%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO209^5 : 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 : n025.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 09:53:40 AM UTC 2026
% Result : Theorem 1.69s 1.50s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 105 ( 39 equ; 0 cnn)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 190 ( 34 ~; 13 |; 0 &; 136 @)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% Number of symbols : 5 ( 2 usr; 2 con; 0-2 aty)
% Number of variables : 93 ( 39 ^; 38 !; 16 ?; 93 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > $o ).
thf(func_def_5,type,
sK1: ( a > $o ) > a ).
thf(f98,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f93,f96]) ).
thf(f96,plain,
( ( sK0
@ ( sK1
@ ^ [Y0: a] :
~ ( sK0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: a] :
~ ( sK0 @ Y0 @ Y0 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
= ( ^ [Y0: a] :
( sK0
@ ( ^ [Y1: a] : Y1
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( sK1
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
( sK0
@ ( ^ [Y2: a] : Y2
@ Y1 )
@ ( ^ [Y2: a] : Y2
@ Y1 ) )
@ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
( ( $false
= ( ^ [Y0: a] :
( sK0
@ ( ^ [Y1: a] : Y1
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( sK1
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
( sK0
@ ( ^ [Y2: a] : Y2
@ Y1 )
@ ( ^ [Y2: a] : Y2
@ Y1 ) )
@ Y0 ) ) ) )
| ( $false != $false ) ),
inference(equality_factoring,[status(thm)],[f88]) ).
thf(f88,plain,
! [X1: a,X4: a > $o] :
( ( $false
= ( sK0
@ ( sK1
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) )
@ X1 ) )
| ( $false
= ( X4 @ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: a,X4: a > $o] :
( ( ( sK0
@ ( sK1
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) )
@ X1 )
= ( ~ $true ) )
| ( $false
= ( X4 @ X1 ) ) ),
inference(cases_simplifying,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: a,X4: a > $o] :
( ( sK0
@ ( sK1
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) )
@ X1 )
= ( ~ ( X4 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
! [X1: a,X4: a > $o] :
( ( sK0
@ ( sK1
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) )
@ X1 )
= ( ^ [Y0: a] :
~ ( X4 @ Y0 )
@ X1 ) ),
inference(primitive_instantiation,[status(thm)],[f49]) ).
thf(f49,plain,
! [X0: a > $o,X1: a] :
( ( X0 @ X1 )
= ( sK0 @ ( sK1 @ X0 ) @ X1 ) ),
inference(argument_congruence,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: a > $o] :
( ( sK0 @ ( sK1 @ X0 ) )
= X0 ),
inference(leibniz_equality_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X3: ( a > $o ) > $o,X1: a > $o] :
( ( $true
!= ( X3 @ ( sK0 @ ( sK1 @ X1 ) ) ) )
| ( ( X3 @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X1: a > $o,X3: ( a > $o ) > $o] :
( ( ( X3 @ X1 )
= $true )
| ( $true
!= ( X3 @ ( sK0 @ ( sK1 @ X1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( ( X3 @ X1 )
= $true )
| ( ( X3 @ ( X0 @ X2 ) )
!= $true ) )
=> ! [X1: a > $o] :
? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( ( X3 @ X1 )
= $true )
| ( $true
!= ( X3 @ ( sK0 @ X2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
! [X1: a > $o] :
( ? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( ( X3 @ X1 )
= $true )
| ( $true
!= ( X3 @ ( sK0 @ X2 ) ) ) )
=> ! [X3: ( a > $o ) > $o] :
( ( ( X3 @ X1 )
= $true )
| ( $true
!= ( X3 @ ( sK0 @ ( sK1 @ X1 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( ( X3 @ X1 )
= $true )
| ( ( X3 @ ( X0 @ X2 ) )
!= $true ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( ( X3 @ ( X0 @ X2 ) )
= $true )
=> ( ( X3 @ X1 )
= $true ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ~ ? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( ( X3 @ ( X0 @ X2 ) )
= $true )
=> ( ( X3 @ X1 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ~ ? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( X3 @ ( X0 @ X2 ) )
=> ( X3 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ~ ? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( X3 @ ( X0 @ X2 ) )
=> ( X3 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
~ ? [X0: a > a > $o] :
! [X1: a > $o] :
? [X2: a] :
! [X3: ( a > $o ) > $o] :
( ( X3 @ ( X0 @ X2 ) )
=> ( X3 @ X1 ) ),
file('/export/starexec/sandbox/tmp/tmp.L4cKLBnvY2/DTF2THF_8246.p',cCT29) ).
thf(f93,plain,
( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a] :
~ ( sK0 @ Y0 @ Y0 ) )
@ ( sK1
@ ^ [Y0: a] :
~ ( sK0 @ Y0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f92]) ).
thf(f92,plain,
( $true
= ( ^ [Y0: a] :
( sK0
@ ( ^ [Y1: a] : Y1
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( sK1
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
( sK0
@ ( ^ [Y2: a] : Y2
@ Y1 )
@ ( ^ [Y2: a] : Y2
@ Y1 ) )
@ Y0 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
( ( $true != $true )
| ( $true
= ( ^ [Y0: a] :
( sK0
@ ( ^ [Y1: a] : Y1
@ Y0 )
@ ( ^ [Y1: a] : Y1
@ Y0 ) )
@ ( sK1
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
( sK0
@ ( ^ [Y2: a] : Y2
@ Y1 )
@ ( ^ [Y2: a] : Y2
@ Y1 ) )
@ Y0 ) ) ) ) ),
inference(equality_factoring,[status(thm)],[f87]) ).
thf(f87,plain,
! [X1: a,X4: a > $o] :
( ( $true
= ( sK0
@ ( sK1
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) )
@ X1 ) )
| ( $true
= ( X4 @ X1 ) ) ),
inference(boolean_simplification,[status(thm)],[f86]) ).
thf(f86,plain,
! [X1: a,X4: a > $o] :
( ( $true
= ( X4 @ X1 ) )
| ( ( sK0
@ ( sK1
@ ^ [Y0: a] :
~ ( X4 @ Y0 ) )
@ X1 )
= ( ~ $false ) ) ),
inference(cases_simplifying,[status(thm)],[f84]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO209^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n025.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 14:26:12 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
% 0.32/0.49 ---- Original DTF file ---
% 0.32/0.49 thf(spec,logic,$$dhol).
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 % File : SYO209^5 : TPTP v9.2.1. Released v4.0.0.
% 0.32/0.49 % Domain : Syntactic
% 0.32/0.49 % Problem : TPS problem CT29
% 0.32/0.49 % Version : Especial.
% 0.32/0.49 % English :
% 0.32/0.49
% 0.32/0.49 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.32/0.49 % Source : [Bro09]
% 0.32/0.49 % Names : tps_0374 [Bro09]
% 0.32/0.49 % : CT29 [TPS]
% 0.32/0.49
% 0.32/0.49 % Status : Theorem
% 0.32/0.49 % Rating : 0.58 v9.1.0, 0.62 v9.0.0, 0.50 v8.2.0, 0.55 v8.1.0, 0.42 v7.5.0, 0.50 v7.4.0, 0.44 v7.3.0, 0.50 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.50 v6.4.0, 0.43 v6.3.0, 0.50 v6.2.0, 0.67 v6.1.0, 0.50 v5.5.0, 0.60 v5.4.0, 0.50 v4.1.0, 0.67 v4.0.0
% 0.32/0.49 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.32/0.49 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.32/0.49 % Maximal formula atoms : 0 ( 0 avg)
% 0.32/0.49 % Number of connectives : 5 ( 1 ~; 0 |; 0 &; 3 @)
% 0.32/0.49 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.32/0.49 % Maximal formula depth : 9 ( 9 avg)
% 0.32/0.49 % Number of types : 2 ( 1 usr)
% 0.32/0.49 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.32/0.49 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.32/0.49 % Number of variables : 4 ( 0 ^; 2 !; 2 ?; 4 :)
% 0.32/0.49 % SPC : TH0_THM_NEQ_NAR
% 0.32/0.49
% 0.32/0.49 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.32/0.49 % project in the Department of Mathematical Sciences at Carnegie
% 0.32/0.49 % Mellon University. Distributed under the Creative Commons copyleft
% 0.32/0.49 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 thf(a_type,type,
% 0.32/0.49 a: $tType ).
% 0.32/0.49
% 0.32/0.49 thf(cCT29,conjecture,
% 0.32/0.49 ~ ? [Xg: a > a > $o] :
% 0.32/0.49 ! [Xf: a > $o] :
% 0.32/0.49 ? [Xj: a] :
% 0.32/0.49 ! [Xp: ( a > $o ) > $o] :
% 0.32/0.49 ( ( Xp @ ( Xg @ Xj ) )
% 0.32/0.49 => ( Xp @ Xf ) ) ).
% 0.32/0.49
% 0.32/0.49 %------------------------------------------------------------------------------
% 0.32/0.49 ------------------------
% 1.64/1.42 ---- Embedded in THF ---
% 1.64/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.42 %%% Generated on Tue Feb 24 14:26:13 EST 2026
% 1.64/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.42 %%% Logic specification used:
% 1.64/1.42 %%% thf(spec, logic, $$dhol).
% 1.64/1.42
% 1.64/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.L4cKLBnvY2/DTF2DTF8246.p
% See solution above
% 1.64/1.42 ------------------------
% 1.64/1.43 ---- Cleaned THF ---
% 1.64/1.43 thf(a_type,type,
% 1.64/1.43 a: $tType ).
% 1.64/1.43
% 1.64/1.43 thf(cCT29,conjecture,
% 1.64/1.43 ~ ? [Xg: a > a > $o] :
% 1.64/1.43 ! [Xf: a > $o] :
% 1.64/1.43 ? [Xj: a] :
% 1.64/1.43 ! [Xp: ( a > $o ) > $o] :
% 1.64/1.43 ( ( Xp @ ( Xg @ Xj ) )
% 1.64/1.43 => ( Xp @ Xf ) ) ).
% 1.64/1.43 ------------------------
% 1.64/1.45 % (8344)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_8246 for (3000ds/4Mi)
% 1.64/1.45 % (8345)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_8246 for (3000ds/27Mi)
% 1.64/1.45 % (8343)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8246 for (3000ds/183Mi)
% 1.64/1.45 % (8346)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8246 for (3000ds/2Mi)
% 1.64/1.45 % (8347)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_8246 for (3000ds/2Mi)
% 1.64/1.45 % (8348)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_8246 for (3000ds/275Mi)
% 1.64/1.45 % (8349)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8246 for (3000ds/18Mi)
% 1.64/1.45 % (8345)Refutation not found, incomplete strategy
% 1.64/1.45 % (8345)------------------------------
% 1.64/1.45 % (8345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.45 % (8345)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.45
% 1.64/1.45
% 1.64/1.45 % (8345)Memory used [KB]: 5500
% 1.64/1.45 % (8345)Time elapsed: 0.002 s
% 1.64/1.45 % (8345)Instructions burned: 1 (million)
% 1.64/1.45 % (8345)------------------------------
% 1.64/1.45 % (8345)------------------------------
% 1.64/1.45 % (8346)Instruction limit reached!
% 1.64/1.45 % (8346)------------------------------
% 1.64/1.45 % (8346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.45 % (8346)Termination reason: Unknown
% 1.64/1.45 % (8346)Termination phase: Saturation
% 1.64/1.45 % (8347)Instruction limit reached!
% 1.64/1.45 % (8347)------------------------------
% 1.64/1.45 % (8347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.45
% 1.64/1.45 % (8346)Memory used [KB]: 5500
% 1.64/1.45 % (8346)Time elapsed: 0.003 s
% 1.64/1.45 % (8346)Instructions burned: 2 (million)
% 1.64/1.45 % (8346)------------------------------
% 1.64/1.45 % (8346)------------------------------
% 1.64/1.45 % (8347)Termination reason: Unknown
% 1.64/1.45 % (8347)Termination phase: Saturation
% 1.64/1.45
% 1.64/1.45 % (8347)Memory used [KB]: 5500
% 1.64/1.45 % (8347)Time elapsed: 0.003 s
% 1.64/1.45 % (8347)Instructions burned: 2 (million)
% 1.64/1.45 % (8347)------------------------------
% 1.64/1.45 % (8347)------------------------------
% 1.64/1.45 % (8344)Instruction limit reached!
% 1.64/1.45 % (8344)------------------------------
% 1.64/1.45 % (8344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.45 % (8344)Termination reason: Unknown
% 1.64/1.45 % (8344)Termination phase: Saturation
% 1.64/1.45
% 1.64/1.45 % (8344)Memory used [KB]: 5500
% 1.64/1.45 % (8344)Time elapsed: 0.004 s
% 1.64/1.45 % (8344)Instructions burned: 4 (million)
% 1.64/1.45 % (8344)------------------------------
% 1.64/1.45 % (8344)------------------------------
% 1.64/1.45 % (8348)Refutation not found, incomplete strategy
% 1.64/1.45 % (8348)------------------------------
% 1.64/1.45 % (8348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.45 % (8348)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.45
% 1.64/1.45
% 1.64/1.45 % (8348)Memory used [KB]: 5500
% 1.64/1.45 % (8348)Time elapsed: 0.004 s
% 1.64/1.45 % (8348)Instructions burned: 4 (million)
% 1.64/1.45 % (8348)------------------------------
% 1.64/1.45 % (8348)------------------------------
% 1.64/1.46 % (8349)Instruction limit reached!
% 1.64/1.46 % (8349)------------------------------
% 1.64/1.46 % (8349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.46 % (8349)Termination reason: Unknown
% 1.64/1.46 % (8349)Termination phase: Saturation
% 1.64/1.46
% 1.64/1.46 % (8349)Memory used [KB]: 5628
% 1.64/1.46 % (8349)Time elapsed: 0.012 s
% 1.64/1.46 % (8349)Instructions burned: 19 (million)
% 1.64/1.46 % (8349)------------------------------
% 1.64/1.46 % (8349)------------------------------
% 1.64/1.47 % (8350)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8246 for (2999ds/3Mi)
% 1.64/1.47 % (8351)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_8246 for (2999ds/37Mi)
% 1.64/1.47 % (8352)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_8246 for (2999ds/15Mi)
% 1.64/1.47 % (8353)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_8246 for (2999ds/3Mi)
% 1.64/1.47 % (8353)Refutation not found, incomplete strategy
% 1.64/1.47 % (8353)------------------------------
% 1.64/1.47 % (8353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (8353)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.47
% 1.64/1.47
% 1.64/1.47 % (8353)Memory used [KB]: 5373
% 1.64/1.47 % (8353)Time elapsed: 0.002 s
% 1.64/1.47 % (8353)Instructions burned: 1 (million)
% 1.64/1.47 % (8353)------------------------------
% 1.64/1.47 % (8353)------------------------------
% 1.64/1.47 % (8354)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_8246 for (2999ds/1041Mi)
% 1.64/1.47 % (8350)Instruction limit reached!
% 1.64/1.47 % (8350)------------------------------
% 1.64/1.47 % (8350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (8350)Termination reason: Unknown
% 1.64/1.47 % (8350)Termination phase: Saturation
% 1.64/1.47
% 1.64/1.47 % (8350)Memory used [KB]: 5500
% 1.64/1.47 % (8350)Time elapsed: 0.004 s
% 1.64/1.47 % (8350)Instructions burned: 4 (million)
% 1.64/1.47 % (8350)------------------------------
% 1.64/1.47 % (8350)------------------------------
% 1.64/1.47 % (8352)Refutation not found, incomplete strategy
% 1.64/1.47 % (8352)------------------------------
% 1.64/1.47 % (8352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.47 % (8352)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.47
% 1.64/1.47
% 1.64/1.47 % (8352)Memory used [KB]: 5500
% 1.64/1.47 % (8352)Time elapsed: 0.004 s
% 1.64/1.47 % (8352)Instructions burned: 4 (million)
% 1.64/1.47 % (8352)------------------------------
% 1.64/1.47 % (8352)------------------------------
% 1.64/1.48 % (8355)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_8246 for (2999ds/7Mi)
% 1.64/1.48 % (8355)Instruction limit reached!
% 1.64/1.48 % (8355)------------------------------
% 1.64/1.48 % (8355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.48 % (8355)Termination reason: Unknown
% 1.64/1.48 % (8355)Termination phase: Saturation
% 1.64/1.48
% 1.64/1.48 % (8355)Memory used [KB]: 1023
% 1.64/1.48 % (8355)Time elapsed: 0.006 s
% 1.64/1.48 % (8355)Instructions burned: 8 (million)
% 1.64/1.48 % (8355)------------------------------
% 1.64/1.48 % (8355)------------------------------
% 1.64/1.49 % (8356)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_8246 for (2999ds/16Mi)
% 1.64/1.49 % (8357)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_8246 for (2999ds/3Mi)
% 1.64/1.49 % (8354)Refutation not found, incomplete strategy
% 1.64/1.49 % (8354)------------------------------
% 1.64/1.49 % (8354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (8354)Termination reason: Refutation not found, incomplete strategy
% 1.64/1.49
% 1.64/1.49
% 1.64/1.49 % (8354)Memory used [KB]: 5628
% 1.64/1.49 % (8354)Time elapsed: 0.019 s
% 1.64/1.49 % (8354)Instructions burned: 31 (million)
% 1.64/1.49 % (8354)------------------------------
% 1.64/1.49 % (8354)------------------------------
% 1.64/1.49 % (8351)Instruction limit reached!
% 1.64/1.49 % (8351)------------------------------
% 1.64/1.49 % (8351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (8358)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_8246 for (2999ds/3Mi)
% 1.64/1.49 % (8351)Termination reason: Unknown
% 1.64/1.49 % (8351)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (8351)Memory used [KB]: 5756
% 1.64/1.49 % (8351)Time elapsed: 0.021 s
% 1.64/1.49 % (8351)Instructions burned: 38 (million)
% 1.64/1.49 % (8351)------------------------------
% 1.64/1.49 % (8351)------------------------------
% 1.64/1.49 % (8357)Instruction limit reached!
% 1.64/1.49 % (8357)------------------------------
% 1.64/1.49 % (8357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (8357)Termination reason: Unknown
% 1.64/1.49 % (8357)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (8357)Memory used [KB]: 5500
% 1.64/1.49 % (8357)Time elapsed: 0.004 s
% 1.64/1.49 % (8357)Instructions burned: 3 (million)
% 1.64/1.49 % (8357)------------------------------
% 1.64/1.49 % (8357)------------------------------
% 1.64/1.49 % (8358)Instruction limit reached!
% 1.64/1.49 % (8358)------------------------------
% 1.64/1.49 % (8358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (8358)Termination reason: Unknown
% 1.64/1.49 % (8358)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (8358)Memory used [KB]: 1023
% 1.64/1.49 % (8358)Time elapsed: 0.003 s
% 1.64/1.49 % (8358)Instructions burned: 3 (million)
% 1.64/1.49 % (8358)------------------------------
% 1.64/1.49 % (8358)------------------------------
% 1.64/1.49 % (8356)Instruction limit reached!
% 1.64/1.49 % (8356)------------------------------
% 1.64/1.49 % (8356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.49 % (8356)Termination reason: Unknown
% 1.64/1.49 % (8356)Termination phase: Saturation
% 1.64/1.49
% 1.64/1.49 % (8356)Memory used [KB]: 5628
% 1.64/1.49 % (8356)Time elapsed: 0.010 s
% 1.64/1.49 % (8356)Instructions burned: 16 (million)
% 1.64/1.49 % (8356)------------------------------
% 1.64/1.49 % (8356)------------------------------
% 1.69/1.50 % (8359)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_8246 for (2999ds/7Mi)
% 1.69/1.50 % (8359)First to succeed.
% 1.69/1.50 % (8359)Refutation found. Thanks to Tanya!
% 1.69/1.50 % SZS status Theorem for DTF2THF_8246
% 1.69/1.50 % SZS output start Proof for DTF2THF_8246
% 1.69/1.50 thf(type_def_5, type, a: $tType).
% 1.69/1.50 thf(func_def_0, type, a: $tType).
% 1.69/1.50 thf(func_def_4, type, sK0: a > a > $o).
% 1.69/1.50 thf(func_def_5, type, sK1: (a > $o) > a).
% 1.69/1.50 thf(f98,plain,(
% 1.69/1.50 $false),
% 1.69/1.50 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.69/1.50 thf(f97,plain,(
% 1.69/1.50 ($true = $false)),
% 1.69/1.50 inference(backward_demodulation,[status(thm)],[f93,f96])).
% 1.69/1.50 thf(f96,plain,(
% 1.69/1.50 ((sK0 @ (sK1 @ (^[Y0 : a]: (~ (sK0 @ Y0 @ Y0)))) @ (sK1 @ (^[Y0 : a]: (~ (sK0 @ Y0 @ Y0))))) = $false)),
% 1.69/1.50 inference(beta_eta_normalization,[status(thm)],[f95])).
% 1.69/1.50 thf(f95,plain,(
% 1.69/1.50 ($false = ((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0) @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK1 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK0 @ ((^[Y2 : a]: (Y2)) @ Y1) @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))),
% 1.69/1.50 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.69/1.50 thf(f94,plain,(
% 1.69/1.50 ($false = ((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0) @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK1 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK0 @ ((^[Y2 : a]: (Y2)) @ Y1) @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0)))))) | ($false != $false)),
% 1.69/1.50 inference(equality_factoring,[status(thm)],[f88])).
% 1.69/1.50 thf(f88,plain,(
% 1.69/1.50 ( ! [X1 : a,X4 : a > $o] : (($false = (sK0 @ (sK1 @ (^[Y0 : a]: (~ (X4 @ Y0)))) @ X1)) | ($false = (X4 @ X1))) )),
% 1.69/1.50 inference(boolean_simplification,[status(thm)],[f85])).
% 1.69/1.50 thf(f85,plain,(
% 1.69/1.50 ( ! [X1 : a,X4 : a > $o] : (((sK0 @ (sK1 @ (^[Y0 : a]: (~ (X4 @ Y0)))) @ X1) = (~ $true)) | ($false = (X4 @ X1))) )),
% 1.69/1.50 inference(cases_simplifying,[status(thm)],[f84])).
% 1.69/1.50 thf(f84,plain,(
% 1.69/1.50 ( ! [X1 : a,X4 : a > $o] : (((sK0 @ (sK1 @ (^[Y0 : a]: (~ (X4 @ Y0)))) @ X1) = (~ (X4 @ X1)))) )),
% 1.69/1.50 inference(beta_eta_normalization,[status(thm)],[f83])).
% 1.69/1.50 thf(f83,plain,(
% 1.69/1.50 ( ! [X1 : a,X4 : a > $o] : (((sK0 @ (sK1 @ (^[Y0 : a]: (~ (X4 @ Y0)))) @ X1) = ((^[Y0 : a]: (~ (X4 @ Y0))) @ X1))) )),
% 1.69/1.50 inference(primitive_instantiation,[status(thm)],[f49])).
% 1.69/1.50 thf(f49,plain,(
% 1.69/1.50 ( ! [X0 : a > $o,X1 : a] : (((X0 @ X1) = (sK0 @ (sK1 @ X0) @ X1))) )),
% 1.69/1.50 inference(argument_congruence,[status(thm)],[f12])).
% 1.69/1.50 thf(f12,plain,(
% 1.69/1.50 ( ! [X0 : a > $o] : (((sK0 @ (sK1 @ X0)) = X0)) )),
% 1.69/1.50 inference(leibniz_equality_elimination,[status(thm)],[f11])).
% 1.69/1.50 thf(f11,plain,(
% 1.69/1.50 ( ! [X3 : (a > $o) > $o,X1 : a > $o] : (($true != (X3 @ (sK0 @ (sK1 @ X1)))) | ((X3 @ X1) = $true)) )),
% 1.69/1.50 inference(cnf_transformation,[status(thm)],[f10])).
% 1.69/1.50 thf(f10,plain,(
% 1.69/1.50 ! [X1 : a > $o] : ! [X3 : (a > $o) > $o] : (((X3 @ X1) = $true) | ($true != (X3 @ (sK0 @ (sK1 @ X1)))))),
% 1.69/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.69/1.50 thf(f8,plain,(
% 1.69/1.50 ? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : ! [X3 : (a > $o) > $o] : (((X3 @ X1) = $true) | ((X3 @ (X0 @ X2)) != $true)) => ! [X1 : a > $o] : ? [X2 : a] : ! [X3 : (a > $o) > $o] : (((X3 @ X1) = $true) | ($true != (X3 @ (sK0 @ X2))))),
% 1.69/1.50 introduced(definition,[],[choice_axiom])).
% 1.69/1.50 thf(f9,plain,(
% 1.69/1.50 ! [X1 : a > $o] : (? [X2 : a] : ! [X3 : (a > $o) > $o] : (((X3 @ X1) = $true) | ($true != (X3 @ (sK0 @ X2)))) => ! [X3 : (a > $o) > $o] : (((X3 @ X1) = $true) | ($true != (X3 @ (sK0 @ (sK1 @ X1))))))),
% 1.69/1.50 introduced(definition,[],[choice_axiom])).
% 1.69/1.50 thf(f7,plain,(
% 1.69/1.50 ? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : ! [X3 : (a > $o) > $o] : (((X3 @ X1) = $true) | ((X3 @ (X0 @ X2)) != $true))),
% 1.69/1.50 inference(ennf_transformation,[status(thm)],[f6])).
% 1.69/1.50 thf(f6,plain,(
% 1.69/1.50 ? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : ! [X3 : (a > $o) > $o] : (((X3 @ (X0 @ X2)) = $true) => ((X3 @ X1) = $true))),
% 1.69/1.50 inference(flattening,[status(thm)],[f5])).
% 1.69/1.50 thf(f5,plain,(
% 1.69/1.50 ~~? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : ! [X3 : (a > $o) > $o] : (((X3 @ (X0 @ X2)) = $true) => ((X3 @ X1) = $true))),
% 1.69/1.50 inference(fool_elimination,[status(thm)],[f4])).
% 1.69/1.50 thf(f4,plain,(
% 1.69/1.50 ~~? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : ! [X3 : (a > $o) > $o] : ((X3 @ (X0 @ X2)) => (X3 @ X1))),
% 1.69/1.50 inference(rectify,[status(thm)],[f2])).
% 1.69/1.50 thf(f2,negated_conjecture,(
% 1.69/1.50 ~~? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : ! [X3 : (a > $o) > $o] : ((X3 @ (X0 @ X2)) => (X3 @ X1))),
% 1.69/1.50 inference(negated_conjecture,[status(cth)],[f1])).
% 1.69/1.50 thf(f1,conjecture,(
% 1.69/1.50 ~? [X0 : a > a > $o] : ! [X1 : a > $o] : ? [X2 : a] : ! [X3 : (a > $o) > $o] : ((X3 @ (X0 @ X2)) => (X3 @ X1))),
% 1.69/1.50 file('/export/starexec/sandbox/tmp/tmp.L4cKLBnvY2/DTF2THF_8246.p',cCT29)).
% 1.69/1.50 thf(f93,plain,(
% 1.69/1.50 ($true = (sK0 @ (sK1 @ (^[Y0 : a]: (~ (sK0 @ Y0 @ Y0)))) @ (sK1 @ (^[Y0 : a]: (~ (sK0 @ Y0 @ Y0))))))),
% 1.69/1.50 inference(beta_eta_normalization,[status(thm)],[f92])).
% 1.69/1.50 thf(f92,plain,(
% 1.69/1.50 ($true = ((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0) @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK1 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK0 @ ((^[Y2 : a]: (Y2)) @ Y1) @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))),
% 1.69/1.50 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.69/1.50 thf(f91,plain,(
% 1.69/1.50 ($true != $true) | ($true = ((^[Y0 : a]: (sK0 @ ((^[Y1 : a]: (Y1)) @ Y0) @ ((^[Y1 : a]: (Y1)) @ Y0))) @ (sK1 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (sK0 @ ((^[Y2 : a]: (Y2)) @ Y1) @ ((^[Y2 : a]: (Y2)) @ Y1))) @ Y0))))))),
% 1.69/1.50 inference(equality_factoring,[status(thm)],[f87])).
% 1.69/1.50 thf(f87,plain,(
% 1.69/1.50 ( ! [X1 : a,X4 : a > $o] : (($true = (sK0 @ (sK1 @ (^[Y0 : a]: (~ (X4 @ Y0)))) @ X1)) | ($true = (X4 @ X1))) )),
% 1.69/1.50 inference(boolean_simplification,[status(thm)],[f86])).
% 1.69/1.50 thf(f86,plain,(
% 1.69/1.50 ( ! [X1 : a,X4 : a > $o] : (($true = (X4 @ X1)) | ((sK0 @ (sK1 @ (^[Y0 : a]: (~ (X4 @ Y0)))) @ X1) = (~ $false))) )),
% 1.69/1.50 inference(cases_simplifying,[status(thm)],[f84])).
% 1.69/1.50 % SZS output end Proof for DTF2THF_8246
% 1.69/1.50 % (8359)------------------------------
% 1.69/1.50 % (8359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.50 % (8359)Termination reason: Refutation
% 1.69/1.50
% 1.69/1.50 % (8359)Memory used [KB]: 5500
% 1.69/1.50 % (8359)Time elapsed: 0.006 s
% 1.69/1.50 % (8359)Instructions burned: 6 (million)
% 1.69/1.50 % (8359)------------------------------
% 1.69/1.50 % (8359)------------------------------
% 1.69/1.50 % (8342)Success in time 0.061 s
%------------------------------------------------------------------------------