%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV603^1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 : Tue May 5 06:51:15 PM UTC 2026
% Result : Theorem 1.68s 1.42s
% Output : Refutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 35 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 209 ( 72 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 351 ( 27 ~; 25 |; 7 &; 288 @)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 93 ( 0 ^; 86 !; 7 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK1: $tType ).
thf(func_def_0,type,
in:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
univ:
!>[X0: $tType] : ( X0 > $o ) ).
thf(func_def_2,type,
insert:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_6,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK2: sK1 ).
thf(func_def_9,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
sK5: sK1 ).
thf(func_def_11,type,
sK6:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 ) ).
thf(func_def_12,type,
sK7:
!>[X0: $tType] : ( X0 > ( X0 > $o ) > X0 > ( X0 > $o ) > X0 ) ).
thf(func_def_13,type,
sK8:
!>[X0: $tType] : ( X0 > X0 > ( X0 > $o ) > X0 ) ).
thf(f215,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f214,f154]) ).
thf(f154,plain,
! [X0: $tType,X1: X0] :
( univ
@ ( X0
= ( insert @ X0 @ X1 @ univ @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
! [X0: $tType,X1: X0] :
( ( univ
@ ( X0
= ( insert @ X0 @ X1 @ univ @ X0 ) ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f128,f56]) ).
thf(f56,plain,
! [X0: $tType,X2: X0,X1: X0] :
( $true
= ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ univ @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: $tType,X2: X0,X1: X0] :
( ( $true != $true )
| ( $true
= ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ univ @ X0 ) ) ) ),
inference(superposition,[status(thm)],[f26,f27]) ).
thf(f27,plain,
! [X0: $tType,X1: X0] :
( ( in @ X0 @ X1 @ univ @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0] :
( ( in @ X0 @ X1 @ univ @ X0 )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0] : ( in @ X0 @ X1 @ univ @ X0 ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0] : ( in @ X0 @ X1 @ univ @ X0 ),
file('/export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2THF_13143.p','pred_set/IN_UNIV_') ).
thf(f26,plain,
! [X0: $tType,X2: X0,X3: X0 > $o,X1: X0] :
( ( ( in @ X0 @ X1 @ X3 )
!= $true )
| ( ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ X3 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( ( ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ X3 ) )
= $true )
| ( ( ( in @ X0 @ X1 @ X3 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X0 @ X1 @ X3 )
= $true )
| ( X1 = X2 )
| ( ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ X3 ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( ( ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ X3 ) )
= $true )
| ( ( ( in @ X0 @ X1 @ X3 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X0 @ X1 @ X3 )
= $true )
| ( X1 = X2 )
| ( ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ X3 ) )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ X3 ) )
= $true )
<=> ( ( ( in @ X0 @ X1 @ X3 )
= $true )
| ( X1 = X2 ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( in @ X0 @ X1 @ X3 )
| ( ( X1 = X2 )
= ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0,X2: X0,X3: X0 > $o] :
( ( in @ X0 @ X1 @ X3 )
| ( ( X1 = X2 )
= ( in @ X0 @ X1 @ ( insert @ X0 @ X2 @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2THF_13143.p','pred_set/IN_INSERT_') ).
thf(f128,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( in @ X0 @ ( sK0 @ X0 @ X1 @ univ @ X0 ) @ X1 )
= $false )
| ( univ @ ( X0 = X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
! [X0: $tType,X1: X0 > $o] :
( ( ( in @ X0 @ ( sK0 @ X0 @ X1 @ univ @ X0 ) @ X1 )
= $false )
| ( $true = $false )
| ( univ @ ( X0 = X1 ) ) ),
inference(superposition,[status(thm)],[f32,f27]) ).
thf(f32,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( in @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 )
= $false )
| ( ( in @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 )
= $false )
| ( X1 = X2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( X1 = X2 )
| ( ( in @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 )
!= ( in @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( in @ X0 @ X3 @ X1 )
= ( in @ X0 @ X3 @ X2 ) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ( ( in @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 )
!= ( in @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ? [X4: X0] :
( ( in @ X0 @ X4 @ X1 )
!= ( in @ X0 @ X4 @ X2 ) )
=> ( ( in @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 )
!= ( in @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( in @ X0 @ X3 @ X1 )
= ( in @ X0 @ X3 @ X2 ) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ? [X4: X0] :
( ( in @ X0 @ X4 @ X1 )
!= ( in @ X0 @ X4 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( in @ X0 @ X3 @ X1 )
= ( in @ X0 @ X3 @ X2 ) )
| ( X1 != X2 ) )
& ( ( X1 = X2 )
| ? [X3: X0] :
( ( in @ X0 @ X3 @ X1 )
!= ( in @ X0 @ X3 @ X2 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ! [X3: X0] :
( ( in @ X0 @ X3 @ X1 )
= ( in @ X0 @ X3 @ X2 ) )
<=> ( X1 = X2 ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( X1 = X2 )
= ( ! [X3: X0] :
( ( in @ X0 @ X3 @ X1 )
= ( in @ X0 @ X3 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X3: X0 > $o,X4: X0 > $o] :
( ( X3 = X4 )
= ( ! [X1: X0] :
( ( in @ X0 @ X1 @ X3 )
= ( in @ X0 @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2THF_13143.p','pred_set/EXTENSION_') ).
thf(f214,plain,
! [X0: sK1] :
( ( ( insert @ sK1 @ X0 @ univ @ sK1 )
!= univ )
@ sK1 ),
inference(forward_demodulation,[status(thm)],[f201,f154]) ).
thf(f201,plain,
! [X0: sK1] :
( ( insert @ sK1 @ X0 @ univ @ sK1 )
!= ( insert @ sK1 @ sK2 @ univ @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f194]) ).
thf(f194,plain,
! [X0: sK1] :
( ( ( insert @ sK1 @ X0 @ univ @ sK1 )
!= ( insert @ sK1 @ sK2 @ univ @ sK1 ) )
| ( univ @ ( sK1 != univ ) @ sK1 ) ),
inference(constrained_superposition,[status(thm)],[f28,f154]) ).
thf(f28,plain,
( univ
@ ( sK1
!= ( insert @ sK1 @ sK2 @ univ @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( univ
@ ( sK1
!= ( insert @ sK1 @ sK2 @ univ @ sK1 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f20]) ).
thf(f20,plain,
( ? [X0: $tType,X1: X0] :
( univ
@ ( X0
!= ( insert @ X0 @ X1 @ univ @ X0 ) ) )
=> ( univ
@ ( sK1
!= ( insert @ sK1 @ sK2 @ univ @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $tType,X1: X0] :
( univ
@ ( X0
!= ( insert @ X0 @ X1 @ univ @ X0 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X1: X0] :
( univ
@ ( X0
= ( insert @ X0 @ X1 @ univ @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X1: X0] :
( univ
@ ( X0
= ( insert @ X0 @ X1 @ univ @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2THF_13143.p','pred_set/INSERT_UNIV_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV603^1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n002.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
% 0.17/0.35 % DateTime : Tue May 5 05:17:16 EDT 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.48 ---- Original DTF file ---
% 0.28/0.48 thf(spec,logic,$$dhol).
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 % File : SEV603^1 : TPTP v9.3.0. Released v9.3.0.
% 0.28/0.48 % Domain : Set Theory
% 0.28/0.48 % Problem : Predicate insert in Univ
% 0.28/0.48 % Version : Especial.
% 0.28/0.48 % English :
% 0.28/0.48
% 0.28/0.48 % Refs :
% 0.28/0.48 % Source : [TPTP]
% 0.28/0.48 % Names : 001 [TPTP]
% 0.28/0.48
% 0.28/0.48 % Status : Theorem
% 0.28/0.48 % Rating : ? v9.3.0
% 0.28/0.48 % Syntax : Number of formulae : 7 ( 3 unt; 3 typ; 0 def)
% 0.28/0.48 % Number of atoms : 16 ( 6 equ; 0 cnn)
% 0.28/0.48 % Maximal formula atoms : 2 ( 4 avg)
% 0.28/0.48 % Number of connectives : 25 ( 0 ~; 1 |; 0 &; 24 @)
% 0.28/0.48 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.28/0.48 % Maximal formula depth : 6 ( 5 avg)
% 0.28/0.48 % Number of types : 1 ( 0 usr)
% 0.28/0.48 % Number of type decls : 3 ( 3 !>P; 0 !>D)
% 0.28/0.48 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.28/0.48 % Number of symbols : 4 ( 3 usr; 0 con; 2-4 aty)
% 0.28/0.48 % Number of variables : 15 ( 0 ^; 12 !; 0 ?; 15 :)
% 0.28/0.48 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.28/0.48 % SPC : TH1_THM_EQU_NAR
% 0.28/0.48
% 0.28/0.48 % Comments : Originally HOL4 Kananaskis 10
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 thf(in,type,
% 0.28/0.48 in:
% 0.28/0.48 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.28/0.48
% 0.28/0.48 thf(univ,type,
% 0.28/0.48 univ:
% 0.28/0.48 !>[A: $tType] : ( A > $o ) ).
% 0.28/0.48
% 0.28/0.48 thf(insert,type,
% 0.28/0.48 insert:
% 0.28/0.48 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.28/0.48
% 0.28/0.48 thf('pred_set/IN_INSERT_',axiom,
% 0.28/0.48 ! [A: $tType,X: A,Y: A,S: A > $o] :
% 0.28/0.48 ( ( in @ A @ X @ ( insert @ A @ Y @ S ) )
% 0.28/0.48 = ( ( X = Y )
% 0.28/0.48 | ( in @ A @ X @ S ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf('pred_set/IN_UNIV_',axiom,
% 0.28/0.48 ! [A: $tType,X: A] : ( in @ A @ X @ ( univ @ A ) ) ).
% 0.28/0.48
% 0.28/0.48 thf('pred_set/EXTENSION_',axiom,
% 0.28/0.48 ! [A: $tType,S: A > $o,T: A > $o] :
% 0.28/0.48 ( ( S = T )
% 0.28/0.48 = ( ! [X: A] :
% 0.28/0.48 ( ( in @ A @ X @ S )
% 0.28/0.48 = ( in @ A @ X @ T ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf('pred_set/INSERT_UNIV_',conjecture,
% 0.28/0.48 ! [A: $tType,X: A] :
% 0.28/0.48 ( ( insert @ A @ X @ ( univ @ A ) )
% 0.28/0.48 = ( univ @ A ) ) ).
% 0.28/0.48
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 ------------------------
% 1.63/1.32 ---- Embedded in THF ---
% 1.63/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.32 %%% Generated on Tue May 05 05:17:17 EDT 2026
% 1.63/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.32 %%% Logic specification used:
% 1.63/1.32 %%% thf(spec, logic, $$dhol).
% 1.63/1.32
% 1.63/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2DTF13143.p
% See solution above
% 1.63/1.32 ------------------------
% 1.63/1.33 ---- Cleaned THF ---
% 1.63/1.33 thf(in,type,
% 1.63/1.33 in:
% 1.63/1.33 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.63/1.33
% 1.63/1.33 thf(univ,type,
% 1.63/1.33 univ:
% 1.63/1.33 !>[A: $tType] : ( A > $o ) ).
% 1.63/1.33
% 1.63/1.33 thf(insert,type,
% 1.63/1.33 insert:
% 1.63/1.33 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.63/1.33
% 1.63/1.33 thf('pred_set/IN_INSERT_',axiom,
% 1.63/1.33 ! [A: $tType,X: A,Y: A,S: A > $o] :
% 1.63/1.33 ( ( in @ A @ X @ ( insert @ A @ Y @ S ) )
% 1.63/1.33 = ( ( X = Y )
% 1.63/1.33 | ( in @ A @ X @ S ) ) ) ).
% 1.63/1.33
% 1.63/1.33 thf('pred_set/IN_UNIV_',axiom,
% 1.63/1.33 ! [A: $tType,X: A] : ( in @ A @ X @ ( univ @ A ) ) ).
% 1.63/1.33
% 1.63/1.33 thf('pred_set/EXTENSION_',axiom,
% 1.63/1.33 ! [A: $tType,S: A > $o,T: A > $o] :
% 1.63/1.33 ( ( S = T )
% 1.63/1.33 = ( ! [X: A] :
% 1.63/1.33 ( ( in @ A @ X @ S )
% 1.63/1.33 = ( in @ A @ X @ T ) ) ) ) ).
% 1.63/1.33
% 1.63/1.33 thf('pred_set/INSERT_UNIV_',conjecture,
% 1.63/1.33 ! [A: $tType,X: A] :
% 1.63/1.33 ( ( insert @ A @ X @ ( univ @ A ) )
% 1.63/1.33 = ( univ @ A ) ) ).
% 1.63/1.33 ------------------------
% 1.63/1.34 % (13246)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13143 for (3000ds/18Mi)
% 1.63/1.34 % (13241)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_13143 for (3000ds/4Mi)
% 1.63/1.35 % (13241)Instruction limit reached!
% 1.63/1.35 % (13241)------------------------------
% 1.63/1.35 % (13241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (13241)Termination reason: Unknown
% 1.63/1.35 % (13241)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (13241)Memory used [KB]: 5500
% 1.63/1.35 % (13241)Time elapsed: 0.003 s
% 1.63/1.35 % (13241)Instructions burned: 5 (million)
% 1.63/1.35 % (13241)------------------------------
% 1.63/1.35 % (13241)------------------------------
% 1.63/1.35 % (13246)Instruction limit reached!
% 1.63/1.35 % (13246)------------------------------
% 1.63/1.35 % (13246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (13246)Termination reason: Unknown
% 1.63/1.35 % (13246)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (13246)Memory used [KB]: 5628
% 1.63/1.35 % (13246)Time elapsed: 0.008 s
% 1.63/1.35 % (13246)Instructions burned: 18 (million)
% 1.63/1.35 % (13246)------------------------------
% 1.63/1.35 % (13246)------------------------------
% 1.63/1.35 % (13240)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13143 for (3000ds/183Mi)
% 1.63/1.35 % (13242)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_13143 for (3000ds/27Mi)
% 1.63/1.35 % (13244)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_13143 for (3000ds/2Mi)
% 1.63/1.35 % (13245)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_13143 for (3000ds/275Mi)
% 1.63/1.35 % (13243)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13143 for (3000ds/2Mi)
% 1.63/1.35 % Exception at run slice level
% 1.63/1.35 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.63/1.35 % (13243)Instruction limit reached!
% 1.63/1.35 % (13243)------------------------------
% 1.63/1.35 % (13243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (13243)Termination reason: Unknown
% 1.63/1.35 % (13243)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (13243)Memory used [KB]: 5500
% 1.63/1.35 % (13243)Time elapsed: 0.004 s
% 1.63/1.35 % (13243)Instructions burned: 2 (million)
% 1.63/1.35 % (13243)------------------------------
% 1.63/1.35 % (13243)------------------------------
% 1.63/1.35 % (13245)Refutation not found, incomplete strategy
% 1.63/1.35 % (13245)------------------------------
% 1.63/1.35 % (13245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (13245)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.35
% 1.63/1.35
% 1.63/1.35 % (13245)Memory used [KB]: 5500
% 1.63/1.35 % (13245)Time elapsed: 0.005 s
% 1.63/1.35 % (13245)Instructions burned: 4 (million)
% 1.63/1.35 % (13245)------------------------------
% 1.63/1.35 % (13245)------------------------------
% 1.63/1.36 % (13248)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_13143 for (2999ds/37Mi)
% 1.63/1.36 % Exception at run slice level
% 1.63/1.36 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.63/1.36 % (13247)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/3Mi)
% 1.63/1.36 % (13247)Instruction limit reached!
% 1.63/1.36 % (13247)------------------------------
% 1.63/1.36 % (13247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (13247)Termination reason: Unknown
% 1.63/1.36 % (13247)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (13247)Memory used [KB]: 5500
% 1.63/1.36 % (13247)Time elapsed: 0.003 s
% 1.63/1.36 % (13247)Instructions burned: 3 (million)
% 1.63/1.36 % (13247)------------------------------
% 1.63/1.36 % (13247)------------------------------
% 1.63/1.37 % (13242)Instruction limit reached!
% 1.63/1.37 % (13242)------------------------------
% 1.63/1.37 % (13242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (13242)Termination reason: Unknown
% 1.63/1.37 % (13242)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (13242)Memory used [KB]: 5500
% 1.63/1.37 % (13242)Time elapsed: 0.019 s
% 1.63/1.37 % (13242)Instructions burned: 27 (million)
% 1.63/1.37 % (13242)------------------------------
% 1.63/1.37 % (13242)------------------------------
% 1.63/1.37 % (13252)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/7Mi)
% 1.63/1.37 % (13249)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_13143 for (2999ds/15Mi)
% 1.63/1.37 % (13250)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_13143 for (2999ds/3Mi)
% 1.63/1.37 % (13251)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_13143 for (2999ds/1041Mi)
% 1.63/1.37 % (13252)Instruction limit reached!
% 1.63/1.37 % (13252)------------------------------
% 1.63/1.37 % (13252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (13252)Termination reason: Unknown
% 1.63/1.37 % (13252)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (13252)Memory used [KB]: 1023
% 1.63/1.37 % (13252)Time elapsed: 0.004 s
% 1.63/1.37 % (13252)Instructions burned: 7 (million)
% 1.63/1.37 % (13252)------------------------------
% 1.63/1.37 % (13252)------------------------------
% 1.63/1.37 % (13253)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/16Mi)
% 1.63/1.37 % (13249)Refutation not found, incomplete strategy
% 1.63/1.37 % (13249)------------------------------
% 1.63/1.37 % (13249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % Exception at run slice level
% 1.63/1.37 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.63/1.37 % (13250)Instruction limit reached!
% 1.63/1.37 % (13250)------------------------------
% 1.63/1.37 % (13250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.37 % (13250)Termination reason: Unknown
% 1.63/1.37 % (13250)Termination phase: Saturation
% 1.63/1.37
% 1.63/1.37 % (13250)Memory used [KB]: 5500
% 1.63/1.37 % (13250)Time elapsed: 0.004 s
% 1.63/1.37 % (13250)Instructions burned: 3 (million)
% 1.63/1.37 % (13250)------------------------------
% 1.63/1.37 % (13250)------------------------------
% 1.63/1.37 % (13249)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.37
% 1.63/1.37
% 1.63/1.37 % (13249)Memory used [KB]: 5500
% 1.63/1.37 % (13249)Time elapsed: 0.005 s
% 1.63/1.37 % (13249)Instructions burned: 3 (million)
% 1.63/1.37 % (13249)------------------------------
% 1.63/1.37 % (13249)------------------------------
% 1.63/1.38 % (13253)Instruction limit reached!
% 1.63/1.38 % (13253)------------------------------
% 1.63/1.38 % (13253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (13253)Termination reason: Unknown
% 1.63/1.38 % (13253)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (13253)Memory used [KB]: 5628
% 1.63/1.38 % (13253)Time elapsed: 0.008 s
% 1.63/1.38 % (13253)Instructions burned: 18 (million)
% 1.63/1.38 % (13253)------------------------------
% 1.63/1.38 % (13253)------------------------------
% 1.63/1.38 % (13255)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_13143 for (2999ds/3Mi)
% 1.63/1.38 % (13255)Instruction limit reached!
% 1.63/1.38 % (13255)------------------------------
% 1.63/1.38 % (13255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.38 % (13255)Termination reason: Unknown
% 1.63/1.38 % (13255)Termination phase: Saturation
% 1.63/1.38
% 1.63/1.38 % (13255)Memory used [KB]: 1023
% 1.63/1.38 % (13255)Time elapsed: 0.002 s
% 1.63/1.38 % (13255)Instructions burned: 3 (million)
% 1.63/1.38 % (13255)------------------------------
% 1.63/1.38 % (13255)------------------------------
% 1.63/1.39 % (13254)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_13143 for (2999ds/3Mi)
% 1.63/1.39 % (13254)Instruction limit reached!
% 1.63/1.39 % (13254)------------------------------
% 1.63/1.39 % (13254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (13254)Termination reason: Unknown
% 1.63/1.39 % (13254)Termination phase: Saturation
% 1.63/1.39
% 1.63/1.39 % (13254)Memory used [KB]: 5500
% 1.63/1.39 % (13254)Time elapsed: 0.005 s
% 1.63/1.39 % (13254)Instructions burned: 4 (million)
% 1.63/1.39 % (13254)------------------------------
% 1.63/1.39 % (13254)------------------------------
% 1.63/1.39 % (13259)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/18Mi)
% 1.63/1.39 % (13256)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/7Mi)
% 1.63/1.39 % (13257)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/3Mi)
% 1.63/1.39 % (13258)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/4Mi)
% 1.63/1.39 % Exception at run slice level
% 1.63/1.39 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.63/1.39 % (13260)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/710Mi)
% 1.63/1.39 % (13256)Refutation not found, incomplete strategy
% 1.63/1.39 % (13256)------------------------------
% 1.63/1.39 % (13256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (13256)Termination reason: Refutation not found, incomplete strategy
% 1.63/1.39
% 1.63/1.39
% 1.63/1.39 % (13256)Memory used [KB]: 5500
% 1.63/1.39 % (13256)Time elapsed: 0.004 s
% 1.63/1.39 % (13256)Instructions burned: 4 (million)
% 1.63/1.39 % (13256)------------------------------
% 1.63/1.39 % (13256)------------------------------
% 1.63/1.39 % (13258)Instruction limit reached!
% 1.63/1.39 % (13258)------------------------------
% 1.63/1.39 % (13258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.39 % (13258)Termination reason: Unknown
% 1.63/1.39 % (13258)Termination phase: Saturation
% 1.63/1.39
% 1.63/1.39 % (13258)Memory used [KB]: 5500
% 1.63/1.39 % (13258)Time elapsed: 0.005 s
% 1.63/1.39 % (13258)Instructions burned: 4 (million)
% 1.63/1.39 % (13258)------------------------------
% 1.63/1.39 % (13258)------------------------------
% 1.68/1.40 % (13259)Instruction limit reached!
% 1.68/1.40 % (13259)------------------------------
% 1.68/1.40 % (13259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.40 % (13259)Termination reason: Unknown
% 1.68/1.40 % (13259)Termination phase: Saturation
% 1.68/1.40
% 1.68/1.40 % (13259)Memory used [KB]: 5500
% 1.68/1.40 % (13259)Time elapsed: 0.032 s
% 1.68/1.40 % (13259)Instructions burned: 19 (million)
% 1.68/1.40 % (13259)------------------------------
% 1.68/1.40 % (13259)------------------------------
% 1.68/1.41 % (13263)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_13143 for (2999ds/21Mi)
% 1.68/1.41 % (13261)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/6Mi)
% 1.68/1.41 % (13265)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_13143 for (2999ds/6Mi)
% 1.68/1.41 % Exception at run slice level
% 1.68/1.41 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.68/1.41 % (13262)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_13143 for (2999ds/902Mi)
% 1.68/1.41 % (13261)Instruction limit reached!
% 1.68/1.41 % (13261)------------------------------
% 1.68/1.41 % (13261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.41 % (13261)Termination reason: Unknown
% 1.68/1.41 % (13261)Termination phase: Saturation
% 1.68/1.41
% 1.68/1.41 % (13261)Memory used [KB]: 5500
% 1.68/1.41 % (13261)Time elapsed: 0.006 s
% 1.68/1.41 % (13261)Instructions burned: 6 (million)
% 1.68/1.41 % (13261)------------------------------
% 1.68/1.41 % (13261)------------------------------
% 1.68/1.41 % (13264)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13143 for (2999ds/5Mi)
% 1.68/1.41 % (13262)Refutation not found, incomplete strategy
% 1.68/1.41 % (13262)------------------------------
% 1.68/1.41 % (13262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.41 % (13262)Termination reason: Refutation not found, incomplete strategy
% 1.68/1.41
% 1.68/1.41
% 1.68/1.41 % (13262)Memory used [KB]: 5500
% 1.68/1.41 % (13262)Time elapsed: 0.005 s
% 1.68/1.41 % (13262)Instructions burned: 2 (million)
% 1.68/1.41 % (13262)------------------------------
% 1.68/1.41 % (13262)------------------------------
% 1.68/1.41 % Exception at run slice level
% 1.68/1.41 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.68/1.41 % (13263)Instruction limit reached!
% 1.68/1.41 % (13263)------------------------------
% 1.68/1.41 % (13263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.41 % (13263)Termination reason: Unknown
% 1.68/1.41 % (13263)Termination phase: Saturation
% 1.68/1.41
% 1.68/1.41 % (13263)Memory used [KB]: 5628
% 1.68/1.41 % (13263)Time elapsed: 0.011 s
% 1.68/1.41 % (13263)Instructions burned: 22 (million)
% 1.68/1.41 % (13263)------------------------------
% 1.68/1.41 % (13263)------------------------------
% 1.68/1.42 % (13260)First to succeed.
% 1.68/1.42 % (13260)Refutation found. Thanks to Tanya!
% 1.68/1.42 % SZS status Theorem for DTF2THF_13143
% 1.68/1.42 % SZS output start Proof for DTF2THF_13143
% 1.68/1.42 thf(type_def_6, type, sK1: $tType).
% 1.68/1.42 thf(func_def_0, type, in: !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.68/1.42 thf(func_def_1, type, univ: !>[X0: $tType]:(X0 > $o)).
% 1.68/1.42 thf(func_def_2, type, insert: !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.68/1.42 thf(func_def_6, type, sK0: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.68/1.42 thf(func_def_7, type, sK2: sK1).
% 1.68/1.42 thf(func_def_9, type, ph4: !>[X0: $tType]:(X0)).
% 1.68/1.42 thf(func_def_10, type, sK5: sK1).
% 1.68/1.42 thf(func_def_11, type, sK6: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 1.68/1.42 thf(func_def_12, type, sK7: !>[X0: $tType]:(X0 > (X0 > $o) > X0 > (X0 > $o) > X0)).
% 1.68/1.42 thf(func_def_13, type, sK8: !>[X0: $tType]:(X0 > X0 > (X0 > $o) > X0)).
% 1.68/1.42 thf(f215,plain,(
% 1.68/1.42 $false),
% 1.68/1.42 inference(subsumption_resolution,[status(thm)],[f214,f154])).
% 1.68/1.42 thf(f154,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X1 : X0] : ((univ @ X0 = (insert @ X0 @ X1 @ univ @ X0))) )),
% 1.68/1.42 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.68/1.42 thf(f140,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X1 : X0] : ((univ @ X0 = (insert @ X0 @ X1 @ univ @ X0)) | ($true = $false)) )),
% 1.68/1.42 inference(superposition,[status(thm)],[f128,f56])).
% 1.68/1.42 thf(f56,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true = (in @ X0 @ X1 @ (insert @ X0 @ X2 @ univ @ X0)))) )),
% 1.68/1.42 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.68/1.42 thf(f55,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X2 : X0,X1 : X0] : (($true != $true) | ($true = (in @ X0 @ X1 @ (insert @ X0 @ X2 @ univ @ X0)))) )),
% 1.68/1.42 inference(superposition,[status(thm)],[f26,f27])).
% 1.68/1.42 thf(f27,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X1 : X0] : (((in @ X0 @ X1 @ univ @ X0) = $true)) )),
% 1.68/1.42 inference(cnf_transformation,[status(thm)],[f12])).
% 1.68/1.42 thf(f12,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0] : ((in @ X0 @ X1 @ univ @ X0) = $true)),
% 1.68/1.42 inference(fool_elimination,[status(thm)],[f11])).
% 1.68/1.42 thf(f11,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0] : (in @ X0 @ X1 @ univ @ X0)),
% 1.68/1.42 inference(rectify,[status(thm)],[f2])).
% 1.68/1.42 thf(f2,axiom,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0] : (in @ X0 @ X1 @ univ @ X0)),
% 1.68/1.42 file('/export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2THF_13143.p','pred_set/IN_UNIV_')).
% 1.68/1.42 thf(f26,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X2 : X0,X3 : X0 > $o,X1 : X0] : (((in @ X0 @ X1 @ X3) != $true) | ((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $true)) )),
% 1.68/1.42 inference(cnf_transformation,[status(thm)],[f19])).
% 1.68/1.42 thf(f19,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $true) | (((in @ X0 @ X1 @ X3) != $true) & (X1 != X2))) & (((in @ X0 @ X1 @ X3) = $true) | (X1 = X2) | ((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) != $true)))),
% 1.68/1.42 inference(flattening,[status(thm)],[f18])).
% 1.68/1.42 thf(f18,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $true) | (((in @ X0 @ X1 @ X3) != $true) & (X1 != X2))) & ((((in @ X0 @ X1 @ X3) = $true) | (X1 = X2)) | ((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) != $true)))),
% 1.68/1.42 inference(nnf_transformation,[status(thm)],[f8])).
% 1.68/1.42 thf(f8,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : (((in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $true) <=> (((in @ X0 @ X1 @ X3) = $true) | (X1 = X2)))),
% 1.68/1.42 inference(fool_elimination,[status(thm)],[f7])).
% 1.68/1.42 thf(f7,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((in @ X0 @ X1 @ X3) | (X1 = X2) = (in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)))),
% 1.68/1.42 inference(rectify,[status(thm)],[f1])).
% 1.68/1.42 thf(f1,axiom,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : X0 > $o] : ((in @ X0 @ X1 @ X3) | (X1 = X2) = (in @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)))),
% 1.68/1.42 file('/export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2THF_13143.p','pred_set/IN_INSERT_')).
% 1.68/1.42 thf(f128,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X1 : X0 > $o] : (((in @ X0 @ (sK0 @ X0 @ X1 @ univ @ X0) @ X1) = $false) | (univ @ X0 = X1)) )),
% 1.68/1.42 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.68/1.42 thf(f100,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X1 : X0 > $o] : (((in @ X0 @ (sK0 @ X0 @ X1 @ univ @ X0) @ X1) = $false) | ($true = $false) | (univ @ X0 = X1)) )),
% 1.68/1.42 inference(superposition,[status(thm)],[f32,f27])).
% 1.68/1.42 thf(f32,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : (((in @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2) = $false) | ((in @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1) = $false) | (X1 = X2)) )),
% 1.68/1.42 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.68/1.42 thf(f22,plain,(
% 1.68/1.42 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((X1 = X2) | ((in @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1) != (in @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2))) )),
% 1.68/1.42 inference(cnf_transformation,[status(thm)],[f17])).
% 1.68/1.42 thf(f17,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : ((in @ X0 @ X3 @ X1) = (in @ X0 @ X3 @ X2)) | (X1 != X2)) & ((X1 = X2) | ((in @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1) != (in @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2))))),
% 1.68/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f15,f16])).
% 1.68/1.42 thf(f16,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X4 : X0] : ((in @ X0 @ X4 @ X1) != (in @ X0 @ X4 @ X2)) => ((in @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1) != (in @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2)))),
% 1.68/1.42 introduced(definition,[],[choice_axiom])).
% 1.68/1.42 thf(f15,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : ((in @ X0 @ X3 @ X1) = (in @ X0 @ X3 @ X2)) | (X1 != X2)) & ((X1 = X2) | ? [X4 : X0] : ((in @ X0 @ X4 @ X1) != (in @ X0 @ X4 @ X2))))),
% 1.68/1.42 inference(rectify,[status(thm)],[f14])).
% 1.68/1.42 thf(f14,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : ((in @ X0 @ X3 @ X1) = (in @ X0 @ X3 @ X2)) | (X1 != X2)) & ((X1 = X2) | ? [X3 : X0] : ((in @ X0 @ X3 @ X1) != (in @ X0 @ X3 @ X2))))),
% 1.68/1.42 inference(nnf_transformation,[status(thm)],[f10])).
% 1.68/1.42 thf(f10,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : ((in @ X0 @ X3 @ X1) = (in @ X0 @ X3 @ X2)) <=> (X1 = X2))),
% 1.68/1.42 inference(fool_elimination,[status(thm)],[f9])).
% 1.68/1.42 thf(f9,plain,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((X1 = X2) = ! [X3 : X0] : ((in @ X0 @ X3 @ X1) = (in @ X0 @ X3 @ X2)))),
% 1.68/1.42 inference(rectify,[status(thm)],[f3])).
% 1.68/1.42 thf(f3,axiom,(
% 1.68/1.42 ! [X0 : $tType,X3 : X0 > $o,X4 : X0 > $o] : ((X3 = X4) = ! [X1 : X0] : ((in @ X0 @ X1 @ X3) = (in @ X0 @ X1 @ X4)))),
% 1.68/1.42 file('/export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2THF_13143.p','pred_set/EXTENSION_')).
% 1.68/1.42 thf(f214,plain,(
% 1.68/1.42 ( ! [X0 : sK1] : (((insert @ sK1 @ X0 @ univ @ sK1) != univ @ sK1)) )),
% 1.68/1.42 inference(forward_demodulation,[status(thm)],[f201,f154])).
% 1.68/1.42 thf(f201,plain,(
% 1.68/1.42 ( ! [X0 : sK1] : (((insert @ sK1 @ X0 @ univ @ sK1) != (insert @ sK1 @ sK2 @ univ @ sK1))) )),
% 1.68/1.42 inference(trivial_inequality_removal,[status(thm)],[f194])).
% 1.68/1.42 thf(f194,plain,(
% 1.68/1.42 ( ! [X0 : sK1] : (((insert @ sK1 @ X0 @ univ @ sK1) != (insert @ sK1 @ sK2 @ univ @ sK1)) | (univ @ sK1 != univ @ sK1)) )),
% 1.68/1.42 inference(constrained_superposition,[status(thm)],[f28,f154])).
% 1.68/1.42 thf(f28,plain,(
% 1.68/1.42 (univ @ sK1 != (insert @ sK1 @ sK2 @ univ @ sK1))),
% 1.68/1.42 inference(cnf_transformation,[status(thm)],[f21])).
% 1.68/1.42 thf(f21,plain,(
% 1.68/1.42 (univ @ sK1 != (insert @ sK1 @ sK2 @ univ @ sK1))),
% 1.68/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f13,f20])).
% 1.68/1.42 thf(f20,plain,(
% 1.68/1.42 ? [X0 : $tType,X1 : X0] : (univ @ X0 != (insert @ X0 @ X1 @ univ @ X0)) => (univ @ sK1 != (insert @ sK1 @ sK2 @ univ @ sK1))),
% 1.68/1.42 introduced(definition,[],[choice_axiom])).
% 1.68/1.42 thf(f13,plain,(
% 1.68/1.42 ? [X0 : $tType,X1 : X0] : (univ @ X0 != (insert @ X0 @ X1 @ univ @ X0))),
% 1.68/1.42 inference(ennf_transformation,[status(thm)],[f5])).
% 1.68/1.42 thf(f5,negated_conjecture,(
% 1.68/1.42 ~! [X0 : $tType,X1 : X0] : (univ @ X0 = (insert @ X0 @ X1 @ univ @ X0))),
% 1.68/1.42 inference(negated_conjecture,[status(cth)],[f4])).
% 1.68/1.42 thf(f4,conjecture,(
% 1.68/1.42 ! [X0 : $tType,X1 : X0] : (univ @ X0 = (insert @ X0 @ X1 @ univ @ X0))),
% 1.68/1.42 file('/export/starexec/sandbox2/tmp/tmp.PH0ggzuWp3/DTF2THF_13143.p','pred_set/INSERT_UNIV_')).
% 1.68/1.42 % SZS output end Proof for DTF2THF_13143
% 1.68/1.42 % (13260)------------------------------
% 1.68/1.42 % (13260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.68/1.42 % (13260)Termination reason: Refutation
% 1.68/1.42
% 1.68/1.42 % (13260)Memory used [KB]: 5756
% 1.68/1.42 % (13260)Time elapsed: 0.051 s
% 1.68/1.42 % (13260)Instructions burned: 75 (million)
% 1.68/1.42 % (13260)------------------------------
% 1.68/1.42 % (13260)------------------------------
% 1.68/1.42 % (13239)Success in time 0.084 s
%------------------------------------------------------------------------------