% 0.19/0.44 h: $o > $i ).
% 0.19/0.44
% 0.19/0.44 thf(x,type,
% 0.19/0.44 x: $o ).
% 0.19/0.44
% 0.19/0.44 thf(2,conjecture,
% 0.19/0.44 ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
% 0.19/0.44 = ( h @ ( f @ x ) ) ) ).
% 0.19/0.44
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 ------------------------
% 1.38/1.19 ---- Embedded in THF ---
% 1.38/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.38/1.20 %%% Generated on Tue Feb 24 14:22:28 EST 2026
% 1.38/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.38/1.20 %%% Logic specification used:
% 1.38/1.20 %%% thf(spec, logic, $$dhol).
% 1.38/1.20
% 1.38/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KDrLZYz61F/DTF2DTF19699.p
% See solution above
% 1.38/1.20 ------------------------
% 1.51/1.21 ---- Cleaned THF ---
% 1.51/1.21 thf(f,type,
% 1.51/1.21 f: $o > $o ).
% 1.51/1.21
% 1.51/1.21 thf(h,type,
% 1.51/1.21 h: $o > $i ).
% 1.51/1.21
% 1.51/1.21 thf(x,type,
% 1.51/1.21 x: $o ).
% 1.51/1.21
% 1.51/1.21 thf(2,conjecture,
% 1.51/1.21 ( ( h @ ( f @ ( f @ ( f @ x ) ) ) )
% 1.51/1.21 = ( h @ ( f @ x ) ) ) ).
% 1.51/1.21 ------------------------
% 1.51/1.22 % (19842)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19699 for (2999ds/183Mi)
% 1.51/1.22 % (19845)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19699 for (2999ds/2Mi)
% 1.51/1.22 % (19845)Refutation not found, incomplete strategy
% 1.51/1.22 % (19845)------------------------------
% 1.51/1.22 % (19845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (19845)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.22
% 1.51/1.22
% 1.51/1.22 % (19845)Memory used [KB]: 5373
% 1.51/1.22 % (19845)Time elapsed: 0.001 s
% 1.51/1.22 % (19845)------------------------------
% 1.51/1.22 % (19845)------------------------------
% 1.51/1.22 % (19847)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_19699 for (2999ds/275Mi)
% 1.51/1.22 % (19847)Refutation not found, incomplete strategy
% 1.51/1.22 % (19847)------------------------------
% 1.51/1.22 % (19847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.22 % (19847)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.22
% 1.51/1.22
% 1.51/1.22 % (19847)Memory used [KB]: 5373
% 1.51/1.22 % (19847)Time elapsed: 0.001 s
% 1.51/1.22 % (19847)------------------------------
% 1.51/1.22 % (19847)------------------------------
% 1.51/1.22 % (19848)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19699 for (2999ds/18Mi)
% 1.51/1.23 % (19848)First to succeed.
% 1.51/1.23 % (19848)Refutation found. Thanks to Tanya!
% 1.51/1.23 % SZS status Theorem for DTF2THF_19699
% 1.51/1.23 % SZS output start Proof for DTF2THF_19699
% 1.51/1.23 thf(func_def_0, type, f: $o > $o).
% 1.51/1.23 thf(func_def_1, type, h: $o > $i).
% 1.51/1.23 thf(func_def_7, type, ph1: !>[X0: $tType]:(X0)).
% 1.51/1.23 thf(f174,plain,(
% 1.51/1.23 $false),
% 1.51/1.23 inference(avatar_sat_refutation,[status(thm)],[f17,f26,f30,f64,f65,f66,f71,f73,f75,f78,f103,f113,f130,f134,f162])).
% 1.51/1.23 thf(f162,plain,(
% 1.51/1.23 ~spl0_2 | ~spl0_4 | spl0_6 | spl0_9),
% 1.51/1.23 inference(avatar_contradiction_clause,[status(thm)],[f161])).
% 1.51/1.23 thf(f161,plain,(
% 1.51/1.23 $false | (~spl0_2 | ~spl0_4 | spl0_6 | spl0_9)),
% 1.51/1.23 inference(subsumption_resolution,[status(thm)],[f160,f69])).
% 1.51/1.23 thf(f69,plain,(
% 1.51/1.23 ($true != (f @ $true)) | spl0_9),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.51/1.23 thf(f68,definition,(
% 1.51/1.23 spl0_9 <=> ($true = (f @ $true))),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.51/1.23 thf(f160,plain,(
% 1.51/1.23 ($true = (f @ $true)) | (~spl0_2 | ~spl0_4 | spl0_6)),
% 1.51/1.23 inference(subsumption_resolution,[status(thm)],[f158,f52])).
% 1.51/1.23 thf(f52,plain,(
% 1.51/1.23 (x != $true) | spl0_6),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.51/1.23 thf(f51,definition,(
% 1.51/1.23 spl0_6 <=> (x = $true)),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.51/1.23 thf(f158,plain,(
% 1.51/1.23 (x = $true) | ($true = (f @ $true)) | (~spl0_2 | ~spl0_4)),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f157])).
% 1.51/1.23 thf(f157,plain,(
% 1.51/1.23 (x != (f @ $true)) | (~spl0_2 | ~spl0_4)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.51/1.23 thf(f150,plain,(
% 1.51/1.23 ($false = $true) | (x != (f @ $true)) | (~spl0_2 | ~spl0_4)),
% 1.51/1.23 inference(constrained_superposition,[status(thm)],[f16,f126])).
% 1.51/1.23 thf(f126,plain,(
% 1.51/1.23 ($false = (f @ (f @ $true))) | (~spl0_2 | ~spl0_4)),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f25,f16])).
% 1.51/1.23 thf(f25,plain,(
% 1.51/1.23 ((f @ (f @ (f @ x))) = $false) | ~spl0_4),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.51/1.23 thf(f23,definition,(
% 1.51/1.23 spl0_4 <=> ((f @ (f @ (f @ x))) = $false)),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.51/1.23 thf(f16,plain,(
% 1.51/1.23 ((f @ x) = $true) | ~spl0_2),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f14])).
% 1.51/1.23 thf(f14,definition,(
% 1.51/1.23 spl0_2 <=> ((f @ x) = $true)),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.51/1.23 thf(f134,plain,(
% 1.51/1.23 ~spl0_6 | ~spl0_2 | spl0_9),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f133,f68,f14,f51])).
% 1.51/1.23 thf(f133,plain,(
% 1.51/1.23 (x != $true) | (~spl0_2 | spl0_9)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.51/1.23 thf(f132,plain,(
% 1.51/1.23 (x != $true) | ($true != $true) | (~spl0_2 | spl0_9)),
% 1.51/1.23 inference(constrained_superposition,[status(thm)],[f69,f16])).
% 1.51/1.23 thf(f130,plain,(
% 1.51/1.23 ~spl0_2 | ~spl0_4 | ~spl0_9),
% 1.51/1.23 inference(avatar_contradiction_clause,[status(thm)],[f129])).
% 1.51/1.23 thf(f129,plain,(
% 1.51/1.23 $false | (~spl0_2 | ~spl0_4 | ~spl0_9)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.51/1.23 thf(f128,plain,(
% 1.51/1.23 ($false = $true) | (~spl0_2 | ~spl0_4 | ~spl0_9)),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f70,f127])).
% 1.51/1.23 thf(f127,plain,(
% 1.51/1.23 ($false = (f @ $true)) | (~spl0_2 | ~spl0_4 | ~spl0_9)),
% 1.51/1.23 inference(forward_demodulation,[status(thm)],[f126,f70])).
% 1.51/1.23 thf(f70,plain,(
% 1.51/1.23 ($true = (f @ $true)) | ~spl0_9),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f68])).
% 1.51/1.23 thf(f113,plain,(
% 1.51/1.23 ~spl0_1 | ~spl0_6 | ~spl0_9),
% 1.51/1.23 inference(avatar_contradiction_clause,[status(thm)],[f112])).
% 1.51/1.23 thf(f112,plain,(
% 1.51/1.23 $false | (~spl0_1 | ~spl0_6 | ~spl0_9)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.51/1.23 thf(f111,plain,(
% 1.51/1.23 ((h @ $true) != (h @ $true)) | (~spl0_1 | ~spl0_6 | ~spl0_9)),
% 1.51/1.23 inference(forward_demodulation,[status(thm)],[f106,f70])).
% 1.51/1.23 thf(f106,plain,(
% 1.51/1.23 ((h @ (f @ $true)) != (h @ $true)) | (~spl0_1 | ~spl0_6)),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f100,f53])).
% 1.51/1.23 thf(f53,plain,(
% 1.51/1.23 (x = $true) | ~spl0_6),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.51/1.23 thf(f100,plain,(
% 1.51/1.23 ((h @ (f @ x)) != (h @ $true)) | ~spl0_1),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f5,f12])).
% 1.51/1.23 thf(f12,plain,(
% 1.51/1.23 ((f @ (f @ (f @ x))) = $true) | ~spl0_1),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f10])).
% 1.51/1.23 thf(f10,definition,(
% 1.51/1.23 spl0_1 <=> ((f @ (f @ (f @ x))) = $true)),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.51/1.23 thf(f5,plain,(
% 1.51/1.23 ((h @ (f @ (f @ (f @ x)))) != (h @ (f @ x)))),
% 1.51/1.23 inference(cnf_transformation,[status(thm)],[f4])).
% 1.51/1.23 thf(f4,plain,(
% 1.51/1.23 ((h @ (f @ (f @ (f @ x)))) != (h @ (f @ x)))),
% 1.51/1.23 inference(flattening,[status(thm)],[f2])).
% 1.51/1.23 thf(f2,negated_conjecture,(
% 1.51/1.23 ~((h @ (f @ (f @ (f @ x)))) = (h @ (f @ x)))),
% 1.51/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.23 thf(f1,conjecture,(
% 1.51/1.23 ((h @ (f @ (f @ (f @ x)))) = (h @ (f @ x)))),
% 1.51/1.23 file('/export/starexec/sandbox2/tmp/tmp.KDrLZYz61F/DTF2THF_19699.p',2)).
% 1.51/1.23 thf(f103,plain,(
% 1.51/1.23 ~spl0_1 | ~spl0_4),
% 1.51/1.23 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 1.51/1.23 thf(f102,plain,(
% 1.51/1.23 $false | (~spl0_1 | ~spl0_4)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.51/1.23 thf(f101,plain,(
% 1.51/1.23 ($false = $true) | (~spl0_1 | ~spl0_4)),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f12,f25])).
% 1.51/1.23 thf(f78,plain,(
% 1.51/1.23 ~spl0_5 | ~spl0_8),
% 1.51/1.23 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.51/1.23 thf(f77,plain,(
% 1.51/1.23 $false | (~spl0_5 | ~spl0_8)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.51/1.23 thf(f76,plain,(
% 1.51/1.23 ($false = $true) | (~spl0_5 | ~spl0_8)),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f49,f62])).
% 1.51/1.23 thf(f62,plain,(
% 1.51/1.23 ($false = (f @ $false)) | ~spl0_8),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.51/1.23 thf(f60,definition,(
% 1.51/1.23 spl0_8 <=> ($false = (f @ $false))),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.51/1.23 thf(f49,plain,(
% 1.51/1.23 ($true = (f @ $false)) | ~spl0_5),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.51/1.23 thf(f47,definition,(
% 1.51/1.23 spl0_5 <=> ($true = (f @ $false))),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.51/1.23 thf(f75,plain,(
% 1.51/1.23 spl0_9 | ~spl0_1 | ~spl0_3 | ~spl0_5),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f74,f47,f19,f10,f68])).
% 1.51/1.23 thf(f19,definition,(
% 1.51/1.23 spl0_3 <=> ((f @ x) = $false)),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.51/1.23 thf(f74,plain,(
% 1.51/1.23 ($true = (f @ $true)) | (~spl0_1 | ~spl0_3 | ~spl0_5)),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f31,f49])).
% 1.51/1.23 thf(f31,plain,(
% 1.51/1.23 ($true = (f @ (f @ $false))) | (~spl0_1 | ~spl0_3)),
% 1.51/1.23 inference(forward_demodulation,[status(thm)],[f12,f21])).
% 1.51/1.23 thf(f21,plain,(
% 1.51/1.23 ((f @ x) = $false) | ~spl0_3),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.51/1.23 thf(f73,plain,(
% 1.51/1.23 spl0_8 | ~spl0_3 | ~spl0_7),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f72,f56,f19,f60])).
% 1.51/1.23 thf(f56,definition,(
% 1.51/1.23 spl0_7 <=> (x = $false)),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.51/1.23 thf(f72,plain,(
% 1.51/1.23 ($false = (f @ $false)) | (~spl0_3 | ~spl0_7)),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f21,f58])).
% 1.51/1.23 thf(f58,plain,(
% 1.51/1.23 (x = $false) | ~spl0_7),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.51/1.23 thf(f71,plain,(
% 1.51/1.23 spl0_9 | ~spl0_8 | ~spl0_1 | ~spl0_3),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f36,f19,f10,f60,f68])).
% 1.51/1.23 thf(f36,plain,(
% 1.51/1.23 ($true = (f @ $true)) | ($false != (f @ $false)) | (~spl0_1 | ~spl0_3)),
% 1.51/1.23 inference(constrained_superposition,[status(thm)],[f31,f31])).
% 1.51/1.23 thf(f66,plain,(
% 1.51/1.23 spl0_7 | spl0_8 | ~spl0_1 | ~spl0_3),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f42,f19,f10,f60,f56])).
% 1.51/1.23 thf(f42,plain,(
% 1.51/1.23 ($false = (f @ $false)) | (x = $false) | (~spl0_1 | ~spl0_3)),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.51/1.23 thf(f40,plain,(
% 1.51/1.23 (x != (f @ $false)) | (~spl0_1 | ~spl0_3)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.51/1.23 thf(f39,plain,(
% 1.51/1.23 (x != (f @ $false)) | ($false = $true) | (~spl0_1 | ~spl0_3)),
% 1.51/1.23 inference(constrained_superposition,[status(thm)],[f21,f31])).
% 1.51/1.23 thf(f65,plain,(
% 1.51/1.23 spl0_6 | spl0_5 | ~spl0_1 | ~spl0_3),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f41,f19,f10,f47,f51])).
% 1.51/1.23 thf(f41,plain,(
% 1.51/1.23 (x = $true) | ($true = (f @ $false)) | (~spl0_1 | ~spl0_3)),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.51/1.23 thf(f64,plain,(
% 1.51/1.23 ~spl0_7 | spl0_5 | ~spl0_1 | ~spl0_3),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f37,f19,f10,f47,f56])).
% 1.51/1.23 thf(f37,plain,(
% 1.51/1.23 ($true = (f @ $false)) | (x != $false) | (~spl0_1 | ~spl0_3)),
% 1.51/1.23 inference(constrained_superposition,[status(thm)],[f31,f21])).
% 1.51/1.23 thf(f30,plain,(
% 1.51/1.23 ~spl0_2 | ~spl0_3),
% 1.51/1.23 inference(avatar_contradiction_clause,[status(thm)],[f29])).
% 1.51/1.23 thf(f29,plain,(
% 1.51/1.23 $false | (~spl0_2 | ~spl0_3)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.51/1.23 thf(f28,plain,(
% 1.51/1.23 ($false = $true) | (~spl0_2 | ~spl0_3)),
% 1.51/1.23 inference(backward_demodulation,[status(thm)],[f16,f21])).
% 1.51/1.23 thf(f26,plain,(
% 1.51/1.23 spl0_3 | spl0_4),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f8,f23,f19])).
% 1.51/1.23 thf(f8,plain,(
% 1.51/1.23 ((f @ x) = $false) | ((f @ (f @ (f @ x))) = $false)),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f6])).
% 1.51/1.23 thf(f6,plain,(
% 1.51/1.23 ((f @ x) != (f @ (f @ (f @ x))))),
% 1.51/1.23 inference(equality_resolution,[status(thm)],[f5])).
% 1.51/1.23 thf(f17,plain,(
% 1.51/1.23 spl0_1 | spl0_2),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f7,f14,f10])).
% 1.51/1.23 thf(f7,plain,(
% 1.51/1.23 ((f @ (f @ (f @ x))) = $true) | ((f @ x) = $true)),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f6])).
% 1.51/1.23 % SZS output end Proof for DTF2THF_19699
% 1.51/1.23 % (19848)------------------------------
% 1.51/1.23 % (19848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (19848)Termination reason: Refutation
% 1.51/1.23
% 1.51/1.23 % (19848)Memory used [KB]: 5500
% 1.51/1.23 % (19848)Time elapsed: 0.005 s
% 1.51/1.23 % (19848)Instructions burned: 7 (million)
% 1.51/1.23 % (19848)------------------------------
% 1.51/1.23 % (19848)------------------------------
% 1.51/1.23 % (19841)Success in time 0.017 s
%------------------------------------------------------------------------------