%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO304^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n021.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 09:53:54 AM UTC 2026
% Result : Theorem 1.52s 1.23s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 182 ( 76 equ; 5 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 237 ( 38 ~; 34 |; 4 &; 114 @)
% ( 4 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 9 usr; 10 con; 0-2 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 75 ( 61 ^; 12 !; 2 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_11,type,
sK0: ( a > a > $o ) > $o ).
thf(func_def_14,type,
ph2:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK3: a ).
thf(func_def_16,type,
sK4: a ).
thf(func_def_17,type,
sK5: a > $o ).
thf(f109,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f36,f41,f46,f71,f108]) ).
thf(f108,plain,
( ~ spl1_1
| ~ spl1_3
| ~ spl1_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f107]) ).
thf(f107,plain,
( $false
| ~ spl1_1
| ~ spl1_3
| ~ spl1_4 ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ( $true = $false )
| ~ spl1_1
| ~ spl1_3
| ~ spl1_4 ),
inference(superposition,[status(thm)],[f45,f73]) ).
thf(f73,plain,
( ( ( sK5 @ sK3 )
= $false )
| ~ spl1_1
| ~ spl1_3 ),
inference(superposition,[status(thm)],[f40,f32]) ).
thf(f32,plain,
( ( sK4 = sK3 )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl1_1
<=> ( sK4 = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f40,plain,
( ( ( sK5 @ sK4 )
= $false )
| ~ spl1_3 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl1_3
<=> ( ( sK5 @ sK4 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition]) ).
thf(f45,plain,
( ( ( sK5 @ sK3 )
= $true )
| ~ spl1_4 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl1_4
<=> ( ( sK5 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition]) ).
thf(f71,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f48,f34,f30]) ).
thf(f34,definition,
( spl1_2
<=> ! [X1: a > $o] :
( ( $true
= ( X1 @ sK4 ) )
| ( ( X1 @ sK3 )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f48,plain,
( ( sK4 = sK3 )
| ~ spl1_2 ),
inference(leibniz_equality_elimination,[status(thm)],[f35]) ).
thf(f35,plain,
( ! [X1: a > $o] :
( ( $true
= ( X1 @ sK4 ) )
| ( ( X1 @ sK3 )
= $false ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f46,plain,
( ~ spl1_1
| spl1_4 ),
inference(avatar_split_clause,[status(thm)],[f24,f43,f30]) ).
thf(f24,plain,
( ( ( sK5 @ sK3 )
= $true )
| ( sK4 != sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( ( sK5 @ sK3 )
=> ( sK5 @ sK4 ) )
= $false )
| ( sK4 != sK3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ( sK3 = sK4 )
= $false )
| ( ( ( sK5 @ sK3 )
=> ( sK5 @ sK4 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f20]) ).
thf(f20,plain,
( ( ( sK3 = sK4 )
= $false )
| ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
=> ( Y0 @ sK4 ) )
@ sK5 )
= $false ) ),
inference(sigma_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
=> ( Y0 @ sK4 ) ) )
= $false )
| ( ( sK3 = sK4 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( sK3 = sK4 )
!= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
=> ( Y0 @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( ( sK3 = sK4 )
!= ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK3 )
=> ( Y1 @ Y0 ) ) )
@ sK4 ) ),
inference(negative_extensionality,[status(thm)],[f15]) ).
thf(f15,plain,
( ( ^ [Y0: a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y1 @ sK3 )
=> ( Y1 @ Y0 ) ) ) )
!= ( (=) @ sK3 ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) )
@ sK3 )
!= ( (=) @ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f13]) ).
thf(f13,plain,
( (=)
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f12]) ).
thf(f12,plain,
( ( $true != $true )
| ( (=)
!= ( ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(constrained_superposition,[status(thm)],[f11,f10]) ).
thf(f10,plain,
( ( sK0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( sK0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
= $true )
& ( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7]) ).
thf(f7,plain,
( ? [X0: ( a > a > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) )
& ( ( X0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
!= $true ) )
=> ( ( ( sK0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) )
= $true )
& ( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f6,plain,
? [X0: ( a > a > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) )
& ( ( X0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > a > $o ) > $o] :
( ( $true
= ( X0
@ ^ [Y0: a,Y1: a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y2 @ Y0 )
=> ( Y2 @ Y1 ) ) ) ) )
=> ( ( X0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > a > $o ) > $o] :
( ( X0
@ ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ( X0
@ ^ [X4: a,X5: a] : ( X4 = X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > a > $o ) > $o] :
( ( X0
@ ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ( X0
@ ^ [X1: a,X2: a] : ( X1 = X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > a > $o ) > $o] :
( ( X0
@ ^ [X1: a,X2: a] :
! [X3: a > $o] :
( ( X3 @ X1 )
=> ( X3 @ X2 ) ) )
=> ( X0
@ ^ [X1: a,X2: a] : ( X1 = X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gePadZBGB7/DTF2THF_10510.p',cE2_eq__pme) ).
thf(f11,plain,
( ( sK0 @ (=) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
( $true
!= ( sK0
@ ^ [Y0: a,Y1: a] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f41,plain,
( ~ spl1_1
| spl1_3 ),
inference(avatar_split_clause,[status(thm)],[f23,f38,f30]) ).
thf(f23,plain,
( ( ( sK5 @ sK4 )
= $false )
| ( sK4 != sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f36,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f34,f30]) ).
thf(f28,plain,
! [X1: a > $o] :
( ( $true
= ( X1 @ sK4 ) )
| ( sK4 = sK3 )
| ( ( X1 @ sK3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: a > $o] :
( ( sK4 = sK3 )
| ( $true
= ( ( X1 @ sK3 )
=> ( X1 @ sK4 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: a > $o] :
( ( sK4 = sK3 )
| ( ( ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
=> ( Y0 @ sK4 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
( ( sK4 = sK3 )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
=> ( Y0 @ sK4 ) ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( sK3 = sK4 )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( Y0 @ sK3 )
=> ( Y0 @ sK4 ) ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO304^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.34 % Computer : n021.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 14:27:54 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SYO304^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Syntactic
% 0.30/0.45 % Problem : TPS problem from UNKNOWN
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_0800 [Bro09]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.27 v7.5.0, 0.43 v7.4.0, 0.33 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.57 v6.1.0, 0.43 v6.0.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.60 v5.3.0, 0.80 v4.1.0, 1.00 v4.0.0
% 0.30/0.45 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.45 % Number of connectives : 6 ( 0 ~; 0 |; 0 &; 4 @)
% 0.30/0.45 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 9 ( 9 avg)
% 0.30/0.45 % Number of types : 2 ( 1 usr)
% 0.30/0.45 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.45 % Number of variables : 6 ( 4 ^; 2 !; 0 ?; 6 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(a_type,type,
% 0.30/0.45 a: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(cE2_eq__pme,conjecture,
% 0.30/0.45 ! [Xq: ( a > a > $o ) > $o] :
% 0.30/0.45 ( ( Xq
% 0.30/0.45 @ ^ [X: a,Y: a] :
% 0.30/0.45 ! [Xq0: a > $o] :
% 0.30/0.45 ( ( Xq0 @ X )
% 0.30/0.45 => ( Xq0 @ Y ) ) )
% 0.30/0.45 => ( Xq
% 0.30/0.45 @ ^ [X: a,Y: a] : ( X = Y ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.39/1.19 ---- Embedded in THF ---
% 1.39/1.19 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.19 %%% Generated on Tue Feb 24 14:27:54 EST 2026
% 1.39/1.19 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.19 %%% Logic specification used:
% 1.39/1.19 %%% thf(spec, logic, $$dhol).
% 1.39/1.19
% 1.39/1.19 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gePadZBGB7/DTF2DTF10510.p
% See solution above
% 1.39/1.19 ------------------------
% 1.39/1.19 ---- Cleaned THF ---
% 1.39/1.20 thf(a_type,type,
% 1.39/1.20 a: $tType ).
% 1.39/1.20
% 1.39/1.20 thf(cE2_eq__pme,conjecture,
% 1.39/1.20 ! [Xq: ( a > a > $o ) > $o] :
% 1.39/1.20 ( ( Xq
% 1.39/1.20 @ ^ [X: a,Y: a] :
% 1.39/1.20 ! [Xq0: a > $o] :
% 1.39/1.20 ( ( Xq0 @ X )
% 1.39/1.20 => ( Xq0 @ Y ) ) )
% 1.39/1.20 => ( Xq
% 1.39/1.20 @ ^ [X: a,Y: a] : ( X = Y ) ) ) ).
% 1.39/1.20 ------------------------
% 1.52/1.21 % (10703)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_10510 for (3000ds/275Mi)
% 1.52/1.21 % (10699)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_10510 for (3000ds/4Mi)
% 1.52/1.21 % (10703)Refutation not found, incomplete strategy
% 1.52/1.21 % (10703)------------------------------
% 1.52/1.21 % (10703)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.21 % (10703)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.21
% 1.52/1.21
% 1.52/1.21 % (10703)Memory used [KB]: 5500
% 1.52/1.21 % (10703)Time elapsed: 0.002 s
% 1.52/1.21 % (10703)------------------------------
% 1.52/1.21 % (10703)------------------------------
% 1.52/1.21 % (10699)Refutation not found, incomplete strategy
% 1.52/1.21 % (10699)------------------------------
% 1.52/1.21 % (10699)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.21 % (10699)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.21
% 1.52/1.21
% 1.52/1.21 % (10699)Memory used [KB]: 5500
% 1.52/1.21 % (10699)Time elapsed: 0.002 s
% 1.52/1.21 % (10699)Instructions burned: 1 (million)
% 1.52/1.21 % (10699)------------------------------
% 1.52/1.21 % (10699)------------------------------
% 1.52/1.22 % (10698)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10510 for (3000ds/183Mi)
% 1.52/1.22 % (10700)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_10510 for (3000ds/27Mi)
% 1.52/1.22 % (10702)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_10510 for (3000ds/2Mi)
% 1.52/1.22 % (10700)Refutation not found, incomplete strategy
% 1.52/1.22 % (10700)------------------------------
% 1.52/1.22 % (10700)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.22 % (10700)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.22
% 1.52/1.22
% 1.52/1.22 % (10700)Memory used [KB]: 5500
% 1.52/1.22 % (10700)Time elapsed: 0.003 s
% 1.52/1.22 % (10700)Instructions burned: 1 (million)
% 1.52/1.22 % (10700)------------------------------
% 1.52/1.22 % (10700)------------------------------
% 1.52/1.22 % (10702)Refutation not found, incomplete strategy
% 1.52/1.22 % (10702)------------------------------
% 1.52/1.22 % (10702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.22 % (10701)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10510 for (3000ds/2Mi)
% 1.52/1.22 % (10702)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.22
% 1.52/1.22
% 1.52/1.22 % (10702)Memory used [KB]: 5500
% 1.52/1.22 % (10702)Time elapsed: 0.004 s
% 1.52/1.22 % (10702)Instructions burned: 1 (million)
% 1.52/1.22 % (10702)------------------------------
% 1.52/1.22 % (10702)------------------------------
% 1.52/1.22 % (10705)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10510 for (2999ds/3Mi)
% 1.52/1.22 % (10701)Refutation not found, incomplete strategy
% 1.52/1.22 % (10701)------------------------------
% 1.52/1.22 % (10701)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.22 % (10701)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.22
% 1.52/1.22
% 1.52/1.22 % (10701)Memory used [KB]: 5500
% 1.52/1.22 % (10701)Time elapsed: 0.003 s
% 1.52/1.22 % (10701)Instructions burned: 1 (million)
% 1.52/1.22 % (10701)------------------------------
% 1.52/1.22 % (10701)------------------------------
% 1.52/1.22 % (10705)Refutation not found, incomplete strategy
% 1.52/1.22 % (10705)------------------------------
% 1.52/1.22 % (10705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.22 % (10705)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.22
% 1.52/1.22
% 1.52/1.22 % (10705)Memory used [KB]: 5500
% 1.52/1.22 % (10705)Time elapsed: 0.001 s
% 1.52/1.22 % (10705)Instructions burned: 1 (million)
% 1.52/1.22 % (10705)------------------------------
% 1.52/1.22 % (10705)------------------------------
% 1.52/1.22 % (10706)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_10510 for (2999ds/37Mi)
% 1.52/1.22 % (10698)First to succeed.
% 1.52/1.22 % (10704)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10510 for (3000ds/18Mi)
% 1.52/1.23 % (10698)Refutation found. Thanks to Tanya!
% 1.52/1.23 % SZS status Theorem for DTF2THF_10510
% 1.52/1.23 % SZS output start Proof for DTF2THF_10510
% 1.52/1.23 thf(type_def_5, type, a: $tType).
% 1.52/1.23 thf(func_def_0, type, a: $tType).
% 1.52/1.23 thf(func_def_11, type, sK0: (a > a > $o) > $o).
% 1.52/1.23 thf(func_def_14, type, ph2: !>[X0: $tType]:(X0)).
% 1.52/1.23 thf(func_def_15, type, sK3: a).
% 1.52/1.23 thf(func_def_16, type, sK4: a).
% 1.52/1.23 thf(func_def_17, type, sK5: a > $o).
% 1.52/1.23 thf(f109,plain,(
% 1.52/1.23 $false),
% 1.52/1.23 inference(avatar_sat_refutation,[status(thm)],[f36,f41,f46,f71,f108])).
% 1.52/1.23 thf(f108,plain,(
% 1.52/1.23 ~spl1_1 | ~spl1_3 | ~spl1_4),
% 1.52/1.23 inference(avatar_contradiction_clause,[status(thm)],[f107])).
% 1.52/1.23 thf(f107,plain,(
% 1.52/1.23 $false | (~spl1_1 | ~spl1_3 | ~spl1_4)),
% 1.52/1.23 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.52/1.23 thf(f104,plain,(
% 1.52/1.23 ($true = $false) | (~spl1_1 | ~spl1_3 | ~spl1_4)),
% 1.52/1.23 inference(superposition,[status(thm)],[f45,f73])).
% 1.52/1.23 thf(f73,plain,(
% 1.52/1.23 ((sK5 @ sK3) = $false) | (~spl1_1 | ~spl1_3)),
% 1.52/1.23 inference(superposition,[status(thm)],[f40,f32])).
% 1.52/1.23 thf(f32,plain,(
% 1.52/1.23 (sK4 = sK3) | ~spl1_1),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.52/1.23 thf(f30,definition,(
% 1.52/1.23 spl1_1 <=> (sK4 = sK3)),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.52/1.23 thf(f40,plain,(
% 1.52/1.23 ((sK5 @ sK4) = $false) | ~spl1_3),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.52/1.23 thf(f38,definition,(
% 1.52/1.23 spl1_3 <=> ((sK5 @ sK4) = $false)),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl1_3])],[avatar_definition])).
% 1.52/1.23 thf(f45,plain,(
% 1.52/1.23 ((sK5 @ sK3) = $true) | ~spl1_4),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.52/1.23 thf(f43,definition,(
% 1.52/1.23 spl1_4 <=> ((sK5 @ sK3) = $true)),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl1_4])],[avatar_definition])).
% 1.52/1.23 thf(f71,plain,(
% 1.52/1.23 spl1_1 | ~spl1_2),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f48,f34,f30])).
% 1.52/1.23 thf(f34,definition,(
% 1.52/1.23 spl1_2 <=> ! [X1 : a > $o] : (($true = (X1 @ sK4)) | ((X1 @ sK3) = $false))),
% 1.52/1.23 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.52/1.23 thf(f48,plain,(
% 1.52/1.23 (sK4 = sK3) | ~spl1_2),
% 1.52/1.23 inference(leibniz_equality_elimination,[status(thm)],[f35])).
% 1.52/1.23 thf(f35,plain,(
% 1.52/1.23 ( ! [X1 : a > $o] : (($true = (X1 @ sK4)) | ((X1 @ sK3) = $false)) ) | ~spl1_2),
% 1.52/1.23 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.52/1.23 thf(f46,plain,(
% 1.52/1.23 ~spl1_1 | spl1_4),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f24,f43,f30])).
% 1.52/1.23 thf(f24,plain,(
% 1.52/1.23 ((sK5 @ sK3) = $true) | (sK4 != sK3)),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.52/1.23 thf(f22,plain,(
% 1.52/1.23 (((sK5 @ sK3) => (sK5 @ sK4)) = $false) | (sK4 != sK3)),
% 1.52/1.23 inference(equality_proxy_clausification,[status(thm)],[f21])).
% 1.52/1.23 thf(f21,plain,(
% 1.52/1.23 ((sK3 = sK4) = $false) | (((sK5 @ sK3) => (sK5 @ sK4)) = $false)),
% 1.52/1.23 inference(beta_eta_normalization,[status(thm)],[f20])).
% 1.52/1.23 thf(f20,plain,(
% 1.52/1.23 ((sK3 = sK4) = $false) | (((^[Y0 : a > $o]: ((Y0 @ sK3) => (Y0 @ sK4))) @ sK5) = $false)),
% 1.52/1.23 inference(sigma_clausification,[status(thm)],[f19])).
% 1.52/1.23 thf(f19,plain,(
% 1.52/1.23 ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK3) => (Y0 @ sK4)))) = $false) | ((sK3 = sK4) = $false)),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.52/1.23 thf(f17,plain,(
% 1.52/1.23 ((sK3 = sK4) != (!! @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK3) => (Y0 @ sK4)))))),
% 1.52/1.23 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.52/1.23 thf(f16,plain,(
% 1.52/1.23 ((sK3 = sK4) != ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK3) => (Y1 @ Y0))))) @ sK4))),
% 1.52/1.23 inference(negative_extensionality,[status(thm)],[f15])).
% 1.52/1.23 thf(f15,plain,(
% 1.52/1.23 ((^[Y0 : a]: (!! @ (a > $o) @ (^[Y1 : a > $o]: ((Y1 @ sK3) => (Y1 @ Y0))))) != (= @ sK3))),
% 1.52/1.23 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.52/1.23 thf(f14,plain,(
% 1.52/1.23 (((^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))) @ sK3) != (= @ sK3))),
% 1.52/1.23 inference(negative_extensionality,[status(thm)],[f13])).
% 1.52/1.23 thf(f13,plain,(
% 1.52/1.23 (= != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.52/1.23 inference(trivial_inequality_removal,[status(thm)],[f12])).
% 1.52/1.23 thf(f12,plain,(
% 1.52/1.23 ($true != $true) | (= != (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))),
% 1.52/1.23 inference(constrained_superposition,[status(thm)],[f11,f10])).
% 1.52/1.23 thf(f10,plain,(
% 1.52/1.23 ((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1)))))))) = $true)),
% 1.52/1.23 inference(cnf_transformation,[status(thm)],[f8])).
% 1.52/1.23 thf(f8,plain,(
% 1.52/1.23 ((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1)))))))) = $true) & ($true != (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1))))))),
% 1.52/1.23 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f7])).
% 1.52/1.23 thf(f7,plain,(
% 1.52/1.23 ? [X0 : (a > a > $o) > $o] : (($true = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))) & ((X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1))))) != $true)) => (((sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1)))))))) = $true) & ($true != (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1)))))))),
% 1.52/1.23 introduced(definition,[],[choice_axiom])).
% 1.52/1.23 thf(f6,plain,(
% 1.52/1.23 ? [X0 : (a > a > $o) > $o] : (($true = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))) & ((X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1))))) != $true))),
% 1.52/1.23 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.23 thf(f5,plain,(
% 1.52/1.23 ~! [X0 : (a > a > $o) > $o] : (($true = (X0 @ (^[Y0 : a]: ((^[Y1 : a]: (!! @ (a > $o) @ (^[Y2 : a > $o]: ((Y2 @ Y0) => (Y2 @ Y1))))))))) => ((X0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1))))) = $true))),
% 1.52/1.23 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.23 thf(f4,plain,(
% 1.52/1.23 ~! [X0 : (a > a > $o) > $o] : ((X0 @ (^[X1 : a, X2 : a] : (! [X3 : a > $o] : ((X3 @ X1) => (X3 @ X2))))) => (X0 @ (^[X4 : a, X5 : a] : ((X4 = X5)))))),
% 1.52/1.23 inference(rectify,[status(thm)],[f2])).
% 1.52/1.23 thf(f2,negated_conjecture,(
% 1.52/1.23 ~! [X0 : (a > a > $o) > $o] : ((X0 @ (^[X1 : a, X2 : a] : (! [X3 : a > $o] : ((X3 @ X1) => (X3 @ X2))))) => (X0 @ (^[X1 : a, X2 : a] : ((X1 = X2)))))),
% 1.52/1.23 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.23 thf(f1,conjecture,(
% 1.52/1.23 ! [X0 : (a > a > $o) > $o] : ((X0 @ (^[X1 : a, X2 : a] : (! [X3 : a > $o] : ((X3 @ X1) => (X3 @ X2))))) => (X0 @ (^[X1 : a, X2 : a] : ((X1 = X2)))))),
% 1.52/1.23 file('/export/starexec/sandbox/tmp/tmp.gePadZBGB7/DTF2THF_10510.p',cE2_eq__pme)).
% 1.52/1.23 thf(f11,plain,(
% 1.52/1.23 ((sK0 @ =) != $true)),
% 1.52/1.23 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.52/1.23 thf(f9,plain,(
% 1.52/1.23 ($true != (sK0 @ (^[Y0 : a]: ((^[Y1 : a]: (Y0 = Y1))))))),
% 1.52/1.23 inference(cnf_transformation,[status(thm)],[f8])).
% 1.52/1.23 thf(f41,plain,(
% 1.52/1.23 ~spl1_1 | spl1_3),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f23,f38,f30])).
% 1.52/1.23 thf(f23,plain,(
% 1.52/1.23 ((sK5 @ sK4) = $false) | (sK4 != sK3)),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.52/1.23 thf(f36,plain,(
% 1.52/1.23 spl1_1 | spl1_2),
% 1.52/1.23 inference(avatar_split_clause,[status(thm)],[f28,f34,f30])).
% 1.52/1.23 thf(f28,plain,(
% 1.52/1.23 ( ! [X1 : a > $o] : (($true = (X1 @ sK4)) | (sK4 = sK3) | ((X1 @ sK3) = $false)) )),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.52/1.23 thf(f27,plain,(
% 1.52/1.23 ( ! [X1 : a > $o] : ((sK4 = sK3) | ($true = ((X1 @ sK3) => (X1 @ sK4)))) )),
% 1.52/1.23 inference(beta_eta_normalization,[status(thm)],[f26])).
% 1.52/1.23 thf(f26,plain,(
% 1.52/1.23 ( ! [X1 : a > $o] : ((sK4 = sK3) | (((^[Y0 : a > $o]: ((Y0 @ sK3) => (Y0 @ sK4))) @ X1) = $true)) )),
% 1.52/1.23 inference(pi_clausification,[status(thm)],[f25])).
% 1.52/1.23 thf(f25,plain,(
% 1.52/1.23 (sK4 = sK3) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK3) => (Y0 @ sK4)))) = $true)),
% 1.52/1.23 inference(equality_proxy_clausification,[status(thm)],[f18])).
% 1.52/1.23 thf(f18,plain,(
% 1.52/1.23 ((sK3 = sK4) = $true) | ((!! @ (a > $o) @ (^[Y0 : a > $o]: ((Y0 @ sK3) => (Y0 @ sK4)))) = $true)),
% 1.52/1.23 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.52/1.23 % SZS output end Proof for DTF2THF_10510
% 1.52/1.23 % (10698)------------------------------
% 1.52/1.23 % (10698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.23 % (10698)Termination reason: Refutation
% 1.52/1.23
% 1.52/1.23 % (10698)Memory used [KB]: 5628
% 1.52/1.23 % (10698)Time elapsed: 0.010 s
% 1.52/1.23 % (10698)Instructions burned: 11 (million)
% 1.52/1.23 % (10698)------------------------------
% 1.52/1.23 % (10698)------------------------------
% 1.52/1.23 % (10697)Success in time 0.015 s
%------------------------------------------------------------------------------