%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU906^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 09:37:43 AM UTC 2026
% Result : Theorem 1.59s 1.42s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 2
% Syntax : Number of formulae : 18 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 54 ( 33 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 145 ( 22 ~; 7 |; 3 &; 101 @)
% ( 3 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 1 con; 0-2 aty)
% Number of variables : 56 ( 15 ^; 34 !; 7 ?; 56 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
f: $i > $i ).
thf(func_def_1,type,
cS: $i > $o ).
thf(func_def_5,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_8,type,
inv_f_2: $i > $i ).
thf(func_def_9,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f32,plain,
$false,
inference(equality_resolution,[status(thm)],[f31]) ).
thf(f31,plain,
! [X0: $i] :
( ( sK0
@ ^ [Y0: $i] : ( cS @ ( inv_f_2 @ Y0 ) ) )
!= X0 ),
inference(beta_eta_normalization,[status(thm)],[f30]) ).
thf(f30,plain,
! [X0: $i] :
( ( sK0
@ ^ [Y0: $i] :
( cS
@ ( inv_f_2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
!= X0 ),
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X0: $i] :
( ( ( sK0
@ ^ [Y0: $i] :
( cS
@ ( inv_f_2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
!= X0 )
| ( ( sK0
@ ^ [Y0: $i] :
( cS
@ ( inv_f_2
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) )
!= X0 ) ),
inference(equality_resolution,[status(thm)],[f23]) ).
thf(f23,plain,
! [X0: $i > $i,X1: $i] :
( ( ( f @ X1 )
!= ( X0
@ ( f
@ ( sK0
@ ^ [Y0: $i] : ( cS @ ( inv_f_2 @ ( X0 @ Y0 ) ) ) ) ) ) )
| ( ( sK0
@ ^ [Y0: $i] : ( cS @ ( inv_f_2 @ ( X0 @ Y0 ) ) ) )
!= X1 ) ),
inference(beta_eta_normalization,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i > $i,X1: $i] :
( ( ( f @ X1 )
!= ( X0
@ ( f
@ ( sK0
@ ^ [Y0: $i] :
( cS
@ ( ^ [Y1: $i] : ( inv_f_2 @ ( X0 @ Y1 ) )
@ Y0 ) ) ) ) ) )
| ( ( sK0
@ ^ [Y0: $i] :
( cS
@ ( ^ [Y1: $i] : ( inv_f_2 @ ( X0 @ Y1 ) )
@ Y0 ) ) )
!= X1 ) ),
inference(constrained_superposition,[status(thm)],[f17,f12]) ).
thf(f12,plain,
! [X3: $i] :
( ( inv_f_2 @ ( f @ X3 ) )
= X3 ),
inference(injectivity,[status(thm)],[f10]) ).
thf(f10,plain,
! [X2: $i,X3: $i] :
( ( ( f @ X3 )
!= ( f @ X2 ) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i > $o] :
( ( cS @ ( sK0 @ X0 ) )
!= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) )
& ! [X2: $i,X3: $i] :
( ( ( f @ X3 )
!= ( f @ X2 ) )
| ( X2 = X3 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ ( f @ X1 ) )
!= ( cS @ X1 ) )
=> ( ( cS @ ( sK0 @ X0 ) )
!= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ ( f @ X1 ) )
!= ( cS @ X1 ) )
& ! [X2: $i,X3: $i] :
( ( ( f @ X3 )
!= ( f @ X2 ) )
| ( X2 = X3 ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X2: $i > $o] :
? [X3: $i] :
( ( cS @ X3 )
!= ( X2 @ ( f @ X3 ) ) )
& ! [X1: $i,X0: $i] :
( ( ( f @ X0 )
!= ( f @ X1 ) )
| ( X0 = X1 ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: $i > $o] :
! [X3: $i] :
( ( cS @ X3 )
= ( X2 @ ( f @ X3 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i,X1: $i] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: $i > $o] :
! [X3: $i] :
( ( X2 @ ( f @ X3 ) )
<=> ( cS @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: $i > $o] :
! [X0: $i] :
( ( X2 @ ( f @ X0 ) )
<=> ( cS @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X0: $i,X1: $i] :
( ( ( f @ X0 )
= ( f @ X1 ) )
=> ( X0 = X1 ) )
=> ? [X2: $i > $o] :
! [X0: $i] :
( ( X2 @ ( f @ X0 ) )
<=> ( cS @ X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.85mFpAmX7E/DTF2THF_665.p',cSV5_pme) ).
thf(f17,plain,
! [X0: $i > $i] :
( ( X0
@ ( f
@ ( sK0
@ ^ [Y0: $i] : ( cS @ ( X0 @ Y0 ) ) ) ) )
!= ( sK0
@ ^ [Y0: $i] : ( cS @ ( X0 @ Y0 ) ) ) ),
inference(equality_resolution,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $i > $o] :
( ( cS @ ( sK0 @ X0 ) )
!= ( X0 @ ( f @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU906^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:36:14 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
% 0.27/0.46 ---- Original DTF file ---
% 0.27/0.46 thf(spec,logic,$$dhol).
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 % File : SEU906^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.46 % Domain : Set Theory
% 0.27/0.46 % Problem : TPS problem from FUNS-AND-SETS-THMS
% 0.27/0.46 % Version : Especial.
% 0.27/0.46 % English :
% 0.27/0.46
% 0.27/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.46 % Source : [Bro09]
% 0.27/0.46 % Names : tps_0808 [Bro09]
% 0.27/0.46
% 0.27/0.46 % Status : Theorem
% 0.27/0.46 % Rating : 0.67 v9.1.0, 0.62 v9.0.0, 0.70 v8.2.0, 0.77 v8.1.0, 0.73 v7.5.0, 0.71 v7.4.0, 0.89 v7.3.0, 1.00 v6.2.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v5.3.0, 1.00 v5.2.0, 0.80 v4.1.0, 0.67 v4.0.0
% 0.27/0.46 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.27/0.46 % Number of atoms : 3 ( 2 equ; 0 cnn)
% 0.27/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.27/0.46 % Number of connectives : 8 ( 0 ~; 0 |; 0 &; 5 @)
% 0.27/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.46 % Maximal formula depth : 7 ( 7 avg)
% 0.27/0.46 % Number of types : 2 ( 0 usr)
% 0.27/0.46 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.27/0.46 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.27/0.46 % Number of variables : 4 ( 0 ^; 3 !; 1 ?; 4 :)
% 0.27/0.46 % SPC : TH0_THM_EQU_NAR
% 0.27/0.46
% 0.27/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 thf(f,type,
% 0.27/0.46 f: $i > $i ).
% 0.27/0.46
% 0.27/0.46 thf(cS,type,
% 0.27/0.46 cS: $i > $o ).
% 0.27/0.46
% 0.27/0.46 thf(cSV5_pme,conjecture,
% 0.27/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.27/0.46 ( ( ( f @ Xx )
% 0.27/0.46 = ( f @ Xy ) )
% 0.27/0.46 => ( Xx = Xy ) )
% 0.27/0.46 => ? [Xu: $i > $o] :
% 0.27/0.46 ! [Xx: $i] :
% 0.27/0.46 ( ( cS @ Xx )
% 0.27/0.46 <=> ( Xu @ ( f @ Xx ) ) ) ) ).
% 0.27/0.46
% 0.27/0.46 %------------------------------------------------------------------------------
% 0.27/0.46 ------------------------
% 1.45/1.26 ---- Embedded in THF ---
% 1.45/1.26 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.45/1.26 %%% Generated on Tue Feb 24 12:36:15 EST 2026
% 1.45/1.26 %%% using '$$dhol' embedding, version 1.3.0.
% 1.45/1.26 %%% Logic specification used:
% 1.45/1.26 %%% thf(spec, logic, $$dhol).
% 1.45/1.26
% 1.45/1.26 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.85mFpAmX7E/DTF2DTF665.p
% See solution above
% 1.45/1.26 ------------------------
% 1.45/1.27 ---- Cleaned THF ---
% 1.45/1.27 thf(f,type,
% 1.45/1.27 f: $i > $i ).
% 1.45/1.27
% 1.45/1.27 thf(cS,type,
% 1.45/1.27 cS: $i > $o ).
% 1.45/1.27
% 1.45/1.27 thf(cSV5_pme,conjecture,
% 1.45/1.27 ( ! [Xx: $i,Xy: $i] :
% 1.45/1.27 ( ( ( f @ Xx )
% 1.45/1.27 = ( f @ Xy ) )
% 1.45/1.27 => ( Xx = Xy ) )
% 1.45/1.27 => ? [Xu: $i > $o] :
% 1.45/1.27 ! [Xx: $i] :
% 1.45/1.27 ( ( cS @ Xx )
% 1.45/1.27 <=> ( Xu @ ( f @ Xx ) ) ) ) ).
% 1.45/1.27 ------------------------
% 1.45/1.29 % (970)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_665 for (2999ds/275Mi)
% 1.45/1.29 % (967)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_665 for (2999ds/27Mi)
% 1.45/1.29 % (967)Refutation not found, incomplete strategy
% 1.45/1.29 % (967)------------------------------
% 1.45/1.29 % (967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (967)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.29
% 1.45/1.29
% 1.45/1.29 % (967)Memory used [KB]: 5500
% 1.45/1.29 % (967)Time elapsed: 0.002 s
% 1.45/1.29 % (967)Instructions burned: 2 (million)
% 1.45/1.29 % (967)------------------------------
% 1.45/1.29 % (967)------------------------------
% 1.45/1.29 % (970)Refutation not found, incomplete strategy
% 1.45/1.29 % (970)------------------------------
% 1.45/1.29 % (970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.45/1.29 % (970)Termination reason: Refutation not found, incomplete strategy
% 1.45/1.29
% 1.45/1.29
% 1.45/1.29 % (970)Memory used [KB]: 5500
% 1.45/1.29 % (970)Time elapsed: 0.004 s
% 1.45/1.29 % (970)Instructions burned: 6 (million)
% 1.45/1.29 % (970)------------------------------
% 1.45/1.29 % (970)------------------------------
% 1.45/1.30 % (965)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/183Mi)
% 1.45/1.30 % (966)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_665 for (2999ds/4Mi)
% 1.59/1.30 % (968)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/2Mi)
% 1.59/1.30 % (969)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_665 for (2999ds/2Mi)
% 1.59/1.30 % (971)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/18Mi)
% 1.59/1.30 % (968)Instruction limit reached!
% 1.59/1.30 % (968)------------------------------
% 1.59/1.30 % (968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (968)Termination reason: Unknown
% 1.59/1.30 % (968)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (968)Memory used [KB]: 5500
% 1.59/1.30 % (968)Time elapsed: 0.004 s
% 1.59/1.30 % (968)Instructions burned: 2 (million)
% 1.59/1.30 % (968)------------------------------
% 1.59/1.30 % (968)------------------------------
% 1.59/1.30 % (969)Instruction limit reached!
% 1.59/1.30 % (969)------------------------------
% 1.59/1.30 % (969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (969)Termination reason: Unknown
% 1.59/1.30 % (969)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (969)Memory used [KB]: 5500
% 1.59/1.30 % (969)Time elapsed: 0.004 s
% 1.59/1.30 % (969)Instructions burned: 2 (million)
% 1.59/1.30 % (969)------------------------------
% 1.59/1.30 % (969)------------------------------
% 1.59/1.30 % (966)Instruction limit reached!
% 1.59/1.30 % (966)------------------------------
% 1.59/1.30 % (966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (966)Termination reason: Unknown
% 1.59/1.30 % (966)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (966)Memory used [KB]: 5500
% 1.59/1.30 % (966)Time elapsed: 0.005 s
% 1.59/1.30 % (966)Instructions burned: 4 (million)
% 1.59/1.30 % (966)------------------------------
% 1.59/1.30 % (966)------------------------------
% 1.59/1.30 % (973)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_665 for (2999ds/37Mi)
% 1.59/1.30 % (972)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/3Mi)
% 1.59/1.30 % (972)Instruction limit reached!
% 1.59/1.30 % (972)------------------------------
% 1.59/1.30 % (972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (972)Termination reason: Unknown
% 1.59/1.30 % (972)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (972)Memory used [KB]: 5500
% 1.59/1.30 % (972)Time elapsed: 0.003 s
% 1.59/1.30 % (972)Instructions burned: 3 (million)
% 1.59/1.30 % (972)------------------------------
% 1.59/1.30 % (972)------------------------------
% 1.59/1.31 % (971)Instruction limit reached!
% 1.59/1.31 % (971)------------------------------
% 1.59/1.31 % (971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (971)Termination reason: Unknown
% 1.59/1.31 % (971)Termination phase: Saturation
% 1.59/1.31
% 1.59/1.31 % (971)Memory used [KB]: 5628
% 1.59/1.31 % (971)Time elapsed: 0.013 s
% 1.59/1.31 % (971)Instructions burned: 18 (million)
% 1.59/1.31 % (971)------------------------------
% 1.59/1.31 % (971)------------------------------
% 1.59/1.31 % (973)Instruction limit reached!
% 1.59/1.31 % (973)------------------------------
% 1.59/1.31 % (973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.31 % (973)Termination reason: Unknown
% 1.59/1.31 % (973)Termination phase: Saturation
% 1.59/1.31
% 1.59/1.31 % (973)Memory used [KB]: 5884
% 1.59/1.31 % (973)Time elapsed: 0.012 s
% 1.59/1.31 % (973)Instructions burned: 38 (million)
% 1.59/1.31 % (973)------------------------------
% 1.59/1.31 % (973)------------------------------
% 1.59/1.31 % (977)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/7Mi)
% 1.59/1.32 % (977)Instruction limit reached!
% 1.59/1.32 % (977)------------------------------
% 1.59/1.32 % (977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (977)Termination reason: Unknown
% 1.59/1.32 % (977)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (977)Memory used [KB]: 1023
% 1.59/1.32 % (977)Time elapsed: 0.005 s
% 1.59/1.32 % (977)Instructions burned: 9 (million)
% 1.59/1.32 % (977)------------------------------
% 1.59/1.32 % (977)------------------------------
% 1.59/1.32 % (974)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_665 for (2999ds/15Mi)
% 1.59/1.32 % (975)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_665 for (2999ds/3Mi)
% 1.59/1.32 % (976)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_665 for (2999ds/1041Mi)
% 1.59/1.32 % (975)Instruction limit reached!
% 1.59/1.32 % (975)------------------------------
% 1.59/1.32 % (975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (975)Termination reason: Unknown
% 1.59/1.32 % (975)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (975)Memory used [KB]: 5500
% 1.59/1.32 % (975)Time elapsed: 0.004 s
% 1.59/1.32 % (975)Instructions burned: 3 (million)
% 1.59/1.32 % (975)------------------------------
% 1.59/1.32 % (975)------------------------------
% 1.59/1.32 % (974)Refutation not found, incomplete strategy
% 1.59/1.32 % (974)------------------------------
% 1.59/1.32 % (974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (974)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.32
% 1.59/1.32
% 1.59/1.32 % (974)Memory used [KB]: 5500
% 1.59/1.32 % (974)Time elapsed: 0.006 s
% 1.59/1.32 % (974)Instructions burned: 5 (million)
% 1.59/1.32 % (974)------------------------------
% 1.59/1.32 % (974)------------------------------
% 1.59/1.32 % (979)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_665 for (2999ds/3Mi)
% 1.59/1.32 % (979)Instruction limit reached!
% 1.59/1.32 % (979)------------------------------
% 1.59/1.32 % (979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (979)Termination reason: Unknown
% 1.59/1.32 % (979)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (979)Memory used [KB]: 5500
% 1.59/1.32 % (979)Time elapsed: 0.003 s
% 1.59/1.32 % (979)Instructions burned: 5 (million)
% 1.59/1.32 % (979)------------------------------
% 1.59/1.32 % (979)------------------------------
% 1.59/1.32 % (978)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/16Mi)
% 1.59/1.33 % (980)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_665 for (2999ds/3Mi)
% 1.59/1.33 % (980)Instruction limit reached!
% 1.59/1.33 % (980)------------------------------
% 1.59/1.33 % (980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (980)Termination reason: Unknown
% 1.59/1.33 % (980)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (980)Memory used [KB]: 5500
% 1.59/1.33 % (980)Time elapsed: 0.003 s
% 1.59/1.33 % (980)Instructions burned: 3 (million)
% 1.59/1.33 % (980)------------------------------
% 1.59/1.33 % (980)------------------------------
% 1.59/1.33 % (983)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/4Mi)
% 1.59/1.33 % (983)Instruction limit reached!
% 1.59/1.33 % (983)------------------------------
% 1.59/1.33 % (983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (983)Termination reason: Unknown
% 1.59/1.33 % (983)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (983)Memory used [KB]: 5500
% 1.59/1.33 % (983)Time elapsed: 0.003 s
% 1.59/1.33 % (983)Instructions burned: 5 (million)
% 1.59/1.33 % (983)------------------------------
% 1.59/1.33 % (983)------------------------------
% 1.59/1.34 % (981)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/7Mi)
% 1.59/1.34 % (978)Instruction limit reached!
% 1.59/1.34 % (978)------------------------------
% 1.59/1.34 % (978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (978)Termination reason: Unknown
% 1.59/1.34 % (978)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (978)Memory used [KB]: 5628
% 1.59/1.34 % (978)Time elapsed: 0.013 s
% 1.59/1.34 % (978)Instructions burned: 17 (million)
% 1.59/1.34 % (978)------------------------------
% 1.59/1.34 % (978)------------------------------
% 1.59/1.34 % (984)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/18Mi)
% 1.59/1.34 % (981)Refutation not found, incomplete strategy
% 1.59/1.34 % (981)------------------------------
% 1.59/1.34 % (981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (981)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.34
% 1.59/1.34
% 1.59/1.34 % (981)Memory used [KB]: 5500
% 1.59/1.34 % (981)Time elapsed: 0.003 s
% 1.59/1.34 % (981)Instructions burned: 1 (million)
% 1.59/1.34 % (981)------------------------------
% 1.59/1.34 % (981)------------------------------
% 1.59/1.34 % (984)Refutation not found, incomplete strategy
% 1.59/1.34 % (984)------------------------------
% 1.59/1.34 % (984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (984)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.34
% 1.59/1.34
% 1.59/1.34 % (984)Memory used [KB]: 5500
% 1.59/1.34 % (984)Time elapsed: 0.002 s
% 1.59/1.34 % (984)Instructions burned: 1 (million)
% 1.59/1.34 % (984)------------------------------
% 1.59/1.34 % (984)------------------------------
% 1.59/1.34 % (982)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/3Mi)
% 1.59/1.34 % (982)Instruction limit reached!
% 1.59/1.34 % (982)------------------------------
% 1.59/1.34 % (982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (982)Termination reason: Unknown
% 1.59/1.34 % (982)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (982)Memory used [KB]: 5500
% 1.59/1.34 % (982)Time elapsed: 0.004 s
% 1.59/1.34 % (982)Instructions burned: 3 (million)
% 1.59/1.34 % (982)------------------------------
% 1.59/1.34 % (982)------------------------------
% 1.59/1.34 % (985)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/710Mi)
% 1.59/1.35 % (990)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_665 for (2999ds/21Mi)
% 1.59/1.35 % (986)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/6Mi)
% 1.59/1.36 % (987)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_665 for (2999ds/902Mi)
% 1.59/1.36 % (990)Instruction limit reached!
% 1.59/1.36 % (990)------------------------------
% 1.59/1.36 % (990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (990)Termination reason: Unknown
% 1.59/1.36 % (990)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (990)Memory used [KB]: 5628
% 1.59/1.36 % (990)Time elapsed: 0.010 s
% 1.59/1.36 % (990)Instructions burned: 22 (million)
% 1.59/1.36 % (990)------------------------------
% 1.59/1.36 % (990)------------------------------
% 1.59/1.36 % (986)Instruction limit reached!
% 1.59/1.36 % (986)------------------------------
% 1.59/1.36 % (986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (986)Termination reason: Unknown
% 1.59/1.36 % (986)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (986)Memory used [KB]: 5500
% 1.59/1.36 % (986)Time elapsed: 0.006 s
% 1.59/1.36 % (986)Instructions burned: 7 (million)
% 1.59/1.36 % (986)------------------------------
% 1.59/1.36 % (986)------------------------------
% 1.59/1.36 % (991)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/5Mi)
% 1.59/1.36 % (991)Instruction limit reached!
% 1.59/1.36 % (991)------------------------------
% 1.59/1.36 % (991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (991)Termination reason: Unknown
% 1.59/1.36 % (991)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (991)Memory used [KB]: 5500
% 1.59/1.36 % (991)Time elapsed: 0.005 s
% 1.59/1.36 % (991)Instructions burned: 5 (million)
% 1.59/1.36 % (991)------------------------------
% 1.59/1.36 % (991)------------------------------
% 1.59/1.37 % (993)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/377Mi)
% 1.59/1.37 % (992)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_665 for (2999ds/6Mi)
% 1.59/1.38 % (992)Instruction limit reached!
% 1.59/1.38 % (992)------------------------------
% 1.59/1.38 % (992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (992)Termination reason: Unknown
% 1.59/1.38 % (992)Termination phase: Saturation
% 1.59/1.38
% 1.59/1.38 % (992)Memory used [KB]: 5500
% 1.59/1.38 % (992)Time elapsed: 0.006 s
% 1.59/1.38 % (992)Instructions burned: 6 (million)
% 1.59/1.38 % (992)------------------------------
% 1.59/1.38 % (992)------------------------------
% 1.59/1.38 % (994)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_665 for (2999ds/779Mi)
% 1.59/1.38 % (965)Instruction limit reached!
% 1.59/1.38 % (965)------------------------------
% 1.59/1.38 % (965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (965)Termination reason: Unknown
% 1.59/1.38 % (965)Termination phase: Saturation
% 1.59/1.38
% 1.59/1.38 % (965)Memory used [KB]: 6908
% 1.59/1.38 % (965)Time elapsed: 0.088 s
% 1.59/1.38 % (965)Instructions burned: 183 (million)
% 1.59/1.38 % (965)------------------------------
% 1.59/1.38 % (965)------------------------------
% 1.59/1.39 % (996)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_665 for (2999ds/879Mi)
% 1.59/1.39 % (996)Refutation not found, incomplete strategy
% 1.59/1.39 % (996)------------------------------
% 1.59/1.39 % (996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.39 % (996)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.39
% 1.59/1.39
% 1.59/1.39 % (996)Memory used [KB]: 5500
% 1.59/1.39 % (996)Time elapsed: 0.004 s
% 1.59/1.39 % (996)Instructions burned: 6 (million)
% 1.59/1.39 % (996)------------------------------
% 1.59/1.39 % (996)------------------------------
% 1.59/1.40 % (995)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_665 for (2999ds/19Mi)
% 1.59/1.40 % (997)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_665 for (2998ds/17Mi)
% 1.59/1.41 % (995)Instruction limit reached!
% 1.59/1.41 % (995)------------------------------
% 1.59/1.41 % (995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.41 % (995)Termination reason: Unknown
% 1.59/1.41 % (995)Termination phase: Saturation
% 1.59/1.41
% 1.59/1.41 % (995)Memory used [KB]: 5628
% 1.59/1.41 % (995)Time elapsed: 0.013 s
% 1.59/1.41 % (995)Instructions burned: 19 (million)
% 1.59/1.41 % (995)------------------------------
% 1.59/1.41 % (995)------------------------------
% 1.59/1.41 % (997)Instruction limit reached!
% 1.59/1.41 % (997)------------------------------
% 1.59/1.41 % (997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.41 % (997)Termination reason: Unknown
% 1.59/1.41 % (997)Termination phase: Saturation
% 1.59/1.41
% 1.59/1.41 % (997)Memory used [KB]: 5500
% 1.59/1.41 % (997)Time elapsed: 0.008 s
% 1.59/1.41 % (997)Instructions burned: 18 (million)
% 1.59/1.41 % (997)------------------------------
% 1.59/1.41 % (997)------------------------------
% 1.59/1.42 % (999)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_665 for (2998ds/30Mi)
% 1.59/1.42 % (999)First to succeed.
% 1.59/1.42 % (998)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_665 for (2998ds/3Mi)
% 1.59/1.42 % (999)Refutation found. Thanks to Tanya!
% 1.59/1.42 % SZS status Theorem for DTF2THF_665
% 1.59/1.42 % SZS output start Proof for DTF2THF_665
% 1.59/1.42 thf(func_def_0, type, f: $i > $i).
% 1.59/1.42 thf(func_def_1, type, cS: $i > $o).
% 1.59/1.42 thf(func_def_5, type, sK0: ($i > $o) > $i).
% 1.59/1.42 thf(func_def_8, type, inv_f_2: $i > $i).
% 1.59/1.42 thf(func_def_9, type, ph3: !>[X0: $tType]:(X0)).
% 1.59/1.42 thf(f32,plain,(
% 1.59/1.42 $false),
% 1.59/1.42 inference(equality_resolution,[status(thm)],[f31])).
% 1.59/1.42 thf(f31,plain,(
% 1.59/1.42 ( ! [X0 : $i] : (((sK0 @ (^[Y0 : $i]: (cS @ (inv_f_2 @ Y0)))) != X0)) )),
% 1.59/1.42 inference(beta_eta_normalization,[status(thm)],[f30])).
% 1.59/1.42 thf(f30,plain,(
% 1.59/1.42 ( ! [X0 : $i] : (((sK0 @ (^[Y0 : $i]: (cS @ (inv_f_2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) != X0)) )),
% 1.59/1.42 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.59/1.42 thf(f26,plain,(
% 1.59/1.42 ( ! [X0 : $i] : (((sK0 @ (^[Y0 : $i]: (cS @ (inv_f_2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) != X0) | ((sK0 @ (^[Y0 : $i]: (cS @ (inv_f_2 @ ((^[Y1 : $i]: (Y1)) @ Y0))))) != X0)) )),
% 1.59/1.42 inference(equality_resolution,[status(thm)],[f23])).
% 1.59/1.42 thf(f23,plain,(
% 1.59/1.42 ( ! [X0 : $i > $i,X1 : $i] : (((f @ X1) != (X0 @ (f @ (sK0 @ (^[Y0 : $i]: (cS @ (inv_f_2 @ (X0 @ Y0)))))))) | ((sK0 @ (^[Y0 : $i]: (cS @ (inv_f_2 @ (X0 @ Y0))))) != X1)) )),
% 1.59/1.42 inference(beta_eta_normalization,[status(thm)],[f21])).
% 1.59/1.42 thf(f21,plain,(
% 1.59/1.42 ( ! [X0 : $i > $i,X1 : $i] : (((f @ X1) != (X0 @ (f @ (sK0 @ (^[Y0 : $i]: (cS @ ((^[Y1 : $i]: (inv_f_2 @ (X0 @ Y1))) @ Y0))))))) | ((sK0 @ (^[Y0 : $i]: (cS @ ((^[Y1 : $i]: (inv_f_2 @ (X0 @ Y1))) @ Y0)))) != X1)) )),
% 1.59/1.42 inference(constrained_superposition,[status(thm)],[f17,f12])).
% 1.59/1.42 thf(f12,plain,(
% 1.59/1.42 ( ! [X3 : $i] : (((inv_f_2 @ (f @ X3)) = X3)) )),
% 1.59/1.42 inference(injectivity,[status(thm)],[f10])).
% 1.59/1.42 thf(f10,plain,(
% 1.59/1.42 ( ! [X2 : $i,X3 : $i] : (((f @ X3) != (f @ X2)) | (X2 = X3)) )),
% 1.59/1.42 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.42 thf(f9,plain,(
% 1.59/1.42 ! [X0 : $i > $o] : ((cS @ (sK0 @ X0)) != (X0 @ (f @ (sK0 @ X0)))) & ! [X2 : $i,X3 : $i] : (((f @ X3) != (f @ X2)) | (X2 = X3))),
% 1.59/1.42 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f7,f8])).
% 1.59/1.42 thf(f8,plain,(
% 1.59/1.42 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ (f @ X1)) != (cS @ X1)) => ((cS @ (sK0 @ X0)) != (X0 @ (f @ (sK0 @ X0)))))),
% 1.59/1.42 introduced(definition,[],[choice_axiom])).
% 1.59/1.42 thf(f7,plain,(
% 1.59/1.42 ! [X0 : $i > $o] : ? [X1 : $i] : ((X0 @ (f @ X1)) != (cS @ X1)) & ! [X2 : $i,X3 : $i] : (((f @ X3) != (f @ X2)) | (X2 = X3))),
% 1.59/1.42 inference(rectify,[status(thm)],[f6])).
% 1.59/1.42 thf(f6,plain,(
% 1.59/1.42 ! [X2 : $i > $o] : ? [X3 : $i] : ((cS @ X3) != (X2 @ (f @ X3))) & ! [X1 : $i,X0 : $i] : (((f @ X0) != (f @ X1)) | (X0 = X1))),
% 1.59/1.42 inference(ennf_transformation,[status(thm)],[f5])).
% 1.59/1.42 thf(f5,plain,(
% 1.59/1.42 ~(! [X0 : $i,X1 : $i] : (((f @ X0) = (f @ X1)) => (X0 = X1)) => ? [X2 : $i > $o] : ! [X3 : $i] : ((cS @ X3) = (X2 @ (f @ X3))))),
% 1.59/1.42 inference(fool_elimination,[status(thm)],[f4])).
% 1.59/1.42 thf(f4,plain,(
% 1.59/1.42 ~(! [X0 : $i,X1 : $i] : (((f @ X0) = (f @ X1)) => (X0 = X1)) => ? [X2 : $i > $o] : ! [X3 : $i] : ((X2 @ (f @ X3)) <=> (cS @ X3)))),
% 1.59/1.42 inference(rectify,[status(thm)],[f2])).
% 1.59/1.42 thf(f2,negated_conjecture,(
% 1.59/1.42 ~(! [X0 : $i,X1 : $i] : (((f @ X0) = (f @ X1)) => (X0 = X1)) => ? [X2 : $i > $o] : ! [X0 : $i] : ((X2 @ (f @ X0)) <=> (cS @ X0)))),
% 1.59/1.42 inference(negated_conjecture,[status(cth)],[f1])).
% 1.59/1.42 thf(f1,conjecture,(
% 1.59/1.42 ! [X0 : $i,X1 : $i] : (((f @ X0) = (f @ X1)) => (X0 = X1)) => ? [X2 : $i > $o] : ! [X0 : $i] : ((X2 @ (f @ X0)) <=> (cS @ X0))),
% 1.59/1.42 file('/export/starexec/sandbox/tmp/tmp.85mFpAmX7E/DTF2THF_665.p',cSV5_pme)).
% 1.59/1.42 thf(f17,plain,(
% 1.59/1.42 ( ! [X0 : $i > $i] : (((X0 @ (f @ (sK0 @ (^[Y0 : $i]: (cS @ (X0 @ Y0)))))) != (sK0 @ (^[Y0 : $i]: (cS @ (X0 @ Y0)))))) )),
% 1.59/1.42 inference(equality_resolution,[status(thm)],[f11])).
% 1.59/1.42 thf(f11,plain,(
% 1.59/1.42 ( ! [X0 : $i > $o] : (((cS @ (sK0 @ X0)) != (X0 @ (f @ (sK0 @ X0))))) )),
% 1.59/1.42 inference(cnf_transformation,[status(thm)],[f9])).
% 1.59/1.42 % SZS output end Proof for DTF2THF_665
% 1.59/1.42 % (999)------------------------------
% 1.59/1.42 % (999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.42 % (999)Termination reason: Refutation
% 1.59/1.42
% 1.59/1.42 % (999)Memory used [KB]: 5500
% 1.59/1.42 % (999)Time elapsed: 0.004 s
% 1.59/1.42 % (999)Instructions burned: 6 (million)
% 1.59/1.42 % (999)------------------------------
% 1.59/1.42 % (999)------------------------------
% 1.59/1.42 % (964)Success in time 0.131 s
%------------------------------------------------------------------------------