%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV604^1 : 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 : n009.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 1.67s 1.31s
% Output : Refutation 1.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV604^1 : 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
% 0.15/0.33 % Computer : n009.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 05:20:10 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEV604^1 : TPTP v9.3.0. Released v9.3.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Set vimage singleton
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English :
% 0.29/0.46
% 0.29/0.46 % Refs :
% 0.29/0.46 % Source : [TPTP]
% 0.29/0.46 % Names : 001 [TPTP]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : ? v9.3.0
% 0.29/0.46 % Syntax : Number of formulae : 15 ( 4 unt; 11 typ; 0 def)
% 0.29/0.46 % Number of atoms : 11 ( 5 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 1 ( 2 avg)
% 0.29/0.46 % Number of connectives : 47 ( 1 ~; 1 |; 0 &; 45 @)
% 0.29/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 7 ( 5 avg)
% 0.29/0.46 % Number of types : 3 ( 2 usr)
% 0.29/0.46 % Number of type decls : 11 ( 4 !>P; 0 !>D)
% 0.29/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 10 ( 9 usr; 2 con; 0-4 aty)
% 0.29/0.46 % Number of variables : 16 ( 0 ^; 11 !; 0 ?; 16 :)
% 0.29/0.46 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.29/0.46 % SPC : TH1_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : Originally from Isabelle 2015
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(ty_set,type,
% 0.29/0.46 set: $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_itself,type,
% 0.29/0.46 itself: $tType > $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_a,type,
% 0.29/0.46 a: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(ty_b,type,
% 0.29/0.46 b: $tType ).
% 0.29/0.46
% 0.29/0.46 thf(c_bot,type,
% 0.29/0.46 bot:
% 0.29/0.46 !>[A: $tType] : A ).
% 0.29/0.46
% 0.29/0.46 %thf(c_type,type,(
% 0.29/0.46 % !>[A: $tType] :
% 0.29/0.46 % ( itself @ A ) )).
% 0.29/0.46
% 0.29/0.46 thf(c_insert,type,
% 0.29/0.46 insert:
% 0.29/0.46 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(c_vimage,type,
% 0.29/0.46 vimage:
% 0.29/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(c_member,type,
% 0.29/0.46 member:
% 0.29/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.29/0.46
% 0.29/0.46 thf(c_a,type,
% 0.29/0.46 a2: a ).
% 0.29/0.46
% 0.29/0.46 thf(c_b,type,
% 0.29/0.46 b2: b ).
% 0.29/0.46
% 0.29/0.46 thf(c_f,type,
% 0.29/0.46 f: a > b ).
% 0.29/0.46
% 0.29/0.46 thf(vimage_eq,axiom,
% 0.29/0.46 ! [A: $tType,B: $tType,A2: A,F: A > B,B2: set @ B] :
% 0.29/0.46 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B2 ) )
% 0.29/0.46 = ( member @ B @ ( F @ A2 ) @ B2 ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(empty_iff,axiom,
% 0.29/0.46 ! [A: $tType,C: A] :
% 0.29/0.46 ~ ( member @ A @ C @ ( bot @ ( set @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(insert_iff,axiom,
% 0.29/0.46 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 0.29/0.46 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 0.29/0.46 = ( ( A2 = B3 )
% 0.29/0.46 | ( member @ A @ A2 @ A3 ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(vimage_singleton_eq,conjecture,
% 0.29/0.46 ( ( member @ a @ a2 @ ( vimage @ a @ b @ f @ ( insert @ b @ b2 @ ( bot @ ( set @ b ) ) ) ) )
% 0.29/0.46 = ( ( f @ a2 )
% 0.29/0.46 = b2 ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 1.51/1.28 ---- Embedded in THF ---
% 1.51/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.28 %%% Generated on Tue May 05 05:20:11 EDT 2026
% 1.51/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.28 %%% Logic specification used:
% 1.51/1.28 %%% thf(spec, logic, $$dhol).
% 1.51/1.28
% 1.51/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.l0jGkukq9r/DTF2DTF12418.p
% 1.51/1.28 thf(ty_set, type, set: ($tType > $tType)).
% 1.51/1.28 thf(ty_itself, type, itself: ($tType > $tType)).
% 1.51/1.28 thf(ty_a, type, a: $tType).
% 1.51/1.28 thf(ty_b, type, b: $tType).
% 1.51/1.28 thf(c_bot, type, bot: (!> [A:$tType]: (A))).
% 1.51/1.28 thf(c_insert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 1.51/1.28 thf(c_vimage, type, vimage: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ B) > (set @ A)))))).
% 1.51/1.28 thf(c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 1.51/1.28 thf(c_a, type, a2: a).
% 1.51/1.28 thf(c_b, type, b2: b).
% 1.51/1.28 thf(c_f, type, f: (a > b)).
% 1.51/1.28 thf(vimage_eq, axiom, (! [A:$tType,B:$tType,A2:A,F:(A > B),B2:(set @ B)]: (((((member @ A) @ A2) @ ((((vimage @ A) @ B) @ F) @ B2)) = (((member @ B) @ (F @ A2)) @ B2))))).
% 1.51/1.28 thf(empty_iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot @ (set @ A)))))))).
% 1.51/1.28 thf(insert_iff, axiom, (! [A:$tType,A2:A,B3:A,A3:(set @ A)]: (((((member @ A) @ A2) @ (((insert @ A) @ B3) @ A3)) = ((A2 = B3) | (((member @ A) @ A2) @ A3)))))).
% 1.51/1.28 thf(vimage_singleton_eq, conjecture, ((((member @ a) @ a2) @ ((((vimage @ a) @ b) @ f) @ (((insert @ b) @ b2) @ (bot @ (set @ b))))) = ((f @ a2) = b2))).
% 1.51/1.28 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.l0jGkukq9r/DTF2DTF12418.p
% 1.51/1.28 ------------------------
% 1.51/1.29 ---- Cleaned THF ---
% 1.51/1.29 thf(ty_set,type,
% 1.51/1.29 set: $tType > $tType ).
% 1.51/1.29
% 1.51/1.29 thf(ty_itself,type,
% 1.51/1.29 itself: $tType > $tType ).
% 1.51/1.29
% 1.51/1.29 thf(ty_a,type,
% 1.51/1.29 a: $tType ).
% 1.51/1.29
% 1.51/1.29 thf(ty_b,type,
% 1.51/1.29 b: $tType ).
% 1.51/1.29
% 1.51/1.29 thf(c_bot,type,
% 1.51/1.29 bot:
% 1.51/1.29 !>[A: $tType] : A ).
% 1.51/1.29
% 1.51/1.29 thf(c_insert,type,
% 1.51/1.29 insert:
% 1.51/1.29 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 1.51/1.29
% 1.51/1.29 thf(c_vimage,type,
% 1.51/1.29 vimage:
% 1.51/1.29 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ B ) > ( set @ A ) ) ).
% 1.51/1.29
% 1.51/1.29 thf(c_member,type,
% 1.51/1.29 member:
% 1.51/1.29 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 1.51/1.29
% 1.51/1.29 thf(c_a,type,
% 1.51/1.29 a2: a ).
% 1.51/1.29
% 1.51/1.29 thf(c_b,type,
% 1.51/1.29 b2: b ).
% 1.51/1.29
% 1.51/1.29 thf(c_f,type,
% 1.51/1.29 f: a > b ).
% 1.51/1.29
% 1.51/1.29 thf(vimage_eq,axiom,
% 1.51/1.29 ! [A: $tType,B: $tType,A2: A,F: A > B,B2: set @ B] :
% 1.51/1.29 ( ( member @ A @ A2 @ ( vimage @ A @ B @ F @ B2 ) )
% 1.51/1.29 = ( member @ B @ ( F @ A2 ) @ B2 ) ) ).
% 1.51/1.29
% 1.51/1.29 thf(empty_iff,axiom,
% 1.51/1.29 ! [A: $tType,C: A] :
% 1.51/1.29 ~ ( member @ A @ C @ ( bot @ ( set @ A ) ) ) ).
% 1.51/1.29
% 1.51/1.29 thf(insert_iff,axiom,
% 1.51/1.29 ! [A: $tType,A2: A,B3: A,A3: set @ A] :
% 1.51/1.29 ( ( member @ A @ A2 @ ( insert @ A @ B3 @ A3 ) )
% 1.51/1.29 = ( ( A2 = B3 )
% 1.51/1.29 | ( member @ A @ A2 @ A3 ) ) ) ).
% 1.51/1.29
% 1.51/1.29 thf(vimage_singleton_eq,conjecture,
% 1.51/1.29 ( ( member @ a @ a2 @ ( vimage @ a @ b @ f @ ( insert @ b @ b2 @ ( bot @ ( set @ b ) ) ) ) )
% 1.51/1.29 = ( ( f @ a2 )
% 1.51/1.29 = b2 ) ) ).
% 1.51/1.29 ------------------------
% 1.67/1.31 % (12517)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_12418 for (2999ds/27Mi)
% 1.67/1.31 % (12519)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_12418 for (2999ds/2Mi)
% 1.67/1.31 % (12519)Instruction limit reached!
% 1.67/1.31 % (12519)------------------------------
% 1.67/1.31 % (12519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (12519)Termination reason: Unknown
% 1.67/1.31 % (12519)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (12519)Memory used [KB]: 5500
% 1.67/1.31 % (12519)Time elapsed: 0.002 s
% 1.67/1.31 % (12519)Instructions burned: 3 (million)
% 1.67/1.31 % (12519)------------------------------
% 1.67/1.31 % (12519)------------------------------
% 1.67/1.31 % (12518)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12418 for (2999ds/2Mi)
% 1.67/1.31 % (12517)First to succeed.
% 1.67/1.31 % (12518)Instruction limit reached!
% 1.67/1.31 % (12518)------------------------------
% 1.67/1.31 % (12518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.31 % (12518)Termination reason: Unknown
% 1.67/1.31 % (12518)Termination phase: Saturation
% 1.67/1.31
% 1.67/1.31 % (12518)Memory used [KB]: 895
% 1.67/1.31 % (12518)Time elapsed: 0.003 s
% 1.67/1.31 % (12518)Instructions burned: 2 (million)
% 1.67/1.31 % (12518)------------------------------
% 1.67/1.31 % (12518)------------------------------
% 1.67/1.31 % (12517)Refutation found. Thanks to Tanya!
% 1.67/1.31 % SZS status Theorem for DTF2THF_12418
% 1.67/1.31 % SZS output start Proof for DTF2THF_12418
% 1.67/1.31 thf(type_def_5, type, set: ($tType) > $tType).
% 1.67/1.31 thf(type_def_7, type, a: $tType).
% 1.67/1.31 thf(type_def_8, type, b: $tType).
% 1.67/1.31 thf(func_def_0, type, set: ($tType) > $tType).
% 1.67/1.31 thf(func_def_1, type, itself: ($tType) > $tType).
% 1.67/1.31 thf(func_def_2, type, a: $tType).
% 1.67/1.31 thf(func_def_3, type, b: $tType).
% 1.67/1.31 thf(func_def_4, type, bot: !>[X0: $tType]:(X0)).
% 1.67/1.31 thf(func_def_5, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 1.67/1.31 thf(func_def_6, type, vimage: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X1 > set @ X0)).
% 1.67/1.31 thf(func_def_7, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 1.67/1.31 thf(func_def_8, type, a2: a).
% 1.67/1.31 thf(func_def_9, type, b2: b).
% 1.67/1.31 thf(func_def_10, type, f: a > b).
% 1.67/1.31 thf(func_def_12, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.67/1.31 thf(func_def_18, type, ph1: !>[X0: $tType]:(X0)).
% 1.67/1.31 thf(f121,plain,(
% 1.67/1.31 $false),
% 1.67/1.31 inference(avatar_sat_refutation,[status(thm)],[f39,f44,f80,f114,f119])).
% 1.67/1.31 thf(f119,plain,(
% 1.67/1.31 ~spl0_4),
% 1.67/1.31 inference(avatar_contradiction_clause,[status(thm)],[f118])).
% 1.67/1.31 thf(f118,plain,(
% 1.67/1.31 $false | ~spl0_4),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f116])).
% 1.67/1.31 thf(f116,plain,(
% 1.67/1.31 ($true != $true) | ~spl0_4),
% 1.67/1.31 inference(superposition,[status(thm)],[f14,f112])).
% 1.67/1.31 thf(f112,plain,(
% 1.67/1.31 ((member @ b @ (f @ a2) @ bot @ set @ b) = $true) | ~spl0_4),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f110])).
% 1.67/1.31 thf(f110,definition,(
% 1.67/1.31 spl0_4 <=> ((member @ b @ (f @ a2) @ bot @ set @ b) = $true)),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.67/1.31 thf(f14,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X1 : X0] : (((member @ X0 @ X1 @ bot @ set @ X0) != $true)) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f12])).
% 1.67/1.31 thf(f12,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0] : ((member @ X0 @ X1 @ bot @ set @ X0) != $true)),
% 1.67/1.31 inference(flattening,[status(thm)],[f10])).
% 1.67/1.31 thf(f10,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0] : ~((member @ X0 @ X1 @ bot @ set @ X0) = $true)),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f9])).
% 1.67/1.31 thf(f9,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0] : ~(member @ X0 @ X1 @ bot @ set @ X0)),
% 1.67/1.31 inference(rectify,[status(thm)],[f2])).
% 1.67/1.31 thf(f2,axiom,(
% 1.67/1.31 ! [X0 : $tType,X5 : X0] : ~(member @ X0 @ X5 @ bot @ set @ X0)),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.l0jGkukq9r/DTF2THF_12418.p',empty_iff)).
% 1.67/1.31 thf(f114,plain,(
% 1.67/1.31 spl0_2 | spl0_4 | ~spl0_1),
% 1.67/1.31 inference(avatar_split_clause,[status(thm)],[f106,f32,f110,f36])).
% 1.67/1.31 thf(f36,definition,(
% 1.67/1.31 spl0_2 <=> (b2 = (f @ a2))),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.67/1.31 thf(f32,definition,(
% 1.67/1.31 spl0_1 <=> ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = $true)),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.67/1.31 thf(f106,plain,(
% 1.67/1.31 (b2 = (f @ a2)) | ((member @ b @ (f @ a2) @ bot @ set @ b) = $true) | ~spl0_1),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.67/1.31 thf(f104,plain,(
% 1.67/1.31 ($false = $true) | (b2 = (f @ a2)) | ((member @ b @ (f @ a2) @ bot @ set @ b) = $true) | ~spl0_1),
% 1.67/1.31 inference(superposition,[status(thm)],[f21,f97])).
% 1.67/1.31 thf(f97,plain,(
% 1.67/1.31 ($true = (member @ b @ (f @ a2) @ (insert @ b @ b2 @ bot @ set @ b))) | ~spl0_1),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.67/1.31 thf(f93,plain,(
% 1.67/1.31 ($true = (member @ b @ (f @ a2) @ (insert @ b @ b2 @ bot @ set @ b))) | ($false = $true) | ~spl0_1),
% 1.67/1.31 inference(superposition,[status(thm)],[f26,f34])).
% 1.67/1.31 thf(f34,plain,(
% 1.67/1.31 ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = $true) | ~spl0_1),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.67/1.31 thf(f26,plain,(
% 1.67/1.31 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0 > X1,X4 : set @ X1] : (((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4)) = $false) | ((member @ X1 @ (X3 @ X2) @ X4) = $true)) )),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.67/1.31 thf(f16,plain,(
% 1.67/1.31 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0 > X1,X4 : set @ X1] : (((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4)) = (member @ X1 @ (X3 @ X2) @ X4))) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f1])).
% 1.67/1.31 thf(f1,axiom,(
% 1.67/1.31 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X0 > X1,X4 : set @ X1] : ((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4)) = (member @ X1 @ (X3 @ X2) @ X4))),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.l0jGkukq9r/DTF2THF_12418.p',vimage_eq)).
% 1.67/1.31 thf(f21,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $false) | (X1 = X2) | ((member @ X0 @ X1 @ X3) = $true)) )),
% 1.67/1.31 inference(equality_proxy_clausification,[status(thm)],[f20])).
% 1.67/1.31 thf(f20,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (((member @ X0 @ X1 @ X3) = $true) | ((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $false) | ((X1 = X2) = $true)) )),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f19])).
% 1.67/1.31 thf(f19,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $false) | ($true = ((member @ X0 @ X1 @ X3) | (X1 = X2)))) )),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.67/1.31 thf(f17,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = ((member @ X0 @ X1 @ X3) | (X1 = X2)))) )),
% 1.67/1.31 inference(cnf_transformation,[status(thm)],[f8])).
% 1.67/1.31 thf(f8,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ X0] : ((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = ((member @ X0 @ X1 @ X3) | (X1 = X2)))),
% 1.67/1.31 inference(fool_elimination,[status(thm)],[f7])).
% 1.67/1.31 thf(f7,plain,(
% 1.67/1.31 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : set @ X0] : ((X1 = X2) | (member @ X0 @ X1 @ X3) = (member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)))),
% 1.67/1.31 inference(rectify,[status(thm)],[f3])).
% 1.67/1.31 thf(f3,axiom,(
% 1.67/1.31 ! [X0 : $tType,X2 : X0,X6 : X0,X7 : set @ X0] : ((X2 = X6) | (member @ X0 @ X2 @ X7) = (member @ X0 @ X2 @ (insert @ X0 @ X6 @ X7)))),
% 1.67/1.31 file('/export/starexec/sandbox2/tmp/tmp.l0jGkukq9r/DTF2THF_12418.p',insert_iff)).
% 1.67/1.31 thf(f80,plain,(
% 1.67/1.31 ~spl0_2 | ~spl0_3),
% 1.67/1.31 inference(avatar_contradiction_clause,[status(thm)],[f79])).
% 1.67/1.31 thf(f79,plain,(
% 1.67/1.31 $false | (~spl0_2 | ~spl0_3)),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f73])).
% 1.67/1.31 thf(f73,plain,(
% 1.67/1.31 (b2 != b2) | ($false = $true) | (~spl0_2 | ~spl0_3)),
% 1.67/1.31 inference(superposition,[status(thm)],[f70,f24])).
% 1.67/1.31 thf(f24,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $true) | (X1 != X2)) )),
% 1.67/1.31 inference(equality_proxy_clausification,[status(thm)],[f22])).
% 1.67/1.31 thf(f22,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (($false = (X1 = X2)) | ((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $true)) )),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f18])).
% 1.67/1.31 thf(f18,plain,(
% 1.67/1.31 ( ! [X0 : $tType,X2 : X0,X3 : set @ X0,X1 : X0] : (((member @ X0 @ X1 @ (insert @ X0 @ X2 @ X3)) = $true) | ($false = ((member @ X0 @ X1 @ X3) | (X1 = X2)))) )),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.67/1.31 thf(f70,plain,(
% 1.67/1.31 ($false = (member @ b @ b2 @ (insert @ b @ b2 @ bot @ set @ b))) | (~spl0_2 | ~spl0_3)),
% 1.67/1.31 inference(forward_demodulation,[status(thm)],[f68,f38])).
% 1.67/1.31 thf(f38,plain,(
% 1.67/1.31 (b2 = (f @ a2)) | ~spl0_2),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.67/1.31 thf(f68,plain,(
% 1.67/1.31 ($false = (member @ b @ (f @ a2) @ (insert @ b @ b2 @ bot @ set @ b))) | ~spl0_3),
% 1.67/1.31 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.67/1.31 thf(f66,plain,(
% 1.67/1.31 ($false = (member @ b @ (f @ a2) @ (insert @ b @ b2 @ bot @ set @ b))) | ($false = $true) | ~spl0_3),
% 1.67/1.31 inference(superposition,[status(thm)],[f43,f25])).
% 1.67/1.31 thf(f25,plain,(
% 1.67/1.31 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X0 > X1,X4 : set @ X1] : (((member @ X0 @ X2 @ (vimage @ X0 @ X1 @ X3 @ X4)) = $true) | ((member @ X1 @ (X3 @ X2) @ X4) = $false)) )),
% 1.67/1.31 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.67/1.31 thf(f43,plain,(
% 1.67/1.31 ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = $false) | ~spl0_3),
% 1.67/1.31 inference(avatar_component_clause,[status(thm)],[f41])).
% 1.67/1.31 thf(f41,definition,(
% 1.67/1.31 spl0_3 <=> ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = $false)),
% 1.67/1.31 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.67/1.32 thf(f44,plain,(
% 1.67/1.32 ~spl0_2 | spl0_3),
% 1.67/1.32 inference(avatar_split_clause,[status(thm)],[f29,f41,f36])).
% 1.67/1.32 thf(f29,plain,(
% 1.67/1.32 ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = $false) | (b2 != (f @ a2))),
% 1.67/1.32 inference(equality_proxy_clausification,[status(thm)],[f28])).
% 1.67/1.32 thf(f28,plain,(
% 1.67/1.32 ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = $false) | ((b2 = (f @ a2)) = $false)),
% 1.67/1.32 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.67/1.32 thf(f15,plain,(
% 1.67/1.32 ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) != (b2 = (f @ a2)))),
% 1.67/1.32 inference(cnf_transformation,[status(thm)],[f13])).
% 1.67/1.32 thf(f13,plain,(
% 1.67/1.32 ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) != (b2 = (f @ a2)))),
% 1.67/1.32 inference(flattening,[status(thm)],[f11])).
% 1.67/1.32 thf(f11,plain,(
% 1.67/1.32 ~((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = (b2 = (f @ a2)))),
% 1.67/1.32 inference(fool_elimination,[status(thm)],[f5])).
% 1.67/1.32 thf(f5,negated_conjecture,(
% 1.67/1.32 ~((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = (b2 = (f @ a2)))),
% 1.67/1.32 inference(negated_conjecture,[status(cth)],[f4])).
% 1.67/1.32 thf(f4,conjecture,(
% 1.67/1.32 ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = (b2 = (f @ a2)))),
% 1.67/1.32 file('/export/starexec/sandbox2/tmp/tmp.l0jGkukq9r/DTF2THF_12418.p',vimage_singleton_eq)).
% 1.67/1.32 thf(f39,plain,(
% 1.67/1.32 spl0_1 | spl0_2),
% 1.67/1.32 inference(avatar_split_clause,[status(thm)],[f30,f36,f32])).
% 1.67/1.32 thf(f30,plain,(
% 1.67/1.32 ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = $true) | (b2 = (f @ a2))),
% 1.67/1.32 inference(equality_proxy_clausification,[status(thm)],[f27])).
% 1.67/1.32 thf(f27,plain,(
% 1.67/1.32 ((b2 = (f @ a2)) = $true) | ((member @ a @ a2 @ (vimage @ a @ b @ f @ (insert @ b @ b2 @ bot @ set @ b))) = $true)),
% 1.67/1.32 inference(binary_proxy_clausification,[status(thm)],[f15])).
% 1.67/1.32 % SZS output end Proof for DTF2THF_12418
% 1.67/1.32 % (12517)------------------------------
% 1.67/1.32 % (12517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.32 % (12517)Termination reason: Refutation
% 1.67/1.32
% 1.67/1.32 % (12517)Memory used [KB]: 5628
% 1.67/1.32 % (12517)Time elapsed: 0.008 s
% 1.67/1.32 % (12517)Instructions burned: 15 (million)
% 1.67/1.32 % (12517)------------------------------
% 1.67/1.32 % (12517)------------------------------
% 1.67/1.32 % (12514)Success in time 0.016 s
%------------------------------------------------------------------------------