%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT286^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 08:45:23 AM UTC 2026
% Result : Theorem 1.65s 1.41s
% Output : Refutation 1.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT286^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n004.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 Feb 24 06:13:56 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.46 ---- Original DTF file ---
% 0.18/0.46 thf(spec,logic,$$dhol).
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 % File : DAT286^1 : TPTP v9.2.1. Released v7.0.0.
% 0.18/0.46 % Domain : Analysis
% 0.18/0.46 % Problem : APPEND_ASSOC
% 0.18/0.46 % Version : Especial.
% 0.18/0.46 % English :
% 0.18/0.46
% 0.18/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.18/0.46 % Source : [Kal16]
% 0.18/0.46 % Names : APPEND_ASSOC_.p [Kal16]
% 0.18/0.46
% 0.18/0.46 % Status : Theorem
% 0.18/0.46 % Rating : 0.67 v9.0.0, 1.00 v7.1.0
% 0.18/0.46 % Syntax : Number of formulae : 8 ( 3 unt; 4 typ; 0 def)
% 0.18/0.46 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.18/0.46 % Maximal formula atoms : 1 ( 0 avg)
% 0.18/0.46 % Number of connectives : 54 ( 0 ~; 0 |; 1 &; 51 @)
% 0.18/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.18/0.46 % Maximal formula depth : 12 ( 6 avg)
% 0.18/0.46 % Number of types : 1 ( 0 usr)
% 0.18/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.18/0.46 % Number of symbols : 5 ( 4 usr; 0 con; 1-3 aty)
% 0.18/0.46 % Number of variables : 18 ( 0 ^; 15 !; 0 ?; 18 :)
% 0.18/0.46 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.18/0.46 % SPC : TH1_THM_EQU_NAR
% 0.18/0.46
% 0.18/0.46 % Comments : Exported from core HOL Light.
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 thf('thf_type_type/ind_types/list',type,
% 0.18/0.46 'type/ind_types/list': $tType > $tType ).
% 0.18/0.46
% 0.18/0.46 thf('thf_const_const/lists/APPEND',type,
% 0.18/0.46 'const/lists/APPEND':
% 0.18/0.46 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.18/0.46
% 0.18/0.46 thf('thf_const_const/ind_types/NIL',type,
% 0.18/0.46 'const/ind_types/NIL':
% 0.18/0.46 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.18/0.46
% 0.18/0.46 thf('thf_const_const/ind_types/CONS',type,
% 0.18/0.46 'const/ind_types/CONS':
% 0.18/0.46 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.18/0.46
% 0.18/0.46 thf('thm/ind_types/list_INDUCT_',axiom,
% 0.18/0.46 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 0.18/0.46 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 0.18/0.46 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 0.18/0.46 ( ( P @ A1 )
% 0.18/0.46 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 0.18/0.46 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 0.18/0.46
% 0.18/0.46 thf('thm/lists/APPEND_1',axiom,
% 0.18/0.46 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A,A2: 'type/ind_types/list' @ A] :
% 0.18/0.46 ( ( 'const/lists/APPEND' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) @ A2 )
% 0.18/0.46 = ( 'const/ind_types/CONS' @ A @ A0 @ ( 'const/lists/APPEND' @ A @ A1 @ A2 ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf('thm/lists/APPEND_0',axiom,
% 0.18/0.46 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 0.18/0.46 ( ( 'const/lists/APPEND' @ A @ ( 'const/ind_types/NIL' @ A ) @ A0 )
% 0.18/0.46 = A0 ) ).
% 0.18/0.46
% 0.18/0.46 thf('thm/lists/APPEND_ASSOC_',conjecture,
% 0.18/0.46 ! [A: $tType,A0: 'type/ind_types/list' @ A,A1: 'type/ind_types/list' @ A,A2: 'type/ind_types/list' @ A] :
% 0.18/0.46 ( ( 'const/lists/APPEND' @ A @ A0 @ ( 'const/lists/APPEND' @ A @ A1 @ A2 ) )
% 0.18/0.46 = ( 'const/lists/APPEND' @ A @ ( 'const/lists/APPEND' @ A @ A0 @ A1 ) @ A2 ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 1.52/1.26 ---- Embedded in THF ---
% 1.52/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.26 %%% Generated on Tue Feb 24 06:13:57 EST 2026
% 1.52/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.26 %%% Logic specification used:
% 1.52/1.26 %%% thf(spec, logic, $$dhol).
% 1.52/1.26
% 1.52/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.THAOAeOfE7/DTF2DTF15015.p
% 1.52/1.26 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.52/1.26 thf('thf_const_const/lists/APPEND', type, 'const/lists/APPEND': (!> [A:$tType]: ((('type/ind_types/list' @ A) > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.52/1.26 thf('thf_const_const/ind_types/NIL', type, 'const/ind_types/NIL': (!> [A:$tType]: (('type/ind_types/list' @ A)))).
% 1.52/1.26 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.52/1.26 thf('thm/ind_types/list_INDUCT_', axiom, (! [A:$tType,P:(('type/ind_types/list' @ A) > $o)]: ((((P @ ('const/ind_types/NIL' @ A)) & (! [A0:A,A1:('type/ind_types/list' @ A)]: (((P @ A1) => (P @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)))))) => (! [A0:('type/ind_types/list' @ A)]: ((P @ A0))))))).
% 1.52/1.26 thf('thm/lists/APPEND_1', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A),A2:('type/ind_types/list' @ A)]: ((((('const/lists/APPEND' @ A) @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)) @ A2) = ((('const/ind_types/CONS' @ A) @ A0) @ ((('const/lists/APPEND' @ A) @ A1) @ A2)))))).
% 1.52/1.26 thf('thm/lists/APPEND_0', axiom, (! [A:$tType,A0:('type/ind_types/list' @ A)]: ((((('const/lists/APPEND' @ A) @ ('const/ind_types/NIL' @ A)) @ A0) = A0)))).
% 1.52/1.26 thf('thm/lists/APPEND_ASSOC_', conjecture, (! [A:$tType,A0:('type/ind_types/list' @ A),A1:('type/ind_types/list' @ A),A2:('type/ind_types/list' @ A)]: ((((('const/lists/APPEND' @ A) @ A0) @ ((('const/lists/APPEND' @ A) @ A1) @ A2)) = ((('const/lists/APPEND' @ A) @ ((('const/lists/APPEND' @ A) @ A0) @ A1)) @ A2))))).
% 1.52/1.26 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.THAOAeOfE7/DTF2DTF15015.p
% 1.52/1.26 ------------------------
% 1.52/1.27 ---- Cleaned THF ---
% 1.52/1.27 thf('thf_type_type/ind_types/list',type,
% 1.52/1.27 'type/ind_types/list': $tType > $tType ).
% 1.52/1.27
% 1.52/1.27 thf('thf_const_const/lists/APPEND',type,
% 1.52/1.27 'const/lists/APPEND':
% 1.52/1.27 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.52/1.27
% 1.52/1.27 thf('thf_const_const/ind_types/NIL',type,
% 1.52/1.27 'const/ind_types/NIL':
% 1.52/1.27 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 1.52/1.27
% 1.52/1.27 thf('thf_const_const/ind_types/CONS',type,
% 1.52/1.27 'const/ind_types/CONS':
% 1.52/1.27 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.52/1.27
% 1.52/1.27 thf('thm/ind_types/list_INDUCT_',axiom,
% 1.52/1.27 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 1.52/1.27 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 1.52/1.27 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 1.52/1.27 ( ( P @ A1 )
% 1.52/1.27 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 1.52/1.27 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 1.52/1.27
% 1.52/1.27 thf('thm/lists/APPEND_1',axiom,
% 1.52/1.27 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A,A2: 'type/ind_types/list' @ A] :
% 1.52/1.27 ( ( 'const/lists/APPEND' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) @ A2 )
% 1.52/1.27 = ( 'const/ind_types/CONS' @ A @ A0 @ ( 'const/lists/APPEND' @ A @ A1 @ A2 ) ) ) ).
% 1.52/1.27
% 1.52/1.27 thf('thm/lists/APPEND_0',axiom,
% 1.52/1.27 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 1.52/1.27 ( ( 'const/lists/APPEND' @ A @ ( 'const/ind_types/NIL' @ A ) @ A0 )
% 1.52/1.27 = A0 ) ).
% 1.52/1.27
% 1.52/1.27 thf('thm/lists/APPEND_ASSOC_',conjecture,
% 1.52/1.27 ! [A: $tType,A0: 'type/ind_types/list' @ A,A1: 'type/ind_types/list' @ A,A2: 'type/ind_types/list' @ A] :
% 1.52/1.27 ( ( 'const/lists/APPEND' @ A @ A0 @ ( 'const/lists/APPEND' @ A @ A1 @ A2 ) )
% 1.52/1.27 = ( 'const/lists/APPEND' @ A @ ( 'const/lists/APPEND' @ A @ A0 @ A1 ) @ A2 ) ) ).
% 1.52/1.27 ------------------------
% 1.52/1.29 % (15355)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_15015 for (2999ds/275Mi)
% 1.52/1.29 % (15355)Refutation not found, incomplete strategy
% 1.52/1.29 % (15355)------------------------------
% 1.52/1.29 % (15355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (15355)Termination reason: Refutation not found, incomplete strategy
% 1.52/1.29
% 1.52/1.29
% 1.52/1.29 % (15355)Memory used [KB]: 5373
% 1.52/1.29 % (15355)Time elapsed: 0.003 s
% 1.52/1.29 % (15355)Instructions burned: 2 (million)
% 1.52/1.29 % (15355)------------------------------
% 1.52/1.29 % (15355)------------------------------
% 1.52/1.30 % (15351)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_15015 for (2999ds/4Mi)
% 1.52/1.30 % (15350)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/183Mi)
% 1.52/1.30 % (15352)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_15015 for (2999ds/27Mi)
% 1.52/1.30 % (15353)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/2Mi)
% 1.52/1.30 % (15354)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_15015 for (2999ds/2Mi)
% 1.65/1.30 % (15356)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/18Mi)
% 1.65/1.30 % (15353)Instruction limit reached!
% 1.65/1.30 % (15353)------------------------------
% 1.65/1.30 % (15353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (15353)Termination reason: Unknown
% 1.65/1.30 % (15353)Termination phase: Saturation
% 1.65/1.30
% 1.65/1.30 % (15353)Memory used [KB]: 895
% 1.65/1.30 % (15353)Time elapsed: 0.003 s
% 1.65/1.30 % (15353)Instructions burned: 2 (million)
% 1.65/1.30 % (15353)------------------------------
% 1.65/1.30 % (15353)------------------------------
% 1.65/1.30 % (15354)Instruction limit reached!
% 1.65/1.30 % (15354)------------------------------
% 1.65/1.30 % (15354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (15354)Termination reason: Unknown
% 1.65/1.30 % (15354)Termination phase: shuffling
% 1.65/1.30
% 1.65/1.30 % (15354)Memory used [KB]: 895
% 1.65/1.30 % (15354)Time elapsed: 0.003 s
% 1.65/1.30 % (15354)Instructions burned: 2 (million)
% 1.65/1.30 % (15354)------------------------------
% 1.65/1.30 % (15354)------------------------------
% 1.65/1.30 % (15351)Instruction limit reached!
% 1.65/1.30 % (15351)------------------------------
% 1.65/1.30 % (15351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (15351)Termination reason: Unknown
% 1.65/1.30 % (15351)Termination phase: Saturation
% 1.65/1.30
% 1.65/1.30 % (15351)Memory used [KB]: 5500
% 1.65/1.30 % (15351)Time elapsed: 0.005 s
% 1.65/1.30 % (15351)Instructions burned: 5 (million)
% 1.65/1.30 % (15351)------------------------------
% 1.65/1.30 % (15351)------------------------------
% 1.65/1.30 % (15352)Refutation not found, incomplete strategy
% 1.65/1.30 % (15352)------------------------------
% 1.65/1.30 % (15352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.30 % (15352)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.30
% 1.65/1.30
% 1.65/1.30 % (15352)Memory used [KB]: 5500
% 1.65/1.30 % (15352)Time elapsed: 0.005 s
% 1.65/1.30 % (15352)Instructions burned: 4 (million)
% 1.65/1.30 % (15352)------------------------------
% 1.65/1.30 % (15352)------------------------------
% 1.65/1.30 % (15357)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/3Mi)
% 1.65/1.31 % (15357)Instruction limit reached!
% 1.65/1.31 % (15357)------------------------------
% 1.65/1.31 % (15357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (15357)Termination reason: Unknown
% 1.65/1.31 % (15357)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (15357)Memory used [KB]: 5500
% 1.65/1.31 % (15357)Time elapsed: 0.002 s
% 1.65/1.31 % (15357)Instructions burned: 3 (million)
% 1.65/1.31 % (15357)------------------------------
% 1.65/1.31 % (15357)------------------------------
% 1.65/1.31 % (15356)Instruction limit reached!
% 1.65/1.31 % (15356)------------------------------
% 1.65/1.31 % (15356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.31 % (15356)Termination reason: Unknown
% 1.65/1.31 % (15356)Termination phase: Saturation
% 1.65/1.31
% 1.65/1.31 % (15356)Memory used [KB]: 5628
% 1.65/1.31 % (15356)Time elapsed: 0.014 s
% 1.65/1.31 % (15356)Instructions burned: 19 (million)
% 1.65/1.31 % (15356)------------------------------
% 1.65/1.31 % (15356)------------------------------
% 1.65/1.31 % (15358)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_15015 for (2999ds/37Mi)
% 1.65/1.31 % (15359)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_15015 for (2999ds/15Mi)
% 1.65/1.32 % Exception at run slice level
% 1.65/1.32 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
% 1.65/1.32 % (15362)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/7Mi)
% 1.65/1.32 % (15360)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_15015 for (2999ds/3Mi)
% 1.65/1.32 % (15359)Refutation not found, incomplete strategy
% 1.65/1.32 % (15359)------------------------------
% 1.65/1.32 % (15359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (15359)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.32
% 1.65/1.32
% 1.65/1.32 % (15359)Memory used [KB]: 5500
% 1.65/1.32 % (15359)Time elapsed: 0.004 s
% 1.65/1.32 % (15359)Instructions burned: 2 (million)
% 1.65/1.32 % (15359)------------------------------
% 1.65/1.32 % (15359)------------------------------
% 1.65/1.32 % (15361)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_15015 for (2999ds/1041Mi)
% 1.65/1.32 % Exception at run slice level
% 1.65/1.32 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
% 1.65/1.32 % (15360)Instruction limit reached!
% 1.65/1.32 % (15360)------------------------------
% 1.65/1.32 % (15360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (15360)Termination reason: Unknown
% 1.65/1.32 % (15360)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (15360)Memory used [KB]: 5500
% 1.65/1.32 % (15360)Time elapsed: 0.004 s
% 1.65/1.32 % (15360)Instructions burned: 3 (million)
% 1.65/1.32 % (15360)------------------------------
% 1.65/1.32 % (15360)------------------------------
% 1.65/1.32 % (15362)Instruction limit reached!
% 1.65/1.32 % (15362)------------------------------
% 1.65/1.32 % (15362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.32 % (15362)Termination reason: Unknown
% 1.65/1.32 % (15362)Termination phase: Saturation
% 1.65/1.32
% 1.65/1.32 % (15362)Memory used [KB]: 1023
% 1.65/1.32 % (15362)Time elapsed: 0.005 s
% 1.65/1.32 % (15362)Instructions burned: 8 (million)
% 1.65/1.32 % (15362)------------------------------
% 1.65/1.32 % (15362)------------------------------
% 1.65/1.33 % (15363)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/16Mi)
% 1.65/1.33 % (15368)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/4Mi)
% 1.65/1.33 % (15366)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/7Mi)
% 1.65/1.33 % (15368)Instruction limit reached!
% 1.65/1.33 % (15368)------------------------------
% 1.65/1.33 % (15368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (15368)Termination reason: Unknown
% 1.65/1.33 % (15368)Termination phase: Saturation
% 1.65/1.33
% 1.65/1.33 % (15368)Memory used [KB]: 5500
% 1.65/1.33 % (15368)Time elapsed: 0.004 s
% 1.65/1.33 % (15368)Instructions burned: 6 (million)
% 1.65/1.33 % (15368)------------------------------
% 1.65/1.33 % (15368)------------------------------
% 1.65/1.33 % (15364)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_15015 for (2999ds/3Mi)
% 1.65/1.33 % (15365)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_15015 for (2999ds/3Mi)
% 1.65/1.33 % (15364)Instruction limit reached!
% 1.65/1.33 % (15364)------------------------------
% 1.65/1.33 % (15364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (15364)Termination reason: Unknown
% 1.65/1.33 % (15364)Termination phase: Saturation
% 1.65/1.33
% 1.65/1.33 % (15364)Memory used [KB]: 5500
% 1.65/1.33 % (15364)Time elapsed: 0.004 s
% 1.65/1.33 % (15364)Instructions burned: 3 (million)
% 1.65/1.33 % (15364)------------------------------
% 1.65/1.33 % (15364)------------------------------
% 1.65/1.33 % (15366)Instruction limit reached!
% 1.65/1.33 % (15366)------------------------------
% 1.65/1.33 % (15366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.33 % (15366)Termination reason: Unknown
% 1.65/1.33 % (15366)Termination phase: Saturation
% 1.65/1.33
% 1.65/1.33 % (15366)Memory used [KB]: 5500
% 1.65/1.33 % (15366)Time elapsed: 0.005 s
% 1.65/1.33 % (15366)Instructions burned: 9 (million)
% 1.65/1.33 % (15366)------------------------------
% 1.65/1.33 % (15366)------------------------------
% 1.65/1.34 % (15363)Instruction limit reached!
% 1.65/1.34 % (15363)------------------------------
% 1.65/1.34 % (15363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (15363)Termination reason: Unknown
% 1.65/1.34 % (15363)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (15363)Memory used [KB]: 5628
% 1.65/1.34 % (15363)Time elapsed: 0.012 s
% 1.65/1.34 % (15363)Instructions burned: 16 (million)
% 1.65/1.34 % (15363)------------------------------
% 1.65/1.34 % (15363)------------------------------
% 1.65/1.34 % (15367)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/3Mi)
% 1.65/1.34 % (15365)Instruction limit reached!
% 1.65/1.34 % (15365)------------------------------
% 1.65/1.34 % (15365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (15365)Termination reason: Unknown
% 1.65/1.34 % (15365)Termination phase: Saturation
% 1.65/1.34
% 1.65/1.34 % (15365)Memory used [KB]: 1023
% 1.65/1.34 % (15365)Time elapsed: 0.004 s
% 1.65/1.34 % (15365)Instructions burned: 4 (million)
% 1.65/1.34 % (15365)------------------------------
% 1.65/1.34 % (15365)------------------------------
% 1.65/1.34 % Exception at run slice level
% 1.65/1.34 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
% 1.65/1.34 % (15369)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/18Mi)
% 1.65/1.34 % (15369)Refutation not found, incomplete strategy
% 1.65/1.34 % (15369)------------------------------
% 1.65/1.34 % (15369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.34 % (15369)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.34
% 1.65/1.34
% 1.65/1.34 % (15369)Memory used [KB]: 5500
% 1.65/1.34 % (15369)Time elapsed: 0.003 s
% 1.65/1.34 % (15369)Instructions burned: 3 (million)
% 1.65/1.34 % (15369)------------------------------
% 1.65/1.34 % (15369)------------------------------
% 1.65/1.34 % (15370)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/710Mi)
% 1.65/1.35 % (15373)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_15015 for (2999ds/21Mi)
% 1.65/1.35 % (15371)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/6Mi)
% 1.65/1.35 % (15372)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_15015 for (2999ds/902Mi)
% 1.65/1.35 % (15375)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_15015 for (2999ds/6Mi)
% 1.65/1.35 % (15374)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/5Mi)
% 1.65/1.35 % Exception at run slice level
% 1.65/1.35 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
% 1.65/1.35 % Exception at run slice level
% 1.65/1.35 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
% 1.65/1.35 % (15372)Refutation not found, incomplete strategy
% 1.65/1.35 % (15372)------------------------------
% 1.65/1.35 % (15372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.35 % (15372)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.35
% 1.65/1.35
% 1.65/1.35 % (15372)Memory used [KB]: 5500
% 1.65/1.35 % (15372)Time elapsed: 0.003 s
% 1.65/1.35 % (15372)Instructions burned: 2 (million)
% 1.65/1.35 % (15372)------------------------------
% 1.65/1.35 % (15372)------------------------------
% 1.65/1.36 % (15371)Instruction limit reached!
% 1.65/1.36 % (15371)------------------------------
% 1.65/1.36 % (15371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (15371)Termination reason: Unknown
% 1.65/1.36 % (15371)Termination phase: Saturation
% 1.65/1.36
% 1.65/1.36 % (15371)Memory used [KB]: 5500
% 1.65/1.36 % (15371)Time elapsed: 0.006 s
% 1.65/1.36 % (15371)Instructions burned: 6 (million)
% 1.65/1.36 % (15371)------------------------------
% 1.65/1.36 % (15371)------------------------------
% 1.65/1.36 % (15373)Instruction limit reached!
% 1.65/1.36 % (15373)------------------------------
% 1.65/1.36 % (15373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.36 % (15373)Termination reason: Unknown
% 1.65/1.36 % (15373)Termination phase: Saturation
% 1.65/1.36
% 1.65/1.36 % (15373)Memory used [KB]: 5628
% 1.65/1.36 % (15373)Time elapsed: 0.010 s
% 1.65/1.36 % (15373)Instructions burned: 23 (million)
% 1.65/1.36 % (15373)------------------------------
% 1.65/1.36 % (15373)------------------------------
% 1.65/1.36 % (15376)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/377Mi)
% 1.65/1.37 % (15380)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/17Mi)
% 1.65/1.37 % (15377)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/779Mi)
% 1.65/1.37 % (15378)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/19Mi)
% 1.65/1.37 % Exception at run slice level
% 1.65/1.37 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
% 1.65/1.37 % (15379)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/879Mi)
% 1.65/1.37 % Exception at run slice level
% 1.65/1.37 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
% 1.65/1.38 % (15380)Instruction limit reached!
% 1.65/1.38 % (15380)------------------------------
% 1.65/1.38 % (15380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (15380)Termination reason: Unknown
% 1.65/1.38 % (15380)Termination phase: Saturation
% 1.65/1.38
% 1.65/1.38 % (15380)Memory used [KB]: 5500
% 1.65/1.38 % (15380)Time elapsed: 0.008 s
% 1.65/1.38 % (15380)Instructions burned: 18 (million)
% 1.65/1.38 % (15380)------------------------------
% 1.65/1.38 % (15380)------------------------------
% 1.65/1.38 % (15350)Instruction limit reached!
% 1.65/1.38 % (15350)------------------------------
% 1.65/1.38 % (15350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.38 % (15350)Termination reason: Unknown
% 1.65/1.38 % (15350)Termination phase: Saturation
% 1.65/1.38
% 1.65/1.38 % (15350)Memory used [KB]: 6140
% 1.65/1.38 % (15350)Time elapsed: 0.086 s
% 1.65/1.38 % (15350)Instructions burned: 183 (million)
% 1.65/1.38 % (15350)------------------------------
% 1.65/1.38 % (15350)------------------------------
% 1.65/1.39 % (15383)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/127Mi)
% 1.65/1.39 % (15381)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/3Mi)
% 1.65/1.39 % (15384)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/100Mi)
% 1.65/1.39 % (15382)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/30Mi)
% 1.65/1.39 % (15381)Instruction limit reached!
% 1.65/1.39 % (15381)------------------------------
% 1.65/1.39 % (15381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.39 % (15381)Termination reason: Unknown
% 1.65/1.39 % (15381)Termination phase: Property scanning
% 1.65/1.39
% 1.65/1.39 % (15381)Memory used [KB]: 1023
% 1.65/1.39 % (15381)Time elapsed: 0.003 s
% 1.65/1.39 % (15381)Instructions burned: 3 (million)
% 1.65/1.39 % (15381)------------------------------
% 1.65/1.39 % (15381)------------------------------
% 1.65/1.40 % (15382)Refutation not found, incomplete strategy
% 1.65/1.40 % (15382)------------------------------
% 1.65/1.40 % (15382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (15382)Termination reason: Refutation not found, incomplete strategy
% 1.65/1.40
% 1.65/1.40
% 1.65/1.40 % (15382)Memory used [KB]: 5500
% 1.65/1.40 % (15382)Time elapsed: 0.008 s
% 1.65/1.40 % (15382)Instructions burned: 10 (million)
% 1.65/1.40 % (15382)------------------------------
% 1.65/1.40 % (15382)------------------------------
% 1.65/1.40 % (15384)First to succeed.
% 1.65/1.40 % (15385)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_15015 for (2999ds/3Mi)
% 1.65/1.40 % Exception at run slice level
% 1.65/1.40 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
% 1.65/1.41 % (15384)Refutation found. Thanks to Tanya!
% 1.65/1.41 % SZS status Theorem for DTF2THF_15015
% 1.65/1.41 % SZS output start Proof for DTF2THF_15015
% 1.65/1.41 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 1.65/1.41 thf(type_def_7, type, sK0: $tType).
% 1.65/1.41 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 1.65/1.41 thf(func_def_1, type, 'const/lists/APPEND': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.65/1.41 thf(func_def_2, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 1.65/1.41 thf(func_def_3, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.65/1.41 thf(func_def_15, type, sK1: 'type/ind_types/list' @ sK0).
% 1.65/1.41 thf(func_def_16, type, sK2: 'type/ind_types/list' @ sK0).
% 1.65/1.41 thf(func_def_17, type, sK3: 'type/ind_types/list' @ sK0).
% 1.65/1.41 thf(func_def_19, type, sK5: 'type/ind_types/list' @ sK0).
% 1.65/1.41 thf(func_def_20, type, sK6: sK0).
% 1.65/1.41 thf(func_def_21, type, sK7: 'type/ind_types/list' @ sK0).
% 1.65/1.41 thf(func_def_22, type, sK8: sK0).
% 1.65/1.41 thf(func_def_23, type, sK9: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0)).
% 1.65/1.41 thf(func_def_24, type, sK10: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > X0)).
% 1.65/1.41 thf(func_def_25, type, sK11: 'type/ind_types/list' @ sK0).
% 1.65/1.41 thf(func_def_26, type, sK12: sK0).
% 1.65/1.41 thf(func_def_27, type, sK13: 'type/ind_types/list' @ sK0).
% 1.65/1.41 thf(func_def_28, type, sK14: sK0).
% 1.65/1.41 thf(func_def_29, type, ph15: !>[X0: $tType]:(X0)).
% 1.65/1.41 thf(f220,plain,(
% 1.65/1.41 $false),
% 1.65/1.41 inference(avatar_sat_refutation,[status(thm)],[f158,f165,f206,f209,f218])).
% 1.65/1.41 thf(f218,plain,(
% 1.65/1.41 ~spl4_10),
% 1.65/1.41 inference(avatar_contradiction_clause,[status(thm)],[f217])).
% 1.65/1.41 thf(f217,plain,(
% 1.65/1.41 $false | ~spl4_10),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f216])).
% 1.65/1.41 thf(f216,plain,(
% 1.65/1.41 (('const/lists/APPEND' @ sK0 @ sK1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) != ('const/lists/APPEND' @ sK0 @ sK1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | ~spl4_10),
% 1.65/1.41 inference(superposition,[status(thm)],[f23,f153])).
% 1.65/1.41 thf(f153,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) ) | ~spl4_10),
% 1.65/1.41 inference(avatar_component_clause,[status(thm)],[f152])).
% 1.65/1.41 thf(f152,definition,(
% 1.65/1.41 spl4_10 <=> ! [X1 : 'type/ind_types/list' @ sK0] : (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))),
% 1.65/1.41 introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition])).
% 1.65/1.41 thf(f23,plain,(
% 1.65/1.41 (('const/lists/APPEND' @ sK0 @ sK1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) != ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK1 @ sK2) @ sK3))),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f19])).
% 1.65/1.41 thf(f19,plain,(
% 1.65/1.41 (('const/lists/APPEND' @ sK0 @ sK1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) != ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK1 @ sK2) @ sK3))),
% 1.65/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f17,f18])).
% 1.65/1.41 thf(f18,plain,(
% 1.65/1.41 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ ('const/lists/APPEND' @ X0 @ X1 @ X2) @ X3) != ('const/lists/APPEND' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))) => (('const/lists/APPEND' @ sK0 @ sK1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) != ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK1 @ sK2) @ sK3))),
% 1.65/1.41 introduced(definition,[],[choice_axiom])).
% 1.65/1.41 thf(f17,plain,(
% 1.65/1.41 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ ('const/lists/APPEND' @ X0 @ X1 @ X2) @ X3) != ('const/lists/APPEND' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)))),
% 1.65/1.41 inference(ennf_transformation,[status(thm)],[f15])).
% 1.65/1.41 thf(f15,plain,(
% 1.65/1.41 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ ('const/lists/APPEND' @ X0 @ X1 @ X2) @ X3) = ('const/lists/APPEND' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)))),
% 1.65/1.41 inference(rectify,[status(thm)],[f5])).
% 1.65/1.41 thf(f5,negated_conjecture,(
% 1.65/1.41 ~! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X2 @ ('const/lists/APPEND' @ X0 @ X3 @ X4)) = ('const/lists/APPEND' @ X0 @ ('const/lists/APPEND' @ X0 @ X2 @ X3) @ X4))),
% 1.65/1.41 inference(negated_conjecture,[status(cth)],[f4])).
% 1.65/1.41 thf(f4,conjecture,(
% 1.65/1.41 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ X2 @ ('const/lists/APPEND' @ X0 @ X3 @ X4)) = ('const/lists/APPEND' @ X0 @ ('const/lists/APPEND' @ X0 @ X2 @ X3) @ X4))),
% 1.65/1.41 file('/export/starexec/sandbox/tmp/tmp.THAOAeOfE7/DTF2THF_15015.p','thm/lists/APPEND_ASSOC_')).
% 1.65/1.41 thf(f209,plain,(
% 1.65/1.41 spl4_9 | ~spl4_12),
% 1.65/1.41 inference(avatar_contradiction_clause,[status(thm)],[f208])).
% 1.65/1.41 thf(f208,plain,(
% 1.65/1.41 $false | (spl4_9 | ~spl4_12)),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.65/1.41 thf(f207,plain,(
% 1.65/1.41 (('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) != ('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)))) | (spl4_9 | ~spl4_12)),
% 1.65/1.41 inference(forward_demodulation,[status(thm)],[f150,f164])).
% 1.65/1.41 thf(f164,plain,(
% 1.65/1.41 (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3) = ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | ~spl4_12),
% 1.65/1.41 inference(avatar_component_clause,[status(thm)],[f162])).
% 1.65/1.41 thf(f162,definition,(
% 1.65/1.41 spl4_12 <=> (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3) = ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)))),
% 1.65/1.41 introduced(definition,[new_symbols(naming,[spl4_12])],[avatar_definition])).
% 1.65/1.41 thf(f150,plain,(
% 1.65/1.41 (('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) != ('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)))) | spl4_9),
% 1.65/1.41 inference(avatar_component_clause,[status(thm)],[f148])).
% 1.65/1.41 thf(f148,definition,(
% 1.65/1.41 spl4_9 <=> (('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) = ('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))))),
% 1.65/1.41 introduced(definition,[new_symbols(naming,[spl4_9])],[avatar_definition])).
% 1.65/1.41 thf(f206,plain,(
% 1.65/1.41 spl4_11),
% 1.65/1.41 inference(avatar_contradiction_clause,[status(thm)],[f205])).
% 1.65/1.41 thf(f205,plain,(
% 1.65/1.41 $false | spl4_11),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f204])).
% 1.65/1.41 thf(f204,plain,(
% 1.65/1.41 (('const/lists/APPEND' @ sK0 @ sK2 @ sK3) != ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) | spl4_11),
% 1.65/1.41 inference(forward_demodulation,[status(thm)],[f203,f201])).
% 1.65/1.41 thf(f201,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ X1) = X1)) )),
% 1.65/1.41 inference(equality_proxy_clausification,[status(thm)],[f200])).
% 1.65/1.41 thf(f200,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ X1) = X1) = $true)) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f199])).
% 1.65/1.41 thf(f199,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((((^[Y0 : 'type/ind_types/list' @ X0]: (('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ Y0) = Y0)) @ X1) = $true)) )),
% 1.65/1.41 inference(pi_clausification,[status(thm)],[f21])).
% 1.65/1.41 thf(f21,plain,(
% 1.65/1.41 ( ! [X0 : $tType] : (($true = (!! @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ Y0) = Y0))))) )),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f13])).
% 1.65/1.41 thf(f13,plain,(
% 1.65/1.41 ! [X0 : $tType] : ($true = (!! @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ Y0) = Y0))))),
% 1.65/1.41 inference(closure,[status(thm)],[f8])).
% 1.65/1.41 thf(f8,plain,(
% 1.65/1.41 ( ! [X0 : $tType] : (($true = (!! @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ Y0) = Y0))))) )),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.41 thf(f7,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ X1) = X1)),
% 1.65/1.41 inference(rectify,[status(thm)],[f3])).
% 1.65/1.41 thf(f3,axiom,(
% 1.65/1.41 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ 'const/ind_types/NIL' @ X0 @ X2) = X2)),
% 1.65/1.41 file('/export/starexec/sandbox/tmp/tmp.THAOAeOfE7/DTF2THF_15015.p','thm/lists/APPEND_0')).
% 1.65/1.41 thf(f203,plain,(
% 1.65/1.41 (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) | spl4_11),
% 1.65/1.41 inference(forward_demodulation,[status(thm)],[f157,f201])).
% 1.65/1.41 thf(f157,plain,(
% 1.65/1.41 (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | spl4_11),
% 1.65/1.41 inference(avatar_component_clause,[status(thm)],[f155])).
% 1.65/1.41 thf(f155,definition,(
% 1.65/1.41 spl4_11 <=> (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) = ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)))),
% 1.65/1.41 introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition])).
% 1.65/1.41 thf(f165,plain,(
% 1.65/1.41 ~spl4_11 | spl4_12),
% 1.65/1.41 inference(avatar_split_clause,[status(thm)],[f160,f162,f155])).
% 1.65/1.41 thf(f160,plain,(
% 1.65/1.41 (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3) = ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)))),
% 1.65/1.41 inference(condensation,[status(thm)],[f159])).
% 1.65/1.41 thf(f159,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3) = ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) )),
% 1.65/1.41 inference(equality_proxy_clausification,[status(thm)],[f145])).
% 1.65/1.41 thf(f145,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | ((('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) = $true) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.65/1.41 thf(f143,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3)) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | ($false = ((('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) => (('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) = ('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)))))) )),
% 1.65/1.41 inference(forward_demodulation,[status(thm)],[f142,f42])).
% 1.65/1.41 thf(f42,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : X0,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2) @ X1))) )),
% 1.65/1.41 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.65/1.41 thf(f35,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : X0,X1 : 'type/ind_types/list' @ X0] : (((('const/ind_types/CONS' @ X0 @ X3 @ ('const/lists/APPEND' @ X0 @ X2 @ X1)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X3 @ X2) @ X1)) = $true)) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f33])).
% 1.65/1.41 thf(f33,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : X0,X1 : 'type/ind_types/list' @ X0] : ((((^[Y0 : X0]: (('const/ind_types/CONS' @ X0 @ Y0 @ ('const/lists/APPEND' @ X0 @ X2 @ X1)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ Y0 @ X2) @ X1))) @ X3) = $true)) )),
% 1.65/1.41 inference(pi_clausification,[status(thm)],[f28])).
% 1.65/1.41 thf(f28,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : (((!! @ X0 @ (^[Y0 : X0]: (('const/ind_types/CONS' @ X0 @ Y0 @ ('const/lists/APPEND' @ X0 @ X2 @ X1)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ Y0 @ X2) @ X1)))) = $true)) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f27])).
% 1.65/1.41 thf(f27,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0] : ((((^[Y0 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y1 : X0]: (('const/ind_types/CONS' @ X0 @ Y1 @ ('const/lists/APPEND' @ X0 @ Y0 @ X1)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ Y1 @ Y0) @ X1))))) @ X2) = $true)) )),
% 1.65/1.41 inference(pi_clausification,[status(thm)],[f26])).
% 1.65/1.41 thf(f26,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((!! @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y1 : X0]: (('const/ind_types/CONS' @ X0 @ Y1 @ ('const/lists/APPEND' @ X0 @ Y0 @ X1)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ Y1 @ Y0) @ X1)))))) = $true)) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f25])).
% 1.65/1.41 thf(f25,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (($true = ((^[Y0 : 'type/ind_types/list' @ X0]: (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y2 : X0]: (('const/ind_types/CONS' @ X0 @ Y2 @ ('const/lists/APPEND' @ X0 @ Y1 @ Y0)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ Y2 @ Y1) @ Y0))))))) @ X1))) )),
% 1.65/1.41 inference(pi_clausification,[status(thm)],[f20])).
% 1.65/1.41 thf(f20,plain,(
% 1.65/1.41 ( ! [X0 : $tType] : (((!! @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y2 : X0]: (('const/ind_types/CONS' @ X0 @ Y2 @ ('const/lists/APPEND' @ X0 @ Y1 @ Y0)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ Y2 @ Y1) @ Y0)))))))) = $true)) )),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f14])).
% 1.65/1.41 thf(f14,plain,(
% 1.65/1.41 ! [X0 : $tType] : ((!! @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y2 : X0]: (('const/ind_types/CONS' @ X0 @ Y2 @ ('const/lists/APPEND' @ X0 @ Y1 @ Y0)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ Y2 @ Y1) @ Y0)))))))) = $true)),
% 1.65/1.41 inference(closure,[status(thm)],[f10])).
% 1.65/1.41 thf(f10,plain,(
% 1.65/1.41 ( ! [X0 : $tType] : (((!! @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y2 : X0]: (('const/ind_types/CONS' @ X0 @ Y2 @ ('const/lists/APPEND' @ X0 @ Y1 @ Y0)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ Y2 @ Y1) @ Y0)))))))) = $true)) )),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f9])).
% 1.65/1.41 thf(f9,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : (('const/ind_types/CONS' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3)) = ('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2) @ X3))),
% 1.65/1.41 inference(rectify,[status(thm)],[f2])).
% 1.65/1.41 thf(f2,axiom,(
% 1.65/1.41 ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (('const/lists/APPEND' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3) @ X4) = ('const/ind_types/CONS' @ X0 @ X2 @ ('const/lists/APPEND' @ X0 @ X3 @ X4)))),
% 1.65/1.41 file('/export/starexec/sandbox/tmp/tmp.THAOAeOfE7/DTF2THF_15015.p','thm/lists/APPEND_1')).
% 1.65/1.41 thf(f142,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3)) | ($false = ((('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) => (('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) = ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2)) @ sK3))))) )),
% 1.65/1.41 inference(forward_demodulation,[status(thm)],[f141,f42])).
% 1.65/1.41 thf(f141,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((((('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) => (('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ sK12 @ sK11) @ sK2) @ sK3))) = $false) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3)) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)))) )),
% 1.65/1.41 inference(forward_demodulation,[status(thm)],[f140,f42])).
% 1.65/1.41 thf(f140,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | ($false = ((('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ sK12 @ sK11) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ sK12 @ sK11) @ sK2) @ sK3)))) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f139])).
% 1.65/1.41 thf(f139,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((((^[Y0 : sK0]: ((('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y0 @ sK11) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y0 @ sK11) @ sK2) @ sK3)))) @ sK12) = $false) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3)) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)))) )),
% 1.65/1.41 inference(sigma_clausification,[status(thm)],[f138])).
% 1.65/1.41 thf(f138,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : (($false = (!! @ sK0 @ (^[Y0 : sK0]: ((('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y0 @ sK11) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y0 @ sK11) @ sK2) @ sK3)))))) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f137])).
% 1.65/1.41 thf(f137,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((((^[Y0 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ sK2) @ sK3)))))) @ sK11) = $false) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) )),
% 1.65/1.41 inference(sigma_clausification,[status(thm)],[f136])).
% 1.65/1.41 thf(f136,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : (((!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ sK2) @ sK3))))))) = $false) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) )),
% 1.65/1.41 inference(equality_proxy_clausification,[status(thm)],[f135])).
% 1.65/1.41 thf(f135,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : (((('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3)) = $false) | ((!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ sK2) @ sK3))))))) = $false) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f134])).
% 1.65/1.41 thf(f134,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((((('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3)) & (!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ sK2) @ sK3)))))))) = $false) | (('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3))) )),
% 1.65/1.41 inference(equality_proxy_clausification,[status(thm)],[f133])).
% 1.65/1.41 thf(f133,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : (((('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3)) = $true) | (((('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3)) & (!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ sK2) @ sK3)))))))) = $false)) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f132])).
% 1.65/1.41 thf(f132,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((((('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3)) & (!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ sK2) @ sK3)))))))) = $false) | (((^[Y0 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3))) @ X1) = $true)) )),
% 1.65/1.41 inference(pi_clausification,[status(thm)],[f131])).
% 1.65/1.41 thf(f131,plain,(
% 1.65/1.41 ((!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)))) = $true) | (((('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3)) & (!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ sK2) @ sK3)))))))) = $false)),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f51])).
% 1.65/1.41 thf(f51,plain,(
% 1.65/1.41 ($true = (((('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3)) & (!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y1 : sK0]: ((('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)) => (('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ ('const/ind_types/CONS' @ sK0 @ Y1 @ Y0) @ sK2) @ sK3)))))))) => (!! @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3))))))),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f47])).
% 1.65/1.41 thf(f47,plain,(
% 1.65/1.41 (((^[Y0 : 'type/ind_types/list' @ sK0 > $o]: (((Y0 @ 'const/ind_types/NIL' @ sK0) & (!! @ 'type/ind_types/list' @ sK0 @ (^[Y1 : 'type/ind_types/list' @ sK0]: (!! @ sK0 @ (^[Y2 : sK0]: ((Y0 @ Y1) => (Y0 @ ('const/ind_types/CONS' @ sK0 @ Y2 @ Y1)))))))) => (!! @ 'type/ind_types/list' @ sK0 @ Y0))) @ (^[Y0 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ Y0 @ sK2) @ sK3)))) = $true)),
% 1.65/1.41 inference(heuristic_instantiation,[status(thm)],[f24])).
% 1.65/1.41 thf(f24,plain,(
% 1.65/1.41 ( ! [X0 : $tType] : (((!! @ ('type/ind_types/list' @ X0 > $o) @ (^[Y0 : 'type/ind_types/list' @ X0 > $o]: (((Y0 @ 'const/ind_types/NIL' @ X0) & (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y2 : X0]: ((Y0 @ Y1) => (Y0 @ ('const/ind_types/CONS' @ X0 @ Y2 @ Y1)))))))) => (!! @ 'type/ind_types/list' @ X0 @ Y0)))) = $true)) )),
% 1.65/1.41 inference(beta_eta_normalization,[status(thm)],[f22])).
% 1.65/1.41 thf(f22,plain,(
% 1.65/1.41 ( ! [X0 : $tType] : (((!! @ ('type/ind_types/list' @ X0 > $o) @ (^[Y0 : 'type/ind_types/list' @ X0 > $o]: (((Y0 @ 'const/ind_types/NIL' @ X0) & (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y2 : X0]: ((Y0 @ Y1) => (Y0 @ ('const/ind_types/CONS' @ X0 @ Y2 @ Y1)))))))) => (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (Y0 @ Y1)))))) = $true)) )),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f16])).
% 1.65/1.41 thf(f16,plain,(
% 1.65/1.41 ! [X0 : $tType] : ((!! @ ('type/ind_types/list' @ X0 > $o) @ (^[Y0 : 'type/ind_types/list' @ X0 > $o]: (((Y0 @ 'const/ind_types/NIL' @ X0) & (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y2 : X0]: ((Y0 @ Y1) => (Y0 @ ('const/ind_types/CONS' @ X0 @ Y2 @ Y1)))))))) => (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (Y0 @ Y1)))))) = $true)),
% 1.65/1.41 inference(closure,[status(thm)],[f12])).
% 1.65/1.41 thf(f12,plain,(
% 1.65/1.41 ( ! [X0 : $tType] : (((!! @ ('type/ind_types/list' @ X0 > $o) @ (^[Y0 : 'type/ind_types/list' @ X0 > $o]: (((Y0 @ 'const/ind_types/NIL' @ X0) & (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (!! @ X0 @ (^[Y2 : X0]: ((Y0 @ Y1) => (Y0 @ ('const/ind_types/CONS' @ X0 @ Y2 @ Y1)))))))) => (!! @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (Y0 @ Y1)))))) = $true)) )),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f11])).
% 1.65/1.41 thf(f11,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 1.65/1.41 inference(rectify,[status(thm)],[f1])).
% 1.65/1.41 thf(f1,axiom,(
% 1.65/1.41 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3))) & (X1 @ 'const/ind_types/NIL' @ X0)) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 1.65/1.41 file('/export/starexec/sandbox/tmp/tmp.THAOAeOfE7/DTF2THF_15015.p','thm/ind_types/list_INDUCT_')).
% 1.65/1.41 thf(f158,plain,(
% 1.65/1.41 ~spl4_9 | spl4_10 | ~spl4_11),
% 1.65/1.41 inference(avatar_split_clause,[status(thm)],[f146,f155,f152,f148])).
% 1.65/1.41 thf(f146,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3)) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) | (('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3)) != ('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))))) )),
% 1.65/1.41 inference(equality_proxy_clausification,[status(thm)],[f144])).
% 1.65/1.41 thf(f144,plain,(
% 1.65/1.41 ( ! [X1 : 'type/ind_types/list' @ sK0] : ((('const/lists/APPEND' @ sK0 @ X1 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)) = ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ X1 @ sK2) @ sK3)) | ((('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ sK11 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3))) = ('const/ind_types/CONS' @ sK0 @ sK12 @ ('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK11 @ sK2) @ sK3))) = $false) | (('const/lists/APPEND' @ sK0 @ ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ sK2) @ sK3) != ('const/lists/APPEND' @ sK0 @ 'const/ind_types/NIL' @ sK0 @ ('const/lists/APPEND' @ sK0 @ sK2 @ sK3)))) )),
% 1.65/1.41 inference(binary_proxy_clausification,[status(thm)],[f143])).
% 1.65/1.41 % SZS output end Proof for DTF2THF_15015
% 1.65/1.41 % (15384)------------------------------
% 1.65/1.41 % (15384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (15384)Termination reason: Refutation
% 1.65/1.41
% 1.65/1.41 % (15384)Memory used [KB]: 5884
% 1.65/1.41 % (15384)Time elapsed: 0.018 s
% 1.65/1.41 % (15384)Instructions burned: 41 (million)
% 1.65/1.41 % (15384)------------------------------
% 1.65/1.41 % (15384)------------------------------
% 1.65/1.41 % (15349)Success in time 0.113 s
%------------------------------------------------------------------------------