%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO022^1 : 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 : n016.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 09:53:09 AM UTC 2026
% Result : Theorem 1.66s 1.30s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 4
% Syntax : Number of formulae : 53 ( 26 unt; 0 typ; 2 def)
% Number of atoms : 243 ( 69 equ; 8 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 234 ( 98 ~; 57 |; 20 &; 45 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 7 usr; 8 con; 0-2 aty)
% ( 4 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 59 ^; 2 !; 0 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).
thf(func_def_14,type,
sK1: ( $o > $o > $o ) > $o ).
thf(func_def_15,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f70,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f57,f63,f69]) ).
thf(f69,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f68]) ).
thf(f68,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false = $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f41,f52]) ).
thf(f52,plain,
( ( sK3 = $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f50]) ).
thf(f50,definition,
( spl0_1
<=> ( sK3 = $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f41,plain,
sK3 = $true,
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
( ( sK3 = $true )
| ( sK3 = $true ) ),
inference(not_proxy_clausification,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $false = ( ~ sK3 ) )
| ( sK3 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $false
= ( ~ sK3
| ~ sK4 ) )
| ( sK3 = $true ) ),
inference(not_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ~ ( ~ sK3
| ~ sK4 ) )
= $true )
| ( sK3 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ( sK3
& sK4 )
= $true )
| ( ( ~ ( ~ sK3
| ~ sK4 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( sK3
& sK4 )
!= ( ~ ( ~ sK3
| ~ sK4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f24]) ).
thf(f24,plain,
( ( sK3
& sK4 )
!= ( ^ [Y0: $o] :
~ ( ~ sK3
| ~ Y0 )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f23]) ).
thf(f23,plain,
( ( (&) @ sK3 )
!= ( ^ [Y0: $o] :
~ ( ~ sK3
| ~ Y0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 )
@ sK3 )
!= ( (&) @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f21]) ).
thf(f21,plain,
( (&)
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f19]) ).
thf(f19,plain,
( ( (&)
!= ( ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) ) )
| ( $false = $true ) ),
inference(constrained_superposition,[status(thm)],[f17,f16]) ).
thf(f16,plain,
( $false
= ( sK1
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
= ( ( sK1 @ (&) )
=> ( sK1
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( $false
= ( ^ [Y0: ( $o > $o > $o ) > $o] :
( ( Y0 @ (&) )
=> ( Y0
@ ^ [Y1: $o,Y2: $o] :
~ ( ~ Y1
| ~ Y2 ) ) )
@ sK1 ) ),
inference(sigma_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( !! @ ( ( $o > $o > $o ) > $o )
@ ^ [Y0: ( $o > $o > $o ) > $o] :
( ( Y0 @ (&) )
=> ( Y0
@ ^ [Y1: $o,Y2: $o] :
~ ( ~ Y1
| ~ Y2 ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
( !! @ ( ( $o > $o > $o ) > $o )
@ ^ [Y2: ( $o > $o > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ ^ [Y0: $o,Y1: $o] :
( Y0
& Y1 )
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f11,f10]) ).
thf(f10,plain,
( leibeq
= ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
( !! @ ( ( $o > $o > $o ) > $o )
@ ^ [Y2: ( $o > $o > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( leibeq
= ( ^ [Y0: $o > $o > $o,Y1: $o > $o > $o] :
( !! @ ( ( $o > $o > $o ) > $o )
@ ^ [Y2: ( $o > $o > $o ) > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
( leibeq
= ( ^ [X0: $o > $o > $o,X1: $o > $o > $o] :
! [X2: ( $o > $o > $o ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( leibeq
= ( ^ [X0: $o > $o > $o,X1: $o > $o > $o] :
! [X2: ( $o > $o > $o ) > $o] :
( ( X2 @ X0 )
=> ( X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.4YKvQSFCbF/DTF2THF_18514.p',leibeq) ).
thf(f11,plain,
( ( leibeq
@ ^ [Y0: $o,Y1: $o] :
( Y0
& Y1 )
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ( leibeq
@ ^ [Y0: $o,Y1: $o] :
( Y0
& Y1 )
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) )
!= $true ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( leibeq
@ ^ [Y0: $o,Y1: $o] :
( Y0
& Y1 )
@ ^ [Y0: $o,Y1: $o] :
~ ( ~ Y0
| ~ Y1 ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ( leibeq
@ ^ [X0: $o,X1: $o] :
( X1
& X0 )
@ ^ [X2: $o,X3: $o] :
~ ( ~ X3
| ~ X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ( leibeq
@ ^ [X3: $o,X4: $o] :
( X4
& X3 )
@ ^ [X0: $o,X1: $o] :
~ ( ~ X1
| ~ X0 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
( leibeq
@ ^ [X3: $o,X4: $o] :
( X4
& X3 )
@ ^ [X0: $o,X1: $o] :
~ ( ~ X1
| ~ X0 ) ),
file('/export/starexec/sandbox/tmp/tmp.4YKvQSFCbF/DTF2THF_18514.p',conj) ).
thf(f17,plain,
( ( sK1 @ (&) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f15]) ).
thf(f63,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f62]) ).
thf(f62,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $false = $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f48,f56]) ).
thf(f56,plain,
( ( $false = sK4 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f54,definition,
( spl0_2
<=> ( $false = sK4 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f48,plain,
sK4 = $true,
inference(duplicate_literal_removal,[status(thm)],[f47]) ).
thf(f47,plain,
( ( sK4 = $true )
| ( sK4 = $true ) ),
inference(not_proxy_clausification,[status(thm)],[f44]) ).
thf(f44,plain,
( ( sK4 = $true )
| ( $false = ( ~ sK4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f43]) ).
thf(f43,plain,
( ( sK4 = $true )
| ( $false
= ( ~ sK3
| ~ sK4 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ~ ( ~ sK3
| ~ sK4 ) )
= $true )
| ( sK4 = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f26]) ).
thf(f57,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f34,f54,f50]) ).
thf(f34,plain,
( ( sK3 = $false )
| ( $false = sK4 ) ),
inference(duplicate_literal_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $false = sK4 )
| ( $false = sK4 )
| ( sK3 = $false ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
( ( sK3 = $false )
| ( $false = sK4 )
| ( ( ~ sK4 ) = $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( sK3 = $false )
| ( ( ~ sK4 ) = $true )
| ( sK3 = $false )
| ( $false = sK4 ) ),
inference(not_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
( ( sK3 = $false )
| ( ( ~ sK3 ) = $true )
| ( $false = sK4 )
| ( ( ~ sK4 ) = $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f29]) ).
thf(f29,plain,
( ( ( ~ sK3
| ~ sK4 )
= $true )
| ( $false = sK4 )
| ( sK3 = $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f28]) ).
thf(f28,plain,
( ( ( sK3
& sK4 )
= $false )
| ( ( ~ sK3
| ~ sK4 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
( ( $false
= ( ~ ( ~ sK3
| ~ sK4 ) ) )
| ( ( sK3
& sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO022^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n016.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 14:22:06 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SYO022^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Syntactic
% 0.20/0.46 % Problem : De Morgan lambda terms by Leibnitz
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BB05] Benzmueller & Brown (2005), A Structured Set of Higher
% 0.20/0.46 % : [Ben09] Benzmueller (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Ben09]
% 0.20/0.46 % Names : Example 20c [BB05]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % : Without Boolean extensionality : CounterSatisfiable
% 0.20/0.46 % : Without xi extensionality : CounterSatisfiable
% 0.20/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.36 v7.5.0, 0.14 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 v4.1.0, 0.33 v4.0.0, 0.00 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 3 ( 2 unt; 1 typ; 1 def)
% 0.20/0.46 % Number of atoms : 3 ( 1 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.20/0.46 % Number of connectives : 10 ( 3 ~; 1 |; 1 &; 4 @)
% 0.20/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 7 ( 4 avg)
% 0.20/0.46 % Number of types : 1 ( 0 usr)
% 0.20/0.46 % Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.20/0.46 % Number of variables : 7 ( 6 ^; 1 !; 0 ?; 7 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(leibeq_decl,type,
% 0.20/0.46 leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(leibeq,definition,
% 0.20/0.46 ( leibeq
% 0.20/0.46 = ( ^ [X: $o > $o > $o,Y: $o > $o > $o] :
% 0.20/0.46 ! [P: ( $o > $o > $o ) > $o] :
% 0.20/0.46 ( ( P @ X )
% 0.20/0.46 => ( P @ Y ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(conj,conjecture,
% 0.20/0.46 ( leibeq
% 0.20/0.46 @ ^ [U: $o,V: $o] :
% 0.20/0.46 ( U
% 0.20/0.46 & V )
% 0.20/0.46 @ ^ [X: $o,Y: $o] :
% 0.20/0.46 ~ ( ~ X
% 0.20/0.46 | ~ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.50/1.27 ---- Embedded in THF ---
% 1.50/1.27 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.27 %%% Generated on Tue Feb 24 14:22:07 EST 2026
% 1.50/1.27 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.27 %%% Logic specification used:
% 1.50/1.27 %%% thf(spec, logic, $$dhol).
% 1.50/1.27
% 1.50/1.27 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.4YKvQSFCbF/DTF2DTF18514.p
% See solution above
% 1.50/1.27 ------------------------
% 1.50/1.28 ---- Cleaned THF ---
% 1.50/1.28 thf(leibeq_decl,type,
% 1.50/1.28 leibeq: ( $o > $o > $o ) > ( $o > $o > $o ) > $o ).
% 1.50/1.28
% 1.50/1.28 thf(leibeq,definition,
% 1.50/1.28 ( leibeq
% 1.50/1.28 = ( ^ [X: $o > $o > $o,Y: $o > $o > $o] :
% 1.50/1.28 ! [P: ( $o > $o > $o ) > $o] :
% 1.50/1.28 ( ( P @ X )
% 1.50/1.28 => ( P @ Y ) ) ) ) ).
% 1.50/1.28
% 1.50/1.28 thf(conj,conjecture,
% 1.50/1.28 ( leibeq
% 1.50/1.28 @ ^ [U: $o,V: $o] :
% 1.50/1.28 ( U
% 1.50/1.28 & V )
% 1.50/1.28 @ ^ [X: $o,Y: $o] :
% 1.50/1.28 ~ ( ~ X
% 1.50/1.28 | ~ Y ) ) ).
% 1.50/1.28 ------------------------
% 1.50/1.29 % (18703)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_18514 for (3000ds/4Mi)
% 1.50/1.29 % (18706)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_18514 for (3000ds/2Mi)
% 1.50/1.29 % (18706)Instruction limit reached!
% 1.50/1.29 % (18706)------------------------------
% 1.50/1.29 % (18706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (18706)Termination reason: Unknown
% 1.50/1.29 % (18706)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (18706)Memory used [KB]: 5500
% 1.50/1.29 % (18706)Time elapsed: 0.002 s
% 1.50/1.29 % (18706)Instructions burned: 2 (million)
% 1.50/1.29 % (18706)------------------------------
% 1.50/1.29 % (18706)------------------------------
% 1.50/1.29 % (18703)Refutation not found, incomplete strategy
% 1.50/1.29 % (18703)------------------------------
% 1.50/1.29 % (18703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (18703)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.29
% 1.50/1.29
% 1.50/1.29 % (18703)Memory used [KB]: 5500
% 1.50/1.29 % (18703)Time elapsed: 0.002 s
% 1.50/1.29 % (18703)Instructions burned: 2 (million)
% 1.50/1.29 % (18703)------------------------------
% 1.50/1.29 % (18703)------------------------------
% 1.66/1.30 % (18707)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_18514 for (3000ds/275Mi)
% 1.66/1.30 % (18702)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_18514 for (3000ds/183Mi)
% 1.66/1.30 % (18705)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_18514 for (3000ds/2Mi)
% 1.66/1.30 % (18704)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_18514 for (3000ds/27Mi)
% 1.66/1.30 % (18707)Refutation not found, incomplete strategy
% 1.66/1.30 % (18707)------------------------------
% 1.66/1.30 % (18707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (18707)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.30
% 1.66/1.30
% 1.66/1.30 % (18707)Memory used [KB]: 5373
% 1.66/1.30 % (18707)Time elapsed: 0.002 s
% 1.66/1.30 % (18707)Instructions burned: 1 (million)
% 1.66/1.30 % (18707)------------------------------
% 1.66/1.30 % (18707)------------------------------
% 1.66/1.30 % (18705)Instruction limit reached!
% 1.66/1.30 % (18705)------------------------------
% 1.66/1.30 % (18705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (18705)Termination reason: Unknown
% 1.66/1.30 % (18705)Termination phase: Saturation
% 1.66/1.30
% 1.66/1.30 % (18705)Memory used [KB]: 895
% 1.66/1.30 % (18705)Time elapsed: 0.003 s
% 1.66/1.30 % (18705)Instructions burned: 2 (million)
% 1.66/1.30 % (18705)------------------------------
% 1.66/1.30 % (18705)------------------------------
% 1.66/1.30 % (18704)Refutation not found, incomplete strategy
% 1.66/1.30 % (18704)------------------------------
% 1.66/1.30 % (18704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (18704)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.30
% 1.66/1.30
% 1.66/1.30 % (18704)Memory used [KB]: 5500
% 1.66/1.30 % (18704)Time elapsed: 0.004 s
% 1.66/1.30 % (18704)Instructions burned: 2 (million)
% 1.66/1.30 % (18704)------------------------------
% 1.66/1.30 % (18704)------------------------------
% 1.66/1.30 % (18702)First to succeed.
% 1.66/1.30 % (18702)Refutation found. Thanks to Tanya!
% 1.66/1.30 % SZS status Theorem for DTF2THF_18514
% 1.66/1.30 % SZS output start Proof for DTF2THF_18514
% 1.66/1.30 thf(func_def_0, type, leibeq: ($o > $o > $o) > ($o > $o > $o) > $o).
% 1.66/1.30 thf(func_def_14, type, sK1: ($o > $o > $o) > $o).
% 1.66/1.30 thf(func_def_15, type, ph2: !>[X0: $tType]:(X0)).
% 1.66/1.30 thf(f70,plain,(
% 1.66/1.30 $false),
% 1.66/1.30 inference(avatar_sat_refutation,[status(thm)],[f57,f63,f69])).
% 1.66/1.30 thf(f69,plain,(
% 1.66/1.30 ~spl0_1),
% 1.66/1.30 inference(avatar_contradiction_clause,[status(thm)],[f68])).
% 1.66/1.30 thf(f68,plain,(
% 1.66/1.30 $false | ~spl0_1),
% 1.66/1.30 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.66/1.30 thf(f65,plain,(
% 1.66/1.30 ($false = $true) | ~spl0_1),
% 1.66/1.30 inference(superposition,[status(thm)],[f41,f52])).
% 1.66/1.30 thf(f52,plain,(
% 1.66/1.30 (sK3 = $false) | ~spl0_1),
% 1.66/1.30 inference(avatar_component_clause,[status(thm)],[f50])).
% 1.66/1.30 thf(f50,definition,(
% 1.66/1.30 spl0_1 <=> (sK3 = $false)),
% 1.66/1.30 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.66/1.30 thf(f41,plain,(
% 1.66/1.30 (sK3 = $true)),
% 1.66/1.30 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.66/1.30 thf(f40,plain,(
% 1.66/1.30 (sK3 = $true) | (sK3 = $true)),
% 1.66/1.30 inference(not_proxy_clausification,[status(thm)],[f39])).
% 1.66/1.30 thf(f39,plain,(
% 1.66/1.30 ($false = (~ sK3)) | (sK3 = $true)),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f37])).
% 1.66/1.30 thf(f37,plain,(
% 1.66/1.30 ($false = ((~ sK3) | (~ sK4))) | (sK3 = $true)),
% 1.66/1.30 inference(not_proxy_clausification,[status(thm)],[f36])).
% 1.66/1.30 thf(f36,plain,(
% 1.66/1.30 ((~ ((~ sK3) | (~ sK4))) = $true) | (sK3 = $true)),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.66/1.30 thf(f26,plain,(
% 1.66/1.30 ((sK3 & sK4) = $true) | ((~ ((~ sK3) | (~ sK4))) = $true)),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.66/1.30 thf(f25,plain,(
% 1.66/1.30 ((sK3 & sK4) != (~ ((~ sK3) | (~ sK4))))),
% 1.66/1.30 inference(beta_eta_normalization,[status(thm)],[f24])).
% 1.66/1.30 thf(f24,plain,(
% 1.66/1.30 ((sK3 & sK4) != ((^[Y0 : $o]: (~ ((~ sK3) | (~ Y0)))) @ sK4))),
% 1.66/1.30 inference(negative_extensionality,[status(thm)],[f23])).
% 1.66/1.30 thf(f23,plain,(
% 1.66/1.30 ((& @ sK3) != (^[Y0 : $o]: (~ ((~ sK3) | (~ Y0)))))),
% 1.66/1.30 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.66/1.30 thf(f22,plain,(
% 1.66/1.30 (((^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1)))))) @ sK3) != (& @ sK3))),
% 1.66/1.30 inference(negative_extensionality,[status(thm)],[f21])).
% 1.66/1.30 thf(f21,plain,(
% 1.66/1.30 (& != (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1)))))))),
% 1.66/1.30 inference(trivial_inequality_removal,[status(thm)],[f19])).
% 1.66/1.30 thf(f19,plain,(
% 1.66/1.30 (& != (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1))))))) | ($false = $true)),
% 1.66/1.30 inference(constrained_superposition,[status(thm)],[f17,f16])).
% 1.66/1.30 thf(f16,plain,(
% 1.66/1.30 ($false = (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1))))))))),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.66/1.30 thf(f15,plain,(
% 1.66/1.30 ($false = ((sK1 @ &) => (sK1 @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1)))))))))),
% 1.66/1.30 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.66/1.30 thf(f14,plain,(
% 1.66/1.30 ($false = ((^[Y0 : ($o > $o > $o) > $o]: ((Y0 @ &) => (Y0 @ (^[Y1 : $o]: ((^[Y2 : $o]: (~ ((~ Y1) | (~ Y2))))))))) @ sK1))),
% 1.66/1.30 inference(sigma_clausification,[status(thm)],[f13])).
% 1.66/1.30 thf(f13,plain,(
% 1.66/1.30 ((!! @ (($o > $o > $o) > $o) @ (^[Y0 : ($o > $o > $o) > $o]: ((Y0 @ &) => (Y0 @ (^[Y1 : $o]: ((^[Y2 : $o]: (~ ((~ Y1) | (~ Y2)))))))))) != $true)),
% 1.66/1.30 inference(beta_eta_normalization,[status(thm)],[f12])).
% 1.66/1.30 thf(f12,plain,(
% 1.66/1.30 (((^[Y0 : $o > $o > $o]: ((^[Y1 : $o > $o > $o]: (!! @ (($o > $o > $o) > $o) @ (^[Y2 : ($o > $o > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1))))))) != $true)),
% 1.66/1.30 inference(definition_unfolding,[status(thm)],[f11,f10])).
% 1.66/1.30 thf(f10,plain,(
% 1.66/1.30 (leibeq = (^[Y0 : $o > $o > $o]: ((^[Y1 : $o > $o > $o]: (!! @ (($o > $o > $o) > $o) @ (^[Y2 : ($o > $o > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.66/1.30 inference(cnf_transformation,[status(thm)],[f6])).
% 1.66/1.30 thf(f6,plain,(
% 1.66/1.30 (leibeq = (^[Y0 : $o > $o > $o]: ((^[Y1 : $o > $o > $o]: (!! @ (($o > $o > $o) > $o) @ (^[Y2 : ($o > $o > $o) > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.66/1.30 inference(fool_elimination,[status(thm)],[f5])).
% 1.66/1.30 thf(f5,plain,(
% 1.66/1.30 (leibeq = (^[X0 : $o > $o > $o, X1 : $o > $o > $o] : (! [X2 : ($o > $o > $o) > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.66/1.30 inference(rectify,[status(thm)],[f1])).
% 1.66/1.30 thf(f1,axiom,(
% 1.66/1.30 (leibeq = (^[X0 : $o > $o > $o, X1 : $o > $o > $o] : (! [X2 : ($o > $o > $o) > $o] : ((X2 @ X0) => (X2 @ X1)))))),
% 1.66/1.30 file('/export/starexec/sandbox/tmp/tmp.4YKvQSFCbF/DTF2THF_18514.p',leibeq)).
% 1.66/1.30 thf(f11,plain,(
% 1.66/1.30 ((leibeq @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1))))))) != $true)),
% 1.66/1.30 inference(cnf_transformation,[status(thm)],[f9])).
% 1.66/1.30 thf(f9,plain,(
% 1.66/1.30 ((leibeq @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1))))))) != $true)),
% 1.66/1.30 inference(flattening,[status(thm)],[f8])).
% 1.66/1.30 thf(f8,plain,(
% 1.66/1.30 ~((leibeq @ (^[Y0 : $o]: ((^[Y1 : $o]: (Y0 & Y1)))) @ (^[Y0 : $o]: ((^[Y1 : $o]: (~ ((~ Y0) | (~ Y1))))))) = $true)),
% 1.66/1.30 inference(fool_elimination,[status(thm)],[f7])).
% 1.66/1.30 thf(f7,plain,(
% 1.66/1.30 ~(leibeq @ (^[X0 : $o, X1 : $o] : (X1 & X0)) @ (^[X2 : $o, X3 : $o] : (~(~X3 | ~X2))))),
% 1.66/1.30 inference(rectify,[status(thm)],[f3])).
% 1.66/1.30 thf(f3,negated_conjecture,(
% 1.66/1.30 ~(leibeq @ (^[X3 : $o, X4 : $o] : (X4 & X3)) @ (^[X0 : $o, X1 : $o] : (~(~X1 | ~X0))))),
% 1.66/1.30 inference(negated_conjecture,[status(cth)],[f2])).
% 1.66/1.30 thf(f2,conjecture,(
% 1.66/1.30 (leibeq @ (^[X3 : $o, X4 : $o] : (X4 & X3)) @ (^[X0 : $o, X1 : $o] : (~(~X1 | ~X0))))),
% 1.66/1.30 file('/export/starexec/sandbox/tmp/tmp.4YKvQSFCbF/DTF2THF_18514.p',conj)).
% 1.66/1.30 thf(f17,plain,(
% 1.66/1.30 ((sK1 @ &) = $true)),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.66/1.30 thf(f63,plain,(
% 1.66/1.30 ~spl0_2),
% 1.66/1.30 inference(avatar_contradiction_clause,[status(thm)],[f62])).
% 1.66/1.30 thf(f62,plain,(
% 1.66/1.30 $false | ~spl0_2),
% 1.66/1.30 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.66/1.30 thf(f58,plain,(
% 1.66/1.30 ($false = $true) | ~spl0_2),
% 1.66/1.30 inference(superposition,[status(thm)],[f48,f56])).
% 1.66/1.30 thf(f56,plain,(
% 1.66/1.30 ($false = sK4) | ~spl0_2),
% 1.66/1.30 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.66/1.30 thf(f54,definition,(
% 1.66/1.30 spl0_2 <=> ($false = sK4)),
% 1.66/1.30 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.66/1.30 thf(f48,plain,(
% 1.66/1.30 (sK4 = $true)),
% 1.66/1.30 inference(duplicate_literal_removal,[status(thm)],[f47])).
% 1.66/1.30 thf(f47,plain,(
% 1.66/1.30 (sK4 = $true) | (sK4 = $true)),
% 1.66/1.30 inference(not_proxy_clausification,[status(thm)],[f44])).
% 1.66/1.30 thf(f44,plain,(
% 1.66/1.30 (sK4 = $true) | ($false = (~ sK4))),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f43])).
% 1.66/1.30 thf(f43,plain,(
% 1.66/1.30 (sK4 = $true) | ($false = ((~ sK3) | (~ sK4)))),
% 1.66/1.30 inference(not_proxy_clausification,[status(thm)],[f35])).
% 1.66/1.30 thf(f35,plain,(
% 1.66/1.30 ((~ ((~ sK3) | (~ sK4))) = $true) | (sK4 = $true)),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f26])).
% 1.66/1.30 thf(f57,plain,(
% 1.66/1.30 spl0_1 | spl0_2),
% 1.66/1.30 inference(avatar_split_clause,[status(thm)],[f34,f54,f50])).
% 1.66/1.30 thf(f34,plain,(
% 1.66/1.30 (sK3 = $false) | ($false = sK4)),
% 1.66/1.30 inference(duplicate_literal_removal,[status(thm)],[f33])).
% 1.66/1.30 thf(f33,plain,(
% 1.66/1.30 ($false = sK4) | ($false = sK4) | (sK3 = $false)),
% 1.66/1.30 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.66/1.30 thf(f32,plain,(
% 1.66/1.30 (sK3 = $false) | ($false = sK4) | ((~ sK4) = $true)),
% 1.66/1.30 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.66/1.30 thf(f31,plain,(
% 1.66/1.30 (sK3 = $false) | ((~ sK4) = $true) | (sK3 = $false) | ($false = sK4)),
% 1.66/1.30 inference(not_proxy_clausification,[status(thm)],[f30])).
% 1.66/1.30 thf(f30,plain,(
% 1.66/1.30 (sK3 = $false) | ((~ sK3) = $true) | ($false = sK4) | ((~ sK4) = $true)),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f29])).
% 1.66/1.30 thf(f29,plain,(
% 1.66/1.30 (((~ sK3) | (~ sK4)) = $true) | ($false = sK4) | (sK3 = $false)),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f28])).
% 1.66/1.30 thf(f28,plain,(
% 1.66/1.30 ((sK3 & sK4) = $false) | (((~ sK3) | (~ sK4)) = $true)),
% 1.66/1.30 inference(not_proxy_clausification,[status(thm)],[f27])).
% 1.66/1.30 thf(f27,plain,(
% 1.66/1.30 ($false = (~ ((~ sK3) | (~ sK4)))) | ((sK3 & sK4) = $false)),
% 1.66/1.30 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.66/1.30 % SZS output end Proof for DTF2THF_18514
% 1.66/1.30 % (18702)------------------------------
% 1.66/1.30 % (18702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.30 % (18702)Termination reason: Refutation
% 1.66/1.30
% 1.66/1.30 % (18702)Memory used [KB]: 5500
% 1.66/1.30 % (18702)Time elapsed: 0.006 s
% 1.66/1.30 % (18702)Instructions burned: 2 (million)
% 1.66/1.30 % (18702)------------------------------
% 1.66/1.30 % (18702)------------------------------
% 1.66/1.30 % (18701)Success in time 0.009 s
%------------------------------------------------------------------------------