%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET557^1 : TPTP v9.2.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.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 09:31:46 AM UTC 2026
% Result : Theorem 1.52s 1.31s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 33 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 160 ( 61 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 315 ( 55 ~; 20 |; 0 &; 225 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 51 ( 51 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 2 usr; 4 con; 0-2 aty)
% ( 5 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 108 ( 69 ^; 35 !; 4 ?; 108 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_12,type,
sK1: $i > $i > $o ).
thf(func_def_13,type,
sK2: ( $i > $o ) > $i ).
thf(f62,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f61]) ).
thf(f61,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f55,f59]) ).
thf(f59,plain,
( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ Y0 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
@ ( ^ [Y0: $i] : Y0
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
= $false ),
inference(equality_resolution,[status(thm)],[f48]) ).
thf(f48,plain,
! [X0: $i > $i] :
( ( ( X0
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) )
!= ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) )
| ( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) ) )
= $false ) ),
inference(equality_resolution,[status(thm)],[f44]) ).
thf(f44,plain,
! [X0: $i > $i,X1: $i] :
( ( ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
!= X1 )
| ( ( sK1 @ X1 @ ( X0 @ X1 ) )
= $false )
| ( ( X0 @ X1 )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f43]) ).
thf(f43,plain,
! [X0: $i > $i,X1: $i] :
( ( ( X0 @ X1 )
!= X1 )
| ( ( ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( X0 @ Y0 ) )
@ X1 )
= $false )
| ( ( sK2
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( sK1
@ ( ^ [Y2: $i] : Y2
@ Y1 )
@ ( X0 @ Y1 ) )
@ Y0 ) )
!= X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i > $i,X1: $i] :
( ( ( X0 @ X1 )
!= X1 )
| ( $false != $false )
| ( ( ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( X0 @ Y0 ) )
@ X1 )
= $false )
| ( ( sK2
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( sK1
@ ( ^ [Y2: $i] : Y2
@ Y1 )
@ ( X0 @ Y1 ) )
@ Y0 ) )
!= X1 ) ),
inference(equality_factoring,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i,X5: $i > $o] :
( ( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( X5 @ Y0 ) )
@ X2 )
= $false )
| ( ( X5 @ X2 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i,X5: $i > $o] :
( ( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( X5 @ Y0 ) )
@ X2 )
= $false )
| ( ( ~ ( X5 @ X2 ) )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X2: $i,X5: $i > $o] :
( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( X5 @ Y0 ) )
@ X2 )
= ( ~ ( X5 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X2: $i,X5: $i > $o] :
( ( ^ [Y0: $i] :
~ ( X5 @ Y0 )
@ X2 )
= ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( X5 @ Y0 ) )
@ X2 ) ),
inference(primitive_instantiation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X2: $i,X1: $i > $o] :
( ( X1 @ X2 )
= ( sK1 @ ( sK2 @ X1 ) @ X2 ) ),
inference(argument_congruence,[status(thm)],[f13]) ).
thf(f13,plain,
! [X1: $i > $o] :
( ( sK1 @ ( sK2 @ X1 ) )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f12]) ).
thf(f12,plain,
! [X1: $i > $o] :
( ( ( sK1 @ ( sK2 @ X1 ) )
= X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f11]) ).
thf(f11,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
= X1 )
@ ( sK2 @ X1 ) )
= $true ),
inference(sigma_clausification,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: $i > $o] :
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
= X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f9]) ).
thf(f9,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
= Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f8]) ).
thf(f8,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
= Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK1 )
= $true ),
inference(sigma_clausification,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f5]) ).
thf(f5,plain,
( ( ~ ~ ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f4]) ).
thf(f4,plain,
( ( ~ ~ ( ?? @ ( $i > $i > $o )
@ ^ [Y0: $i > $i > $o] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
= Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: $i > $i > $o] :
! [X1: $i > $o] :
? [X2: $i] :
( ( X0 @ X2 )
= X1 ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ? [X0: $i > $i > $o] :
! [X1: $i > $o] :
? [X2: $i] :
( ( X0 @ X2 )
= X1 ),
file('/export/starexec/sandbox/tmp/tmp.YiTSxwEGXQ/DTF2THF_26621.p',surjectiveCantorThm) ).
thf(f55,plain,
( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ Y0 ) )
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f53]) ).
thf(f53,plain,
( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) )
@ ( ^ [Y0: $i] : Y0
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
= $true ),
inference(equality_resolution,[status(thm)],[f47]) ).
thf(f47,plain,
! [X0: $i > $i] :
( ( ( X0
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) )
!= ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) )
| ( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
@ ( X0
@ ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) ) ) )
= $true ) ),
inference(equality_resolution,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: $i > $i,X1: $i] :
( ( ( sK2
@ ^ [Y0: $i] :
~ ( sK1 @ Y0 @ ( X0 @ Y0 ) ) )
!= X1 )
| ( ( sK1 @ X1 @ ( X0 @ X1 ) )
= $true )
| ( ( X0 @ X1 )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: $i > $i,X1: $i] :
( ( ( sK2
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( sK1
@ ( ^ [Y2: $i] : Y2
@ Y1 )
@ ( X0 @ Y1 ) )
@ Y0 ) )
!= X1 )
| ( ( X0 @ X1 )
!= X1 )
| ( ( ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( X0 @ Y0 ) )
@ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: $i > $i,X1: $i] :
( ( $true != $true )
| ( ( X0 @ X1 )
!= X1 )
| ( ( sK2
@ ^ [Y0: $i] :
~ ( ^ [Y1: $i] :
( sK1
@ ( ^ [Y2: $i] : Y2
@ Y1 )
@ ( X0 @ Y1 ) )
@ Y0 ) )
!= X1 )
| ( ( ^ [Y0: $i] :
( sK1
@ ( ^ [Y1: $i] : Y1
@ Y0 )
@ ( X0 @ Y0 ) )
@ X1 )
= $true ) ),
inference(equality_factoring,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i,X5: $i > $o] :
( ( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( X5 @ Y0 ) )
@ X2 )
= $true )
| ( ( X5 @ X2 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i,X5: $i > $o] :
( ( ( sK1
@ ( sK2
@ ^ [Y0: $i] :
~ ( X5 @ Y0 ) )
@ X2 )
= $true )
| ( ( ~ ( X5 @ X2 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET557^1 : TPTP v9.2.1. Released v3.6.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n003.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 11:58:55 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SET557^1 : TPTP v9.2.1. Released v3.6.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : Cantor's theorem
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.29/0.45 % : [Qua92] Quaife (1992), Automated Deduction in von Neumann-Bern
% 0.29/0.45 % Source : [TPTP]
% 0.29/0.45 % Names : tps_0048 [Bro09]
% 0.29/0.45 % : CT28 [TPS]
% 0.29/0.45 % : X5304 [TPS]
% 0.29/0.45 % : THM5 [TPS]
% 0.29/0.45 % : tps_0666 [Bro09]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.45 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.1, 0.67 v4.0.0, 0.33 v3.7.0
% 0.29/0.45 % Syntax : Number of formulae : 1 ( 1 unt; 0 typ; 0 def)
% 0.29/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.29/0.45 % Number of connectives : 2 ( 1 ~; 0 |; 0 &; 1 @)
% 0.29/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 5 ( 5 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.29/0.45 % Number of variables : 3 ( 0 ^; 1 !; 2 ?; 3 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments :
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(surjectiveCantorThm,conjecture,
% 0.29/0.45 ~ ? [G: $i > $i > $o] :
% 0.29/0.45 ! [F: $i > $o] :
% 0.29/0.45 ? [X: $i] :
% 0.29/0.45 ( ( G @ X )
% 0.29/0.45 = F ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.36/1.20 ---- Embedded in THF ---
% 1.50/1.20 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.20 %%% Generated on Tue Feb 24 11:58:56 EST 2026
% 1.50/1.20 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.20 %%% Logic specification used:
% 1.50/1.20 %%% thf(spec, logic, $$dhol).
% 1.50/1.20
% 1.50/1.20 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.YiTSxwEGXQ/DTF2DTF26621.p
% See solution above
% 1.50/1.20 ------------------------
% 1.50/1.21 ---- Cleaned THF ---
% 1.50/1.21 thf(surjectiveCantorThm,conjecture,
% 1.50/1.21 ~ ? [G: $i > $i > $o] :
% 1.50/1.21 ! [F: $i > $o] :
% 1.50/1.21 ? [X: $i] :
% 1.50/1.21 ( ( G @ X )
% 1.50/1.21 = F ) ).
% 1.50/1.21 ------------------------
% 1.50/1.22 % (26724)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26621 for (3000ds/18Mi)
% 1.50/1.22 % (26719)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_26621 for (3000ds/4Mi)
% 1.50/1.23 % (26719)Instruction limit reached!
% 1.50/1.23 % (26719)------------------------------
% 1.50/1.23 % (26719)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (26719)Termination reason: Unknown
% 1.50/1.23 % (26719)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (26719)Memory used [KB]: 5500
% 1.50/1.23 % (26719)Time elapsed: 0.004 s
% 1.50/1.23 % (26719)Instructions burned: 4 (million)
% 1.50/1.23 % (26719)------------------------------
% 1.50/1.23 % (26719)------------------------------
% 1.50/1.23 % (26724)Instruction limit reached!
% 1.50/1.23 % (26724)------------------------------
% 1.50/1.23 % (26724)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (26724)Termination reason: Unknown
% 1.50/1.23 % (26724)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (26724)Memory used [KB]: 5628
% 1.50/1.23 % (26724)Time elapsed: 0.008 s
% 1.50/1.23 % (26724)Instructions burned: 21 (million)
% 1.50/1.23 % (26724)------------------------------
% 1.50/1.23 % (26724)------------------------------
% 1.50/1.23 % (26718)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26621 for (3000ds/183Mi)
% 1.50/1.23 % (26721)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26621 for (3000ds/2Mi)
% 1.50/1.23 % (26722)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_26621 for (3000ds/2Mi)
% 1.50/1.23 % (26720)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_26621 for (3000ds/27Mi)
% 1.50/1.23 % (26721)Instruction limit reached!
% 1.50/1.23 % (26721)------------------------------
% 1.50/1.23 % (26721)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (26722)Instruction limit reached!
% 1.50/1.23 % (26722)------------------------------
% 1.50/1.23 % (26722)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (26721)Termination reason: Unknown
% 1.50/1.23 % (26721)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (26721)Memory used [KB]: 5500
% 1.50/1.23 % (26721)Time elapsed: 0.004 s
% 1.50/1.23 % (26721)Instructions burned: 2 (million)
% 1.50/1.23 % (26721)------------------------------
% 1.50/1.23 % (26721)------------------------------
% 1.50/1.23 % (26722)Termination reason: Unknown
% 1.50/1.23 % (26722)Termination phase: Saturation
% 1.50/1.23
% 1.50/1.23 % (26722)Memory used [KB]: 5500
% 1.50/1.23 % (26722)Time elapsed: 0.004 s
% 1.50/1.23 % (26722)Instructions burned: 3 (million)
% 1.50/1.23 % (26722)------------------------------
% 1.50/1.23 % (26722)------------------------------
% 1.50/1.23 % (26720)Refutation not found, incomplete strategy
% 1.50/1.23 % (26720)------------------------------
% 1.50/1.23 % (26720)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.23 % (26720)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.23
% 1.50/1.23
% 1.50/1.23 % (26720)Memory used [KB]: 5500
% 1.50/1.23 % (26720)Time elapsed: 0.004 s
% 1.50/1.23 % (26720)Instructions burned: 2 (million)
% 1.50/1.23 % (26720)------------------------------
% 1.50/1.23 % (26720)------------------------------
% 1.50/1.23 % (26725)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/3Mi)
% 1.50/1.24 % (26725)Instruction limit reached!
% 1.50/1.24 % (26725)------------------------------
% 1.50/1.24 % (26725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (26725)Termination reason: Unknown
% 1.50/1.24 % (26725)Termination phase: Saturation
% 1.50/1.24
% 1.50/1.24 % (26725)Memory used [KB]: 5500
% 1.50/1.24 % (26725)Time elapsed: 0.002 s
% 1.50/1.24 % (26725)Instructions burned: 3 (million)
% 1.50/1.24 % (26725)------------------------------
% 1.50/1.24 % (26725)------------------------------
% 1.50/1.24 % (26726)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_26621 for (2999ds/37Mi)
% 1.50/1.24 % (26723)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_26621 for (3000ds/275Mi)
% 1.50/1.24 % (26723)Refutation not found, incomplete strategy
% 1.50/1.24 % (26723)------------------------------
% 1.50/1.24 % (26723)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (26723)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.24
% 1.50/1.24
% 1.50/1.24 % (26723)Memory used [KB]: 5500
% 1.50/1.24 % (26723)Time elapsed: 0.006 s
% 1.50/1.24 % (26723)Instructions burned: 2 (million)
% 1.50/1.24 % (26723)------------------------------
% 1.50/1.24 % (26723)------------------------------
% 1.50/1.25 % (26730)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/7Mi)
% 1.50/1.25 % (26727)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/15Mi)
% 1.50/1.25 % (26728)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/3Mi)
% 1.50/1.25 % (26729)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/1041Mi)
% 1.50/1.25 % (26727)Refutation not found, incomplete strategy
% 1.50/1.25 % (26727)------------------------------
% 1.50/1.25 % (26727)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (26727)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.25
% 1.50/1.25
% 1.50/1.25 % (26727)Memory used [KB]: 5500
% 1.50/1.25 % (26727)Time elapsed: 0.004 s
% 1.50/1.25 % (26727)Instructions burned: 1 (million)
% 1.50/1.25 % (26727)------------------------------
% 1.50/1.25 % (26727)------------------------------
% 1.50/1.25 % (26728)Instruction limit reached!
% 1.50/1.25 % (26728)------------------------------
% 1.50/1.25 % (26728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (26728)Termination reason: Unknown
% 1.50/1.25 % (26728)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (26728)Memory used [KB]: 5500
% 1.50/1.25 % (26728)Time elapsed: 0.004 s
% 1.50/1.25 % (26728)Instructions burned: 3 (million)
% 1.50/1.25 % (26730)Instruction limit reached!
% 1.50/1.25 % (26730)------------------------------
% 1.50/1.25 % (26730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (26730)Termination reason: Unknown
% 1.50/1.25 % (26730)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (26730)Memory used [KB]: 1023
% 1.50/1.25 % (26730)Time elapsed: 0.004 s
% 1.50/1.25 % (26730)Instructions burned: 9 (million)
% 1.50/1.25 % (26730)------------------------------
% 1.50/1.25 % (26730)------------------------------
% 1.50/1.25 % (26728)------------------------------
% 1.50/1.25 % (26728)------------------------------
% 1.50/1.25 % (26726)Instruction limit reached!
% 1.50/1.25 % (26726)------------------------------
% 1.50/1.25 % (26726)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (26726)Termination reason: Unknown
% 1.50/1.25 % (26726)Termination phase: Saturation
% 1.50/1.25
% 1.50/1.25 % (26726)Memory used [KB]: 5756
% 1.50/1.25 % (26726)Time elapsed: 0.015 s
% 1.50/1.25 % (26726)Instructions burned: 38 (million)
% 1.50/1.25 % (26726)------------------------------
% 1.50/1.25 % (26726)------------------------------
% 1.50/1.26 % (26732)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/3Mi)
% 1.50/1.26 % (26732)Refutation not found, incomplete strategy
% 1.50/1.26 % (26732)------------------------------
% 1.50/1.26 % (26732)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (26732)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.26
% 1.50/1.26
% 1.50/1.26 % (26732)Memory used [KB]: 5500
% 1.50/1.26 % (26732)Time elapsed: 0.001 s
% 1.50/1.26 % (26732)Instructions burned: 1 (million)
% 1.50/1.26 % (26732)------------------------------
% 1.50/1.26 % (26732)------------------------------
% 1.50/1.26 % (26729)Refutation not found, incomplete strategy
% 1.50/1.26 % (26729)------------------------------
% 1.50/1.26 % (26729)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.26 % (26729)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.26
% 1.50/1.26
% 1.50/1.26 % (26729)Memory used [KB]: 5500
% 1.50/1.26 % (26729)Time elapsed: 0.017 s
% 1.50/1.26 % (26729)Instructions burned: 24 (million)
% 1.50/1.26 % (26729)------------------------------
% 1.50/1.26 % (26729)------------------------------
% 1.50/1.27 % (26733)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/3Mi)
% 1.50/1.27 % (26734)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/7Mi)
% 1.50/1.27 % (26735)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/3Mi)
% 1.50/1.27 % (26734)Refutation not found, incomplete strategy
% 1.50/1.27 % (26734)------------------------------
% 1.50/1.27 % (26734)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (26734)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.27
% 1.50/1.27
% 1.50/1.27 % (26734)Memory used [KB]: 5373
% 1.50/1.27 % (26734)Time elapsed: 0.003 s
% 1.50/1.27 % (26734)Instructions burned: 1 (million)
% 1.50/1.27 % (26734)------------------------------
% 1.50/1.27 % (26734)------------------------------
% 1.50/1.27 % (26733)Instruction limit reached!
% 1.50/1.27 % (26733)------------------------------
% 1.50/1.27 % (26733)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (26733)Termination reason: Unknown
% 1.50/1.27 % (26733)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (26733)Memory used [KB]: 5500
% 1.50/1.27 % (26733)Time elapsed: 0.004 s
% 1.50/1.27 % (26733)Instructions burned: 3 (million)
% 1.50/1.27 % (26733)------------------------------
% 1.50/1.27 % (26733)------------------------------
% 1.50/1.27 % (26736)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/4Mi)
% 1.50/1.27 % (26731)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/16Mi)
% 1.50/1.27 % (26735)Instruction limit reached!
% 1.50/1.27 % (26735)------------------------------
% 1.50/1.27 % (26735)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (26735)Termination reason: Unknown
% 1.50/1.27 % (26735)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (26735)Memory used [KB]: 5500
% 1.50/1.27 % (26735)Time elapsed: 0.004 s
% 1.50/1.27 % (26735)Instructions burned: 4 (million)
% 1.50/1.27 % (26735)------------------------------
% 1.50/1.27 % (26735)------------------------------
% 1.50/1.27 % (26736)Instruction limit reached!
% 1.50/1.27 % (26736)------------------------------
% 1.50/1.27 % (26736)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.27 % (26736)Termination reason: Unknown
% 1.50/1.27 % (26736)Termination phase: Saturation
% 1.50/1.27
% 1.50/1.27 % (26736)Memory used [KB]: 5500
% 1.50/1.27 % (26736)Time elapsed: 0.003 s
% 1.50/1.27 % (26736)Instructions burned: 5 (million)
% 1.50/1.27 % (26736)------------------------------
% 1.50/1.27 % (26736)------------------------------
% 1.50/1.28 % (26739)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/6Mi)
% 1.50/1.28 % (26731)Instruction limit reached!
% 1.50/1.28 % (26731)------------------------------
% 1.50/1.28 % (26731)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (26731)Termination reason: Unknown
% 1.50/1.28 % (26731)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (26731)Memory used [KB]: 5500
% 1.50/1.28 % (26731)Time elapsed: 0.013 s
% 1.50/1.28 % (26731)Instructions burned: 17 (million)
% 1.50/1.28 % (26731)------------------------------
% 1.50/1.28 % (26731)------------------------------
% 1.50/1.28 % (26741)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/21Mi)
% 1.50/1.28 % (26739)Instruction limit reached!
% 1.50/1.28 % (26739)------------------------------
% 1.50/1.28 % (26739)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (26739)Termination reason: Unknown
% 1.50/1.28 % (26739)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (26739)Memory used [KB]: 5500
% 1.50/1.28 % (26739)Time elapsed: 0.004 s
% 1.50/1.28 % (26739)Instructions burned: 6 (million)
% 1.50/1.28 % (26739)------------------------------
% 1.50/1.28 % (26739)------------------------------
% 1.50/1.28 % (26737)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/18Mi)
% 1.50/1.28 % (26737)Refutation not found, incomplete strategy
% 1.50/1.28 % (26737)------------------------------
% 1.50/1.28 % (26737)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (26737)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.28
% 1.50/1.28
% 1.50/1.28 % (26737)Memory used [KB]: 5500
% 1.50/1.28 % (26737)Time elapsed: 0.003 s
% 1.50/1.28 % (26737)Instructions burned: 1 (million)
% 1.50/1.28 % (26737)------------------------------
% 1.50/1.28 % (26737)------------------------------
% 1.50/1.29 % (26738)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/710Mi)
% 1.50/1.29 % (26740)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/902Mi)
% 1.50/1.29 % (26741)Instruction limit reached!
% 1.50/1.29 % (26741)------------------------------
% 1.50/1.29 % (26741)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (26741)Termination reason: Unknown
% 1.50/1.29 % (26741)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (26741)Memory used [KB]: 5628
% 1.50/1.29 % (26741)Time elapsed: 0.031 s
% 1.50/1.29 % (26741)Instructions burned: 23 (million)
% 1.50/1.29 % (26741)------------------------------
% 1.50/1.29 % (26741)------------------------------
% 1.50/1.29 % (26718)Instruction limit reached!
% 1.50/1.29 % (26718)------------------------------
% 1.50/1.29 % (26718)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (26718)Termination reason: Unknown
% 1.50/1.29 % (26718)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (26718)Memory used [KB]: 6140
% 1.50/1.29 % (26718)Time elapsed: 0.064 s
% 1.50/1.29 % (26718)Instructions burned: 183 (million)
% 1.50/1.29 % (26718)------------------------------
% 1.50/1.29 % (26718)------------------------------
% 1.50/1.29 % (26743)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/6Mi)
% 1.50/1.29 % (26743)Instruction limit reached!
% 1.50/1.29 % (26743)------------------------------
% 1.50/1.29 % (26743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (26743)Termination reason: Unknown
% 1.50/1.29 % (26743)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (26743)Memory used [KB]: 5500
% 1.50/1.29 % (26743)Time elapsed: 0.004 s
% 1.50/1.29 % (26743)Instructions burned: 6 (million)
% 1.50/1.29 % (26743)------------------------------
% 1.50/1.29 % (26743)------------------------------
% 1.52/1.30 % (26745)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/779Mi)
% 1.52/1.30 % (26742)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/5Mi)
% 1.52/1.30 % (26745)Refutation not found, incomplete strategy
% 1.52/1.30 % (26745)------------------------------
% 1.52/1.30 % (26745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (26745)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.30
% 1.52/1.30
% 1.52/1.30 % (26745)Memory used [KB]: 5500
% 1.52/1.30 % (26745)Time elapsed: 0.002 s
% 1.52/1.30 % (26745)Instructions burned: 3 (million)
% 1.52/1.30 % (26745)------------------------------
% 1.52/1.30 % (26745)------------------------------
% 1.52/1.30 % (26746)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/19Mi)
% 1.52/1.30 % (26744)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/377Mi)
% 1.52/1.30 % (26742)Instruction limit reached!
% 1.52/1.30 % (26742)------------------------------
% 1.52/1.30 % (26742)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (26742)Termination reason: Unknown
% 1.52/1.30 % (26742)Termination phase: Saturation
% 1.52/1.30
% 1.52/1.30 % (26742)Memory used [KB]: 5500
% 1.52/1.30 % (26742)Time elapsed: 0.027 s
% 1.52/1.30 % (26742)Instructions burned: 5 (million)
% 1.52/1.30 % (26742)------------------------------
% 1.52/1.30 % (26742)------------------------------
% 1.52/1.30 % (26744)Refutation not found, incomplete strategy
% 1.52/1.30 % (26744)------------------------------
% 1.52/1.30 % (26744)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (26744)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.30
% 1.52/1.30
% 1.52/1.30 % (26744)Memory used [KB]: 5500
% 1.52/1.30 % (26744)Time elapsed: 0.003 s
% 1.52/1.30 % (26744)Instructions burned: 2 (million)
% 1.52/1.30 % (26744)------------------------------
% 1.52/1.30 % (26744)------------------------------
% 1.52/1.30 % (26747)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26621 for (2999ds/879Mi)
% 1.52/1.30 % (26747)Refutation not found, incomplete strategy
% 1.52/1.30 % (26747)------------------------------
% 1.52/1.30 % (26747)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.30 % (26747)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.30
% 1.52/1.30
% 1.52/1.30 % (26747)Memory used [KB]: 5500
% 1.52/1.30 % (26747)Time elapsed: 0.003 s
% 1.52/1.30 % (26747)Instructions burned: 1 (million)
% 1.52/1.30 % (26746)First to succeed.
% 1.52/1.30 % (26747)------------------------------
% 1.52/1.30 % (26747)------------------------------
% 1.52/1.31 % (26746)Refutation found. Thanks to Tanya!
% 1.52/1.31 % SZS status Theorem for DTF2THF_26621
% 1.52/1.31 % SZS output start Proof for DTF2THF_26621
% 1.52/1.31 thf(func_def_12, type, sK1: $i > $i > $o).
% 1.52/1.31 thf(func_def_13, type, sK2: ($i > $o) > $i).
% 1.52/1.31 thf(f62,plain,(
% 1.52/1.31 $false),
% 1.52/1.31 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.52/1.31 thf(f61,plain,(
% 1.52/1.31 ($true = $false)),
% 1.52/1.31 inference(backward_demodulation,[status(thm)],[f55,f59])).
% 1.52/1.31 thf(f59,plain,(
% 1.52/1.31 ((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ Y0)))) @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ Y0))))) = $false)),
% 1.52/1.31 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.52/1.31 thf(f57,plain,(
% 1.52/1.31 ((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) @ ((^[Y0 : $i]: (Y0)) @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) = $false)),
% 1.52/1.31 inference(equality_resolution,[status(thm)],[f48])).
% 1.52/1.31 thf(f48,plain,(
% 1.52/1.31 ( ! [X0 : $i > $i] : (((X0 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0)))))) != (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0)))))) | ((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) @ (X0 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0))))))) = $false)) )),
% 1.52/1.31 inference(equality_resolution,[status(thm)],[f44])).
% 1.52/1.31 thf(f44,plain,(
% 1.52/1.31 ( ! [X0 : $i > $i,X1 : $i] : (((sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) != X1) | ((sK1 @ X1 @ (X0 @ X1)) = $false) | ((X0 @ X1) != X1)) )),
% 1.52/1.31 inference(beta_eta_normalization,[status(thm)],[f43])).
% 1.52/1.31 thf(f43,plain,(
% 1.52/1.31 ( ! [X0 : $i > $i,X1 : $i] : (((X0 @ X1) != X1) | (((^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ (X0 @ Y0))) @ X1) = $false) | ((sK2 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK1 @ ((^[Y2 : $i]: (Y2)) @ Y1) @ (X0 @ Y1))) @ Y0)))) != X1)) )),
% 1.52/1.31 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.52/1.31 thf(f41,plain,(
% 1.52/1.31 ( ! [X0 : $i > $i,X1 : $i] : (((X0 @ X1) != X1) | ($false != $false) | (((^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ (X0 @ Y0))) @ X1) = $false) | ((sK2 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK1 @ ((^[Y2 : $i]: (Y2)) @ Y1) @ (X0 @ Y1))) @ Y0)))) != X1)) )),
% 1.52/1.31 inference(equality_factoring,[status(thm)],[f40])).
% 1.52/1.31 thf(f40,plain,(
% 1.52/1.31 ( ! [X2 : $i,X5 : $i > $o] : (((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0)))) @ X2) = $false) | ((X5 @ X2) = $false)) )),
% 1.52/1.31 inference(not_proxy_clausification,[status(thm)],[f32])).
% 1.52/1.31 thf(f32,plain,(
% 1.52/1.31 ( ! [X2 : $i,X5 : $i > $o] : (((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0)))) @ X2) = $false) | ((~ (X5 @ X2)) = $true)) )),
% 1.52/1.31 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.52/1.31 thf(f21,plain,(
% 1.52/1.31 ( ! [X2 : $i,X5 : $i > $o] : (((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0)))) @ X2) = (~ (X5 @ X2)))) )),
% 1.52/1.31 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.52/1.31 thf(f19,plain,(
% 1.52/1.31 ( ! [X2 : $i,X5 : $i > $o] : ((((^[Y0 : $i]: (~ (X5 @ Y0))) @ X2) = (sK1 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0)))) @ X2))) )),
% 1.52/1.31 inference(primitive_instantiation,[status(thm)],[f14])).
% 1.52/1.31 thf(f14,plain,(
% 1.52/1.31 ( ! [X2 : $i,X1 : $i > $o] : (((X1 @ X2) = (sK1 @ (sK2 @ X1) @ X2))) )),
% 1.52/1.31 inference(argument_congruence,[status(thm)],[f13])).
% 1.52/1.31 thf(f13,plain,(
% 1.52/1.31 ( ! [X1 : $i > $o] : (((sK1 @ (sK2 @ X1)) = X1)) )),
% 1.52/1.31 inference(equality_proxy_clausification,[status(thm)],[f12])).
% 1.52/1.31 thf(f12,plain,(
% 1.52/1.31 ( ! [X1 : $i > $o] : ((((sK1 @ (sK2 @ X1)) = X1) = $true)) )),
% 1.52/1.31 inference(beta_eta_normalization,[status(thm)],[f11])).
% 1.52/1.31 thf(f11,plain,(
% 1.52/1.31 ( ! [X1 : $i > $o] : ((((^[Y0 : $i]: ((sK1 @ Y0) = X1)) @ (sK2 @ X1)) = $true)) )),
% 1.52/1.31 inference(sigma_clausification,[status(thm)],[f10])).
% 1.52/1.31 thf(f10,plain,(
% 1.52/1.31 ( ! [X1 : $i > $o] : (($true = (?? @ $i @ (^[Y0 : $i]: ((sK1 @ Y0) = X1))))) )),
% 1.52/1.31 inference(beta_eta_normalization,[status(thm)],[f9])).
% 1.52/1.31 thf(f9,plain,(
% 1.52/1.31 ( ! [X1 : $i > $o] : (($true = ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) = Y0)))) @ X1))) )),
% 1.52/1.31 inference(pi_clausification,[status(thm)],[f8])).
% 1.52/1.31 thf(f8,plain,(
% 1.52/1.31 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((sK1 @ Y1) = Y0))))) = $true)),
% 1.52/1.31 inference(beta_eta_normalization,[status(thm)],[f7])).
% 1.52/1.31 thf(f7,plain,(
% 1.52/1.31 (((^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1)))))) @ sK1) = $true)),
% 1.52/1.31 inference(sigma_clausification,[status(thm)],[f6])).
% 1.52/1.31 thf(f6,plain,(
% 1.52/1.31 ((?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1))))))) = $true)),
% 1.52/1.31 inference(boolean_simplification,[status(thm)],[f5])).
% 1.52/1.31 thf(f5,plain,(
% 1.52/1.31 ((~ (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1))))))))) = $true)),
% 1.52/1.31 inference(cnf_transformation,[status(thm)],[f4])).
% 1.52/1.31 thf(f4,plain,(
% 1.52/1.31 ((~ (~ (?? @ ($i > $i > $o) @ (^[Y0 : $i > $i > $o]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) = Y1))))))))) = $true)),
% 1.52/1.31 inference(fool_elimination,[status(thm)],[f2])).
% 1.52/1.31 thf(f2,negated_conjecture,(
% 1.52/1.31 ~~? [X0 : $i > $i > $o] : ! [X1 : $i > $o] : ? [X2 : $i] : ((X0 @ X2) = X1)),
% 1.52/1.31 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.31 thf(f1,conjecture,(
% 1.52/1.31 ~? [X0 : $i > $i > $o] : ! [X1 : $i > $o] : ? [X2 : $i] : ((X0 @ X2) = X1)),
% 1.52/1.31 file('/export/starexec/sandbox/tmp/tmp.YiTSxwEGXQ/DTF2THF_26621.p',surjectiveCantorThm)).
% 1.52/1.31 thf(f55,plain,(
% 1.52/1.31 ((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ Y0)))) @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ Y0))))) = $true)),
% 1.52/1.31 inference(beta_eta_normalization,[status(thm)],[f53])).
% 1.52/1.31 thf(f53,plain,(
% 1.52/1.31 ((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) @ ((^[Y0 : $i]: (Y0)) @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ ((^[Y1 : $i]: (Y1)) @ Y0))))))) = $true)),
% 1.52/1.31 inference(equality_resolution,[status(thm)],[f47])).
% 1.52/1.31 thf(f47,plain,(
% 1.52/1.31 ( ! [X0 : $i > $i] : (((X0 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0)))))) != (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0)))))) | ((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) @ (X0 @ (sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0))))))) = $true)) )),
% 1.52/1.31 inference(equality_resolution,[status(thm)],[f37])).
% 1.52/1.31 thf(f37,plain,(
% 1.52/1.31 ( ! [X0 : $i > $i,X1 : $i] : (((sK2 @ (^[Y0 : $i]: (~ (sK1 @ Y0 @ (X0 @ Y0))))) != X1) | ((sK1 @ X1 @ (X0 @ X1)) = $true) | ((X0 @ X1) != X1)) )),
% 1.52/1.31 inference(beta_eta_normalization,[status(thm)],[f36])).
% 1.52/1.31 thf(f36,plain,(
% 1.52/1.31 ( ! [X0 : $i > $i,X1 : $i] : (((sK2 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK1 @ ((^[Y2 : $i]: (Y2)) @ Y1) @ (X0 @ Y1))) @ Y0)))) != X1) | ((X0 @ X1) != X1) | (((^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ (X0 @ Y0))) @ X1) = $true)) )),
% 1.52/1.31 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 1.52/1.31 thf(f34,plain,(
% 1.52/1.31 ( ! [X0 : $i > $i,X1 : $i] : (($true != $true) | ((X0 @ X1) != X1) | ((sK2 @ (^[Y0 : $i]: (~ ((^[Y1 : $i]: (sK1 @ ((^[Y2 : $i]: (Y2)) @ Y1) @ (X0 @ Y1))) @ Y0)))) != X1) | (((^[Y0 : $i]: (sK1 @ ((^[Y1 : $i]: (Y1)) @ Y0) @ (X0 @ Y0))) @ X1) = $true)) )),
% 1.52/1.31 inference(equality_factoring,[status(thm)],[f33])).
% 1.52/1.31 thf(f33,plain,(
% 1.52/1.31 ( ! [X2 : $i,X5 : $i > $o] : (((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0)))) @ X2) = $true) | ((X5 @ X2) = $true)) )),
% 1.52/1.31 inference(not_proxy_clausification,[status(thm)],[f31])).
% 1.52/1.31 thf(f31,plain,(
% 1.52/1.31 ( ! [X2 : $i,X5 : $i > $o] : (((sK1 @ (sK2 @ (^[Y0 : $i]: (~ (X5 @ Y0)))) @ X2) = $true) | ((~ (X5 @ X2)) = $false)) )),
% 1.52/1.31 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.52/1.31 % SZS output end Proof for DTF2THF_26621
% 1.52/1.31 % (26746)------------------------------
% 1.52/1.31 % (26746)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.31 % (26746)Termination reason: Refutation
% 1.52/1.31
% 1.52/1.31 % (26746)Memory used [KB]: 5628
% 1.52/1.31 % (26746)Time elapsed: 0.008 s
% 1.52/1.31 % (26746)Instructions burned: 15 (million)
% 1.52/1.31 % (26746)------------------------------
% 1.52/1.31 % (26746)------------------------------
% 1.52/1.31 % (26717)Success in time 0.094 s
%------------------------------------------------------------------------------