%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT320^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 08:45:27 AM UTC 2026
% Result : Theorem 1.15s 1.04s
% Output : Refutation 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : DAT320^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.26 % Computer : n012.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue Feb 24 06:14:30 EST 2026
% 0.07/0.26 % CPUTime :
% 0.07/0.26 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 ---- Original DTF file ---
% 0.15/0.33 thf(spec,logic,$$dhol).
% 0.15/0.33 %------------------------------------------------------------------------------
% 0.15/0.33 % File : DAT320^1 : TPTP v9.2.1. Released v7.0.0.
% 0.15/0.33 % Domain : Analysis
% 0.15/0.33 % Problem : MEM_APPEND_DECOMPOSE
% 0.15/0.33 % Version : Especial.
% 0.15/0.33 % English :
% 0.15/0.33
% 0.15/0.33 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.15/0.33 % Source : [Kal16]
% 0.15/0.33 % Names : MEM_APPEND_DECOMPOSE_.p [Kal16]
% 0.15/0.33
% 0.15/0.33 % Status : Theorem
% 0.15/0.33 % Rating : 0.00 v7.1.0
% 0.15/0.33 % Syntax : Number of formulae : 8 ( 4 unt; 4 typ; 0 def)
% 0.15/0.33 % Number of atoms : 15 ( 7 equ; 0 cnn)
% 0.15/0.33 % Maximal formula atoms : 1 ( 3 avg)
% 0.15/0.33 % Number of connectives : 61 ( 1 ~; 2 |; 1 &; 57 @)
% 0.15/0.33 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.15/0.33 % Maximal formula depth : 5 ( 5 avg)
% 0.15/0.33 % Number of types : 1 ( 0 usr)
% 0.15/0.33 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.15/0.33 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.15/0.33 % Number of variables : 21 ( 0 ^; 14 !; 4 ?; 21 :)
% 0.15/0.33 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.15/0.33 % SPC : TH1_THM_EQU_NAR
% 0.15/0.33
% 0.15/0.33 % Comments : Exported from core HOL Light.
% 0.15/0.33 %------------------------------------------------------------------------------
% 0.15/0.33 thf('thf_type_type/ind_types/list',type,
% 0.15/0.33 'type/ind_types/list': $tType > $tType ).
% 0.15/0.33
% 0.15/0.33 thf('thf_const_const/lists/MEM',type,
% 0.15/0.33 'const/lists/MEM':
% 0.15/0.33 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > $o ) ).
% 0.15/0.33
% 0.15/0.33 thf('thf_const_const/lists/APPEND',type,
% 0.15/0.33 'const/lists/APPEND':
% 0.15/0.33 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.15/0.33
% 0.15/0.33 thf('thf_const_const/ind_types/CONS',type,
% 0.15/0.33 'const/ind_types/CONS':
% 0.15/0.33 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.15/0.33
% 0.15/0.33 thf('thm/lists/MEM_APPEND_DECOMPOSE_LEFT_',axiom,
% 0.15/0.33 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.15/0.33 ( ( 'const/lists/MEM' @ A @ A0 @ A1 )
% 0.15/0.33 = ( ? [A2: 'type/ind_types/list' @ A,A3: 'type/ind_types/list' @ A] :
% 0.15/0.33 ( ~ ( 'const/lists/MEM' @ A @ A0 @ A2 )
% 0.15/0.33 & ( A1
% 0.15/0.33 = ( 'const/lists/APPEND' @ A @ A2 @ ( 'const/ind_types/CONS' @ A @ A0 @ A3 ) ) ) ) ) ) ).
% 0.15/0.33
% 0.15/0.33 thf('thm/lists/MEM_1',axiom,
% 0.15/0.33 ! [A: $tType,A0: A,A1: A,A2: 'type/ind_types/list' @ A] :
% 0.15/0.33 ( ( 'const/lists/MEM' @ A @ A1 @ ( 'const/ind_types/CONS' @ A @ A0 @ A2 ) )
% 0.15/0.33 = ( ( A1 = A0 )
% 0.15/0.33 | ( 'const/lists/MEM' @ A @ A1 @ A2 ) ) ) ).
% 0.15/0.33
% 0.15/0.33 thf('thm/lists/MEM_APPEND_',axiom,
% 0.15/0.33 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A,A2: 'type/ind_types/list' @ A] :
% 0.15/0.33 ( ( 'const/lists/MEM' @ A @ A0 @ ( 'const/lists/APPEND' @ A @ A1 @ A2 ) )
% 0.15/0.33 = ( ( 'const/lists/MEM' @ A @ A0 @ A1 )
% 0.15/0.33 | ( 'const/lists/MEM' @ A @ A0 @ A2 ) ) ) ).
% 0.15/0.33
% 0.15/0.33 thf('thm/lists/MEM_APPEND_DECOMPOSE_',conjecture,
% 0.15/0.33 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.15/0.33 ( ( 'const/lists/MEM' @ A @ A0 @ A1 )
% 0.15/0.33 = ( ? [A2: 'type/ind_types/list' @ A,A3: 'type/ind_types/list' @ A] :
% 0.15/0.33 ( A1
% 0.15/0.33 = ( 'const/lists/APPEND' @ A @ A2 @ ( 'const/ind_types/CONS' @ A @ A0 @ A3 ) ) ) ) ) ).
% 0.15/0.33
% 0.15/0.33 %------------------------------------------------------------------------------
% 0.15/0.33 ------------------------
% 1.15/1.01 ---- Embedded in THF ---
% 1.15/1.01 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.15/1.01 %%% Generated on Tue Feb 24 06:14:31 EST 2026
% 1.15/1.01 %%% using '$$dhol' embedding, version 1.3.0.
% 1.15/1.01 %%% Logic specification used:
% 1.15/1.01 %%% thf(spec, logic, $$dhol).
% 1.15/1.01
% 1.15/1.01 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rKUjhMko3l/DTF2DTF10047.p
% 1.15/1.01 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.15/1.01 thf('thf_const_const/lists/MEM', type, 'const/lists/MEM': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > $o))))).
% 1.15/1.01 thf('thf_const_const/lists/APPEND', type, 'const/lists/APPEND': (!> [A:$tType]: ((('type/ind_types/list' @ A) > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.15/1.01 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.15/1.01 thf('thm/lists/MEM_APPEND_DECOMPOSE_LEFT_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: ((((('const/lists/MEM' @ A) @ A0) @ A1) = (? [A2:('type/ind_types/list' @ A),A3:('type/ind_types/list' @ A)]: (((~ (((('const/lists/MEM' @ A) @ A0) @ A2))) & (A1 = ((('const/lists/APPEND' @ A) @ A2) @ ((('const/ind_types/CONS' @ A) @ A0) @ A3)))))))))).
% 1.15/1.01 thf('thm/lists/MEM_1', axiom, (! [A:$tType,A0:A,A1:A,A2:('type/ind_types/list' @ A)]: ((((('const/lists/MEM' @ A) @ A1) @ ((('const/ind_types/CONS' @ A) @ A0) @ A2)) = ((A1 = A0) | ((('const/lists/MEM' @ A) @ A1) @ A2)))))).
% 1.15/1.01 thf('thm/lists/MEM_APPEND_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A),A2:('type/ind_types/list' @ A)]: ((((('const/lists/MEM' @ A) @ A0) @ ((('const/lists/APPEND' @ A) @ A1) @ A2)) = (((('const/lists/MEM' @ A) @ A0) @ A1) | ((('const/lists/MEM' @ A) @ A0) @ A2)))))).
% 1.15/1.01 thf('thm/lists/MEM_APPEND_DECOMPOSE_', conjecture, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: ((((('const/lists/MEM' @ A) @ A0) @ A1) = (? [A2:('type/ind_types/list' @ A),A3:('type/ind_types/list' @ A)]: ((A1 = ((('const/lists/APPEND' @ A) @ A2) @ ((('const/ind_types/CONS' @ A) @ A0) @ A3))))))))).
% 1.15/1.01 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rKUjhMko3l/DTF2DTF10047.p
% 1.15/1.01 ------------------------
% 1.15/1.02 ---- Cleaned THF ---
% 1.15/1.02 thf('thf_type_type/ind_types/list',type,
% 1.15/1.02 'type/ind_types/list': $tType > $tType ).
% 1.15/1.02
% 1.15/1.02 thf('thf_const_const/lists/MEM',type,
% 1.15/1.02 'const/lists/MEM':
% 1.15/1.02 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > $o ) ).
% 1.15/1.02
% 1.15/1.02 thf('thf_const_const/lists/APPEND',type,
% 1.15/1.02 'const/lists/APPEND':
% 1.15/1.02 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.15/1.02
% 1.15/1.02 thf('thf_const_const/ind_types/CONS',type,
% 1.15/1.02 'const/ind_types/CONS':
% 1.15/1.02 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.15/1.02
% 1.15/1.02 thf('thm/lists/MEM_APPEND_DECOMPOSE_LEFT_',axiom,
% 1.15/1.02 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.15/1.02 ( ( 'const/lists/MEM' @ A @ A0 @ A1 )
% 1.15/1.02 = ( ? [A2: 'type/ind_types/list' @ A,A3: 'type/ind_types/list' @ A] :
% 1.15/1.02 ( ~ ( 'const/lists/MEM' @ A @ A0 @ A2 )
% 1.15/1.02 & ( A1
% 1.15/1.02 = ( 'const/lists/APPEND' @ A @ A2 @ ( 'const/ind_types/CONS' @ A @ A0 @ A3 ) ) ) ) ) ) ).
% 1.15/1.02
% 1.15/1.02 thf('thm/lists/MEM_1',axiom,
% 1.15/1.02 ! [A: $tType,A0: A,A1: A,A2: 'type/ind_types/list' @ A] :
% 1.15/1.02 ( ( 'const/lists/MEM' @ A @ A1 @ ( 'const/ind_types/CONS' @ A @ A0 @ A2 ) )
% 1.15/1.02 = ( ( A1 = A0 )
% 1.15/1.02 | ( 'const/lists/MEM' @ A @ A1 @ A2 ) ) ) ).
% 1.15/1.02
% 1.15/1.02 thf('thm/lists/MEM_APPEND_',axiom,
% 1.15/1.02 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A,A2: 'type/ind_types/list' @ A] :
% 1.15/1.02 ( ( 'const/lists/MEM' @ A @ A0 @ ( 'const/lists/APPEND' @ A @ A1 @ A2 ) )
% 1.15/1.02 = ( ( 'const/lists/MEM' @ A @ A0 @ A1 )
% 1.15/1.02 | ( 'const/lists/MEM' @ A @ A0 @ A2 ) ) ) ).
% 1.15/1.02
% 1.15/1.02 thf('thm/lists/MEM_APPEND_DECOMPOSE_',conjecture,
% 1.15/1.02 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.15/1.02 ( ( 'const/lists/MEM' @ A @ A0 @ A1 )
% 1.15/1.02 = ( ? [A2: 'type/ind_types/list' @ A,A3: 'type/ind_types/list' @ A] :
% 1.15/1.02 ( A1
% 1.15/1.02 = ( 'const/lists/APPEND' @ A @ A2 @ ( 'const/ind_types/CONS' @ A @ A0 @ A3 ) ) ) ) ) ).
% 1.15/1.02 ------------------------
% 1.15/1.03 % (10325)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10047 for (3000ds/183Mi)
% 1.15/1.03 % (10326)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_10047 for (3000ds/4Mi)
% 1.15/1.03 % (10327)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_10047 for (3000ds/27Mi)
% 1.15/1.03 % (10329)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_10047 for (3000ds/2Mi)
% 1.15/1.03 % (10330)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_10047 for (3000ds/275Mi)
% 1.15/1.03 % (10328)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10047 for (3000ds/2Mi)
% 1.15/1.03 % (10331)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10047 for (3000ds/18Mi)
% 1.15/1.03 % Exception at run slice level
% 1.15/1.03 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
% 1.15/1.03 % (10328)Instruction limit reached!
% 1.15/1.03 % (10328)------------------------------
% 1.15/1.03 % (10328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/1.03 % (10328)Termination reason: Unknown
% 1.15/1.03 % (10328)Termination phase: Saturation
% 1.15/1.03
% 1.15/1.03 % (10328)Memory used [KB]: 5500
% 1.15/1.03 % (10328)Time elapsed: 0.003 s
% 1.15/1.03 % (10328)Instructions burned: 4 (million)
% 1.15/1.03 % (10328)------------------------------
% 1.15/1.03 % (10328)------------------------------
% 1.15/1.04 % (10326)Instruction limit reached!
% 1.15/1.04 % (10326)------------------------------
% 1.15/1.04 % (10326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/1.04 % (10326)Termination reason: Unknown
% 1.15/1.04 % (10326)Termination phase: Saturation
% 1.15/1.04
% 1.15/1.04 % (10326)Memory used [KB]: 5500
% 1.15/1.04 % (10326)Time elapsed: 0.004 s
% 1.15/1.04 % (10326)Instructions burned: 7 (million)
% 1.15/1.04 % (10326)------------------------------
% 1.15/1.04 % (10326)------------------------------
% 1.15/1.04 % (10330)First to succeed.
% 1.15/1.04 % (10330)Refutation found. Thanks to Tanya!
% 1.15/1.04 % SZS status Theorem for DTF2THF_10047
% 1.15/1.04 % SZS output start Proof for DTF2THF_10047
% 1.15/1.04 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 1.15/1.04 thf(type_def_7, type, sK2: $tType).
% 1.15/1.04 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 1.15/1.04 thf(func_def_1, type, 'const/lists/MEM': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > $o)).
% 1.15/1.04 thf(func_def_2, type, 'const/lists/APPEND': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.15/1.04 thf(func_def_3, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.15/1.04 thf(func_def_7, type, sK0: !>[X0: $tType]:('type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0)).
% 1.15/1.04 thf(func_def_8, type, sK1: !>[X0: $tType]:('type/ind_types/list' @ X0 > X0 > 'type/ind_types/list' @ X0)).
% 1.15/1.04 thf(func_def_9, type, sK3: sK2).
% 1.15/1.04 thf(func_def_10, type, sK4: 'type/ind_types/list' @ sK2).
% 1.15/1.04 thf(func_def_11, type, sK5: 'type/ind_types/list' @ sK2).
% 1.15/1.04 thf(func_def_12, type, sK6: 'type/ind_types/list' @ sK2).
% 1.15/1.04 thf(f80,plain,(
% 1.15/1.04 $false),
% 1.15/1.04 inference(avatar_sat_refutation,[status(thm)],[f50,f54,f68,f79])).
% 1.15/1.04 thf(f79,plain,(
% 1.15/1.04 ~spl7_1 | spl7_2),
% 1.15/1.04 inference(avatar_contradiction_clause,[status(thm)],[f78])).
% 1.15/1.04 thf(f78,plain,(
% 1.15/1.04 $false | (~spl7_1 | spl7_2)),
% 1.15/1.04 inference(subsumption_resolution,[status(thm)],[f77,f75])).
% 1.15/1.04 thf(f75,plain,(
% 1.15/1.04 ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK5)) | (~spl7_1 | spl7_2)),
% 1.15/1.04 inference(subsumption_resolution,[status(thm)],[f71,f48])).
% 1.15/1.04 thf(f48,plain,(
% 1.15/1.04 ($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | spl7_2),
% 1.15/1.04 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.15/1.04 thf(f47,definition,(
% 1.15/1.04 spl7_2 <=> ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4))),
% 1.15/1.04 introduced(definition,[new_symbols(naming,[spl7_2])],[avatar_definition])).
% 1.15/1.04 thf(f71,plain,(
% 1.15/1.04 ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK5)) | ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ~spl7_1),
% 1.15/1.04 inference(superposition,[status(thm)],[f41,f45])).
% 1.15/1.04 thf(f45,plain,(
% 1.15/1.04 (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4) | ~spl7_1),
% 1.15/1.04 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.15/1.04 thf(f43,definition,(
% 1.15/1.04 spl7_1 <=> (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4)),
% 1.15/1.04 introduced(definition,[new_symbols(naming,[spl7_1])],[avatar_definition])).
% 1.15/1.04 thf(f41,plain,(
% 1.15/1.04 ( ! [X0 : $tType,X1 : X0,X6 : 'type/ind_types/list' @ X0,X5 : 'type/ind_types/list' @ X0] : (($true = ('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)))) | ($true = ('const/lists/MEM' @ X0 @ X1 @ X5))) )),
% 1.15/1.04 inference(equality_resolution,[status(thm)],[f35])).
% 1.15/1.04 thf(f35,plain,(
% 1.15/1.04 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0,X6 : 'type/ind_types/list' @ X0,X5 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ($true = ('const/lists/MEM' @ X0 @ X1 @ X5)) | (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) != X2)) )),
% 1.15/1.04 inference(cnf_transformation,[status(thm)],[f23])).
% 1.15/1.04 thf(f23,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((($true != ('const/lists/MEM' @ X0 @ X1 @ (sK0 @ X0 @ X2 @ X1))) & (('const/lists/APPEND' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1))) = X2)) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ! [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (($true = ('const/lists/MEM' @ X0 @ X1 @ X5)) | (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) != X2))))),
% 1.15/1.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f21,f22])).
% 1.15/1.04 thf(f22,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) != $true) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)) => (($true != ('const/lists/MEM' @ X0 @ X1 @ (sK0 @ X0 @ X2 @ X1))) & (('const/lists/APPEND' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1))) = X2)))),
% 1.15/1.04 introduced(definition,[],[choice_axiom])).
% 1.15/1.04 thf(f21,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) != $true) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ! [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (($true = ('const/lists/MEM' @ X0 @ X1 @ X5)) | (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) != X2))))),
% 1.15/1.04 inference(rectify,[status(thm)],[f20])).
% 1.15/1.04 thf(f20,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) != $true) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2))))),
% 1.15/1.04 inference(nnf_transformation,[status(thm)],[f14])).
% 1.15/1.04 thf(f14,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X3) != $true) & (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)) <=> (('const/lists/MEM' @ X0 @ X1 @ X2) = $true))),
% 1.15/1.04 inference(flattening,[status(thm)],[f10])).
% 1.15/1.04 thf(f10,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) <=> ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2) & ~(('const/lists/MEM' @ X0 @ X1 @ X3) = $true)))),
% 1.15/1.04 inference(fool_elimination,[status(thm)],[f9])).
% 1.15/1.04 thf(f9,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2) & ~('const/lists/MEM' @ X0 @ X1 @ X3)))),
% 1.15/1.04 inference(rectify,[status(thm)],[f1])).
% 1.15/1.04 thf(f1,axiom,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2) & ~('const/lists/MEM' @ X0 @ X1 @ X3)))),
% 1.15/1.04 file('/export/starexec/sandbox2/tmp/tmp.rKUjhMko3l/DTF2THF_10047.p','thm/lists/MEM_APPEND_DECOMPOSE_LEFT_')).
% 1.15/1.04 thf(f77,plain,(
% 1.15/1.04 ($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK5)) | (~spl7_1 | spl7_2)),
% 1.15/1.04 inference(trivial_inequality_removal,[status(thm)],[f76])).
% 1.15/1.04 thf(f76,plain,(
% 1.15/1.04 ($true != $true) | ($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK5)) | (~spl7_1 | spl7_2)),
% 1.15/1.04 inference(superposition,[status(thm)],[f48,f74])).
% 1.15/1.04 thf(f74,plain,(
% 1.15/1.04 ( ! [X0 : sK2] : (($true = ('const/lists/MEM' @ sK2 @ X0 @ sK4)) | ($true != ('const/lists/MEM' @ sK2 @ X0 @ sK5))) ) | ~spl7_1),
% 1.15/1.04 inference(superposition,[status(thm)],[f30,f45])).
% 1.15/1.04 thf(f30,plain,(
% 1.15/1.04 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)) )),
% 1.15/1.04 inference(cnf_transformation,[status(thm)],[f17])).
% 1.15/1.04 thf(f17,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true) | (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) != $true)) & ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true) | ((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) & (('const/lists/MEM' @ X0 @ X1 @ X3) != $true))))),
% 1.15/1.04 inference(flattening,[status(thm)],[f16])).
% 1.15/1.04 thf(f16,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true)) | (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) != $true)) & ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true) | ((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) & (('const/lists/MEM' @ X0 @ X1 @ X3) != $true))))),
% 1.15/1.04 inference(nnf_transformation,[status(thm)],[f8])).
% 1.15/1.04 thf(f8,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | (('const/lists/MEM' @ X0 @ X1 @ X3) = $true)) <=> (('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = $true))),
% 1.15/1.04 inference(fool_elimination,[status(thm)],[f7])).
% 1.15/1.04 thf(f7,plain,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) | ('const/lists/MEM' @ X0 @ X1 @ X3) = ('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)))),
% 1.15/1.04 inference(rectify,[status(thm)],[f3])).
% 1.15/1.04 thf(f3,axiom,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) | ('const/lists/MEM' @ X0 @ X1 @ X3) = ('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)))),
% 1.15/1.04 file('/export/starexec/sandbox2/tmp/tmp.rKUjhMko3l/DTF2THF_10047.p','thm/lists/MEM_APPEND_')).
% 1.15/1.04 thf(f68,plain,(
% 1.15/1.04 ~spl7_2 | ~spl7_3),
% 1.15/1.04 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.15/1.04 thf(f67,plain,(
% 1.15/1.04 $false | (~spl7_2 | ~spl7_3)),
% 1.15/1.04 inference(trivial_inequality_removal,[status(thm)],[f61])).
% 1.15/1.04 thf(f61,plain,(
% 1.15/1.04 ($true != $true) | (sK4 != sK4) | (~spl7_2 | ~spl7_3)),
% 1.15/1.04 inference(superposition,[status(thm)],[f55,f49])).
% 1.15/1.04 thf(f49,plain,(
% 1.15/1.04 ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ~spl7_2),
% 1.15/1.04 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.15/1.04 thf(f55,plain,(
% 1.15/1.04 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((('const/lists/MEM' @ sK2 @ sK3 @ X0) != $true) | (sK4 != X0)) ) | ~spl7_3),
% 1.15/1.04 inference(superposition,[status(thm)],[f53,f36])).
% 1.15/1.04 thf(f36,plain,(
% 1.15/1.04 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/APPEND' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK1 @ X0 @ X2 @ X1))) = X2) | (('const/lists/MEM' @ X0 @ X1 @ X2) != $true)) )),
% 1.15/1.04 inference(cnf_transformation,[status(thm)],[f23])).
% 1.15/1.04 thf(f53,plain,(
% 1.15/1.04 ( ! [X3 : 'type/ind_types/list' @ sK2,X4 : 'type/ind_types/list' @ sK2] : ((sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)))) ) | ~spl7_3),
% 1.15/1.04 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.15/1.04 thf(f52,definition,(
% 1.15/1.04 spl7_3 <=> ! [X4 : 'type/ind_types/list' @ sK2,X3 : 'type/ind_types/list' @ sK2] : (sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)))),
% 1.15/1.04 introduced(definition,[new_symbols(naming,[spl7_3])],[avatar_definition])).
% 1.15/1.04 thf(f54,plain,(
% 1.15/1.04 ~spl7_2 | spl7_3),
% 1.15/1.04 inference(avatar_split_clause,[status(thm)],[f39,f52,f47])).
% 1.15/1.04 thf(f39,plain,(
% 1.15/1.04 ( ! [X3 : 'type/ind_types/list' @ sK2,X4 : 'type/ind_types/list' @ sK2] : ((sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4))) | ($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK4))) )),
% 1.15/1.04 inference(cnf_transformation,[status(thm)],[f28])).
% 1.15/1.04 thf(f28,plain,(
% 1.15/1.04 (($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)))) & (($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4))),
% 1.15/1.04 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6])],[f25,f27,f26])).
% 1.15/1.04 thf(f26,plain,(
% 1.15/1.04 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ? [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) = X2))) => ((($true != ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ! [X4 : 'type/ind_types/list' @ sK2,X3 : 'type/ind_types/list' @ sK2] : (sK4 != ('const/lists/APPEND' @ sK2 @ X3 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X4)))) & (($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | ? [X6 : 'type/ind_types/list' @ sK2,X5 : 'type/ind_types/list' @ sK2] : (('const/lists/APPEND' @ sK2 @ X5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X6)) = sK4)))),
% 1.15/1.04 introduced(definition,[],[choice_axiom])).
% 1.15/1.04 thf(f27,plain,(
% 1.15/1.04 ? [X6 : 'type/ind_types/list' @ sK2,X5 : 'type/ind_types/list' @ sK2] : (('const/lists/APPEND' @ sK2 @ X5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ X6)) = sK4) => (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4)),
% 1.15/1.04 introduced(definition,[],[choice_axiom])).
% 1.15/1.04 thf(f25,plain,(
% 1.15/1.04 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ? [X5 : 'type/ind_types/list' @ X0,X6 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X5 @ ('const/ind_types/CONS' @ X0 @ X1 @ X6)) = X2)))),
% 1.15/1.04 inference(rectify,[status(thm)],[f24])).
% 1.15/1.04 thf(f24,plain,(
% 1.15/1.04 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2) != $true) | ! [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) != X2)) & ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) | ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2)))),
% 1.15/1.04 inference(nnf_transformation,[status(thm)],[f15])).
% 1.15/1.04 thf(f15,plain,(
% 1.15/1.04 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2) <~> (('const/lists/MEM' @ X0 @ X1 @ X2) = $true))),
% 1.15/1.04 inference(ennf_transformation,[status(thm)],[f13])).
% 1.15/1.04 thf(f13,plain,(
% 1.15/1.04 ~! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2) = $true) <=> ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2))),
% 1.15/1.04 inference(fool_elimination,[status(thm)],[f5])).
% 1.15/1.04 thf(f5,negated_conjecture,(
% 1.15/1.04 ~! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2))),
% 1.15/1.04 inference(negated_conjecture,[status(cth)],[f4])).
% 1.15/1.04 thf(f4,conjecture,(
% 1.15/1.04 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/MEM' @ X0 @ X1 @ X2) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)) = X2))),
% 1.15/1.04 file('/export/starexec/sandbox2/tmp/tmp.rKUjhMko3l/DTF2THF_10047.p','thm/lists/MEM_APPEND_DECOMPOSE_')).
% 1.15/1.04 thf(f50,plain,(
% 1.15/1.04 spl7_1 | spl7_2),
% 1.15/1.04 inference(avatar_split_clause,[status(thm)],[f38,f47,f43])).
% 1.15/1.04 thf(f38,plain,(
% 1.15/1.04 ($true = ('const/lists/MEM' @ sK2 @ sK3 @ sK4)) | (('const/lists/APPEND' @ sK2 @ sK5 @ ('const/ind_types/CONS' @ sK2 @ sK3 @ sK6)) = sK4)),
% 1.15/1.04 inference(cnf_transformation,[status(thm)],[f28])).
% 1.15/1.04 % SZS output end Proof for DTF2THF_10047
% 1.15/1.04 % (10330)------------------------------
% 1.15/1.04 % (10330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.15/1.04 % (10330)Termination reason: Refutation
% 1.15/1.04
% 1.15/1.04 % (10330)Memory used [KB]: 5628
% 1.15/1.04 % (10330)Time elapsed: 0.006 s
% 1.15/1.04 % (10330)Instructions burned: 9 (million)
% 1.15/1.04 % (10330)------------------------------
% 1.15/1.04 % (10330)------------------------------
% 1.15/1.04 % (10323)Success in time 0.013 s
%------------------------------------------------------------------------------