%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT327^1 : 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 : n003.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 08:45:28 AM UTC 2026
% Result : Theorem 1.62s 1.39s
% Output : Refutation 1.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT327^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 06:14:10 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.49 ---- Original DTF file ---
% 0.27/0.49 thf(spec,logic,$$dhol).
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 % File : DAT327^1 : TPTP v9.2.1. Released v7.0.0.
% 0.27/0.49 % Domain : Analysis
% 0.27/0.49 % Problem : SET_OF_LIST_EQ_EMPTY
% 0.27/0.49 % Version : Especial.
% 0.27/0.49 % English :
% 0.27/0.49
% 0.27/0.49 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.27/0.49 % Source : [Kal16]
% 0.27/0.49 % Names : SET_OF_LIST_EQ_EMPTY_.p [Kal16]
% 0.27/0.49
% 0.27/0.49 % Status : Theorem
% 0.27/0.49 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 1.00 v7.1.0
% 0.27/0.49 % Syntax : Number of formulae : 12 ( 5 unt; 6 typ; 0 def)
% 0.27/0.49 % Number of atoms : 16 ( 7 equ; 0 cnn)
% 0.27/0.49 % Maximal formula atoms : 1 ( 2 avg)
% 0.27/0.49 % Number of connectives : 49 ( 2 ~; 0 |; 1 &; 44 @)
% 0.27/0.49 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.49 % Maximal formula depth : 12 ( 5 avg)
% 0.27/0.49 % Number of types : 1 ( 0 usr)
% 0.27/0.49 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.27/0.49 % Number of symbols : 7 ( 6 usr; 0 con; 1-4 aty)
% 0.27/0.49 % Number of variables : 22 ( 0 ^; 17 !; 0 ?; 22 :)
% 0.27/0.49 % ( 5 !>; 0 ?*; 0 @-; 0 @+)
% 0.27/0.49 % SPC : TH1_THM_EQU_NAR
% 0.27/0.49
% 0.27/0.49 % Comments : Exported from core HOL Light.
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 thf('thf_type_type/ind_types/list',type,
% 0.27/0.49 'type/ind_types/list': $tType > $tType ).
% 0.27/0.49
% 0.27/0.49 thf('thf_const_const/sets/set_of_list',type,
% 0.27/0.49 'const/sets/set_of_list':
% 0.27/0.49 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A > $o ) ).
% 0.27/0.49
% 0.27/0.49 thf('thf_const_const/sets/INSERT',type,
% 0.27/0.49 'const/sets/INSERT':
% 0.27/0.49 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 0.27/0.49
% 0.27/0.49 thf('thf_const_const/sets/EMPTY',type,
% 0.27/0.49 'const/sets/EMPTY':
% 0.27/0.49 !>[A: $tType] : ( A > $o ) ).
% 0.27/0.49
% 0.27/0.49 thf('thf_const_const/ind_types/NIL',type,
% 0.27/0.49 'const/ind_types/NIL':
% 0.27/0.49 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.27/0.49
% 0.27/0.49 thf('thf_const_const/ind_types/CONS',type,
% 0.27/0.49 'const/ind_types/CONS':
% 0.27/0.49 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.27/0.49
% 0.27/0.49 thf('thm/ind_types/list_INDUCT_',axiom,
% 0.27/0.49 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 0.27/0.49 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 0.27/0.49 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 0.27/0.49 ( ( P @ A1 )
% 0.27/0.49 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 0.27/0.49 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 0.27/0.49
% 0.27/0.49 thf('thm/lists/NOT_CONS_NIL_',axiom,
% 0.27/0.49 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.27/0.49 ( ( 'const/ind_types/CONS' @ A @ A0 @ A1 )
% 0.27/0.49 != ( 'const/ind_types/NIL' @ A ) ) ).
% 0.27/0.49
% 0.27/0.49 thf('thm/sets/NOT_INSERT_EMPTY_',axiom,
% 0.27/0.49 ! [A: $tType,A0: A,A1: A > $o] :
% 0.27/0.49 ( ( 'const/sets/INSERT' @ A @ A0 @ A1 )
% 0.27/0.49 != ( 'const/sets/EMPTY' @ A ) ) ).
% 0.27/0.49
% 0.27/0.49 thf('thm/sets/set_of_list_1',axiom,
% 0.27/0.49 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 0.27/0.49 ( ( 'const/sets/set_of_list' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.27/0.49 = ( 'const/sets/INSERT' @ A @ A0 @ ( 'const/sets/set_of_list' @ A @ A1 ) ) ) ).
% 0.27/0.49
% 0.27/0.49 thf('thm/sets/set_of_list_0',axiom,
% 0.27/0.49 ! [A: $tType] :
% 0.27/0.49 ( ( 'const/sets/set_of_list' @ A @ ( 'const/ind_types/NIL' @ A ) )
% 0.27/0.49 = ( 'const/sets/EMPTY' @ A ) ) ).
% 0.27/0.49
% 0.27/0.49 thf('thm/sets/SET_OF_LIST_EQ_EMPTY_',conjecture,
% 0.27/0.49 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 0.27/0.49 ( ( ( 'const/sets/set_of_list' @ A @ A0 )
% 0.27/0.49 = ( 'const/sets/EMPTY' @ A ) )
% 0.27/0.49 = ( A0
% 0.27/0.49 = ( 'const/ind_types/NIL' @ A ) ) ) ).
% 0.27/0.49
% 0.27/0.49 %------------------------------------------------------------------------------
% 0.27/0.49 ------------------------
% 1.50/1.25 ---- Embedded in THF ---
% 1.50/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.25 %%% Generated on Tue Feb 24 06:14:11 EST 2026
% 1.50/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.25 %%% Logic specification used:
% 1.50/1.25 %%% thf(spec, logic, $$dhol).
% 1.50/1.25
% 1.50/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.mZd7HkgSwK/DTF2DTF5723.p
% 1.50/1.25 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.50/1.25 thf('thf_const_const/sets/set_of_list', type, 'const/sets/set_of_list': (!> [A:$tType]: ((('type/ind_types/list' @ A) > (A > $o))))).
% 1.50/1.25 thf('thf_const_const/sets/INSERT', type, 'const/sets/INSERT': (!> [A:$tType]: ((A > ((A > $o) > (A > $o)))))).
% 1.50/1.25 thf('thf_const_const/sets/EMPTY', type, 'const/sets/EMPTY': (!> [A:$tType]: ((A > $o)))).
% 1.50/1.25 thf('thf_const_const/ind_types/NIL', type, 'const/ind_types/NIL': (!> [A:$tType]: (('type/ind_types/list' @ A)))).
% 1.50/1.25 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.50/1.25 thf('thm/ind_types/list_INDUCT_', axiom, (! [A:$tType,P:(('type/ind_types/list' @ A) > $o)]: ((((P @ ('const/ind_types/NIL' @ A)) & (! [A0:A,A1:('type/ind_types/list' @ A)]: (((P @ A1) => (P @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)))))) => (! [A0:('type/ind_types/list' @ A)]: ((P @ A0))))))).
% 1.50/1.25 thf('thm/lists/NOT_CONS_NIL_', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: ((((('const/ind_types/CONS' @ A) @ A0) @ A1) != ('const/ind_types/NIL' @ A))))).
% 1.50/1.25 thf('thm/sets/NOT_INSERT_EMPTY_', axiom, (! [A:$tType,A0:A,A1:(A > $o)]: ((((('const/sets/INSERT' @ A) @ A0) @ A1) != ('const/sets/EMPTY' @ A))))).
% 1.50/1.25 thf('thm/sets/set_of_list_1', axiom, (! [A:$tType,A0:A,A1:('type/ind_types/list' @ A)]: (((('const/sets/set_of_list' @ A) @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)) = ((('const/sets/INSERT' @ A) @ A0) @ (('const/sets/set_of_list' @ A) @ A1)))))).
% 1.50/1.25 thf('thm/sets/set_of_list_0', axiom, (! [A:$tType]: (((('const/sets/set_of_list' @ A) @ ('const/ind_types/NIL' @ A)) = ('const/sets/EMPTY' @ A))))).
% 1.50/1.25 thf('thm/sets/SET_OF_LIST_EQ_EMPTY_', conjecture, (! [A:$tType,A0:('type/ind_types/list' @ A)]: ((((('const/sets/set_of_list' @ A) @ A0) = ('const/sets/EMPTY' @ A)) = (A0 = ('const/ind_types/NIL' @ A)))))).
% 1.50/1.25 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.mZd7HkgSwK/DTF2DTF5723.p
% 1.50/1.25 ------------------------
% 1.50/1.26 ---- Cleaned THF ---
% 1.50/1.26 thf('thf_type_type/ind_types/list',type,
% 1.50/1.26 'type/ind_types/list': $tType > $tType ).
% 1.50/1.26
% 1.50/1.26 thf('thf_const_const/sets/set_of_list',type,
% 1.50/1.26 'const/sets/set_of_list':
% 1.50/1.26 !>[A: $tType] : ( ( 'type/ind_types/list' @ A ) > A > $o ) ).
% 1.50/1.26
% 1.50/1.26 thf('thf_const_const/sets/INSERT',type,
% 1.50/1.26 'const/sets/INSERT':
% 1.50/1.26 !>[A: $tType] : ( A > ( A > $o ) > A > $o ) ).
% 1.50/1.26
% 1.50/1.26 thf('thf_const_const/sets/EMPTY',type,
% 1.50/1.26 'const/sets/EMPTY':
% 1.50/1.26 !>[A: $tType] : ( A > $o ) ).
% 1.50/1.26
% 1.50/1.26 thf('thf_const_const/ind_types/NIL',type,
% 1.50/1.26 'const/ind_types/NIL':
% 1.50/1.26 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 1.50/1.26
% 1.50/1.26 thf('thf_const_const/ind_types/CONS',type,
% 1.50/1.26 'const/ind_types/CONS':
% 1.50/1.26 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.50/1.26
% 1.50/1.26 thf('thm/ind_types/list_INDUCT_',axiom,
% 1.50/1.26 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 1.50/1.26 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 1.50/1.26 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 1.50/1.26 ( ( P @ A1 )
% 1.50/1.26 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 1.50/1.26 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 1.50/1.26
% 1.50/1.26 thf('thm/lists/NOT_CONS_NIL_',axiom,
% 1.50/1.26 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.50/1.26 ( ( 'const/ind_types/CONS' @ A @ A0 @ A1 )
% 1.50/1.26 != ( 'const/ind_types/NIL' @ A ) ) ).
% 1.50/1.26
% 1.50/1.26 thf('thm/sets/NOT_INSERT_EMPTY_',axiom,
% 1.50/1.26 ! [A: $tType,A0: A,A1: A > $o] :
% 1.50/1.26 ( ( 'const/sets/INSERT' @ A @ A0 @ A1 )
% 1.50/1.26 != ( 'const/sets/EMPTY' @ A ) ) ).
% 1.50/1.26
% 1.50/1.26 thf('thm/sets/set_of_list_1',axiom,
% 1.50/1.26 ! [A: $tType,A0: A,A1: 'type/ind_types/list' @ A] :
% 1.50/1.26 ( ( 'const/sets/set_of_list' @ A @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 1.50/1.26 = ( 'const/sets/INSERT' @ A @ A0 @ ( 'const/sets/set_of_list' @ A @ A1 ) ) ) ).
% 1.50/1.26
% 1.50/1.26 thf('thm/sets/set_of_list_0',axiom,
% 1.50/1.26 ! [A: $tType] :
% 1.50/1.26 ( ( 'const/sets/set_of_list' @ A @ ( 'const/ind_types/NIL' @ A ) )
% 1.50/1.26 = ( 'const/sets/EMPTY' @ A ) ) ).
% 1.50/1.26
% 1.50/1.26 thf('thm/sets/SET_OF_LIST_EQ_EMPTY_',conjecture,
% 1.50/1.26 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 1.50/1.26 ( ( ( 'const/sets/set_of_list' @ A @ A0 )
% 1.50/1.26 = ( 'const/sets/EMPTY' @ A ) )
% 1.50/1.26 = ( A0
% 1.50/1.26 = ( 'const/ind_types/NIL' @ A ) ) ) ).
% 1.50/1.26 ------------------------
% 1.50/1.28 % (6038)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/2Mi)
% 1.50/1.28 % (6041)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/18Mi)
% 1.50/1.28 % (6038)Instruction limit reached!
% 1.50/1.28 % (6038)------------------------------
% 1.50/1.28 % (6038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (6038)Termination reason: Unknown
% 1.50/1.28 % (6038)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (6038)Memory used [KB]: 5500
% 1.50/1.28 % (6038)Time elapsed: 0.003 s
% 1.50/1.28 % (6038)Instructions burned: 3 (million)
% 1.50/1.28 % (6038)------------------------------
% 1.50/1.28 % (6038)------------------------------
% 1.50/1.28 % (6034)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/183Mi)
% 1.50/1.28 % (6041)Instruction limit reached!
% 1.50/1.28 % (6041)------------------------------
% 1.50/1.28 % (6041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.28 % (6041)Termination reason: Unknown
% 1.50/1.28 % (6041)Termination phase: Saturation
% 1.50/1.28
% 1.50/1.28 % (6041)Memory used [KB]: 5628
% 1.50/1.28 % (6041)Time elapsed: 0.008 s
% 1.50/1.28 % (6041)Instructions burned: 18 (million)
% 1.50/1.28 % (6041)------------------------------
% 1.50/1.28 % (6041)------------------------------
% 1.50/1.28 % (6035)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_5723 for (2999ds/4Mi)
% 1.50/1.28 % (6036)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_5723 for (2999ds/27Mi)
% 1.50/1.28 % (6039)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_5723 for (2999ds/2Mi)
% 1.50/1.28 % (6040)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_5723 for (2999ds/275Mi)
% 1.50/1.28 % Exception at run slice level
% 1.50/1.28 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
% 1.50/1.29 % (6035)Instruction limit reached!
% 1.50/1.29 % (6035)------------------------------
% 1.50/1.29 % (6035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (6035)Termination reason: Unknown
% 1.50/1.29 % (6035)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (6035)Memory used [KB]: 5500
% 1.50/1.29 % (6035)Time elapsed: 0.005 s
% 1.50/1.29 % (6035)Instructions burned: 4 (million)
% 1.50/1.29 % (6035)------------------------------
% 1.50/1.29 % (6035)------------------------------
% 1.50/1.29 % (6040)Refutation not found, incomplete strategy
% 1.50/1.29 % (6040)------------------------------
% 1.50/1.29 % (6040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (6040)Termination reason: Refutation not found, incomplete strategy
% 1.50/1.29
% 1.50/1.29
% 1.50/1.29 % (6040)Memory used [KB]: 5500
% 1.50/1.29 % (6040)Time elapsed: 0.004 s
% 1.50/1.29 % (6040)Instructions burned: 2 (million)
% 1.50/1.29 % (6040)------------------------------
% 1.50/1.29 % (6040)------------------------------
% 1.50/1.29 % (6048)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/3Mi)
% 1.50/1.29 % (6048)Instruction limit reached!
% 1.50/1.29 % (6048)------------------------------
% 1.50/1.29 % (6048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.29 % (6048)Termination reason: Unknown
% 1.50/1.29 % (6048)Termination phase: Saturation
% 1.50/1.29
% 1.50/1.29 % (6048)Memory used [KB]: 5500
% 1.50/1.29 % (6048)Time elapsed: 0.002 s
% 1.50/1.29 % (6048)Instructions burned: 3 (million)
% 1.50/1.29 % (6048)------------------------------
% 1.50/1.29 % (6048)------------------------------
% 1.50/1.29 % (6052)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_5723 for (2999ds/37Mi)
% 1.50/1.29 % Exception at run slice level
% 1.50/1.29 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
% 1.62/1.30 % (6057)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/7Mi)
% 1.62/1.30 % (6057)Instruction limit reached!
% 1.62/1.30 % (6057)------------------------------
% 1.62/1.30 % (6057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (6057)Termination reason: Unknown
% 1.62/1.30 % (6057)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (6057)Memory used [KB]: 1023
% 1.62/1.30 % (6057)Time elapsed: 0.004 s
% 1.62/1.30 % (6057)Instructions burned: 8 (million)
% 1.62/1.30 % (6057)------------------------------
% 1.62/1.30 % (6057)------------------------------
% 1.62/1.30 % (6036)Instruction limit reached!
% 1.62/1.30 % (6036)------------------------------
% 1.62/1.30 % (6036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.30 % (6036)Termination reason: Unknown
% 1.62/1.30 % (6036)Termination phase: Saturation
% 1.62/1.30
% 1.62/1.30 % (6036)Memory used [KB]: 5628
% 1.62/1.30 % (6036)Time elapsed: 0.019 s
% 1.62/1.30 % (6036)Instructions burned: 27 (million)
% 1.62/1.30 % (6036)------------------------------
% 1.62/1.30 % (6036)------------------------------
% 1.62/1.30 % (6053)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_5723 for (2999ds/15Mi)
% 1.62/1.30 % (6054)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_5723 for (2999ds/3Mi)
% 1.62/1.30 % (6059)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/16Mi)
% 1.62/1.30 % (6056)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_5723 for (2999ds/1041Mi)
% 1.62/1.31 % (6054)Instruction limit reached!
% 1.62/1.31 % (6054)------------------------------
% 1.62/1.31 % (6054)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (6054)Termination reason: Unknown
% 1.62/1.31 % (6054)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (6054)Memory used [KB]: 5500
% 1.62/1.31 % (6054)Time elapsed: 0.004 s
% 1.62/1.31 % (6054)Instructions burned: 3 (million)
% 1.62/1.31 % (6054)------------------------------
% 1.62/1.31 % (6054)------------------------------
% 1.62/1.31 % Exception at run slice level
% 1.62/1.31 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
% 1.62/1.31 % (6060)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_5723 for (2999ds/3Mi)
% 1.62/1.31 % (6060)Instruction limit reached!
% 1.62/1.31 % (6060)------------------------------
% 1.62/1.31 % (6060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (6060)Termination reason: Unknown
% 1.62/1.31 % (6060)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (6060)Memory used [KB]: 5500
% 1.62/1.31 % (6060)Time elapsed: 0.002 s
% 1.62/1.31 % (6060)Instructions burned: 3 (million)
% 1.62/1.31 % (6060)------------------------------
% 1.62/1.31 % (6060)------------------------------
% 1.62/1.31 % (6059)Instruction limit reached!
% 1.62/1.31 % (6059)------------------------------
% 1.62/1.31 % (6059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (6059)Termination reason: Unknown
% 1.62/1.31 % (6059)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (6059)Memory used [KB]: 5756
% 1.62/1.31 % (6059)Time elapsed: 0.009 s
% 1.62/1.31 % (6059)Instructions burned: 18 (million)
% 1.62/1.31 % (6059)------------------------------
% 1.62/1.31 % (6059)------------------------------
% 1.62/1.31 % (6053)Instruction limit reached!
% 1.62/1.31 % (6053)------------------------------
% 1.62/1.31 % (6053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.31 % (6053)Termination reason: Unknown
% 1.62/1.31 % (6053)Termination phase: Saturation
% 1.62/1.31
% 1.62/1.31 % (6053)Memory used [KB]: 5628
% 1.62/1.31 % (6053)Time elapsed: 0.012 s
% 1.62/1.31 % (6053)Instructions burned: 15 (million)
% 1.62/1.31 % (6053)------------------------------
% 1.62/1.31 % (6053)------------------------------
% 1.62/1.32 % (6062)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_5723 for (2999ds/3Mi)
% 1.62/1.32 % (6068)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/4Mi)
% 1.62/1.32 % (6062)Instruction limit reached!
% 1.62/1.32 % (6062)------------------------------
% 1.62/1.32 % (6062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (6062)Termination reason: Unknown
% 1.62/1.32 % (6062)Termination phase: Equality resolution with deletion
% 1.62/1.32
% 1.62/1.32 % (6062)Memory used [KB]: 1023
% 1.62/1.32 % (6062)Time elapsed: 0.003 s
% 1.62/1.32 % (6062)Instructions burned: 3 (million)
% 1.62/1.32 % (6062)------------------------------
% 1.62/1.32 % (6062)------------------------------
% 1.62/1.32 % (6068)Instruction limit reached!
% 1.62/1.32 % (6068)------------------------------
% 1.62/1.32 % (6068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.32 % (6068)Termination reason: Unknown
% 1.62/1.32 % (6068)Termination phase: Saturation
% 1.62/1.32
% 1.62/1.32 % (6068)Memory used [KB]: 5500
% 1.62/1.32 % (6068)Time elapsed: 0.003 s
% 1.62/1.32 % (6068)Instructions burned: 5 (million)
% 1.62/1.32 % (6068)------------------------------
% 1.62/1.32 % (6068)------------------------------
% 1.62/1.32 % (6069)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/18Mi)
% 1.62/1.32 % (6065)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/3Mi)
% 1.62/1.32 % (6064)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/7Mi)
% 1.62/1.32 % Exception at run slice level
% 1.62/1.32 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
% 1.62/1.33 % (6064)Instruction limit reached!
% 1.62/1.33 % (6064)------------------------------
% 1.62/1.33 % (6064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (6064)Termination reason: Unknown
% 1.62/1.33 % (6064)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (6064)Memory used [KB]: 5500
% 1.62/1.33 % (6064)Time elapsed: 0.007 s
% 1.62/1.33 % (6064)Instructions burned: 7 (million)
% 1.62/1.33 % (6064)------------------------------
% 1.62/1.33 % (6064)------------------------------
% 1.62/1.33 % (6069)Instruction limit reached!
% 1.62/1.33 % (6069)------------------------------
% 1.62/1.33 % (6069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (6069)Termination reason: Unknown
% 1.62/1.33 % (6069)Termination phase: Saturation
% 1.62/1.33
% 1.62/1.33 % (6069)Memory used [KB]: 5628
% 1.62/1.33 % (6069)Time elapsed: 0.009 s
% 1.62/1.33 % (6069)Instructions burned: 19 (million)
% 1.62/1.33 % (6069)------------------------------
% 1.62/1.33 % (6069)------------------------------
% 1.62/1.33 % (6070)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/710Mi)
% 1.62/1.33 % (6072)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_5723 for (2999ds/902Mi)
% 1.62/1.34 % (6071)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/6Mi)
% 1.62/1.34 % (6075)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_5723 for (2999ds/6Mi)
% 1.62/1.34 % Exception at run slice level
% 1.62/1.34 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
% 1.62/1.34 % (6073)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_5723 for (2999ds/21Mi)
% 1.62/1.34 % (6071)Instruction limit reached!
% 1.62/1.34 % (6071)------------------------------
% 1.62/1.34 % (6071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.34 % (6071)Termination reason: Unknown
% 1.62/1.34 % (6071)Termination phase: Saturation
% 1.62/1.34
% 1.62/1.34 % (6071)Memory used [KB]: 5500
% 1.62/1.34 % (6071)Time elapsed: 0.007 s
% 1.62/1.34 % (6071)Instructions burned: 7 (million)
% 1.62/1.34 % (6071)------------------------------
% 1.62/1.34 % (6071)------------------------------
% 1.62/1.35 % (6074)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/5Mi)
% 1.62/1.35 % Exception at run slice level
% 1.62/1.35 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
% 1.62/1.35 % (6073)Instruction limit reached!
% 1.62/1.35 % (6073)------------------------------
% 1.62/1.35 % (6073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.35 % (6073)Termination reason: Unknown
% 1.62/1.35 % (6073)Termination phase: Saturation
% 1.62/1.35
% 1.62/1.35 % (6073)Memory used [KB]: 5628
% 1.62/1.35 % (6073)Time elapsed: 0.011 s
% 1.62/1.35 % (6073)Instructions burned: 22 (million)
% 1.62/1.35 % (6073)------------------------------
% 1.62/1.35 % (6073)------------------------------
% 1.62/1.35 % (6076)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/377Mi)
% 1.62/1.36 % (6079)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/879Mi)
% 1.62/1.36 % (6077)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_5723 for (2999ds/779Mi)
% 1.62/1.36 % Exception at run slice level
% 1.62/1.36 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
% 1.62/1.36 % (6078)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_5723 for (2999ds/19Mi)
% 1.62/1.36 % Exception at run slice level
% 1.62/1.36 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
% 1.62/1.38 % (6080)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/17Mi)
% 1.62/1.38 % (6081)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5723 for (2999ds/3Mi)
% 1.62/1.38 % (6081)Instruction limit reached!
% 1.62/1.38 % (6081)------------------------------
% 1.62/1.38 % (6081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.38 % (6081)Termination reason: Unknown
% 1.62/1.38 % (6081)Termination phase: Saturation
% 1.62/1.38
% 1.62/1.38 % (6081)Memory used [KB]: 1023
% 1.62/1.38 % (6081)Time elapsed: 0.004 s
% 1.62/1.38 % (6081)Instructions burned: 3 (million)
% 1.62/1.38 % (6081)------------------------------
% 1.62/1.38 % (6081)------------------------------
% 1.62/1.38 % (6076)First to succeed.
% 1.62/1.39 % (6076)Refutation found. Thanks to Tanya!
% 1.62/1.39 % SZS status Theorem for DTF2THF_5723
% 1.62/1.39 % SZS output start Proof for DTF2THF_5723
% 1.62/1.39 thf(type_def_5, type, 'type/ind_types/list': ($tType) > $tType).
% 1.62/1.39 thf(type_def_7, type, sK2: $tType).
% 1.62/1.39 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 1.62/1.39 thf(func_def_1, type, 'const/sets/set_of_list': !>[X0: $tType]:('type/ind_types/list' @ X0 > X0 > $o)).
% 1.62/1.39 thf(func_def_2, type, 'const/sets/INSERT': !>[X0: $tType]:(X0 > (X0 > $o) > X0 > $o)).
% 1.62/1.39 thf(func_def_3, type, 'const/sets/EMPTY': !>[X0: $tType]:(X0 > $o)).
% 1.62/1.39 thf(func_def_4, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 1.62/1.39 thf(func_def_5, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.62/1.39 thf(func_def_10, type, sK0: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > X0)).
% 1.62/1.39 thf(func_def_11, type, sK1: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0)).
% 1.62/1.39 thf(func_def_12, type, sK3: 'type/ind_types/list' @ sK2).
% 1.62/1.39 thf(func_def_14, type, ph5: !>[X0: $tType]:(X0)).
% 1.62/1.39 thf(func_def_18, type, sK6: !>[X0: $tType]:(X0 > (X0 > $o) > X0)).
% 1.62/1.39 thf(func_def_19, type, sK7: !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > X0)).
% 1.62/1.39 thf(func_def_20, type, sK8: !>[X0: $tType]:('type/ind_types/list' @ X0 > X0)).
% 1.62/1.39 thf(func_def_21, type, sK9: 'type/ind_types/list' @ sK2 > sK2).
% 1.62/1.39 thf(f467,plain,(
% 1.62/1.39 $false),
% 1.62/1.39 inference(avatar_sat_refutation,[status(thm)],[f47,f48,f51,f437,f465])).
% 1.62/1.39 thf(f465,plain,(
% 1.62/1.39 spl4_2 | ~spl4_1 | ~spl4_11),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f453,f434,f40,f44])).
% 1.62/1.39 thf(f44,definition,(
% 1.62/1.39 spl4_2 <=> ('const/ind_types/NIL' @ sK2 = sK3)),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.62/1.39 thf(f40,definition,(
% 1.62/1.39 spl4_1 <=> (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.62/1.39 thf(f434,definition,(
% 1.62/1.39 spl4_11 <=> (('const/sets/set_of_list' @ sK2 @ sK3 @ (sK9 @ sK3)) = $true)),
% 1.62/1.39 introduced(definition,[new_symbols(naming,[spl4_11])],[avatar_definition])).
% 1.62/1.39 thf(f453,plain,(
% 1.62/1.39 ('const/ind_types/NIL' @ sK2 = sK3) | (~spl4_1 | ~spl4_11)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f452])).
% 1.62/1.39 thf(f452,plain,(
% 1.62/1.39 ($false = $true) | ('const/ind_types/NIL' @ sK2 = sK3) | (~spl4_1 | ~spl4_11)),
% 1.62/1.39 inference(duplicate_literal_removal,[status(thm)],[f441])).
% 1.62/1.39 thf(f441,plain,(
% 1.62/1.39 ('const/ind_types/NIL' @ sK2 = sK3) | ($false = $true) | ($false = $true) | (~spl4_1 | ~spl4_11)),
% 1.62/1.39 inference(superposition,[status(thm)],[f402,f436])).
% 1.62/1.39 thf(f436,plain,(
% 1.62/1.39 (('const/sets/set_of_list' @ sK2 @ sK3 @ (sK9 @ sK3)) = $true) | ~spl4_11),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f434])).
% 1.62/1.39 thf(f402,plain,(
% 1.62/1.39 ( ! [X0 : 'type/ind_types/list' @ sK2] : (($false = ('const/sets/set_of_list' @ sK2 @ sK3 @ (sK9 @ X0))) | ($false = ('const/sets/set_of_list' @ sK2 @ X0 @ (sK9 @ X0))) | ('const/ind_types/NIL' @ sK2 = X0)) ) | ~spl4_1),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f397])).
% 1.62/1.39 thf(f397,plain,(
% 1.62/1.39 ( ! [X0 : 'type/ind_types/list' @ sK2] : (('const/ind_types/NIL' @ sK2 = X0) | (('const/sets/set_of_list' @ sK2 @ sK3 @ (sK9 @ X0)) != ('const/sets/set_of_list' @ sK2 @ X0 @ (sK9 @ X0)))) ) | ~spl4_1),
% 1.62/1.39 inference(negative_extensionality,[status(thm)],[f391])).
% 1.62/1.39 thf(f391,plain,(
% 1.62/1.39 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((('const/sets/set_of_list' @ sK2 @ sK3) != ('const/sets/set_of_list' @ sK2 @ X0)) | ('const/ind_types/NIL' @ sK2 = X0)) ) | ~spl4_1),
% 1.62/1.39 inference(superposition,[status(thm)],[f375,f42])).
% 1.62/1.39 thf(f42,plain,(
% 1.62/1.39 (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3)) | ~spl4_1),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.62/1.39 thf(f375,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0) != ('const/sets/set_of_list' @ X0 @ X1)) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.62/1.39 inference(superposition,[status(thm)],[f129,f109])).
% 1.62/1.39 thf(f109,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ('const/ind_types/NIL' @ X0 = X1)) )),
% 1.62/1.39 inference(equality_proxy_clausification,[status(thm)],[f108])).
% 1.62/1.39 thf(f108,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (((X1 = 'const/ind_types/NIL' @ X0) = $true) | (('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1)) )),
% 1.62/1.39 inference(not_proxy_clausification,[status(thm)],[f107])).
% 1.62/1.39 thf(f107,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | ((~ (X1 = 'const/ind_types/NIL' @ X0)) != $true)) )),
% 1.62/1.39 inference(beta_eta_normalization,[status(thm)],[f101])).
% 1.62/1.39 thf(f101,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ((('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0)))) @ (sK1 @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))))) = X1) | (((^[Y0 : 'type/ind_types/list' @ X0]: (~ (X1 = Y0))) @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.62/1.39 inference(leibniz_equality_elimination,[status(thm)],[f25])).
% 1.62/1.39 thf(f25,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) != $true) | ((X1 @ X2) = $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.62/1.39 inference(cnf_transformation,[status(thm)],[f21])).
% 1.62/1.39 thf(f21,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ! [X2 : 'type/ind_types/list' @ X0] : ((X1 @ X2) = $true) | (((X1 @ (sK1 @ X0 @ X1)) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) != $true)))),
% 1.62/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f19,f20])).
% 1.62/1.39 thf(f20,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)) != $true)) => (((X1 @ (sK1 @ X0 @ X1)) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1))) != $true)))),
% 1.62/1.39 introduced(definition,[],[choice_axiom])).
% 1.62/1.39 thf(f19,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ! [X2 : 'type/ind_types/list' @ X0] : ((X1 @ X2) = $true) | ? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (((X1 @ X4) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)) != $true)))),
% 1.62/1.39 inference(rectify,[status(thm)],[f18])).
% 1.62/1.39 thf(f18,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ! [X4 : 'type/ind_types/list' @ X0] : ((X1 @ X4) = $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ X3) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true)))),
% 1.62/1.39 inference(flattening,[status(thm)],[f17])).
% 1.62/1.39 thf(f17,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (! [X4 : 'type/ind_types/list' @ X0] : ((X1 @ X4) = $true) | (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ X3) = $true) & ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true)) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)))),
% 1.62/1.39 inference(ennf_transformation,[status(thm)],[f12])).
% 1.62/1.39 thf(f12,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : ((! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ X3) = $true) => ((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) = $true)) & ((X1 @ 'const/ind_types/NIL' @ X0) = $true)) => ! [X4 : 'type/ind_types/list' @ X0] : ((X1 @ X4) = $true))),
% 1.62/1.39 inference(fool_elimination,[status(thm)],[f11])).
% 1.62/1.39 thf(f11,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X4 : 'type/ind_types/list' @ X0] : (X1 @ X4))),
% 1.62/1.39 inference(rectify,[status(thm)],[f1])).
% 1.62/1.39 thf(f1,axiom,(
% 1.62/1.39 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (((X1 @ 'const/ind_types/NIL' @ X0) & ! [X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((X1 @ X3) => (X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)))) => ! [X2 : 'type/ind_types/list' @ X0] : (X1 @ X2))),
% 1.62/1.39 file('/export/starexec/sandbox/tmp/tmp.mZd7HkgSwK/DTF2THF_5723.p','thm/ind_types/list_INDUCT_')).
% 1.62/1.39 thf(f129,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0) != ('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)))) )),
% 1.62/1.39 inference(superposition,[status(thm)],[f32,f28])).
% 1.62/1.39 thf(f28,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/set_of_list' @ X0 @ X2)) = ('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)))) )),
% 1.62/1.39 inference(cnf_transformation,[status(thm)],[f14])).
% 1.62/1.39 thf(f14,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : (('const/sets/INSERT' @ X0 @ X1 @ ('const/sets/set_of_list' @ X0 @ X2)) = ('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X1 @ X2)))),
% 1.62/1.39 inference(rectify,[status(thm)],[f4])).
% 1.62/1.39 thf(f4,axiom,(
% 1.62/1.39 ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0] : (('const/sets/set_of_list' @ X0 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) = ('const/sets/INSERT' @ X0 @ X2 @ ('const/sets/set_of_list' @ X0 @ X3)))),
% 1.62/1.39 file('/export/starexec/sandbox/tmp/tmp.mZd7HkgSwK/DTF2THF_5723.p','thm/sets/set_of_list_1')).
% 1.62/1.39 thf(f32,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : ((('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0) != ('const/sets/INSERT' @ X0 @ X1 @ X2))) )),
% 1.62/1.39 inference(definition_unfolding,[status(thm)],[f30,f24])).
% 1.62/1.39 thf(f24,plain,(
% 1.62/1.39 ( ! [X0 : $tType] : (('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0))) )),
% 1.62/1.39 inference(cnf_transformation,[status(thm)],[f5])).
% 1.62/1.39 thf(f5,axiom,(
% 1.62/1.39 ! [X0 : $tType] : ('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ 'const/ind_types/NIL' @ X0))),
% 1.62/1.39 file('/export/starexec/sandbox/tmp/tmp.mZd7HkgSwK/DTF2THF_5723.p','thm/sets/set_of_list_0')).
% 1.62/1.39 thf(f30,plain,(
% 1.62/1.39 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0] : (('const/sets/EMPTY' @ X0 != ('const/sets/INSERT' @ X0 @ X1 @ X2))) )),
% 1.62/1.39 inference(cnf_transformation,[status(thm)],[f15])).
% 1.62/1.39 thf(f15,plain,(
% 1.62/1.39 ! [X0 : $tType,X1 : X0,X2 : X0 > $o] : ('const/sets/EMPTY' @ X0 != ('const/sets/INSERT' @ X0 @ X1 @ X2))),
% 1.62/1.39 inference(rectify,[status(thm)],[f3])).
% 1.62/1.39 thf(f3,axiom,(
% 1.62/1.39 ! [X0 : $tType,X2 : X0,X3 : X0 > $o] : (('const/sets/INSERT' @ X0 @ X2 @ X3) != 'const/sets/EMPTY' @ X0)),
% 1.62/1.39 file('/export/starexec/sandbox/tmp/tmp.mZd7HkgSwK/DTF2THF_5723.p','thm/sets/NOT_INSERT_EMPTY_')).
% 1.62/1.39 thf(f437,plain,(
% 1.62/1.39 spl4_2 | spl4_11 | ~spl4_1),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f432,f40,f434,f44])).
% 1.62/1.39 thf(f432,plain,(
% 1.62/1.39 (('const/sets/set_of_list' @ sK2 @ sK3 @ (sK9 @ sK3)) = $true) | ('const/ind_types/NIL' @ sK2 = sK3) | ~spl4_1),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f431])).
% 1.62/1.39 thf(f431,plain,(
% 1.62/1.39 ('const/ind_types/NIL' @ sK2 = sK3) | (('const/sets/set_of_list' @ sK2 @ sK3 @ (sK9 @ sK3)) = $true) | ($true != $true) | ~spl4_1),
% 1.62/1.39 inference(equality_factoring,[status(thm)],[f401])).
% 1.62/1.39 thf(f401,plain,(
% 1.62/1.39 ( ! [X0 : 'type/ind_types/list' @ sK2] : ((('const/sets/set_of_list' @ sK2 @ sK3 @ (sK9 @ X0)) = $true) | (('const/sets/set_of_list' @ sK2 @ X0 @ (sK9 @ X0)) = $true) | ('const/ind_types/NIL' @ sK2 = X0)) ) | ~spl4_1),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f397])).
% 1.62/1.39 thf(f51,plain,(
% 1.62/1.39 spl4_1 | ~spl4_2),
% 1.62/1.39 inference(avatar_contradiction_clause,[status(thm)],[f50])).
% 1.62/1.39 thf(f50,plain,(
% 1.62/1.39 $false | (spl4_1 | ~spl4_2)),
% 1.62/1.39 inference(trivial_inequality_removal,[status(thm)],[f49])).
% 1.62/1.39 thf(f49,plain,(
% 1.62/1.39 (('const/sets/set_of_list' @ sK2 @ sK3) != ('const/sets/set_of_list' @ sK2 @ sK3)) | (spl4_1 | ~spl4_2)),
% 1.62/1.39 inference(backward_demodulation,[status(thm)],[f41,f46])).
% 1.62/1.39 thf(f46,plain,(
% 1.62/1.39 ('const/ind_types/NIL' @ sK2 = sK3) | ~spl4_2),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.62/1.39 thf(f41,plain,(
% 1.62/1.39 (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) != ('const/sets/set_of_list' @ sK2 @ sK3)) | spl4_1),
% 1.62/1.39 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.62/1.39 thf(f48,plain,(
% 1.62/1.39 ~spl4_2 | ~spl4_1),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f36,f40,f44])).
% 1.62/1.39 thf(f36,plain,(
% 1.62/1.39 (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) != ('const/sets/set_of_list' @ sK2 @ sK3)) | ('const/ind_types/NIL' @ sK2 != sK3)),
% 1.62/1.39 inference(equality_proxy_clausification,[status(thm)],[f35])).
% 1.62/1.39 thf(f35,plain,(
% 1.62/1.39 (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) != ('const/sets/set_of_list' @ sK2 @ sK3)) | ($false = ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.39 inference(equality_proxy_clausification,[status(thm)],[f34])).
% 1.62/1.39 thf(f34,plain,(
% 1.62/1.39 ($false = (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))) | ($false = ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.62/1.39 thf(f31,plain,(
% 1.62/1.39 (('const/ind_types/NIL' @ sK2 = sK3) != (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3)))),
% 1.62/1.39 inference(definition_unfolding,[status(thm)],[f27,f24])).
% 1.62/1.39 thf(f27,plain,(
% 1.62/1.39 (('const/sets/EMPTY' @ sK2 = ('const/sets/set_of_list' @ sK2 @ sK3)) != ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.62/1.39 thf(f23,plain,(
% 1.62/1.39 (('const/sets/EMPTY' @ sK2 = ('const/sets/set_of_list' @ sK2 @ sK3)) != ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f16,f22])).
% 1.62/1.39 thf(f22,plain,(
% 1.62/1.39 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ X1)) != ('const/ind_types/NIL' @ X0 = X1)) => (('const/sets/EMPTY' @ sK2 = ('const/sets/set_of_list' @ sK2 @ sK3)) != ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.39 introduced(definition,[],[choice_axiom])).
% 1.62/1.39 thf(f16,plain,(
% 1.62/1.39 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ X1)) != ('const/ind_types/NIL' @ X0 = X1))),
% 1.62/1.39 inference(ennf_transformation,[status(thm)],[f10])).
% 1.62/1.39 thf(f10,plain,(
% 1.62/1.39 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ X1)) = ('const/ind_types/NIL' @ X0 = X1))),
% 1.62/1.39 inference(fool_elimination,[status(thm)],[f9])).
% 1.62/1.39 thf(f9,plain,(
% 1.62/1.39 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ X1)) = ('const/ind_types/NIL' @ X0 = X1))),
% 1.62/1.39 inference(rectify,[status(thm)],[f7])).
% 1.62/1.39 thf(f7,negated_conjecture,(
% 1.62/1.39 ~! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ X2)) = ('const/ind_types/NIL' @ X0 = X2))),
% 1.62/1.39 inference(negated_conjecture,[status(cth)],[f6])).
% 1.62/1.39 thf(f6,conjecture,(
% 1.62/1.39 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (('const/sets/EMPTY' @ X0 = ('const/sets/set_of_list' @ X0 @ X2)) = ('const/ind_types/NIL' @ X0 = X2))),
% 1.62/1.39 file('/export/starexec/sandbox/tmp/tmp.mZd7HkgSwK/DTF2THF_5723.p','thm/sets/SET_OF_LIST_EQ_EMPTY_')).
% 1.62/1.39 thf(f47,plain,(
% 1.62/1.39 spl4_1 | spl4_2),
% 1.62/1.39 inference(avatar_split_clause,[status(thm)],[f38,f44,f40])).
% 1.62/1.39 thf(f38,plain,(
% 1.62/1.39 (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3)) | ('const/ind_types/NIL' @ sK2 = sK3)),
% 1.62/1.39 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.62/1.39 thf(f37,plain,(
% 1.62/1.39 ($true = ('const/ind_types/NIL' @ sK2 = sK3)) | (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))),
% 1.62/1.39 inference(equality_proxy_clausification,[status(thm)],[f33])).
% 1.62/1.39 thf(f33,plain,(
% 1.62/1.39 ($true = (('const/sets/set_of_list' @ sK2 @ 'const/ind_types/NIL' @ sK2) = ('const/sets/set_of_list' @ sK2 @ sK3))) | ($true = ('const/ind_types/NIL' @ sK2 = sK3))),
% 1.62/1.39 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.62/1.39 % SZS output end Proof for DTF2THF_5723
% 1.62/1.39 % (6076)------------------------------
% 1.62/1.39 % (6076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.39 % (6076)Termination reason: Refutation
% 1.62/1.39
% 1.62/1.39 % (6076)Memory used [KB]: 5884
% 1.62/1.39 % (6076)Time elapsed: 0.037 s
% 1.62/1.39 % (6076)Instructions burned: 100 (million)
% 1.62/1.39 % (6076)------------------------------
% 1.62/1.39 % (6076)------------------------------
% 1.62/1.39 % (6031)Success in time 0.107 s
%------------------------------------------------------------------------------