%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT276^1 : 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 : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:22 AM UTC 2026
% Result : Theorem 1.77s 1.47s
% Output : Refutation 1.77s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT276^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n002.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 06:13:18 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : DAT276^1 : TPTP v9.2.1. Released v7.0.0.
% 0.27/0.46 % Domain : Analysis
% 0.27/0.46 % Problem : MAP2_
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Kal16]
% 0.27/0.46 % Names : MAP2_1.p [Kal16]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.00 v7.1.0
% 0.27/0.46 % Syntax : Number of formulae : 9 ( 4 unt; 5 typ; 0 def)
% 0.27/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 1 ( 1 avg)
% 0.27/0.46 % Number of connectives : 71 ( 0 ~; 0 |; 0 &; 71 @)
% 0.27/0.46 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 9 ( 6 avg)
% 0.27/0.46 % Number of types : 0 ( 0 usr)
% 0.27/0.46 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 6 ( 5 usr; 0 con; 1-6 aty)
% 0.27/0.46 % Number of variables : 27 ( 0 ^; 21 !; 0 ?; 27 :)
% 0.27/0.46 % ( 6 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.46 % SPC : TH1_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : Exported from core HOL Light.
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf('thf_type_type/ind_types/list',type,
% 0.27/0.46 'type/ind_types/list': $tType > $tType ).
% 0.27/0.46
% 0.27/0.46 thf('thf_const_const/lists/TL',type,
% 0.27/0.46 'const/lists/TL':
% 0.27/0.46 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.27/0.46
% 0.27/0.46 thf('thf_const_const/lists/MAP2',type,
% 0.27/0.46 'const/lists/MAP2':
% 0.27/0.46 !>[A: $tType,A0: $tType,A1: $tType] : ( ( A > A0 > A1 ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A0 ) > ( 'type/ind_types/list' @ A1 ) ) ).
% 0.27/0.46
% 0.27/0.46 thf('thf_const_const/lists/HD',type,
% 0.27/0.46 'const/lists/HD':
% 0.27/0.46 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A ) ).
% 0.27/0.46
% 0.27/0.46 thf('thf_const_const/ind_types/CONS',type,
% 0.27/0.46 'const/ind_types/CONS':
% 0.27/0.46 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.27/0.46
% 0.27/0.46 thf('thm/lists/TL_',axiom,
% 0.27/0.46 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.27/0.46 ( ( 'const/lists/TL' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.27/0.46 = A1 ) ).
% 0.27/0.46
% 0.27/0.46 thf('thm/lists/HD_',axiom,
% 0.27/0.46 ! [A: $tType,A0: 'type/ind_types/list' @ A,A1: A] :
% 0.27/0.46 ( ( 'const/lists/HD' @ A @ ( 'const/ind_types/CONS' @ A @ A1 @ A0 ) )
% 0.27/0.46 = A1 ) ).
% 0.27/0.46
% 0.27/0.46 thf('thm/lists/MAP2_DEF_1',axiom,
% 0.27/0.46 ! [A: $tType,A0: $tType,A1: $tType,A2: A0,A3: A0 > A1 > A,A4: 'type/ind_types/list' @ A0,A5: 'type/ind_types/list' @ A1] :
% 0.27/0.46 ( ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A3 @ ( 'const/ind_types/CONS' @ A0 @ A2 @ A4 ) @ A5 )
% 0.27/0.46 = ( 'const/ind_types/CONS' @ A @ ( A3 @ A2 @ ( 'const/lists/HD' @ A1 @ A5 ) ) @ ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A3 @ A4 @ ( 'const/lists/TL' @ A1 @ A5 ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 thf('thm/lists/MAP2_1',conjecture,
% 0.27/0.46 ! [A: $tType,A0: $tType,A1: $tType,A2: A0,A3: A1,A4: A0 > A1 > A,A5: 'type/ind_types/list' @ A0,A6: 'type/ind_types/list' @ A1] :
% 0.27/0.46 ( ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A4 @ ( 'const/ind_types/CONS' @ A0 @ A2 @ A5 ) @ ( 'const/ind_types/CONS' @ A1 @ A3 @ A6 ) )
% 0.27/0.46 = ( 'const/ind_types/CONS' @ A @ ( A4 @ A2 @ A3 ) @ ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A4 @ A5 @ A6 ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.70/1.32 ---- Embedded in THF ---
% 1.70/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.70/1.33 %%% Generated on Tue Feb 24 06:13:19 EST 2026
% 1.70/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.70/1.33 %%% Logic specification used:
% 1.70/1.33 %%% thf(spec, logic, $$dhol).
% 1.70/1.33
% 1.70/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yalf5SCnLk/DTF2DTF898.p
% 1.70/1.33 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.70/1.33 thf('thf_const_const/lists/TL', type, 'const/lists/TL': (!> [A:$tType]: ((('type/ind_types/list' @ A) > ('type/ind_types/list' @ A))))).
% 1.70/1.33 thf('thf_const_const/lists/MAP2', type, 'const/lists/MAP2': (!> [A:$tType,A0:$tType,A1:$tType]: (((A > (A0 > A1)) > (('type/ind_types/list' @ A) > (('type/ind_types/list' @ A0) > ('type/ind_types/list' @ A1))))))).
% 1.70/1.33 thf('thf_const_const/lists/HD', type, 'const/lists/HD': (!> [A:$tType]: ((('type/ind_types/list' @ A) > A)))).
% 1.70/1.33 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.70/1.33 thf('thm/lists/TL_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: (((('const/lists/TL' @ A) @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)) = A1)))).
% 1.70/1.33 thf('thm/lists/HD_', axiom, (! [A:$tType,A0:('type/ind_types/list' @ A),A1:A]: (((('const/lists/HD' @ A) @ ((('const/ind_types/CONS' @ A) @ A1) @ A0)) = A1)))).
% 1.70/1.33 thf('thm/lists/MAP2_DEF_1', axiom, (! [A:$tType,A0:$tType,A1:$tType,A2:A0,A3:(A0 > (A1 > A)),A4:('type/ind_types/list' @ A0),A5:('type/ind_types/list' @ A1)]: (((((((('const/lists/MAP2' @ A0) @ A1) @ A) @ A3) @ ((('const/ind_types/CONS' @ A0) @ A2) @ A4)) @ A5) = ((('const/ind_types/CONS' @ A) @ ((A3 @ A2) @ (('const/lists/HD' @ A1) @ A5))) @ (((((('const/lists/MAP2' @ A0) @ A1) @ A) @ A3) @ A4) @ (('const/lists/TL' @ A1) @ A5))))))).
% 1.70/1.33 thf('thm/lists/MAP2_1', conjecture, (! [A:$tType,A0:$tType,A1:$tType,A2:A0,A3:A1,A4:(A0 > (A1 > A)),A5:('type/ind_types/list' @ A0),A6:('type/ind_types/list' @ A1)]: (((((((('const/lists/MAP2' @ A0) @ A1) @ A) @ A4) @ ((('const/ind_types/CONS' @ A0) @ A2) @ A5)) @ ((('const/ind_types/CONS' @ A1) @ A3) @ A6)) = ((('const/ind_types/CONS' @ A) @ ((A4 @ A2) @ A3)) @ (((((('const/lists/MAP2' @ A0) @ A1) @ A) @ A4) @ A5) @ A6)))))).
% 1.70/1.33 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yalf5SCnLk/DTF2DTF898.p
% 1.70/1.33 ------------------------
% 1.70/1.34 ---- Cleaned THF ---
% 1.70/1.34 thf('thf_type_type/ind_types/list',type,
% 1.70/1.34 'type/ind_types/list': $tType > $tType ).
% 1.70/1.34
% 1.70/1.34 thf('thf_const_const/lists/TL',type,
% 1.70/1.34 'const/lists/TL':
% 1.70/1.34 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.70/1.34
% 1.70/1.34 thf('thf_const_const/lists/MAP2',type,
% 1.70/1.34 'const/lists/MAP2':
% 1.70/1.34 !>[A: $tType,A0: $tType,A1: $tType] : ( ( A > A0 > A1 ) > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A0 ) > ( 'type/ind_types/list' @ A1 ) ) ).
% 1.70/1.34
% 1.70/1.34 thf('thf_const_const/lists/HD',type,
% 1.70/1.34 'const/lists/HD':
% 1.70/1.34 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A ) ).
% 1.70/1.34
% 1.70/1.34 thf('thf_const_const/ind_types/CONS',type,
% 1.70/1.34 'const/ind_types/CONS':
% 1.70/1.34 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.70/1.34
% 1.70/1.34 thf('thm/lists/TL_',axiom,
% 1.70/1.34 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.70/1.34 ( ( 'const/lists/TL' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 1.70/1.34 = A1 ) ).
% 1.70/1.34
% 1.70/1.34 thf('thm/lists/HD_',axiom,
% 1.70/1.34 ! [A: $tType,A0: 'type/ind_types/list' @ A,A1: A] :
% 1.70/1.34 ( ( 'const/lists/HD' @ A @ ( 'const/ind_types/CONS' @ A @ A1 @ A0 ) )
% 1.70/1.34 = A1 ) ).
% 1.70/1.34
% 1.70/1.34 thf('thm/lists/MAP2_DEF_1',axiom,
% 1.70/1.34 ! [A: $tType,A0: $tType,A1: $tType,A2: A0,A3: A0 > A1 > A,A4: 'type/ind_types/list' @ A0,A5: 'type/ind_types/list' @ A1] :
% 1.70/1.34 ( ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A3 @ ( 'const/ind_types/CONS' @ A0 @ A2 @ A4 ) @ A5 )
% 1.70/1.34 = ( 'const/ind_types/CONS' @ A @ ( A3 @ A2 @ ( 'const/lists/HD' @ A1 @ A5 ) ) @ ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A3 @ A4 @ ( 'const/lists/TL' @ A1 @ A5 ) ) ) ) ).
% 1.70/1.34
% 1.70/1.34 thf('thm/lists/MAP2_1',conjecture,
% 1.70/1.34 ! [A: $tType,A0: $tType,A1: $tType,A2: A0,A3: A1,A4: A0 > A1 > A,A5: 'type/ind_types/list' @ A0,A6: 'type/ind_types/list' @ A1] :
% 1.70/1.34 ( ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A4 @ ( 'const/ind_types/CONS' @ A0 @ A2 @ A5 ) @ ( 'const/ind_types/CONS' @ A1 @ A3 @ A6 ) )
% 1.70/1.34 = ( 'const/ind_types/CONS' @ A @ ( A4 @ A2 @ A3 ) @ ( 'const/lists/MAP2' @ A0 @ A1 @ A @ A4 @ A5 @ A6 ) ) ) ).
% 1.70/1.34 ------------------------
% 1.70/1.35 % (1213)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_898 for (2999ds/4Mi)
% 1.70/1.35 % (1216)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_898 for (2999ds/2Mi)
% 1.70/1.35 % Exception at run slice level
% 1.70/1.35 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
% 1.70/1.35 % (1213)Instruction limit reached!
% 1.70/1.35 % (1213)------------------------------
% 1.70/1.35 % (1213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.35 % (1213)Termination reason: Unknown
% 1.70/1.35 % (1213)Termination phase: Saturation
% 1.70/1.35
% 1.70/1.35 % (1213)Memory used [KB]: 5500
% 1.70/1.35 % (1213)Time elapsed: 0.003 s
% 1.70/1.35 % (1213)Instructions burned: 5 (million)
% 1.70/1.35 % (1213)------------------------------
% 1.70/1.35 % (1213)------------------------------
% 1.70/1.36 % (1212)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/183Mi)
% 1.70/1.36 % (1214)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_898 for (2999ds/27Mi)
% 1.70/1.36 % (1215)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/2Mi)
% 1.70/1.36 % (1218)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/18Mi)
% 1.70/1.36 % (1217)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_898 for (2999ds/275Mi)
% 1.70/1.36 % (1215)Instruction limit reached!
% 1.70/1.36 % (1215)------------------------------
% 1.70/1.36 % (1215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (1215)Termination reason: Unknown
% 1.70/1.36 % (1215)Termination phase: Property scanning
% 1.70/1.36
% 1.70/1.36 % (1215)Memory used [KB]: 895
% 1.70/1.36 % (1215)Time elapsed: 0.003 s
% 1.70/1.36 % (1215)Instructions burned: 2 (million)
% 1.70/1.36 % (1215)------------------------------
% 1.70/1.36 % (1215)------------------------------
% 1.70/1.36 % (1217)Refutation not found, incomplete strategy
% 1.70/1.36 % (1217)------------------------------
% 1.70/1.36 % (1217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (1217)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.36
% 1.70/1.36
% 1.70/1.36 % (1217)Memory used [KB]: 5500
% 1.70/1.36 % (1217)Time elapsed: 0.004 s
% 1.70/1.36 % (1217)Instructions burned: 3 (million)
% 1.70/1.36 % (1217)------------------------------
% 1.70/1.36 % (1217)------------------------------
% 1.70/1.36 % (1219)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/3Mi)
% 1.70/1.36 % (1219)Instruction limit reached!
% 1.70/1.36 % (1219)------------------------------
% 1.70/1.36 % (1219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.36 % (1219)Termination reason: Unknown
% 1.70/1.36 % (1219)Termination phase: Saturation
% 1.70/1.36
% 1.70/1.36 % (1219)Memory used [KB]: 5500
% 1.70/1.36 % (1219)Time elapsed: 0.003 s
% 1.70/1.36 % (1219)Instructions burned: 3 (million)
% 1.70/1.36 % (1219)------------------------------
% 1.70/1.36 % (1219)------------------------------
% 1.70/1.36 % (1220)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_898 for (2999ds/37Mi)
% 1.70/1.36 % Exception at run slice level
% 1.70/1.36 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.70/1.37 % (1218)Instruction limit reached!
% 1.70/1.37 % (1218)------------------------------
% 1.70/1.37 % (1218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (1218)Termination reason: Unknown
% 1.70/1.37 % (1218)Termination phase: Saturation
% 1.70/1.37
% 1.70/1.37 % (1218)Memory used [KB]: 5628
% 1.70/1.37 % (1218)Time elapsed: 0.014 s
% 1.70/1.37 % (1218)Instructions burned: 19 (million)
% 1.70/1.37 % (1218)------------------------------
% 1.70/1.37 % (1218)------------------------------
% 1.70/1.37 % (1214)Instruction limit reached!
% 1.70/1.37 % (1214)------------------------------
% 1.70/1.37 % (1214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.37 % (1214)Termination reason: Unknown
% 1.70/1.37 % (1214)Termination phase: Saturation
% 1.70/1.37
% 1.70/1.37 % (1214)Memory used [KB]: 5628
% 1.70/1.37 % (1214)Time elapsed: 0.017 s
% 1.70/1.37 % (1214)Instructions burned: 27 (million)
% 1.70/1.37 % (1214)------------------------------
% 1.70/1.37 % (1214)------------------------------
% 1.70/1.37 % (1223)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_898 for (2999ds/1041Mi)
% 1.70/1.37 % Exception at run slice level
% 1.70/1.37 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
% 1.70/1.37 % (1224)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/7Mi)
% 1.70/1.38 % (1221)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_898 for (2999ds/15Mi)
% 1.70/1.38 % (1224)Instruction limit reached!
% 1.70/1.38 % (1224)------------------------------
% 1.70/1.38 % (1224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (1224)Termination reason: Unknown
% 1.70/1.38 % (1224)Termination phase: Saturation
% 1.70/1.38
% 1.70/1.38 % (1224)Memory used [KB]: 1151
% 1.70/1.38 % (1224)Time elapsed: 0.005 s
% 1.70/1.38 % (1224)Instructions burned: 9 (million)
% 1.70/1.38 % (1224)------------------------------
% 1.70/1.38 % (1224)------------------------------
% 1.70/1.38 % (1222)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_898 for (2999ds/3Mi)
% 1.70/1.38 % (1221)Refutation not found, incomplete strategy
% 1.70/1.38 % (1221)------------------------------
% 1.70/1.38 % (1221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (1221)Termination reason: Refutation not found, incomplete strategy
% 1.70/1.38
% 1.70/1.38
% 1.70/1.38 % (1221)Memory used [KB]: 5500
% 1.70/1.38 % (1221)Time elapsed: 0.004 s
% 1.70/1.38 % (1221)Instructions burned: 3 (million)
% 1.70/1.38 % (1221)------------------------------
% 1.70/1.38 % (1221)------------------------------
% 1.70/1.38 % (1222)Instruction limit reached!
% 1.70/1.38 % (1222)------------------------------
% 1.70/1.38 % (1222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.38 % (1222)Termination reason: Unknown
% 1.70/1.38 % (1222)Termination phase: Saturation
% 1.70/1.38
% 1.70/1.38 % (1222)Memory used [KB]: 5500
% 1.70/1.38 % (1222)Time elapsed: 0.004 s
% 1.70/1.38 % (1222)Instructions burned: 3 (million)
% 1.70/1.38 % (1222)------------------------------
% 1.70/1.38 % (1222)------------------------------
% 1.70/1.38 % (1227)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_898 for (2999ds/3Mi)
% 1.70/1.39 % (1227)Instruction limit reached!
% 1.70/1.39 % (1227)------------------------------
% 1.70/1.39 % (1227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (1227)Termination reason: Unknown
% 1.70/1.39 % (1227)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (1227)Memory used [KB]: 1023
% 1.70/1.39 % (1227)Time elapsed: 0.003 s
% 1.70/1.39 % (1227)Instructions burned: 4 (million)
% 1.70/1.39 % (1227)------------------------------
% 1.70/1.39 % (1227)------------------------------
% 1.70/1.39 % (1226)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_898 for (2999ds/3Mi)
% 1.70/1.39 % (1228)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/7Mi)
% 1.70/1.39 % (1226)Instruction limit reached!
% 1.70/1.39 % (1226)------------------------------
% 1.70/1.39 % (1226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (1226)Termination reason: Unknown
% 1.70/1.39 % (1226)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (1226)Memory used [KB]: 5500
% 1.70/1.39 % (1226)Time elapsed: 0.003 s
% 1.70/1.39 % (1226)Instructions burned: 3 (million)
% 1.70/1.39 % (1226)------------------------------
% 1.70/1.39 % (1226)------------------------------
% 1.70/1.39 % (1225)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/16Mi)
% 1.70/1.39 % (1228)Instruction limit reached!
% 1.70/1.39 % (1228)------------------------------
% 1.70/1.39 % (1228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.39 % (1228)Termination reason: Unknown
% 1.70/1.39 % (1228)Termination phase: Saturation
% 1.70/1.39
% 1.70/1.39 % (1228)Memory used [KB]: 5500
% 1.70/1.39 % (1228)Time elapsed: 0.005 s
% 1.70/1.39 % (1228)Instructions burned: 9 (million)
% 1.70/1.39 % (1228)------------------------------
% 1.70/1.39 % (1228)------------------------------
% 1.70/1.40 % (1231)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/18Mi)
% 1.77/1.40 % (1229)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/3Mi)
% 1.77/1.40 % (1232)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/710Mi)
% 1.77/1.40 % Exception at run slice level
% 1.77/1.40 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
% 1.77/1.40 % (1230)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/4Mi)
% 1.77/1.40 % (1225)Instruction limit reached!
% 1.77/1.40 % (1225)------------------------------
% 1.77/1.40 % (1225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.40 % (1225)Termination reason: Unknown
% 1.77/1.40 % (1225)Termination phase: Saturation
% 1.77/1.40
% 1.77/1.40 % (1225)Memory used [KB]: 5756
% 1.77/1.40 % (1225)Time elapsed: 0.013 s
% 1.77/1.40 % (1225)Instructions burned: 17 (million)
% 1.77/1.40 % (1225)------------------------------
% 1.77/1.40 % (1225)------------------------------
% 1.77/1.40 % (1233)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/6Mi)
% 1.77/1.40 % (1230)Instruction limit reached!
% 1.77/1.40 % (1230)------------------------------
% 1.77/1.40 % (1230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.40 % (1230)Termination reason: Unknown
% 1.77/1.40 % (1230)Termination phase: Saturation
% 1.77/1.40
% 1.77/1.40 % (1230)Memory used [KB]: 5500
% 1.77/1.40 % (1230)Time elapsed: 0.005 s
% 1.77/1.40 % (1230)Instructions burned: 4 (million)
% 1.77/1.40 % (1230)------------------------------
% 1.77/1.40 % (1230)------------------------------
% 1.77/1.40 % (1231)Instruction limit reached!
% 1.77/1.40 % (1231)------------------------------
% 1.77/1.40 % (1231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.40 % (1231)Termination reason: Unknown
% 1.77/1.40 % (1231)Termination phase: Saturation
% 1.77/1.40
% 1.77/1.40 % (1231)Memory used [KB]: 5628
% 1.77/1.40 % (1231)Time elapsed: 0.009 s
% 1.77/1.40 % (1231)Instructions burned: 20 (million)
% 1.77/1.40 % (1231)------------------------------
% 1.77/1.40 % (1231)------------------------------
% 1.77/1.40 % (1233)Instruction limit reached!
% 1.77/1.40 % (1233)------------------------------
% 1.77/1.40 % (1233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.40 % (1233)Termination reason: Unknown
% 1.77/1.40 % (1233)Termination phase: Saturation
% 1.77/1.40
% 1.77/1.40 % (1233)Memory used [KB]: 5500
% 1.77/1.40 % (1233)Time elapsed: 0.004 s
% 1.77/1.40 % (1233)Instructions burned: 6 (million)
% 1.77/1.40 % (1233)------------------------------
% 1.77/1.40 % (1233)------------------------------
% 1.77/1.41 % (1237)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_898 for (2999ds/6Mi)
% 1.77/1.41 % (1238)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/377Mi)
% 1.77/1.41 % Exception at run slice level
% 1.77/1.41 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.77/1.42 % (1234)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_898 for (2999ds/902Mi)
% 1.77/1.42 % (1235)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_898 for (2999ds/21Mi)
% 1.77/1.42 % (1234)Refutation not found, incomplete strategy
% 1.77/1.42 % (1234)------------------------------
% 1.77/1.42 % (1234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.42 % (1234)Termination reason: Refutation not found, incomplete strategy
% 1.77/1.42
% 1.77/1.42
% 1.77/1.42 % (1234)Memory used [KB]: 5500
% 1.77/1.42 % (1234)Time elapsed: 0.004 s
% 1.77/1.42 % (1234)Instructions burned: 3 (million)
% 1.77/1.42 % (1234)------------------------------
% 1.77/1.42 % (1234)------------------------------
% 1.77/1.42 % (1236)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/5Mi)
% 1.77/1.42 % Exception at run slice level
% 1.77/1.42 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
% 1.77/1.42 % (1239)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_898 for (2999ds/779Mi)
% 1.77/1.42 % Exception at run slice level
% 1.77/1.42 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
% 1.77/1.43 % (1212)Instruction limit reached!
% 1.77/1.43 % (1212)------------------------------
% 1.77/1.43 % (1212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.43 % (1212)Termination reason: Unknown
% 1.77/1.43 % (1212)Termination phase: Saturation
% 1.77/1.43
% 1.77/1.43 % (1212)Memory used [KB]: 6396
% 1.77/1.43 % (1212)Time elapsed: 0.070 s
% 1.77/1.43 % (1212)Instructions burned: 185 (million)
% 1.77/1.43 % (1212)------------------------------
% 1.77/1.43 % (1212)------------------------------
% 1.77/1.43 % (1235)Instruction limit reached!
% 1.77/1.43 % (1235)------------------------------
% 1.77/1.43 % (1235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.43 % (1235)Termination reason: Unknown
% 1.77/1.43 % (1235)Termination phase: Saturation
% 1.77/1.43
% 1.77/1.43 % (1235)Memory used [KB]: 5628
% 1.77/1.43 % (1235)Time elapsed: 0.015 s
% 1.77/1.43 % (1235)Instructions burned: 21 (million)
% 1.77/1.43 % (1235)------------------------------
% 1.77/1.43 % (1235)------------------------------
% 1.77/1.43 % (1242)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/17Mi)
% 1.77/1.44 % (1240)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_898 for (2999ds/19Mi)
% 1.77/1.44 % (1243)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/3Mi)
% 1.77/1.44 % Exception at run slice level
% 1.77/1.44 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
% 1.77/1.44 % (1241)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/879Mi)
% 1.77/1.44 % (1243)Instruction limit reached!
% 1.77/1.44 % (1243)------------------------------
% 1.77/1.44 % (1243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.44 % (1243)Termination reason: Unknown
% 1.77/1.44 % (1243)Termination phase: Saturation
% 1.77/1.44
% 1.77/1.44 % (1243)Memory used [KB]: 1023
% 1.77/1.44 % (1243)Time elapsed: 0.003 s
% 1.77/1.44 % (1243)Instructions burned: 4 (million)
% 1.77/1.44 % (1243)------------------------------
% 1.77/1.44 % (1243)------------------------------
% 1.77/1.44 % (1242)Instruction limit reached!
% 1.77/1.44 % (1242)------------------------------
% 1.77/1.44 % (1242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.44 % (1242)Termination reason: Unknown
% 1.77/1.44 % (1242)Termination phase: Saturation
% 1.77/1.44
% 1.77/1.44 % (1242)Memory used [KB]: 5628
% 1.77/1.44 % (1242)Time elapsed: 0.008 s
% 1.77/1.44 % (1242)Instructions burned: 18 (million)
% 1.77/1.44 % (1242)------------------------------
% 1.77/1.44 % (1242)------------------------------
% 1.77/1.45 % (1244)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/30Mi)
% 1.77/1.45 % (1246)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/100Mi)
% 1.77/1.45 % (1247)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_898 for (2999ds/3Mi)
% 1.77/1.45 % Exception at run slice level
% 1.77/1.45 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
% 1.77/1.45 % (1245)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/127Mi)
% 1.77/1.46 % (1248)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_898 for (2999ds/20Mi)
% 1.77/1.47 % (1244)Instruction limit reached!
% 1.77/1.47 % (1244)------------------------------
% 1.77/1.47 % (1244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.47 % (1244)Termination reason: Unknown
% 1.77/1.47 % (1244)Termination phase: Saturation
% 1.77/1.47
% 1.77/1.47 % (1244)Memory used [KB]: 5628
% 1.77/1.47 % (1244)Time elapsed: 0.045 s
% 1.77/1.47 % (1244)Instructions burned: 30 (million)
% 1.77/1.47 % (1244)------------------------------
% 1.77/1.47 % (1244)------------------------------
% 1.77/1.47 % (1248)First to succeed.
% 1.77/1.47 % (1248)Refutation found. Thanks to Tanya!
% 1.77/1.47 % SZS status Theorem for DTF2THF_898
% 1.77/1.47 % SZS output start Proof for DTF2THF_898
% 1.77/1.47 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 1.77/1.47 thf(type_def_7, type, sK0: $tType).
% 1.77/1.47 thf(type_def_8, type, sK1: $tType).
% 1.77/1.47 thf(type_def_9, type, sK2: $tType).
% 1.77/1.47 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 1.77/1.47 thf(func_def_1, type, 'const/lists/TL': !>[X0: $tType]:('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.77/1.47 thf(func_def_2, type, 'const/lists/MAP2': !>[X0: $tType, X1: $tType, X2: $tType]:((X0 > X1 > X2) > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X1 > 'type/ind_types/list' @ X2)).
% 1.77/1.47 thf(func_def_3, type, 'const/lists/HD': !>[X0: $tType]:('type/ind_types/list' @ X0 > X0)).
% 1.77/1.47 thf(func_def_4, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.77/1.47 thf(func_def_8, type, sK3: sK1).
% 1.77/1.47 thf(func_def_9, type, sK4: sK2).
% 1.77/1.47 thf(func_def_10, type, sK5: sK1 > sK2 > sK0).
% 1.77/1.47 thf(func_def_11, type, sK6: 'type/ind_types/list' @ sK1).
% 1.77/1.47 thf(func_def_12, type, sK7: 'type/ind_types/list' @ sK2).
% 1.77/1.47 thf(func_def_13, type, sP8: 'type/ind_types/list' @ sK0 > $o).
% 1.77/1.47 thf(func_def_15, type, ph10: !>[X0: $tType]:(X0)).
% 1.77/1.47 thf(f27,plain,(
% 1.77/1.47 $false),
% 1.77/1.47 inference(trivial_inequality_removal,[status(thm)],[f26])).
% 1.77/1.47 thf(f26,plain,(
% 1.77/1.47 ($true = $false)),
% 1.77/1.47 inference(backward_demodulation,[status(thm)],[f15,f25])).
% 1.77/1.47 thf(f25,plain,(
% 1.77/1.47 ((sP8 @ ('const/ind_types/CONS' @ sK0 @ (sK5 @ sK3 @ sK4) @ ('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ sK6 @ sK7))) = $false)),
% 1.77/1.47 inference(backward_demodulation,[status(thm)],[f14,f24])).
% 1.77/1.47 thf(f24,plain,(
% 1.77/1.47 ( ! [X4 : $tType,X0 : $tType,X3 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0,X6 : X4,X7 : 'type/ind_types/list' @ X4,X5 : X4 > X0 > X3] : ((('const/ind_types/CONS' @ X3 @ (X5 @ X6 @ X1) @ ('const/lists/MAP2' @ X4 @ X0 @ X3 @ X5 @ X7 @ X2)) = ('const/lists/MAP2' @ X4 @ X0 @ X3 @ X5 @ ('const/ind_types/CONS' @ X4 @ X6 @ X7) @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)))) )),
% 1.77/1.47 inference(forward_demodulation,[status(thm)],[f18,f13])).
% 1.77/1.47 thf(f13,plain,(
% 1.77/1.47 ( ! [X0 : $tType,X2 : X0,X1 : 'type/ind_types/list' @ X0] : ((('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1)) = X2)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f2])).
% 1.77/1.47 thf(f2,axiom,(
% 1.77/1.47 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0,X2 : X0] : (('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X1)) = X2)),
% 1.77/1.47 file('/export/starexec/sandbox2/tmp/tmp.yalf5SCnLk/DTF2THF_898.p','thm/lists/HD_')).
% 1.77/1.47 thf(f18,plain,(
% 1.77/1.47 ( ! [X4 : $tType,X0 : $tType,X3 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0,X6 : X4,X7 : 'type/ind_types/list' @ X4,X5 : X4 > X0 > X3] : ((('const/lists/MAP2' @ X4 @ X0 @ X3 @ X5 @ ('const/ind_types/CONS' @ X4 @ X6 @ X7) @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = ('const/ind_types/CONS' @ X3 @ (X5 @ X6 @ ('const/lists/HD' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2))) @ ('const/lists/MAP2' @ X4 @ X0 @ X3 @ X5 @ X7 @ X2)))) )),
% 1.77/1.47 inference(superposition,[status(thm)],[f12,f10])).
% 1.77/1.47 thf(f10,plain,(
% 1.77/1.47 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = X2)) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f1])).
% 1.77/1.47 thf(f1,axiom,(
% 1.77/1.47 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/lists/TL' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)) = X2)),
% 1.77/1.47 file('/export/starexec/sandbox2/tmp/tmp.yalf5SCnLk/DTF2THF_898.p','thm/lists/TL_')).
% 1.77/1.47 thf(f12,plain,(
% 1.77/1.47 ( ! [X1 : $tType,X0 : $tType,X2 : $tType,X3 : X1,X6 : 'type/ind_types/list' @ X2,X4 : X1 > X2 > X0,X5 : 'type/ind_types/list' @ X1] : ((('const/lists/MAP2' @ X1 @ X2 @ X0 @ X4 @ ('const/ind_types/CONS' @ X1 @ X3 @ X5) @ X6) = ('const/ind_types/CONS' @ X0 @ (X4 @ X3 @ ('const/lists/HD' @ X2 @ X6)) @ ('const/lists/MAP2' @ X1 @ X2 @ X0 @ X4 @ X5 @ ('const/lists/TL' @ X2 @ X6))))) )),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f3])).
% 1.77/1.47 thf(f3,axiom,(
% 1.77/1.47 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1,X4 : X1 > X2 > X0,X5 : 'type/ind_types/list' @ X1,X6 : 'type/ind_types/list' @ X2] : (('const/lists/MAP2' @ X1 @ X2 @ X0 @ X4 @ ('const/ind_types/CONS' @ X1 @ X3 @ X5) @ X6) = ('const/ind_types/CONS' @ X0 @ (X4 @ X3 @ ('const/lists/HD' @ X2 @ X6)) @ ('const/lists/MAP2' @ X1 @ X2 @ X0 @ X4 @ X5 @ ('const/lists/TL' @ X2 @ X6))))),
% 1.77/1.47 file('/export/starexec/sandbox2/tmp/tmp.yalf5SCnLk/DTF2THF_898.p','thm/lists/MAP2_DEF_1')).
% 1.77/1.47 thf(f14,plain,(
% 1.77/1.47 ((sP8 @ ('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ ('const/ind_types/CONS' @ sK1 @ sK3 @ sK6) @ ('const/ind_types/CONS' @ sK2 @ sK4 @ sK7))) = $false)),
% 1.77/1.47 introduced(definition,[new_symbols(naming,[sP8])],[inequality_splitting_name_introduction])).
% 1.77/1.47 thf(f15,plain,(
% 1.77/1.47 ($true = (sP8 @ ('const/ind_types/CONS' @ sK0 @ (sK5 @ sK3 @ sK4) @ ('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ sK6 @ sK7))))),
% 1.77/1.47 inference(inequality_splitting,[status(thm)],[f11,f14])).
% 1.77/1.47 thf(f11,plain,(
% 1.77/1.47 (('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ ('const/ind_types/CONS' @ sK1 @ sK3 @ sK6) @ ('const/ind_types/CONS' @ sK2 @ sK4 @ sK7)) != ('const/ind_types/CONS' @ sK0 @ (sK5 @ sK3 @ sK4) @ ('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ sK6 @ sK7)))),
% 1.77/1.47 inference(cnf_transformation,[status(thm)],[f9])).
% 1.77/1.47 thf(f9,plain,(
% 1.77/1.47 (('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ ('const/ind_types/CONS' @ sK1 @ sK3 @ sK6) @ ('const/ind_types/CONS' @ sK2 @ sK4 @ sK7)) != ('const/ind_types/CONS' @ sK0 @ (sK5 @ sK3 @ sK4) @ ('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ sK6 @ sK7)))),
% 1.77/1.47 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7])],[f7,f8])).
% 1.77/1.47 thf(f8,plain,(
% 1.77/1.47 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1,X4 : X2,X5 : X1 > X2 > X0,X6 : 'type/ind_types/list' @ X1,X7 : 'type/ind_types/list' @ X2] : (('const/lists/MAP2' @ X1 @ X2 @ X0 @ X5 @ ('const/ind_types/CONS' @ X1 @ X3 @ X6) @ ('const/ind_types/CONS' @ X2 @ X4 @ X7)) != ('const/ind_types/CONS' @ X0 @ (X5 @ X3 @ X4) @ ('const/lists/MAP2' @ X1 @ X2 @ X0 @ X5 @ X6 @ X7))) => (('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ ('const/ind_types/CONS' @ sK1 @ sK3 @ sK6) @ ('const/ind_types/CONS' @ sK2 @ sK4 @ sK7)) != ('const/ind_types/CONS' @ sK0 @ (sK5 @ sK3 @ sK4) @ ('const/lists/MAP2' @ sK1 @ sK2 @ sK0 @ sK5 @ sK6 @ sK7)))),
% 1.77/1.47 introduced(definition,[],[choice_axiom])).
% 1.77/1.47 thf(f7,plain,(
% 1.77/1.47 ? [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1,X4 : X2,X5 : X1 > X2 > X0,X6 : 'type/ind_types/list' @ X1,X7 : 'type/ind_types/list' @ X2] : (('const/lists/MAP2' @ X1 @ X2 @ X0 @ X5 @ ('const/ind_types/CONS' @ X1 @ X3 @ X6) @ ('const/ind_types/CONS' @ X2 @ X4 @ X7)) != ('const/ind_types/CONS' @ X0 @ (X5 @ X3 @ X4) @ ('const/lists/MAP2' @ X1 @ X2 @ X0 @ X5 @ X6 @ X7)))),
% 1.77/1.47 inference(ennf_transformation,[status(thm)],[f5])).
% 1.77/1.47 thf(f5,negated_conjecture,(
% 1.77/1.47 ~! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1,X4 : X2,X5 : X1 > X2 > X0,X6 : 'type/ind_types/list' @ X1,X7 : 'type/ind_types/list' @ X2] : (('const/lists/MAP2' @ X1 @ X2 @ X0 @ X5 @ ('const/ind_types/CONS' @ X1 @ X3 @ X6) @ ('const/ind_types/CONS' @ X2 @ X4 @ X7)) = ('const/ind_types/CONS' @ X0 @ (X5 @ X3 @ X4) @ ('const/lists/MAP2' @ X1 @ X2 @ X0 @ X5 @ X6 @ X7)))),
% 1.77/1.47 inference(negated_conjecture,[status(cth)],[f4])).
% 1.77/1.47 thf(f4,conjecture,(
% 1.77/1.47 ! [X0 : $tType,X1 : $tType,X2 : $tType,X3 : X1,X4 : X2,X5 : X1 > X2 > X0,X6 : 'type/ind_types/list' @ X1,X7 : 'type/ind_types/list' @ X2] : (('const/lists/MAP2' @ X1 @ X2 @ X0 @ X5 @ ('const/ind_types/CONS' @ X1 @ X3 @ X6) @ ('const/ind_types/CONS' @ X2 @ X4 @ X7)) = ('const/ind_types/CONS' @ X0 @ (X5 @ X3 @ X4) @ ('const/lists/MAP2' @ X1 @ X2 @ X0 @ X5 @ X6 @ X7)))),
% 1.77/1.47 file('/export/starexec/sandbox2/tmp/tmp.yalf5SCnLk/DTF2THF_898.p','thm/lists/MAP2_1')).
% 1.77/1.47 % SZS output end Proof for DTF2THF_898
% 1.77/1.47 % (1248)------------------------------
% 1.77/1.47 % (1248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.77/1.47 % (1248)Termination reason: Refutation
% 1.77/1.47
% 1.77/1.47 % (1248)Memory used [KB]: 5628
% 1.77/1.47 % (1248)Time elapsed: 0.034 s
% 1.77/1.47 % (1248)Instructions burned: 19 (million)
% 1.77/1.47 % (1248)------------------------------
% 1.77/1.47 % (1248)------------------------------
% 1.77/1.47 % (1211)Success in time 0.132 s
%------------------------------------------------------------------------------