%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV181^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 09:40:29 AM UTC 2026
% Result : Theorem 1.31s 1.14s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 3
% Syntax : Number of formulae : 36 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 183 ( 87 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 303 ( 41 ~; 17 |; 25 &; 194 @)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 5 usr; 3 con; 0-2 aty)
% ( 0 !!; 15 ??; 0 @@+; 0 @@-)
% Number of variables : 81 ( 37 ^; 40 !; 4 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
thf(func_def_12,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_14,type,
sK2: $i > $o ).
thf(func_def_15,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_16,type,
sK4: $i > $i > $o ).
thf(f56,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
$true = $false,
inference(duplicate_literal_removal,[status(thm)],[f45]) ).
thf(f45,plain,
( ( $true = $false )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f44,f22]) ).
thf(f22,plain,
( ( sK2 @ ( sK0 @ sK2 ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
= ( ~ ( sK2 @ ( sK0 @ sK2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f19,plain,
( $true
= ( ~ ( sK2 @ ( sK0 @ sK2 ) )
& ( ( sK0 @ sK2 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f18]) ).
thf(f18,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f16]) ).
thf(f16,plain,
( $true
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK0
@ ( sK0
@ ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) )
@ sK0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f13,f15,f15]) ).
thf(f15,plain,
( cD_FOR_X5309
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( cD_FOR_X5309
= ( ^ [Y0: ( $i > $o ) > $i,Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( Y0 @ Y2 ) )
& ( ( Y0 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
? [X2: $i > $o] :
( ( ( X0 @ X2 )
= X1 )
& ~ ( X2 @ ( X0 @ X2 ) ) ) )
= cD_FOR_X5309 ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: ( $i > $o ) > $i,X1: $i] :
? [X2: $i > $o] :
( ( ( X0 @ X2 )
= X1 )
& ~ ( X2 @ ( X0 @ X2 ) ) ) )
= cD_FOR_X5309 ),
file('/export/starexec/sandbox/tmp/tmp.Aw9Tkq5nsg/DTF2THF_30602.p',cD_FOR_X5309_def) ).
thf(f13,plain,
( $true
= ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( sK0 @ X2 )
!= ( sK0 @ X1 ) ) )
& ( $true
= ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11]) ).
thf(f11,plain,
( ? [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X2 )
!= ( X0 @ X1 ) ) )
& ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
= $true ) )
=> ( ! [X2: $i > $o,X1: $i > $o] :
( ( X1 = X2 )
| ( ( sK0 @ X2 )
!= ( sK0 @ X1 ) ) )
& ( $true
= ( cD_FOR_X5309 @ sK0 @ ( sK0 @ ( cD_FOR_X5309 @ sK0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
? [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X2 )
!= ( X0 @ X1 ) ) )
& ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 )
= ( X0 @ X1 ) )
=> ( X1 = X2 ) )
=> ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 )
= ( X0 @ X1 ) )
=> ( X1 = X2 ) )
=> ( ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X2 )
= ( X0 @ X1 ) )
=> ( X1 = X2 ) )
=> ~ ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X4: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 )
= ( X0 @ X4 ) )
=> ( X3 = X4 ) )
=> ~ ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X0: ( $i > $o ) > $i] :
( ! [X4: $i > $o,X3: $i > $o] :
( ( ( X0 @ X3 )
= ( X0 @ X4 ) )
=> ( X3 = X4 ) )
=> ~ ( cD_FOR_X5309 @ X0 @ ( X0 @ ( cD_FOR_X5309 @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Aw9Tkq5nsg/DTF2THF_30602.p',cTHM143C_pme) ).
thf(f44,plain,
! [X0: $i > $o] :
( ( $true
= ( sK2 @ ( sK0 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(equality_resolution,[status(thm)],[f43]) ).
thf(f43,plain,
! [X2: $i > $o,X1: $i] :
( ( ( sK0 @ X2 )
!= X1 )
| ( $true
= ( sK2 @ X1 ) )
| ( $true
= ( X2 @ ( sK0 @ X2 ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( ( sK0 @ X2 )
!= X1 )
| ( $false
= ( ~ ( X2 @ ( sK0 @ X2 ) ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( ( sK0 @ X2 )
= X1 ) )
| ( $false
= ( ~ ( X2 @ ( sK0 @ X2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( ~ ( X2 @ ( sK0 @ X2 ) )
& ( ( sK0 @ X2 )
= X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X2: $i > $o,X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= X1 ) )
@ X2 )
= $false ) ),
inference(pi_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X1: $i] :
( ( $true
= ( sK2 @ X1 ) )
| ( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X1: $i] :
( ( sK2 @ X1 )
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ X1 )
= ( sK2 @ X1 ) ),
inference(argument_congruence,[status(thm)],[f28]) ).
thf(f28,plain,
( sK2
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i > $o] :
( ( ( sK0 @ sK2 )
!= ( sK0 @ X0 ) )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= X0 ) ),
inference(superposition,[status(thm)],[f14,f23]) ).
thf(f23,plain,
( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= ( sK0 @ sK2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
( $true
= ( ( sK0 @ sK2 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f19]) ).
thf(f14,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( sK0 @ X2 )
!= ( sK0 @ X1 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV181^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.10/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.33 % Computer : n018.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue Feb 24 12:41:16 EST 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.42 ---- Original DTF file ---
% 0.16/0.42 thf(spec,logic,$$dhol).
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 % File : SEV181^5 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.16/0.42 % Domain : Set Theory (Sets of sets)
% 0.16/0.42 % Problem : TPS problem from CANTOR-THMS
% 0.16/0.42 % Version : Especial.
% 0.16/0.42 % English :
% 0.16/0.42
% 0.16/0.42 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.42 % Source : [Bro09]
% 0.16/0.42 % Names : tps_0780 [Bro09]
% 0.16/0.42
% 0.16/0.42 % Status : Theorem
% 0.16/0.42 % Rating : 0.00 v8.2.0, 0.15 v8.1.0, 0.09 v7.5.0, 0.00 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, 0.14 v6.1.0, 0.00 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.40 v5.2.0
% 0.16/0.42 % Syntax : Number of formulae : 3 ( 1 unt; 1 typ; 1 def)
% 0.16/0.42 % Number of atoms : 7 ( 4 equ; 0 cnn)
% 0.16/0.42 % Maximal formula atoms : 4 ( 3 avg)
% 0.16/0.42 % Number of connectives : 14 ( 2 ~; 0 |; 1 &; 9 @)
% 0.16/0.42 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.16/0.42 % Maximal formula depth : 7 ( 4 avg)
% 0.16/0.42 % Number of types : 2 ( 0 usr)
% 0.16/0.42 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.16/0.42 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.16/0.42 % Number of variables : 6 ( 2 ^; 3 !; 1 ?; 6 :)
% 0.16/0.42 % SPC : TH0_THM_EQU_NAR
% 0.16/0.42
% 0.16/0.42 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.42 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.42 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.42 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.42 % Bugfixes : v5.2.0 - Added missing type declarations.
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 thf(cD_FOR_X5309_type,type,
% 0.16/0.42 cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
% 0.16/0.42
% 0.16/0.42 thf(cD_FOR_X5309_def,definition,
% 0.16/0.42 ( cD_FOR_X5309
% 0.16/0.42 = ( ^ [Xh: ( $i > $o ) > $i,Xz: $i] :
% 0.16/0.42 ? [Xt: $i > $o] :
% 0.16/0.42 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.16/0.42 & ( Xz
% 0.16/0.42 = ( Xh @ Xt ) ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 thf(cTHM143C_pme,conjecture,
% 0.16/0.42 ! [Xh: ( $i > $o ) > $i] :
% 0.16/0.42 ( ! [Xp: $i > $o,Xq: $i > $o] :
% 0.16/0.42 ( ( ( Xh @ Xp )
% 0.16/0.42 = ( Xh @ Xq ) )
% 0.16/0.42 => ( Xp = Xq ) )
% 0.16/0.42 => ~ ( cD_FOR_X5309 @ Xh @ ( Xh @ ( cD_FOR_X5309 @ Xh ) ) ) ) ).
% 0.16/0.42
% 0.16/0.42 %------------------------------------------------------------------------------
% 0.16/0.42 ------------------------
% 1.14/1.09 ---- Embedded in THF ---
% 1.14/1.09 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.14/1.09 %%% Generated on Tue Feb 24 12:41:16 EST 2026
% 1.14/1.09 %%% using '$$dhol' embedding, version 1.3.0.
% 1.14/1.09 %%% Logic specification used:
% 1.14/1.09 %%% thf(spec, logic, $$dhol).
% 1.14/1.09
% 1.14/1.09 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Aw9Tkq5nsg/DTF2DTF30602.p
% See solution above
% 1.14/1.09 ------------------------
% 1.14/1.10 ---- Cleaned THF ---
% 1.14/1.10 thf(cD_FOR_X5309_type,type,
% 1.14/1.10 cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
% 1.14/1.10
% 1.14/1.10 thf(cD_FOR_X5309_def,definition,
% 1.14/1.10 ( cD_FOR_X5309
% 1.14/1.10 = ( ^ [Xh: ( $i > $o ) > $i,Xz: $i] :
% 1.14/1.10 ? [Xt: $i > $o] :
% 1.14/1.10 ( ~ ( Xt @ ( Xh @ Xt ) )
% 1.14/1.10 & ( Xz
% 1.14/1.10 = ( Xh @ Xt ) ) ) ) ) ).
% 1.14/1.10
% 1.14/1.10 thf(cTHM143C_pme,conjecture,
% 1.14/1.10 ! [Xh: ( $i > $o ) > $i] :
% 1.14/1.10 ( ! [Xp: $i > $o,Xq: $i > $o] :
% 1.14/1.10 ( ( ( Xh @ Xp )
% 1.14/1.10 = ( Xh @ Xq ) )
% 1.14/1.10 => ( Xp = Xq ) )
% 1.14/1.10 => ~ ( cD_FOR_X5309 @ Xh @ ( Xh @ ( cD_FOR_X5309 @ Xh ) ) ) ) ).
% 1.14/1.10 ------------------------
% 1.14/1.11 % (30704)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30602 for (3000ds/2Mi)
% 1.14/1.12 % (30704)Instruction limit reached!
% 1.14/1.12 % (30704)------------------------------
% 1.14/1.12 % (30704)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.12 % (30704)Termination reason: Unknown
% 1.14/1.12 % (30704)Termination phase: Property scanning
% 1.14/1.12
% 1.14/1.12 % (30704)Memory used [KB]: 895
% 1.14/1.12 % (30704)Time elapsed: 0.002 s
% 1.14/1.12 % (30704)Instructions burned: 2 (million)
% 1.14/1.12 % (30704)------------------------------
% 1.14/1.12 % (30704)------------------------------
% 1.14/1.12 % (30702)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_30602 for (3000ds/4Mi)
% 1.14/1.12 % (30703)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_30602 for (3000ds/27Mi)
% 1.14/1.12 % (30701)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30602 for (3000ds/183Mi)
% 1.14/1.12 % (30705)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_30602 for (3000ds/2Mi)
% 1.14/1.12 % (30706)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_30602 for (3000ds/275Mi)
% 1.14/1.12 % (30707)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30602 for (3000ds/18Mi)
% 1.14/1.12 % (30705)Instruction limit reached!
% 1.14/1.12 % (30705)------------------------------
% 1.14/1.12 % (30705)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.12 % (30705)Termination reason: Unknown
% 1.14/1.12 % (30705)Termination phase: Function definition elimination
% 1.14/1.12
% 1.14/1.12 % (30705)Memory used [KB]: 895
% 1.14/1.12 % (30705)Time elapsed: 0.002 s
% 1.14/1.12 % (30705)Instructions burned: 2 (million)
% 1.14/1.12 % (30705)------------------------------
% 1.14/1.12 % (30705)------------------------------
% 1.14/1.12 % (30706)Refutation not found, incomplete strategy
% 1.14/1.12 % (30706)------------------------------
% 1.14/1.12 % (30706)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.14/1.12 % (30706)Termination reason: Refutation not found, incomplete strategy
% 1.14/1.12
% 1.14/1.12
% 1.14/1.12 % (30706)Memory used [KB]: 5500
% 1.14/1.12 % (30706)Time elapsed: 0.002 s
% 1.14/1.12 % (30706)Instructions burned: 1 (million)
% 1.14/1.12 % (30706)------------------------------
% 1.14/1.12 % (30706)------------------------------
% 1.31/1.12 % (30702)Instruction limit reached!
% 1.31/1.12 % (30702)------------------------------
% 1.31/1.12 % (30702)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.12 % (30702)Termination reason: Unknown
% 1.31/1.12 % (30702)Termination phase: Saturation
% 1.31/1.12
% 1.31/1.12 % (30702)Memory used [KB]: 5500
% 1.31/1.12 % (30702)Time elapsed: 0.004 s
% 1.31/1.12 % (30702)Instructions burned: 4 (million)
% 1.31/1.12 % (30702)------------------------------
% 1.31/1.12 % (30702)------------------------------
% 1.31/1.12 % (30707)First to succeed.
% 1.31/1.13 % (30708)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_30602 for (2999ds/3Mi)
% 1.31/1.13 % (30708)Instruction limit reached!
% 1.31/1.13 % (30708)------------------------------
% 1.31/1.13 % (30708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.13 % (30708)Termination reason: Unknown
% 1.31/1.13 % (30708)Termination phase: Saturation
% 1.31/1.13
% 1.31/1.13 % (30708)Memory used [KB]: 5500
% 1.31/1.13 % (30708)Time elapsed: 0.003 s
% 1.31/1.13 % (30708)Instructions burned: 4 (million)
% 1.31/1.13 % (30708)------------------------------
% 1.31/1.13 % (30708)------------------------------
% 1.31/1.14 % (30712)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_30602 for (2999ds/1041Mi)
% 1.31/1.14 % (30709)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_30602 for (2999ds/37Mi)
% 1.31/1.14 % (30710)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_30602 for (2999ds/15Mi)
% 1.31/1.14 % (30711)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_30602 for (2999ds/3Mi)
% 1.31/1.14 % (30711)Instruction limit reached!
% 1.31/1.14 % (30711)------------------------------
% 1.31/1.14 % (30711)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (30711)Termination reason: Unknown
% 1.31/1.14 % (30711)Termination phase: Saturation
% 1.31/1.14
% 1.31/1.14 % (30711)Memory used [KB]: 5500
% 1.31/1.14 % (30711)Time elapsed: 0.003 s
% 1.31/1.14 % (30711)Instructions burned: 3 (million)
% 1.31/1.14 % (30711)------------------------------
% 1.31/1.14 % (30711)------------------------------
% 1.31/1.14 % (30703)Also succeeded, but the first one will report.
% 1.31/1.14 % (30707)Refutation found. Thanks to Tanya!
% 1.31/1.14 % SZS status Theorem for DTF2THF_30602
% 1.31/1.14 % SZS output start Proof for DTF2THF_30602
% 1.31/1.14 thf(func_def_0, type, cD_FOR_X5309: (($i > $o) > $i) > $i > $o).
% 1.31/1.14 thf(func_def_12, type, sK0: ($i > $o) > $i).
% 1.31/1.14 thf(func_def_14, type, sK2: $i > $o).
% 1.31/1.14 thf(func_def_15, type, ph3: !>[X0: $tType]:(X0)).
% 1.31/1.14 thf(func_def_16, type, sK4: $i > $i > $o).
% 1.31/1.14 thf(f56,plain,(
% 1.31/1.14 $false),
% 1.31/1.14 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.31/1.14 thf(f55,plain,(
% 1.31/1.14 ($true = $false)),
% 1.31/1.14 inference(duplicate_literal_removal,[status(thm)],[f45])).
% 1.31/1.14 thf(f45,plain,(
% 1.31/1.14 ($true = $false) | ($true = $false)),
% 1.31/1.14 inference(superposition,[status(thm)],[f44,f22])).
% 1.31/1.14 thf(f22,plain,(
% 1.31/1.14 ((sK2 @ (sK0 @ sK2)) = $false)),
% 1.31/1.14 inference(not_proxy_clausification,[status(thm)],[f21])).
% 1.31/1.14 thf(f21,plain,(
% 1.31/1.14 ($true = (~ (sK2 @ (sK0 @ sK2))))),
% 1.31/1.14 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.31/1.14 thf(f19,plain,(
% 1.31/1.14 ($true = ((~ (sK2 @ (sK0 @ sK2))) & ((sK0 @ sK2) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))))))),
% 1.31/1.14 inference(beta_eta_normalization,[status(thm)],[f18])).
% 1.31/1.14 thf(f18,plain,(
% 1.31/1.14 ($true = ((^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK0 @ Y2))) & ((sK0 @ Y2) = Y1))))))))) @ sK2))),
% 1.31/1.14 inference(sigma_clausification,[status(thm)],[f17])).
% 1.31/1.14 thf(f17,plain,(
% 1.31/1.14 ($true = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = (sK0 @ (^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (sK0 @ Y2))) & ((sK0 @ Y2) = Y1)))))))))))),
% 1.31/1.14 inference(beta_eta_normalization,[status(thm)],[f16])).
% 1.31/1.14 thf(f16,plain,(
% 1.31/1.14 ($true = ((^[Y0 : ($i > $o) > $i]: ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (Y0 @ Y2))) & ((Y0 @ Y2) = Y1))))))) @ sK0 @ (sK0 @ ((^[Y0 : ($i > $o) > $i]: ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (Y0 @ Y2))) & ((Y0 @ Y2) = Y1))))))) @ sK0))))),
% 1.31/1.14 inference(definition_unfolding,[status(thm)],[f13,f15,f15])).
% 1.31/1.14 thf(f15,plain,(
% 1.31/1.14 (cD_FOR_X5309 = (^[Y0 : ($i > $o) > $i]: ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (Y0 @ Y2))) & ((Y0 @ Y2) = Y1))))))))),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f8])).
% 1.31/1.14 thf(f8,plain,(
% 1.31/1.14 (cD_FOR_X5309 = (^[Y0 : ($i > $o) > $i]: ((^[Y1 : $i]: (?? @ ($i > $o) @ (^[Y2 : $i > $o]: ((~ (Y2 @ (Y0 @ Y2))) & ((Y0 @ Y2) = Y1))))))))),
% 1.31/1.14 inference(fool_elimination,[status(thm)],[f7])).
% 1.31/1.14 thf(f7,plain,(
% 1.31/1.14 ((^[X0 : ($i > $o) > $i, X1 : $i] : (? [X2 : $i > $o] : (((X0 @ X2) = X1) & ~(X2 @ (X0 @ X2))))) = cD_FOR_X5309)),
% 1.31/1.14 inference(rectify,[status(thm)],[f1])).
% 1.31/1.14 thf(f1,axiom,(
% 1.31/1.14 ((^[X0 : ($i > $o) > $i, X1 : $i] : (? [X2 : $i > $o] : (((X0 @ X2) = X1) & ~(X2 @ (X0 @ X2))))) = cD_FOR_X5309)),
% 1.31/1.14 file('/export/starexec/sandbox/tmp/tmp.Aw9Tkq5nsg/DTF2THF_30602.p',cD_FOR_X5309_def)).
% 1.31/1.14 thf(f13,plain,(
% 1.31/1.14 ($true = (cD_FOR_X5309 @ sK0 @ (sK0 @ (cD_FOR_X5309 @ sK0))))),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f12])).
% 1.31/1.14 thf(f12,plain,(
% 1.31/1.14 ! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((sK0 @ X2) != (sK0 @ X1))) & ($true = (cD_FOR_X5309 @ sK0 @ (sK0 @ (cD_FOR_X5309 @ sK0))))),
% 1.31/1.14 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f11])).
% 1.31/1.14 thf(f11,plain,(
% 1.31/1.14 ? [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((X0 @ X2) != (X0 @ X1))) & ((cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))) = $true)) => (! [X2 : $i > $o,X1 : $i > $o] : ((X1 = X2) | ((sK0 @ X2) != (sK0 @ X1))) & ($true = (cD_FOR_X5309 @ sK0 @ (sK0 @ (cD_FOR_X5309 @ sK0)))))),
% 1.31/1.14 introduced(definition,[],[choice_axiom])).
% 1.31/1.14 thf(f10,plain,(
% 1.31/1.14 ? [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((X0 @ X2) != (X0 @ X1))) & ((cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))) = $true))),
% 1.31/1.14 inference(ennf_transformation,[status(thm)],[f9])).
% 1.31/1.14 thf(f9,plain,(
% 1.31/1.14 ~! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2) = (X0 @ X1)) => (X1 = X2)) => ((cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))) != $true))),
% 1.31/1.14 inference(flattening,[status(thm)],[f6])).
% 1.31/1.14 thf(f6,plain,(
% 1.31/1.14 ~! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2) = (X0 @ X1)) => (X1 = X2)) => ~((cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))) = $true))),
% 1.31/1.14 inference(fool_elimination,[status(thm)],[f5])).
% 1.31/1.14 thf(f5,plain,(
% 1.31/1.14 ~! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X2) = (X0 @ X1)) => (X1 = X2)) => ~(cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))))),
% 1.31/1.14 inference(rectify,[status(thm)],[f3])).
% 1.31/1.14 thf(f3,negated_conjecture,(
% 1.31/1.14 ~! [X0 : ($i > $o) > $i] : (! [X4 : $i > $o,X3 : $i > $o] : (((X0 @ X3) = (X0 @ X4)) => (X3 = X4)) => ~(cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))))),
% 1.31/1.14 inference(negated_conjecture,[status(cth)],[f2])).
% 1.31/1.14 thf(f2,conjecture,(
% 1.31/1.14 ! [X0 : ($i > $o) > $i] : (! [X4 : $i > $o,X3 : $i > $o] : (((X0 @ X3) = (X0 @ X4)) => (X3 = X4)) => ~(cD_FOR_X5309 @ X0 @ (X0 @ (cD_FOR_X5309 @ X0))))),
% 1.31/1.14 file('/export/starexec/sandbox/tmp/tmp.Aw9Tkq5nsg/DTF2THF_30602.p',cTHM143C_pme)).
% 1.31/1.14 thf(f44,plain,(
% 1.31/1.14 ( ! [X0 : $i > $o] : (($true = (sK2 @ (sK0 @ X0))) | ($true = (X0 @ (sK0 @ X0)))) )),
% 1.31/1.14 inference(equality_resolution,[status(thm)],[f43])).
% 1.31/1.14 thf(f43,plain,(
% 1.31/1.14 ( ! [X2 : $i > $o,X1 : $i] : (((sK0 @ X2) != X1) | ($true = (sK2 @ X1)) | ($true = (X2 @ (sK0 @ X2)))) )),
% 1.31/1.14 inference(not_proxy_clausification,[status(thm)],[f42])).
% 1.31/1.14 thf(f42,plain,(
% 1.31/1.14 ( ! [X2 : $i > $o,X1 : $i] : (($true = (sK2 @ X1)) | ((sK0 @ X2) != X1) | ($false = (~ (X2 @ (sK0 @ X2))))) )),
% 1.31/1.14 inference(equality_proxy_clausification,[status(thm)],[f41])).
% 1.31/1.14 thf(f41,plain,(
% 1.31/1.14 ( ! [X2 : $i > $o,X1 : $i] : (($true = (sK2 @ X1)) | ($false = ((sK0 @ X2) = X1)) | ($false = (~ (X2 @ (sK0 @ X2))))) )),
% 1.31/1.14 inference(binary_proxy_clausification,[status(thm)],[f40])).
% 1.31/1.14 thf(f40,plain,(
% 1.31/1.14 ( ! [X2 : $i > $o,X1 : $i] : (($true = (sK2 @ X1)) | ($false = ((~ (X2 @ (sK0 @ X2))) & ((sK0 @ X2) = X1)))) )),
% 1.31/1.14 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.31/1.14 thf(f39,plain,(
% 1.31/1.14 ( ! [X2 : $i > $o,X1 : $i] : (($true = (sK2 @ X1)) | (((^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = X1))) @ X2) = $false)) )),
% 1.31/1.14 inference(pi_clausification,[status(thm)],[f31])).
% 1.31/1.14 thf(f31,plain,(
% 1.31/1.14 ( ! [X1 : $i] : (($true = (sK2 @ X1)) | ($false = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = X1)))))) )),
% 1.31/1.14 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.31/1.14 thf(f30,plain,(
% 1.31/1.14 ( ! [X1 : $i] : (((sK2 @ X1) = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: ((~ (Y0 @ (sK0 @ Y0))) & ((sK0 @ Y0) = X1)))))) )),
% 1.31/1.14 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.31/1.14 thf(f29,plain,(
% 1.31/1.14 ( ! [X1 : $i] : ((((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) @ X1) = (sK2 @ X1))) )),
% 1.31/1.14 inference(argument_congruence,[status(thm)],[f28])).
% 1.31/1.14 thf(f28,plain,(
% 1.31/1.14 (sK2 = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))),
% 1.31/1.14 inference(equality_resolution,[status(thm)],[f25])).
% 1.31/1.14 thf(f25,plain,(
% 1.31/1.14 ( ! [X0 : $i > $o] : (((sK0 @ sK2) != (sK0 @ X0)) | ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))) = X0)) )),
% 1.31/1.14 inference(superposition,[status(thm)],[f14,f23])).
% 1.31/1.14 thf(f23,plain,(
% 1.31/1.14 ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0)))))) = (sK0 @ sK2))),
% 1.31/1.14 inference(equality_proxy_clausification,[status(thm)],[f20])).
% 1.31/1.14 thf(f20,plain,(
% 1.31/1.14 ($true = ((sK0 @ sK2) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: ((~ (Y1 @ (sK0 @ Y1))) & ((sK0 @ Y1) = Y0))))))))),
% 1.31/1.14 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.31/1.14 thf(f14,plain,(
% 1.31/1.14 ( ! [X2 : $i > $o,X1 : $i > $o] : (((sK0 @ X2) != (sK0 @ X1)) | (X1 = X2)) )),
% 1.31/1.14 inference(cnf_transformation,[status(thm)],[f12])).
% 1.31/1.14 % SZS output end Proof for DTF2THF_30602
% 1.31/1.14 % (30707)------------------------------
% 1.31/1.14 % (30707)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.14 % (30707)Termination reason: Refutation
% 1.31/1.14
% 1.31/1.14 % (30707)Memory used [KB]: 5500
% 1.31/1.14 % (30707)Time elapsed: 0.008 s
% 1.31/1.14 % (30707)Instructions burned: 6 (million)
% 1.31/1.14 % (30707)------------------------------
% 1.31/1.14 % (30707)------------------------------
% 1.31/1.14 % (30700)Success in time 0.035 s
%------------------------------------------------------------------------------