%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT294^1 : 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 : n017.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 08:45:24 AM UTC 2026
% Result : Theorem 1.72s 1.43s
% Output : Refutation 1.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT294^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n017.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 06:11:26 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.48 ---- Original DTF file ---
% 0.31/0.48 thf(spec,logic,$$dhol).
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 % File : DAT294^1 : TPTP v9.2.1. Released v7.0.0.
% 0.31/0.48 % Domain : Analysis
% 0.31/0.48 % Problem : ALL_T
% 0.31/0.48 % Version : Especial.
% 0.31/0.48 % English :
% 0.31/0.48
% 0.31/0.48 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.31/0.48 % Source : [Kal16]
% 0.31/0.48 % Names : ALL_T_.p [Kal16]
% 0.31/0.48
% 0.31/0.48 % Status : Theorem
% 0.31/0.48 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.31/0.48 % Syntax : Number of formulae : 8 ( 2 unt; 4 typ; 0 def)
% 0.31/0.48 % Number of atoms : 8 ( 2 equ; 0 cnn)
% 0.31/0.48 % Maximal formula atoms : 2 ( 2 avg)
% 0.31/0.48 % Number of connectives : 38 ( 0 ~; 0 |; 2 &; 34 @)
% 0.31/0.48 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.31/0.48 % Maximal formula depth : 12 ( 7 avg)
% 0.31/0.48 % Number of types : 1 ( 0 usr)
% 0.31/0.48 % Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% 0.31/0.48 % Number of symbols : 6 ( 4 usr; 1 con; 0-3 aty)
% 0.31/0.48 % Number of variables : 17 ( 1 ^; 13 !; 0 ?; 17 :)
% 0.31/0.48 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.48 % SPC : TH1_THM_EQU_NAR
% 0.31/0.48
% 0.31/0.48 % Comments : Exported from core HOL Light.
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 thf('thf_type_type/ind_types/list',type,
% 0.31/0.48 'type/ind_types/list': $tType > $tType ).
% 0.31/0.48
% 0.31/0.48 thf('thf_const_const/lists/ALL',type,
% 0.31/0.48 'const/lists/ALL':
% 0.31/0.48 !>[A: $tType] : ( ( A > $o ) > ( 'type/ind_types/list' @ A ) > $o ) ).
% 0.31/0.48
% 0.31/0.48 thf('thf_const_const/ind_types/NIL',type,
% 0.31/0.48 'const/ind_types/NIL':
% 0.31/0.48 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 0.31/0.48
% 0.31/0.48 thf('thf_const_const/ind_types/CONS',type,
% 0.31/0.48 'const/ind_types/CONS':
% 0.31/0.48 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 0.31/0.48
% 0.31/0.48 thf('thm/ind_types/list_INDUCT_',axiom,
% 0.31/0.48 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 0.31/0.48 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 0.31/0.48 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 0.31/0.48 ( ( P @ A1 )
% 0.31/0.48 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 0.31/0.48 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 0.31/0.48
% 0.31/0.48 thf('thm/lists/ALL_1',axiom,
% 0.31/0.48 ! [A: $tType,A0: A,P: A > $o,A1: 'type/ind_types/list' @ A] :
% 0.31/0.48 ( ( 'const/lists/ALL' @ A @ P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 0.31/0.48 = ( ( P @ A0 )
% 0.31/0.48 & ( 'const/lists/ALL' @ A @ P @ A1 ) ) ) ).
% 0.31/0.48
% 0.31/0.48 thf('thm/lists/ALL_0',axiom,
% 0.31/0.48 ! [A: $tType,P: A > $o] :
% 0.31/0.48 ( ( 'const/lists/ALL' @ A @ P @ ( 'const/ind_types/NIL' @ A ) )
% 0.31/0.48 = $true ) ).
% 0.31/0.48
% 0.31/0.48 thf('thm/lists/ALL_T_',conjecture,
% 0.31/0.48 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 0.31/0.48 ( 'const/lists/ALL' @ A
% 0.31/0.48 @ ^ [A1: A] : $true
% 0.31/0.48 @ A0 ) ).
% 0.31/0.48
% 0.31/0.48 %------------------------------------------------------------------------------
% 0.31/0.48 ------------------------
% 1.69/1.31 ---- Embedded in THF ---
% 1.69/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.69/1.31 %%% Generated on Tue Feb 24 06:11:27 EST 2026
% 1.69/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.69/1.31 %%% Logic specification used:
% 1.69/1.31 %%% thf(spec, logic, $$dhol).
% 1.69/1.31
% 1.69/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.hiKps8SKu2/DTF2DTF3933.p
% 1.69/1.31 thf('thf_type_type/ind_types/list', type, 'type/ind_types/list': ($tType > $tType)).
% 1.69/1.31 thf('thf_const_const/lists/ALL', type, 'const/lists/ALL': (!> [A:$tType]: (((A > $o) > (('type/ind_types/list' @ A) > $o))))).
% 1.69/1.31 thf('thf_const_const/ind_types/NIL', type, 'const/ind_types/NIL': (!> [A:$tType]: (('type/ind_types/list' @ A)))).
% 1.69/1.31 thf('thf_const_const/ind_types/CONS', type, 'const/ind_types/CONS': (!> [A:$tType]: ((A > (('type/ind_types/list' @ A) > ('type/ind_types/list' @ A)))))).
% 1.69/1.31 thf('thm/ind_types/list_INDUCT_', axiom, (! [A:$tType,P:(('type/ind_types/list' @ A) > $o)]: ((((P @ ('const/ind_types/NIL' @ A)) & (! [A0:A,A1:('type/ind_types/list' @ A)]: (((P @ A1) => (P @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)))))) => (! [A0:('type/ind_types/list' @ A)]: ((P @ A0))))))).
% 1.69/1.31 thf('thm/lists/ALL_1', axiom, (! [A:$tType,A0:A,P:(A > $o),A1:('type/ind_types/list' @ A)]: ((((('const/lists/ALL' @ A) @ P) @ ((('const/ind_types/CONS' @ A) @ A0) @ A1)) = ((P @ A0) & ((('const/lists/ALL' @ A) @ P) @ A1)))))).
% 1.69/1.31 thf('thm/lists/ALL_0', axiom, (! [A:$tType,P:(A > $o)]: ((((('const/lists/ALL' @ A) @ P) @ ('const/ind_types/NIL' @ A)) = $true)))).
% 1.69/1.31 thf('thm/lists/ALL_T_', conjecture, (! [A:$tType,A0:('type/ind_types/list' @ A)]: (((('const/lists/ALL' @ A) @ (^ [A1:A]: ($true))) @ A0)))).
% 1.69/1.31 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.hiKps8SKu2/DTF2DTF3933.p
% 1.69/1.31 ------------------------
% 1.69/1.32 ---- Cleaned THF ---
% 1.69/1.33 thf('thf_type_type/ind_types/list',type,
% 1.69/1.33 'type/ind_types/list': $tType > $tType ).
% 1.69/1.33
% 1.69/1.33 thf('thf_const_const/lists/ALL',type,
% 1.69/1.33 'const/lists/ALL':
% 1.69/1.33 !>[A: $tType] : ( ( A > $o ) > ( 'type/ind_types/list' @ A ) > $o ) ).
% 1.69/1.33
% 1.69/1.33 thf('thf_const_const/ind_types/NIL',type,
% 1.69/1.33 'const/ind_types/NIL':
% 1.69/1.33 !>[A: $tType] : ( 'type/ind_types/list' @ A ) ).
% 1.69/1.33
% 1.69/1.33 thf('thf_const_const/ind_types/CONS',type,
% 1.69/1.33 'const/ind_types/CONS':
% 1.69/1.33 !>[A: $tType] : ( A > ( 'type/ind_types/list' @ A ) > ( 'type/ind_types/list' @ A ) ) ).
% 1.69/1.33
% 1.69/1.33 thf('thm/ind_types/list_INDUCT_',axiom,
% 1.69/1.33 ! [A: $tType,P: ( 'type/ind_types/list' @ A ) > $o] :
% 1.69/1.33 ( ( ( P @ ( 'const/ind_types/NIL' @ A ) )
% 1.69/1.33 & ! [A0: A,A1: 'type/ind_types/list' @ A] :
% 1.69/1.33 ( ( P @ A1 )
% 1.69/1.33 => ( P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) ) ) )
% 1.69/1.33 => ! [A0: 'type/ind_types/list' @ A] : ( P @ A0 ) ) ).
% 1.69/1.33
% 1.69/1.33 thf('thm/lists/ALL_1',axiom,
% 1.69/1.33 ! [A: $tType,A0: A,P: A > $o,A1: 'type/ind_types/list' @ A] :
% 1.69/1.33 ( ( 'const/lists/ALL' @ A @ P @ ( 'const/ind_types/CONS' @ A @ A0 @ A1 ) )
% 1.69/1.33 = ( ( P @ A0 )
% 1.69/1.33 & ( 'const/lists/ALL' @ A @ P @ A1 ) ) ) ).
% 1.69/1.33
% 1.69/1.33 thf('thm/lists/ALL_0',axiom,
% 1.69/1.33 ! [A: $tType,P: A > $o] :
% 1.69/1.33 ( ( 'const/lists/ALL' @ A @ P @ ( 'const/ind_types/NIL' @ A ) )
% 1.69/1.33 = $true ) ).
% 1.69/1.33
% 1.69/1.33 thf('thm/lists/ALL_T_',conjecture,
% 1.69/1.33 ! [A: $tType,A0: 'type/ind_types/list' @ A] :
% 1.69/1.33 ( 'const/lists/ALL' @ A
% 1.69/1.33 @ ^ [A1: A] : $true
% 1.69/1.33 @ A0 ) ).
% 1.69/1.33 ------------------------
% 1.69/1.34 % (4282)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_3933 for (2999ds/275Mi)
% 1.69/1.34 % (4279)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_3933 for (2999ds/27Mi)
% 1.69/1.34 % (4282)Refutation not found, incomplete strategy
% 1.69/1.34 % (4282)------------------------------
% 1.69/1.34 % (4282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.34 % (4282)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.34
% 1.69/1.34
% 1.69/1.34 % (4282)Memory used [KB]: 5373
% 1.69/1.34 % (4282)Time elapsed: 0.002 s
% 1.69/1.34 % (4282)------------------------------
% 1.69/1.34 % (4282)------------------------------
% 1.69/1.35 % (4277)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/183Mi)
% 1.69/1.35 % (4278)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_3933 for (2999ds/4Mi)
% 1.69/1.35 % (4280)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/2Mi)
% 1.69/1.35 % (4281)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_3933 for (2999ds/2Mi)
% 1.69/1.35 % (4283)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/18Mi)
% 1.69/1.35 % (4281)Instruction limit reached!
% 1.69/1.35 % (4281)------------------------------
% 1.69/1.35 % (4281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (4281)Termination reason: Unknown
% 1.69/1.35 % (4281)Termination phase: shuffling
% 1.69/1.35
% 1.69/1.35 % (4281)Memory used [KB]: 895
% 1.69/1.35 % (4281)Time elapsed: 0.003 s
% 1.69/1.35 % (4281)Instructions burned: 2 (million)
% 1.69/1.35 % (4281)------------------------------
% 1.69/1.35 % (4281)------------------------------
% 1.69/1.35 % (4280)Instruction limit reached!
% 1.69/1.35 % (4280)------------------------------
% 1.69/1.35 % (4280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (4280)Termination reason: Unknown
% 1.69/1.35 % (4280)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (4280)Memory used [KB]: 5500
% 1.69/1.35 % (4280)Time elapsed: 0.004 s
% 1.69/1.35 % (4280)Instructions burned: 3 (million)
% 1.69/1.35 % (4280)------------------------------
% 1.69/1.35 % (4280)------------------------------
% 1.69/1.35 % (4278)Instruction limit reached!
% 1.69/1.35 % (4278)------------------------------
% 1.69/1.35 % (4278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (4278)Termination reason: Unknown
% 1.69/1.35 % (4278)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (4278)Memory used [KB]: 5500
% 1.69/1.35 % (4278)Time elapsed: 0.005 s
% 1.69/1.35 % (4278)Instructions burned: 4 (million)
% 1.69/1.35 % (4278)------------------------------
% 1.69/1.35 % (4278)------------------------------
% 1.69/1.35 % (4279)Instruction limit reached!
% 1.69/1.35 % (4279)------------------------------
% 1.69/1.35 % (4279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (4279)Termination reason: Unknown
% 1.69/1.35 % (4279)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (4279)Memory used [KB]: 5628
% 1.69/1.35 % (4279)Time elapsed: 0.011 s
% 1.69/1.35 % (4279)Instructions burned: 27 (million)
% 1.69/1.35 % (4279)------------------------------
% 1.69/1.35 % (4279)------------------------------
% 1.69/1.35 % (4284)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/3Mi)
% 1.69/1.35 % (4284)Instruction limit reached!
% 1.69/1.35 % (4284)------------------------------
% 1.69/1.35 % (4284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (4284)Termination reason: Unknown
% 1.69/1.35 % (4284)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (4284)Memory used [KB]: 5500
% 1.69/1.35 % (4284)Time elapsed: 0.003 s
% 1.69/1.35 % (4284)Instructions burned: 5 (million)
% 1.69/1.35 % (4284)------------------------------
% 1.69/1.35 % (4284)------------------------------
% 1.69/1.36 % (4283)Instruction limit reached!
% 1.69/1.36 % (4283)------------------------------
% 1.69/1.36 % (4283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (4283)Termination reason: Unknown
% 1.69/1.36 % (4283)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (4283)Memory used [KB]: 5628
% 1.69/1.36 % (4283)Time elapsed: 0.014 s
% 1.69/1.36 % (4283)Instructions burned: 19 (million)
% 1.69/1.36 % (4283)------------------------------
% 1.69/1.36 % (4283)------------------------------
% 1.69/1.36 % (4288)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_3933 for (2999ds/1041Mi)
% 1.69/1.36 % Exception at run slice level
% 1.69/1.36 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
% 1.69/1.36 % (4289)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/7Mi)
% 1.69/1.36 % (4289)Instruction limit reached!
% 1.69/1.36 % (4289)------------------------------
% 1.69/1.36 % (4289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (4289)Termination reason: Unknown
% 1.69/1.36 % (4289)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (4289)Memory used [KB]: 1023
% 1.69/1.36 % (4289)Time elapsed: 0.004 s
% 1.69/1.36 % (4289)Instructions burned: 9 (million)
% 1.69/1.36 % (4289)------------------------------
% 1.69/1.36 % (4289)------------------------------
% 1.69/1.37 % (4285)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_3933 for (2999ds/37Mi)
% 1.69/1.37 % Exception at run slice level
% 1.69/1.37 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
% 1.69/1.37 % (4286)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_3933 for (2999ds/15Mi)
% 1.69/1.37 % (4287)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_3933 for (2999ds/3Mi)
% 1.69/1.37 % (4287)Instruction limit reached!
% 1.69/1.37 % (4287)------------------------------
% 1.69/1.37 % (4287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (4287)Termination reason: Unknown
% 1.69/1.37 % (4287)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (4287)Memory used [KB]: 5500
% 1.69/1.37 % (4287)Time elapsed: 0.004 s
% 1.69/1.37 % (4287)Instructions burned: 3 (million)
% 1.69/1.37 % (4287)------------------------------
% 1.69/1.37 % (4287)------------------------------
% 1.69/1.37 % (4291)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_3933 for (2999ds/3Mi)
% 1.69/1.37 % (4291)Instruction limit reached!
% 1.69/1.37 % (4291)------------------------------
% 1.69/1.37 % (4291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (4291)Termination reason: Unknown
% 1.69/1.37 % (4291)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (4291)Memory used [KB]: 5500
% 1.69/1.37 % (4291)Time elapsed: 0.003 s
% 1.69/1.37 % (4291)Instructions burned: 3 (million)
% 1.69/1.37 % (4291)------------------------------
% 1.69/1.37 % (4291)------------------------------
% 1.69/1.37 % (4292)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_3933 for (2999ds/3Mi)
% 1.69/1.37 % (4292)Instruction limit reached!
% 1.69/1.37 % (4292)------------------------------
% 1.69/1.37 % (4292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (4292)Termination reason: Unknown
% 1.69/1.37 % (4292)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (4292)Memory used [KB]: 1023
% 1.69/1.37 % (4292)Time elapsed: 0.002 s
% 1.69/1.37 % (4292)Instructions burned: 3 (million)
% 1.69/1.37 % (4292)------------------------------
% 1.69/1.37 % (4292)------------------------------
% 1.69/1.38 % (4286)Instruction limit reached!
% 1.69/1.38 % (4286)------------------------------
% 1.69/1.38 % (4286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (4286)Termination reason: Unknown
% 1.69/1.38 % (4286)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (4286)Memory used [KB]: 5628
% 1.69/1.38 % (4286)Time elapsed: 0.012 s
% 1.69/1.38 % (4286)Instructions burned: 16 (million)
% 1.69/1.38 % (4286)------------------------------
% 1.69/1.38 % (4286)------------------------------
% 1.69/1.38 % (4290)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/16Mi)
% 1.69/1.38 % (4295)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/4Mi)
% 1.69/1.38 % (4293)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/7Mi)
% 1.69/1.38 % (4296)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/18Mi)
% 1.69/1.38 % (4295)Instruction limit reached!
% 1.69/1.38 % (4295)------------------------------
% 1.69/1.38 % (4295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (4295)Termination reason: Unknown
% 1.69/1.38 % (4295)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (4295)Memory used [KB]: 5500
% 1.69/1.38 % (4295)Time elapsed: 0.004 s
% 1.69/1.38 % (4295)Instructions burned: 6 (million)
% 1.69/1.38 % (4295)------------------------------
% 1.69/1.38 % (4295)------------------------------
% 1.69/1.39 % (4290)Instruction limit reached!
% 1.69/1.39 % (4290)------------------------------
% 1.69/1.39 % (4290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (4290)Termination reason: Unknown
% 1.69/1.39 % (4290)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (4290)Memory used [KB]: 5628
% 1.69/1.39 % (4290)Time elapsed: 0.012 s
% 1.69/1.39 % (4290)Instructions burned: 16 (million)
% 1.69/1.39 % (4290)------------------------------
% 1.69/1.39 % (4290)------------------------------
% 1.69/1.39 % (4294)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/3Mi)
% 1.69/1.39 % Exception at run slice level
% 1.69/1.39 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
% 1.69/1.39 % (4296)Refutation not found, incomplete strategy
% 1.69/1.39 % (4296)------------------------------
% 1.69/1.39 % (4296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (4296)Termination reason: Refutation not found, incomplete strategy
% 1.69/1.39
% 1.69/1.39
% 1.69/1.39 % (4296)Memory used [KB]: 5500
% 1.69/1.39 % (4296)Time elapsed: 0.005 s
% 1.69/1.39 % (4296)Instructions burned: 11 (million)
% 1.69/1.39 % (4296)------------------------------
% 1.69/1.39 % (4296)------------------------------
% 1.69/1.39 % (4293)Instruction limit reached!
% 1.69/1.39 % (4293)------------------------------
% 1.69/1.39 % (4293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (4293)Termination reason: Unknown
% 1.69/1.39 % (4293)Termination phase: Saturation
% 1.69/1.39
% 1.69/1.39 % (4293)Memory used [KB]: 5500
% 1.69/1.39 % (4293)Time elapsed: 0.007 s
% 1.69/1.39 % (4293)Instructions burned: 8 (million)
% 1.69/1.39 % (4293)------------------------------
% 1.69/1.39 % (4293)------------------------------
% 1.69/1.39 % (4297)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/710Mi)
% 1.69/1.39 % (4298)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/6Mi)
% 1.72/1.40 % (4298)Instruction limit reached!
% 1.72/1.40 % (4298)------------------------------
% 1.72/1.40 % (4298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.40 % (4298)Termination reason: Unknown
% 1.72/1.40 % (4298)Termination phase: Saturation
% 1.72/1.40
% 1.72/1.40 % (4298)Memory used [KB]: 5500
% 1.72/1.40 % (4298)Time elapsed: 0.004 s
% 1.72/1.40 % (4298)Instructions burned: 6 (million)
% 1.72/1.40 % (4298)------------------------------
% 1.72/1.40 % (4298)------------------------------
% 1.72/1.40 % (4301)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/5Mi)
% 1.72/1.40 % Exception at run slice level
% 1.72/1.40 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
% 1.72/1.40 % (4299)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_3933 for (2999ds/902Mi)
% 1.72/1.41 % (4300)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_3933 for (2999ds/21Mi)
% 1.72/1.41 % (4302)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_3933 for (2999ds/6Mi)
% 1.72/1.41 % (4299)Refutation not found, incomplete strategy
% 1.72/1.41 % (4299)------------------------------
% 1.72/1.41 % (4299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.41 % (4299)Termination reason: Refutation not found, incomplete strategy
% 1.72/1.41
% 1.72/1.41
% 1.72/1.41 % (4299)Memory used [KB]: 5500
% 1.72/1.41 % (4299)Time elapsed: 0.004 s
% 1.72/1.41 % (4299)Instructions burned: 2 (million)
% 1.72/1.41 % (4299)------------------------------
% 1.72/1.41 % (4299)------------------------------
% 1.72/1.41 % (4303)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/377Mi)
% 1.72/1.41 % Exception at run slice level
% 1.72/1.41 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
% 1.72/1.41 % (4304)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_3933 for (2999ds/779Mi)
% 1.72/1.41 % Exception at run slice level
% 1.72/1.41 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
% 1.72/1.42 % (4307)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/17Mi)
% 1.72/1.42 % (4300)Instruction limit reached!
% 1.72/1.42 % (4300)------------------------------
% 1.72/1.42 % (4300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (4300)Termination reason: Unknown
% 1.72/1.42 % (4300)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (4300)Memory used [KB]: 5628
% 1.72/1.42 % (4300)Time elapsed: 0.016 s
% 1.72/1.42 % (4300)Instructions burned: 21 (million)
% 1.72/1.42 % (4300)------------------------------
% 1.72/1.42 % (4300)------------------------------
% 1.72/1.42 % (4307)Instruction limit reached!
% 1.72/1.42 % (4307)------------------------------
% 1.72/1.42 % (4307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.42 % (4307)Termination reason: Unknown
% 1.72/1.42 % (4307)Termination phase: Saturation
% 1.72/1.42
% 1.72/1.42 % (4307)Memory used [KB]: 5628
% 1.72/1.42 % (4307)Time elapsed: 0.029 s
% 1.72/1.42 % (4307)Instructions burned: 17 (million)
% 1.72/1.42 % (4307)------------------------------
% 1.72/1.42 % (4307)------------------------------
% 1.72/1.42 % (4305)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_3933 for (2999ds/19Mi)
% 1.72/1.42 % (4306)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3933 for (2999ds/879Mi)
% 1.72/1.42 % Exception at run slice level
% 1.72/1.42 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
% 1.72/1.43 % (4303)First to succeed.
% 1.72/1.43 % (4303)Refutation found. Thanks to Tanya!
% 1.72/1.43 % SZS status Theorem for DTF2THF_3933
% 1.72/1.43 % SZS output start Proof for DTF2THF_3933
% 1.72/1.43 thf(type_def_6, type, 'type/ind_types/list': ($tType) > $tType).
% 1.72/1.43 thf(type_def_7, type, sK2: $tType).
% 1.72/1.43 thf(func_def_0, type, 'type/ind_types/list': ($tType) > $tType).
% 1.72/1.43 thf(func_def_1, type, 'const/lists/ALL': !>[X0: $tType]:((X0 > $o) > 'type/ind_types/list' @ X0 > $o)).
% 1.72/1.43 thf(func_def_2, type, 'const/ind_types/NIL': !>[X0: $tType]:('type/ind_types/list' @ X0)).
% 1.72/1.43 thf(func_def_3, type, 'const/ind_types/CONS': !>[X0: $tType]:(X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0)).
% 1.72/1.43 thf(func_def_9, type, sK0: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > X0)).
% 1.72/1.43 thf(func_def_10, type, sK1: !>[X0: $tType]:(('type/ind_types/list' @ X0 > $o) > 'type/ind_types/list' @ X0)).
% 1.72/1.43 thf(func_def_11, type, sK3: 'type/ind_types/list' @ sK2).
% 1.72/1.43 thf(func_def_14, type, ph5: !>[X0: $tType]:(X0)).
% 1.72/1.43 thf(f405,plain,(
% 1.72/1.43 $false),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f388])).
% 1.72/1.43 thf(f388,plain,(
% 1.72/1.43 ($true = $false)),
% 1.72/1.43 inference(superposition,[status(thm)],[f358,f34])).
% 1.72/1.43 thf(f34,plain,(
% 1.72/1.43 ($false = ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ sK3))),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.72/1.43 thf(f33,plain,(
% 1.72/1.43 ($true != $true) | ($false = ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ sK3))),
% 1.72/1.43 inference(fool_paramodulation,[status(thm)],[f26])).
% 1.72/1.43 thf(f26,plain,(
% 1.72/1.43 ($true != ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ sK3))),
% 1.72/1.43 inference(cnf_transformation,[status(thm)],[f21])).
% 1.72/1.43 thf(f21,plain,(
% 1.72/1.43 ($true != ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ sK3))),
% 1.72/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f14,f20])).
% 1.72/1.43 thf(f20,plain,(
% 1.72/1.43 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true)) @ X1) != $true) => ($true != ('const/lists/ALL' @ sK2 @ (^[Y0 : sK2]: ($true)) @ sK3))),
% 1.72/1.43 introduced(definition,[],[choice_axiom])).
% 1.72/1.43 thf(f14,plain,(
% 1.72/1.43 ? [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true)) @ X1) != $true)),
% 1.72/1.43 inference(ennf_transformation,[status(thm)],[f13])).
% 1.72/1.43 thf(f13,plain,(
% 1.72/1.43 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : (('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true)) @ X1) = $true)),
% 1.72/1.43 inference(fool_elimination,[status(thm)],[f12])).
% 1.72/1.43 thf(f12,plain,(
% 1.72/1.43 ~! [X0 : $tType,X1 : 'type/ind_types/list' @ X0] : ('const/lists/ALL' @ X0 @ (^[X2 : X0] : ($true)) @ X1)),
% 1.72/1.43 inference(rectify,[status(thm)],[f5])).
% 1.72/1.43 thf(f5,negated_conjecture,(
% 1.72/1.43 ~! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : ('const/lists/ALL' @ X0 @ (^[X3 : X0] : ($true)) @ X2)),
% 1.72/1.43 inference(negated_conjecture,[status(cth)],[f4])).
% 1.72/1.43 thf(f4,conjecture,(
% 1.72/1.43 ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : ('const/lists/ALL' @ X0 @ (^[X3 : X0] : ($true)) @ X2)),
% 1.72/1.43 file('/export/starexec/sandbox/tmp/tmp.hiKps8SKu2/DTF2THF_3933.p','thm/lists/ALL_T_')).
% 1.72/1.43 thf(f358,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (($true = ('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true)) @ X2))) )),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f357])).
% 1.72/1.43 thf(f357,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (($true = ('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true)) @ X2)) | ($true = $false)) )),
% 1.72/1.43 inference(beta_eta_normalization,[status(thm)],[f345])).
% 1.72/1.43 thf(f345,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0] : (($true = ('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true)) @ X2)) | ($false = ((^[Y0 : X0]: ($true)) @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ (^[Y0 : X0]: ($true))))))) )),
% 1.72/1.43 inference(primitive_instantiation,[status(thm)],[f343])).
% 1.72/1.43 thf(f343,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0 > $o] : (((X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false) | ($true = ('const/lists/ALL' @ X0 @ X1 @ X2))) )),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f342])).
% 1.72/1.43 thf(f342,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0 > $o] : (($true != $true) | ((X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false) | ($true = ('const/lists/ALL' @ X0 @ X1 @ X2))) )),
% 1.72/1.43 inference(forward_demodulation,[status(thm)],[f339,f24])).
% 1.72/1.43 thf(f24,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X1 : X0 > $o] : ((('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) = $true)) )),
% 1.72/1.43 inference(cnf_transformation,[status(thm)],[f7])).
% 1.72/1.43 thf(f7,plain,(
% 1.72/1.43 ! [X0 : $tType,X1 : X0 > $o] : (('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) = $true)),
% 1.72/1.43 inference(fool_elimination,[status(thm)],[f3])).
% 1.72/1.43 thf(f3,axiom,(
% 1.72/1.43 ! [X0 : $tType,X1 : X0 > $o] : (('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) = $true)),
% 1.72/1.43 file('/export/starexec/sandbox/tmp/tmp.hiKps8SKu2/DTF2THF_3933.p','thm/lists/ALL_0')).
% 1.72/1.43 thf(f339,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0 > $o] : ((('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) != $true) | ($true = ('const/lists/ALL' @ X0 @ X1 @ X2)) | ((X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false)) )),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f332])).
% 1.72/1.43 thf(f332,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0 > $o] : (((X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false) | ($true = $false) | ($true = ('const/lists/ALL' @ X0 @ X1 @ X2)) | (('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.72/1.43 inference(superposition,[status(thm)],[f53,f147])).
% 1.72/1.43 thf(f147,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0 > $o] : ((('const/lists/ALL' @ X0 @ X1 @ (sK1 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false) | ((X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false) | ($true = ('const/lists/ALL' @ X0 @ X1 @ X2))) )),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f146])).
% 1.72/1.43 thf(f146,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0 > $o] : (($true != $true) | ((X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false) | ($true = ('const/lists/ALL' @ X0 @ X1 @ X2)) | (('const/lists/ALL' @ X0 @ X1 @ (sK1 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false)) )),
% 1.72/1.43 inference(forward_demodulation,[status(thm)],[f145,f24])).
% 1.72/1.43 thf(f145,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0 > $o] : ((('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) != $true) | ((X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false) | ($true = ('const/lists/ALL' @ X0 @ X1 @ X2)) | (('const/lists/ALL' @ X0 @ X1 @ (sK1 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false)) )),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f137])).
% 1.72/1.43 thf(f137,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0 > $o] : ((('const/lists/ALL' @ X0 @ X1 @ 'const/ind_types/NIL' @ X0) != $true) | ($true = ('const/lists/ALL' @ X0 @ X1 @ X2)) | (('const/lists/ALL' @ X0 @ X1 @ (sK1 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false) | ($true = $false) | ((X1 @ (sK0 @ X0 @ ('const/lists/ALL' @ X0 @ X1))) = $false)) )),
% 1.72/1.43 inference(superposition,[status(thm)],[f86,f31])).
% 1.72/1.43 thf(f31,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : X0 > $o,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (($true = ('const/lists/ALL' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) | ($false = ('const/lists/ALL' @ X0 @ X2 @ X3)) | ((X2 @ X1) = $false)) )),
% 1.72/1.43 inference(binary_proxy_clausification,[status(thm)],[f27])).
% 1.72/1.43 thf(f27,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : X0 > $o,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/ALL' @ X0 @ X2 @ X3) & (X2 @ X1)) = $false) | ($true = ('const/lists/ALL' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3)))) )),
% 1.72/1.43 inference(binary_proxy_clausification,[status(thm)],[f25])).
% 1.72/1.43 thf(f25,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : X0 > $o,X3 : 'type/ind_types/list' @ X0,X1 : X0] : ((('const/lists/ALL' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3)) = (('const/lists/ALL' @ X0 @ X2 @ X3) & (X2 @ X1)))) )),
% 1.72/1.43 inference(cnf_transformation,[status(thm)],[f11])).
% 1.72/1.43 thf(f11,plain,(
% 1.72/1.43 ! [X0 : $tType,X1 : X0,X2 : X0 > $o,X3 : 'type/ind_types/list' @ X0] : (('const/lists/ALL' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3)) = (('const/lists/ALL' @ X0 @ X2 @ X3) & (X2 @ X1)))),
% 1.72/1.43 inference(fool_elimination,[status(thm)],[f10])).
% 1.72/1.43 thf(f10,plain,(
% 1.72/1.43 ! [X0 : $tType,X1 : X0,X2 : X0 > $o,X3 : 'type/ind_types/list' @ X0] : (('const/lists/ALL' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3)) = (X2 @ X1) & ('const/lists/ALL' @ X0 @ X2 @ X3))),
% 1.72/1.43 inference(rectify,[status(thm)],[f2])).
% 1.72/1.43 thf(f2,axiom,(
% 1.72/1.43 ! [X0 : $tType,X2 : X0,X1 : X0 > $o,X3 : 'type/ind_types/list' @ X0] : (('const/lists/ALL' @ X0 @ X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) = (X1 @ X2) & ('const/lists/ALL' @ X0 @ X1 @ X3))),
% 1.72/1.43 file('/export/starexec/sandbox/tmp/tmp.hiKps8SKu2/DTF2THF_3933.p','thm/lists/ALL_1')).
% 1.72/1.43 thf(f86,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0 > $o] : (($false = (X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1)))) | ((X1 @ X2) = $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.72/1.43 thf(f74,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0 > $o] : (($false = (X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1)))) | ($true != $true) | ((X1 @ X2) = $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.72/1.43 inference(fool_paramodulation,[status(thm)],[f23])).
% 1.72/1.43 thf(f23,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0 > $o] : (($true != (X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1)))) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ((X1 @ X2) = $true)) )),
% 1.72/1.43 inference(cnf_transformation,[status(thm)],[f19])).
% 1.72/1.43 thf(f19,plain,(
% 1.72/1.43 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (! [X2 : 'type/ind_types/list' @ X0] : ((X1 @ X2) = $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true) | (($true != (X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1)))) & ($true = (X1 @ (sK1 @ X0 @ X1)))))),
% 1.72/1.43 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f17,f18])).
% 1.72/1.43 thf(f18,plain,(
% 1.72/1.43 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)) != $true) & ($true = (X1 @ X4))) => (($true != (X1 @ ('const/ind_types/CONS' @ X0 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1)))) & ($true = (X1 @ (sK1 @ X0 @ X1)))))),
% 1.72/1.43 introduced(definition,[],[choice_axiom])).
% 1.72/1.43 thf(f17,plain,(
% 1.72/1.43 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (! [X2 : 'type/ind_types/list' @ X0] : ((X1 @ X2) = $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ? [X3 : X0,X4 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X3 @ X4)) != $true) & ($true = (X1 @ X4))))),
% 1.72/1.43 inference(rectify,[status(thm)],[f16])).
% 1.72/1.43 thf(f16,plain,(
% 1.72/1.43 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true) | ? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true) & ((X1 @ X3) = $true)))),
% 1.72/1.43 inference(flattening,[status(thm)],[f15])).
% 1.72/1.43 thf(f15,plain,(
% 1.72/1.43 ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)) | (? [X2 : X0,X3 : 'type/ind_types/list' @ X0] : (((X1 @ ('const/ind_types/CONS' @ X0 @ X2 @ X3)) != $true) & ((X1 @ X3) = $true)) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)))),
% 1.72/1.43 inference(ennf_transformation,[status(thm)],[f9])).
% 1.72/1.43 thf(f9,plain,(
% 1.72/1.43 ! [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) = $true)) => ! [X4 : 'type/ind_types/list' @ X0] : ($true = (X1 @ X4)))),
% 1.72/1.43 inference(fool_elimination,[status(thm)],[f8])).
% 1.72/1.43 thf(f8,plain,(
% 1.72/1.43 ! [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))),
% 1.72/1.43 inference(rectify,[status(thm)],[f1])).
% 1.72/1.43 thf(f1,axiom,(
% 1.72/1.43 ! [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))),
% 1.72/1.43 file('/export/starexec/sandbox/tmp/tmp.hiKps8SKu2/DTF2THF_3933.p','thm/ind_types/list_INDUCT_')).
% 1.72/1.43 thf(f53,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (($true = (X1 @ (sK1 @ X0 @ X1))) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.72/1.43 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.72/1.43 thf(f43,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X1 : 'type/ind_types/list' @ X0 > $o] : (($true = (X1 @ (sK1 @ X0 @ X1))) | ($true != $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.72/1.43 inference(equality_factoring,[status(thm)],[f22])).
% 1.72/1.43 thf(f22,plain,(
% 1.72/1.43 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : 'type/ind_types/list' @ X0 > $o] : (($true = (X1 @ (sK1 @ X0 @ X1))) | ((X1 @ X2) = $true) | ((X1 @ 'const/ind_types/NIL' @ X0) != $true)) )),
% 1.72/1.43 inference(cnf_transformation,[status(thm)],[f19])).
% 1.72/1.43 % SZS output end Proof for DTF2THF_3933
% 1.72/1.43 % (4303)------------------------------
% 1.72/1.43 % (4303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.72/1.43 % (4303)Termination reason: Refutation
% 1.72/1.43
% 1.72/1.43 % (4303)Memory used [KB]: 5756
% 1.72/1.43 % (4303)Time elapsed: 0.043 s
% 1.72/1.43 % (4303)Instructions burned: 55 (million)
% 1.72/1.43 % (4303)------------------------------
% 1.72/1.43 % (4303)------------------------------
% 1.72/1.43 % (4276)Success in time 0.108 s
%------------------------------------------------------------------------------