%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV121^5 : 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 : n027.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 09:40:20 AM UTC 2026
% Result : Theorem 1.34s 1.28s
% Output : Refutation 1.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 5
% Syntax : Number of formulae : 51 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 319 ( 98 equ; 3 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 327 ( 37 ~; 50 |; 0 &; 191 @)
% ( 4 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 66 ( 66 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 9 usr; 10 con; 0-2 aty)
% ( 27 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 92 ( 73 ^; 19 !; 0 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_11,type,
ph1:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK4: $i > $i > $o ).
thf(func_def_16,type,
sK5: ( $i > $i > $o ) > $i ).
thf(f82,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f36,f41,f45,f52,f78]) ).
thf(f78,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f77]) ).
thf(f77,plain,
( $false
| ~ spl0_1
| spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f71,f34]) ).
thf(f34,plain,
( ( sK2 != sK3 )
| spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl0_2
<=> ( sK2 = sK3 ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f71,plain,
( ( sK2 = sK3 )
| ~ spl0_1 ),
inference(equality_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( sK3 = sK2 )
= $true )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f69]) ).
thf(f69,plain,
( ( ( sK3 = sK2 )
= $true )
| ( $false = $true )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f68]) ).
thf(f68,plain,
( ( ( sK3 = sK2 )
= $true )
| ( $false
= ( ( sK5
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK5
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $false
= ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ ( sK5
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
@ ( sK5
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ sK2
@ sK3 )
= $true )
| ~ spl0_1 ),
inference(primitive_instantiation,[status(thm)],[f31]) ).
thf(f31,plain,
( ! [X1: $i > $i > $o] :
( ( ( X1 @ ( sK5 @ X1 ) @ ( sK5 @ X1 ) )
= $false )
| ( ( X1 @ sK2 @ sK3 )
= $true ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl0_1
<=> ! [X1: $i > $i > $o] :
( ( ( X1 @ sK2 @ sK3 )
= $true )
| ( ( X1 @ ( sK5 @ X1 ) @ ( sK5 @ X1 ) )
= $false ) ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f52,plain,
( ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f44,f46]) ).
thf(f46,plain,
( ( ( sK4 @ sK2 @ sK2 )
= $false )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[status(thm)],[f40,f35]) ).
thf(f35,plain,
( ( sK2 = sK3 )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f40,plain,
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl0_3
<=> ( $false
= ( sK4 @ sK2 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f44,plain,
( ! [X1: $i] :
( $true
= ( sK4 @ X1 @ X1 ) )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl0_4
<=> ! [X1: $i] :
( $true
= ( sK4 @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f45,plain,
( ~ spl0_2
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f21,f43,f33]) ).
thf(f21,plain,
! [X1: $i] :
( ( $true
= ( sK4 @ X1 @ X1 ) )
| ( sK2 != sK3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( $false
= ( sK2 = sK3 ) )
| ( $true
= ( sK4 @ X1 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( $true
= ( ^ [Y0: $i] : ( sK4 @ Y0 @ Y0 )
@ X1 ) )
| ( $false
= ( sK2 = sK3 ) ) ),
inference(pi_clausification,[status(thm)],[f18]) ).
thf(f18,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] : ( sK4 @ Y0 @ Y0 ) )
= $true )
| ( $false
= ( sK2 = sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] : ( sK4 @ Y0 @ Y0 ) )
=> ( sK4 @ sK2 @ sK3 ) ) )
| ( $false
= ( sK2 = sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f15]) ).
thf(f15,plain,
( ( $false
= ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ sK4 ) )
| ( $false
= ( sK2 = sK3 ) ) ),
inference(sigma_clausification,[status(thm)],[f14]) ).
thf(f14,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $false )
| ( $false
= ( sK2 = sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
!= ( sK2 = sK3 ) ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
( ( sK2 = sK3 )
!= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
=> ( Y1 @ sK2 @ Y0 ) ) )
@ sK3 ) ),
inference(negative_extensionality,[status(thm)],[f10]) ).
thf(f10,plain,
( ( (=) @ sK2 )
!= ( ^ [Y0: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y1: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y2: $i] : ( Y1 @ Y2 @ Y2 ) )
=> ( Y1 @ sK2 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
( ( (=) @ sK2 )
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) )
@ sK2 ) ),
inference(negative_extensionality,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= (=) ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $i > $o )
@ ^ [Y2: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y3: $i] : ( Y2 @ Y3 @ Y3 ) )
=> ( Y2 @ Y0 @ Y1 ) ) ) )
!= ( ^ [Y0: $i,Y1: $i] : ( Y0 = Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $i > $o] :
( ! [X3: $i] : ( X2 @ X3 @ X3 )
=> ( X2 @ X0 @ X1 ) ) )
!= ( ^ [X4: $i,X5: $i] : ( X4 = X5 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
( ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ( X4 @ X2 @ X3 ) ) )
!= ( ^ [X0: $i,X1: $i] : ( X0 = X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ^ [X2: $i,X3: $i] :
! [X4: $i > $i > $o] :
( ! [X5: $i] : ( X4 @ X5 @ X5 )
=> ( X4 @ X2 @ X3 ) ) )
= ( ^ [X0: $i,X1: $i] : ( X0 = X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.f7H6qgbKSu/DTF2THF_20692.p',cTHM47C_pme) ).
thf(f41,plain,
( ~ spl0_2
| spl0_3 ),
inference(avatar_split_clause,[status(thm)],[f22,f38,f33]) ).
thf(f22,plain,
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( sK2 != sK3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( ( $false
= ( sK4 @ sK2 @ sK3 ) )
| ( $false
= ( sK2 = sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f36,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f28,f33,f30]) ).
thf(f28,plain,
! [X1: $i > $i > $o] :
( ( sK2 = sK3 )
| ( ( X1 @ sK2 @ sK3 )
= $true )
| ( ( X1 @ ( sK5 @ X1 ) @ ( sK5 @ X1 ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f27]) ).
thf(f27,plain,
! [X1: $i > $i > $o] :
( ( ( X1 @ sK2 @ sK3 )
= $true )
| ( ( ^ [Y0: $i] : ( X1 @ Y0 @ Y0 )
@ ( sK5 @ X1 ) )
= $false )
| ( sK2 = sK3 ) ),
inference(sigma_clausification,[status(thm)],[f26]) ).
thf(f26,plain,
! [X1: $i > $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) ) )
| ( sK2 = sK3 )
| ( ( X1 @ sK2 @ sK3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f25]) ).
thf(f25,plain,
! [X1: $i > $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true )
| ( sK2 = sK3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f24]) ).
thf(f24,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( sK2 = sK3 ) )
| ( ( ( !! @ $i
@ ^ [Y0: $i] : ( X1 @ Y0 @ Y0 ) )
=> ( X1 @ sK2 @ sK3 ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f23]) ).
thf(f23,plain,
! [X1: $i > $i > $o] :
( ( $true
= ( sK2 = sK3 ) )
| ( ( ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK2 @ sK3 ) )
@ X1 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ( !! @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 @ Y1 ) )
=> ( Y0 @ sK2 @ sK3 ) ) )
= $true )
| ( $true
= ( sK2 = sK3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV121^5 : 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
% 0.17/0.34 % Computer : n027.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:41:07 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SEV121^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.48 % Domain : Set Theory (Relations)
% 0.20/0.48 % Problem : TPS problem THM47C
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro09]
% 0.20/0.48 % Names : tps_0445 [Bro09]
% 0.20/0.48 % : THM47C [TPS]
% 0.20/0.48 % : tps_0444 [Bro09]
% 0.20/0.48 % : X5303 [TPS]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.0.0, 0.60 v4.1.0, 0.67 v4.0.0
% 0.20/0.48 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.20/0.48 % Number of atoms : 2 ( 2 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 1 ( 2 avg)
% 0.20/0.48 % Number of connectives : 5 ( 0 ~; 0 |; 0 &; 4 @)
% 0.20/0.48 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 1 ( 1 avg)
% 0.20/0.48 % Number of types : 2 ( 0 usr)
% 0.20/0.48 % Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.20/0.48 % Number of variables : 6 ( 4 ^; 2 !; 0 ?; 6 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.48 % : Polymorphic definitions expanded.
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(cTHM47C_pme,conjecture,
% 0.20/0.48 ( ( ^ [Xu: $i,Xv: $i] : ( Xu = Xv ) )
% 0.20/0.48 = ( ^ [Xx: $i,Xy: $i] :
% 0.20/0.48 ! [Xp: $i > $i > $o] :
% 0.20/0.48 ( ! [Xx0: $i] : ( Xp @ Xx0 @ Xx0 )
% 0.20/0.48 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.34/1.25 ---- Embedded in THF ---
% 1.34/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.34/1.25 %%% Generated on Tue Feb 24 12:41:08 EST 2026
% 1.34/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.34/1.25 %%% Logic specification used:
% 1.34/1.25 %%% thf(spec, logic, $$dhol).
% 1.34/1.25
% 1.34/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.f7H6qgbKSu/DTF2DTF20692.p
% See solution above
% 1.34/1.25 ------------------------
% 1.34/1.25 ---- Cleaned THF ---
% 1.34/1.25 thf(cTHM47C_pme,conjecture,
% 1.34/1.25 ( ( ^ [Xu: $i,Xv: $i] : ( Xu = Xv ) )
% 1.34/1.25 = ( ^ [Xx: $i,Xy: $i] :
% 1.34/1.25 ! [Xp: $i > $i > $o] :
% 1.34/1.25 ( ! [Xx0: $i] : ( Xp @ Xx0 @ Xx0 )
% 1.34/1.25 => ( Xp @ Xx @ Xy ) ) ) ) ).
% 1.34/1.25 ------------------------
% 1.34/1.27 % (20795)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_20692 for (3000ds/2Mi)
% 1.34/1.27 % (20793)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_20692 for (3000ds/27Mi)
% 1.34/1.27 % (20795)Refutation not found, incomplete strategy
% 1.34/1.27 % (20795)------------------------------
% 1.34/1.27 % (20795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.27 % (20795)Termination reason: Refutation not found, incomplete strategy
% 1.34/1.27
% 1.34/1.27
% 1.34/1.27 % (20795)Memory used [KB]: 5500
% 1.34/1.27 % (20795)Time elapsed: 0.002 s
% 1.34/1.27 % (20795)Instructions burned: 1 (million)
% 1.34/1.27 % (20795)------------------------------
% 1.34/1.27 % (20795)------------------------------
% 1.34/1.27 % (20793)Refutation not found, incomplete strategy
% 1.34/1.27 % (20793)------------------------------
% 1.34/1.27 % (20793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.27 % (20793)Termination reason: Refutation not found, incomplete strategy
% 1.34/1.27
% 1.34/1.27
% 1.34/1.27 % (20793)Memory used [KB]: 5500
% 1.34/1.27 % (20793)Time elapsed: 0.002 s
% 1.34/1.27 % (20793)Instructions burned: 2 (million)
% 1.34/1.27 % (20793)------------------------------
% 1.34/1.27 % (20793)------------------------------
% 1.34/1.27 % (20796)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_20692 for (3000ds/275Mi)
% 1.34/1.27 % (20797)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20692 for (3000ds/18Mi)
% 1.34/1.27 % (20791)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20692 for (3000ds/183Mi)
% 1.34/1.28 % (20794)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20692 for (3000ds/2Mi)
% 1.34/1.28 % (20796)First to succeed.
% 1.34/1.28 % (20794)Instruction limit reached!
% 1.34/1.28 % (20794)------------------------------
% 1.34/1.28 % (20794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.28 % (20794)Termination reason: Unknown
% 1.34/1.28 % (20794)Termination phase: Saturation
% 1.34/1.28
% 1.34/1.28 % (20794)Memory used [KB]: 5500
% 1.34/1.28 % (20794)Time elapsed: 0.002 s
% 1.34/1.28 % (20794)Instructions burned: 2 (million)
% 1.34/1.28 % (20794)------------------------------
% 1.34/1.28 % (20794)------------------------------
% 1.34/1.28 % (20792)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_20692 for (3000ds/4Mi)
% 1.34/1.28 % (20798)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20692 for (2999ds/3Mi)
% 1.34/1.28 % (20797)Also succeeded, but the first one will report.
% 1.34/1.28 % (20796)Refutation found. Thanks to Tanya!
% 1.34/1.28 % SZS status Theorem for DTF2THF_20692
% 1.34/1.28 % SZS output start Proof for DTF2THF_20692
% 1.34/1.28 thf(func_def_11, type, ph1: !>[X0: $tType]:(X0)).
% 1.34/1.28 thf(func_def_15, type, sK4: $i > $i > $o).
% 1.34/1.28 thf(func_def_16, type, sK5: ($i > $i > $o) > $i).
% 1.34/1.28 thf(f82,plain,(
% 1.34/1.28 $false),
% 1.34/1.28 inference(avatar_sat_refutation,[status(thm)],[f36,f41,f45,f52,f78])).
% 1.34/1.28 thf(f78,plain,(
% 1.34/1.28 ~spl0_1 | spl0_2),
% 1.34/1.28 inference(avatar_contradiction_clause,[status(thm)],[f77])).
% 1.34/1.28 thf(f77,plain,(
% 1.34/1.28 $false | (~spl0_1 | spl0_2)),
% 1.34/1.28 inference(subsumption_resolution,[status(thm)],[f71,f34])).
% 1.34/1.28 thf(f34,plain,(
% 1.34/1.28 (sK2 != sK3) | spl0_2),
% 1.34/1.28 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.34/1.28 thf(f33,definition,(
% 1.34/1.28 spl0_2 <=> (sK2 = sK3)),
% 1.34/1.28 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.34/1.28 thf(f71,plain,(
% 1.34/1.28 (sK2 = sK3) | ~spl0_1),
% 1.34/1.28 inference(equality_proxy_clausification,[status(thm)],[f70])).
% 1.34/1.28 thf(f70,plain,(
% 1.34/1.28 ((sK3 = sK2) = $true) | ~spl0_1),
% 1.34/1.28 inference(trivial_inequality_removal,[status(thm)],[f69])).
% 1.34/1.28 thf(f69,plain,(
% 1.34/1.28 ((sK3 = sK2) = $true) | ($false = $true) | ~spl0_1),
% 1.34/1.28 inference(boolean_simplification,[status(thm)],[f68])).
% 1.34/1.28 thf(f68,plain,(
% 1.34/1.28 ((sK3 = sK2) = $true) | ($false = ((sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) | ~spl0_1),
% 1.34/1.28 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.34/1.28 thf(f53,plain,(
% 1.34/1.28 ($false = ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ (sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) @ (sK5 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ sK2 @ sK3) = $true) | ~spl0_1),
% 1.34/1.28 inference(primitive_instantiation,[status(thm)],[f31])).
% 1.34/1.28 thf(f31,plain,(
% 1.34/1.28 ( ! [X1 : $i > $i > $o] : (((X1 @ (sK5 @ X1) @ (sK5 @ X1)) = $false) | ((X1 @ sK2 @ sK3) = $true)) ) | ~spl0_1),
% 1.34/1.28 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.34/1.28 thf(f30,definition,(
% 1.34/1.28 spl0_1 <=> ! [X1 : $i > $i > $o] : (((X1 @ sK2 @ sK3) = $true) | ((X1 @ (sK5 @ X1) @ (sK5 @ X1)) = $false))),
% 1.34/1.28 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.34/1.28 thf(f52,plain,(
% 1.34/1.28 ~spl0_2 | ~spl0_3 | ~spl0_4),
% 1.34/1.28 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.34/1.28 thf(f51,plain,(
% 1.34/1.28 $false | (~spl0_2 | ~spl0_3 | ~spl0_4)),
% 1.34/1.28 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.34/1.28 thf(f48,plain,(
% 1.34/1.28 ($false = $true) | (~spl0_2 | ~spl0_3 | ~spl0_4)),
% 1.34/1.28 inference(superposition,[status(thm)],[f44,f46])).
% 1.34/1.28 thf(f46,plain,(
% 1.34/1.28 ((sK4 @ sK2 @ sK2) = $false) | (~spl0_2 | ~spl0_3)),
% 1.34/1.28 inference(forward_demodulation,[status(thm)],[f40,f35])).
% 1.34/1.28 thf(f35,plain,(
% 1.34/1.28 (sK2 = sK3) | ~spl0_2),
% 1.34/1.28 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.34/1.28 thf(f40,plain,(
% 1.34/1.28 ($false = (sK4 @ sK2 @ sK3)) | ~spl0_3),
% 1.34/1.28 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.34/1.28 thf(f38,definition,(
% 1.34/1.28 spl0_3 <=> ($false = (sK4 @ sK2 @ sK3))),
% 1.34/1.28 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.34/1.28 thf(f44,plain,(
% 1.34/1.28 ( ! [X1 : $i] : (($true = (sK4 @ X1 @ X1))) ) | ~spl0_4),
% 1.34/1.28 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.34/1.28 thf(f43,definition,(
% 1.34/1.28 spl0_4 <=> ! [X1 : $i] : ($true = (sK4 @ X1 @ X1))),
% 1.34/1.28 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.34/1.28 thf(f45,plain,(
% 1.34/1.28 ~spl0_2 | spl0_4),
% 1.34/1.28 inference(avatar_split_clause,[status(thm)],[f21,f43,f33])).
% 1.34/1.28 thf(f21,plain,(
% 1.34/1.28 ( ! [X1 : $i] : (($true = (sK4 @ X1 @ X1)) | (sK2 != sK3)) )),
% 1.34/1.28 inference(equality_proxy_clausification,[status(thm)],[f20])).
% 1.34/1.28 thf(f20,plain,(
% 1.34/1.28 ( ! [X1 : $i] : (($false = (sK2 = sK3)) | ($true = (sK4 @ X1 @ X1))) )),
% 1.34/1.28 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.34/1.28 thf(f19,plain,(
% 1.34/1.28 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (sK4 @ Y0 @ Y0)) @ X1)) | ($false = (sK2 = sK3))) )),
% 1.34/1.28 inference(pi_clausification,[status(thm)],[f18])).
% 1.34/1.28 thf(f18,plain,(
% 1.34/1.28 ((!! @ $i @ (^[Y0 : $i]: (sK4 @ Y0 @ Y0))) = $true) | ($false = (sK2 = sK3))),
% 1.34/1.28 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.34/1.28 thf(f16,plain,(
% 1.34/1.28 ($false = ((!! @ $i @ (^[Y0 : $i]: (sK4 @ Y0 @ Y0))) => (sK4 @ sK2 @ sK3))) | ($false = (sK2 = sK3))),
% 1.34/1.28 inference(beta_eta_normalization,[status(thm)],[f15])).
% 1.34/1.28 thf(f15,plain,(
% 1.34/1.28 ($false = ((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) => (Y0 @ sK2 @ sK3))) @ sK4)) | ($false = (sK2 = sK3))),
% 1.34/1.28 inference(sigma_clausification,[status(thm)],[f14])).
% 1.34/1.28 thf(f14,plain,(
% 1.34/1.28 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) => (Y0 @ sK2 @ sK3)))) = $false) | ($false = (sK2 = sK3))),
% 1.34/1.28 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.34/1.28 thf(f12,plain,(
% 1.34/1.28 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) => (Y0 @ sK2 @ sK3)))) != (sK2 = sK3))),
% 1.34/1.28 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.34/1.28 thf(f11,plain,(
% 1.34/1.28 ((sK2 = sK3) != ((^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2 @ Y2))) => (Y1 @ sK2 @ Y0))))) @ sK3))),
% 1.34/1.28 inference(negative_extensionality,[status(thm)],[f10])).
% 1.34/1.28 thf(f10,plain,(
% 1.34/1.28 ((= @ sK2) != (^[Y0 : $i]: (!! @ ($i > $i > $o) @ (^[Y1 : $i > $i > $o]: ((!! @ $i @ (^[Y2 : $i]: (Y1 @ Y2 @ Y2))) => (Y1 @ sK2 @ Y0))))))),
% 1.34/1.28 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.34/1.28 thf(f9,plain,(
% 1.34/1.28 ((= @ sK2) != ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (Y2 @ Y3 @ Y3))) => (Y2 @ Y0 @ Y1))))))) @ sK2))),
% 1.34/1.28 inference(negative_extensionality,[status(thm)],[f8])).
% 1.34/1.28 thf(f8,plain,(
% 1.34/1.28 ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (Y2 @ Y3 @ Y3))) => (Y2 @ Y0 @ Y1))))))) != =)),
% 1.34/1.28 inference(beta_eta_normalization,[status(thm)],[f7])).
% 1.34/1.28 thf(f7,plain,(
% 1.34/1.28 ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (Y2 @ Y3 @ Y3))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))))),
% 1.34/1.28 inference(cnf_transformation,[status(thm)],[f6])).
% 1.34/1.28 thf(f6,plain,(
% 1.34/1.28 ((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (Y2 @ Y3 @ Y3))) => (Y2 @ Y0 @ Y1))))))) != (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))))),
% 1.34/1.28 inference(flattening,[status(thm)],[f5])).
% 1.34/1.28 thf(f5,plain,(
% 1.34/1.28 ~((^[Y0 : $i]: ((^[Y1 : $i]: (!! @ ($i > $i > $o) @ (^[Y2 : $i > $i > $o]: ((!! @ $i @ (^[Y3 : $i]: (Y2 @ Y3 @ Y3))) => (Y2 @ Y0 @ Y1))))))) = (^[Y0 : $i]: ((^[Y1 : $i]: (Y0 = Y1)))))),
% 1.34/1.28 inference(fool_elimination,[status(thm)],[f4])).
% 1.34/1.28 thf(f4,plain,(
% 1.34/1.28 ~((^[X0 : $i, X1 : $i] : (! [X2 : $i > $i > $o] : (! [X3 : $i] : (X2 @ X3 @ X3) => (X2 @ X0 @ X1)))) = (^[X4 : $i, X5 : $i] : ((X4 = X5))))),
% 1.34/1.28 inference(rectify,[status(thm)],[f2])).
% 1.34/1.28 thf(f2,negated_conjecture,(
% 1.34/1.28 ~((^[X2 : $i, X3 : $i] : (! [X4 : $i > $i > $o] : (! [X5 : $i] : (X4 @ X5 @ X5) => (X4 @ X2 @ X3)))) = (^[X0 : $i, X1 : $i] : ((X0 = X1))))),
% 1.34/1.28 inference(negated_conjecture,[status(cth)],[f1])).
% 1.34/1.28 thf(f1,conjecture,(
% 1.34/1.28 ((^[X2 : $i, X3 : $i] : (! [X4 : $i > $i > $o] : (! [X5 : $i] : (X4 @ X5 @ X5) => (X4 @ X2 @ X3)))) = (^[X0 : $i, X1 : $i] : ((X0 = X1))))),
% 1.34/1.28 file('/export/starexec/sandbox/tmp/tmp.f7H6qgbKSu/DTF2THF_20692.p',cTHM47C_pme)).
% 1.34/1.28 thf(f41,plain,(
% 1.34/1.28 ~spl0_2 | spl0_3),
% 1.34/1.28 inference(avatar_split_clause,[status(thm)],[f22,f38,f33])).
% 1.34/1.28 thf(f22,plain,(
% 1.34/1.28 ($false = (sK4 @ sK2 @ sK3)) | (sK2 != sK3)),
% 1.34/1.28 inference(equality_proxy_clausification,[status(thm)],[f17])).
% 1.34/1.28 thf(f17,plain,(
% 1.34/1.28 ($false = (sK4 @ sK2 @ sK3)) | ($false = (sK2 = sK3))),
% 1.34/1.28 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.34/1.28 thf(f36,plain,(
% 1.34/1.28 spl0_1 | spl0_2),
% 1.34/1.28 inference(avatar_split_clause,[status(thm)],[f28,f33,f30])).
% 1.34/1.28 thf(f28,plain,(
% 1.34/1.28 ( ! [X1 : $i > $i > $o] : ((sK2 = sK3) | ((X1 @ sK2 @ sK3) = $true) | ((X1 @ (sK5 @ X1) @ (sK5 @ X1)) = $false)) )),
% 1.34/1.28 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.34/1.28 thf(f27,plain,(
% 1.34/1.28 ( ! [X1 : $i > $i > $o] : (((X1 @ sK2 @ sK3) = $true) | (((^[Y0 : $i]: (X1 @ Y0 @ Y0)) @ (sK5 @ X1)) = $false) | (sK2 = sK3)) )),
% 1.34/1.28 inference(sigma_clausification,[status(thm)],[f26])).
% 1.34/1.28 thf(f26,plain,(
% 1.34/1.28 ( ! [X1 : $i > $i > $o] : (($false = (!! @ $i @ (^[Y0 : $i]: (X1 @ Y0 @ Y0)))) | (sK2 = sK3) | ((X1 @ sK2 @ sK3) = $true)) )),
% 1.34/1.28 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.34/1.28 thf(f25,plain,(
% 1.34/1.28 ( ! [X1 : $i > $i > $o] : ((((!! @ $i @ (^[Y0 : $i]: (X1 @ Y0 @ Y0))) => (X1 @ sK2 @ sK3)) = $true) | (sK2 = sK3)) )),
% 1.34/1.28 inference(equality_proxy_clausification,[status(thm)],[f24])).
% 1.34/1.28 thf(f24,plain,(
% 1.34/1.28 ( ! [X1 : $i > $i > $o] : (($true = (sK2 = sK3)) | (((!! @ $i @ (^[Y0 : $i]: (X1 @ Y0 @ Y0))) => (X1 @ sK2 @ sK3)) = $true)) )),
% 1.34/1.28 inference(beta_eta_normalization,[status(thm)],[f23])).
% 1.34/1.28 thf(f23,plain,(
% 1.34/1.28 ( ! [X1 : $i > $i > $o] : (($true = (sK2 = sK3)) | (((^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) => (Y0 @ sK2 @ sK3))) @ X1) = $true)) )),
% 1.34/1.28 inference(pi_clausification,[status(thm)],[f13])).
% 1.34/1.28 thf(f13,plain,(
% 1.34/1.28 ((!! @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: ((!! @ $i @ (^[Y1 : $i]: (Y0 @ Y1 @ Y1))) => (Y0 @ sK2 @ sK3)))) = $true) | ($true = (sK2 = sK3))),
% 1.34/1.28 inference(binary_proxy_clausification,[status(thm)],[f12])).
% 1.34/1.28 % SZS output end Proof for DTF2THF_20692
% 1.34/1.28 % (20796)------------------------------
% 1.34/1.28 % (20796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.34/1.28 % (20796)Termination reason: Refutation
% 1.34/1.28
% 1.34/1.28 % (20796)Memory used [KB]: 5500
% 1.34/1.28 % (20796)Time elapsed: 0.006 s
% 1.34/1.28 % (20796)Instructions burned: 3 (million)
% 1.34/1.28 % (20796)------------------------------
% 1.34/1.28 % (20796)------------------------------
% 1.34/1.28 % (20790)Success in time 0.019 s
%------------------------------------------------------------------------------