%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO241^5 : 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 : n016.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 09:53:45 AM UTC 2026
% Result : Theorem 1.63s 1.36s
% Output : Refutation 1.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 155 ( 87 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 308 ( 49 ~; 17 |; 34 &; 182 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 82 ( 82 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 4 usr; 3 con; 0-2 aty)
% ( 0 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 84 ( 30 ^; 40 !; 14 ?; 84 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_10,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_11,type,
sK1: $i > $o ).
thf(func_def_13,type,
ph3:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
sK4: $i > $i > $o ).
thf(f48,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f44,f12]) ).
thf(f12,plain,
( ( sK1 @ ( sK0 @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) ) )
& ( ( sK1 @ ( sK0 @ sK1 ) )
!= $true )
& ( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ? [X3: $i > $o] :
( ( ( X3 @ ( X0 @ X3 ) )
!= $true )
& ( ( X0 @ X3 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) ) ) )
=> ( ! [X2: $i > $o,X1: $i > $o] :
( ( X1 = X2 )
| ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) ) )
& ? [X3: $i > $o] :
( ( ( X3 @ ( sK0 @ X3 ) )
!= $true )
& ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
= ( sK0 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X3: $i > $o] :
( ( ( X3 @ ( sK0 @ X3 ) )
!= $true )
& ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
= ( sK0 @ X3 ) ) )
=> ( ( ( sK1 @ ( sK0 @ sK1 ) )
!= $true )
& ( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( X1 = X2 )
| ( ( X0 @ X1 )
!= ( X0 @ X2 ) ) )
& ? [X3: $i > $o] :
( ( ( X3 @ ( X0 @ X3 ) )
!= $true )
& ( ( X0 @ X3 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ( ( X3 @ ( X0 @ X3 ) )
!= $true )
& ( ( X0 @ X3 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ( ( X0 @ X3 )
= ( X0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( X0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( X0 @ Y1 ) ) ) ) ) )
& ( ( X3 @ ( X0 @ X3 ) )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X1: $i > $o,X2: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ( ( X0
@ ^ [X4: $i] :
? [X5: $i > $o] :
( ~ ( X5 @ ( X0 @ X5 ) )
& ( ( X0 @ X5 )
= X4 ) ) )
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i] :
( ! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ( ( X0
@ ^ [X4: $i] :
? [X5: $i > $o] :
( ~ ( X5 @ ( X0 @ X5 ) )
& ( ( X0 @ X5 )
= X4 ) ) )
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i] :
( ! [X2: $i > $o,X1: $i > $o] :
( ( ( X0 @ X1 )
= ( X0 @ X2 ) )
=> ( X1 = X2 ) )
=> ~ ? [X3: $i > $o] :
( ( ( X0
@ ^ [X4: $i] :
? [X5: $i > $o] :
( ~ ( X5 @ ( X0 @ X5 ) )
& ( ( X0 @ X5 )
= X4 ) ) )
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LTHERgGu6h/DTF2THF_9246.p',cTHM143_EXPAND) ).
thf(f44,plain,
( ( sK1 @ ( sK0 @ sK1 ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f37]) ).
thf(f37,plain,
( ( $true != $true )
| ( ( sK1 @ ( sK0 @ sK1 ) )
= $true ) ),
inference(superposition,[status(thm)],[f12,f35]) ).
thf(f35,plain,
! [X0: $i > $o] :
( ( $true
= ( sK1 @ ( sK0 @ X0 ) ) )
| ( ( X0 @ ( sK0 @ X0 ) )
= $true ) ),
inference(equality_resolution,[status(thm)],[f33]) ).
thf(f33,plain,
! [X2: $i > $o,X1: $i] :
( ( ( sK0 @ X2 )
!= X1 )
| ( ( sK1 @ X1 )
= $true )
| ( ( X2 @ ( sK0 @ X2 ) )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f32]) ).
thf(f32,plain,
! [X2: $i > $o,X1: $i] :
( ( ( X2 @ ( sK0 @ X2 ) )
= $true )
| ( ( sK1 @ X1 )
= $true )
| ( $false
= ( ( sK0 @ X2 )
= X1 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: $i > $o,X1: $i] :
( ( $false
= ( ~ ( X2 @ ( sK0 @ X2 ) ) ) )
| ( ( sK1 @ X1 )
= $true )
| ( $false
= ( ( sK0 @ X2 )
= X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f30]) ).
thf(f30,plain,
! [X2: $i > $o,X1: $i] :
( ( ( sK1 @ X1 )
= $true )
| ( $false
= ( ( ( sK0 @ X2 )
= X1 )
& ~ ( X2 @ ( sK0 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f29]) ).
thf(f29,plain,
! [X2: $i > $o,X1: $i] :
( ( ( sK1 @ X1 )
= $true )
| ( $false
= ( ^ [Y0: $i > $o] :
( ( ( sK0 @ Y0 )
= X1 )
& ~ ( Y0 @ ( sK0 @ Y0 ) ) )
@ X2 ) ) ),
inference(pi_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X1: $i] :
( ( ( sK1 @ X1 )
= $true )
| ( $false
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( sK0 @ Y0 )
= X1 )
& ~ ( Y0 @ ( sK0 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f20]) ).
thf(f20,plain,
! [X1: $i] :
( ( sK1 @ X1 )
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( sK0 @ Y0 )
= X1 )
& ~ ( Y0 @ ( sK0 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f19]) ).
thf(f19,plain,
! [X1: $i] :
( ( sK1 @ X1 )
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) )
@ X1 ) ),
inference(argument_congruence,[status(thm)],[f18]) ).
thf(f18,plain,
( sK1
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) ) ),
inference(equality_resolution,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $i > $o] :
( ( ( sK0 @ X0 )
!= ( sK0 @ sK1 ) )
| ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) )
= X0 ) ),
inference(superposition,[status(thm)],[f13,f11]) ).
thf(f11,plain,
( ( sK0 @ sK1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( sK0 @ Y1 )
= Y0 )
& ~ ( Y1 @ ( sK0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f13,plain,
! [X2: $i > $o,X1: $i > $o] :
( ( ( sK0 @ X1 )
!= ( sK0 @ X2 ) )
| ( X1 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO241^5 : 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
% 0.16/0.34 % Computer : n016.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 14:27:21 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
% 0.30/0.46 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SYO241^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.46 % Domain : Syntactic
% 0.30/0.46 % Problem : TPS problem from BASIC-HO-EQ-THMS
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English :
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : tps_0431 [Bro09]
% 0.30/0.46 % : tps_0900 [Bro09]
% 0.30/0.46 % : THM143A [TPS]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v6.0.0, 0.43 v5.5.0, 0.17 v5.4.0, 0.40 v5.3.0, 0.60 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v4.0.0
% 0.30/0.46 % Syntax : Number of formulae : 1 ( 0 unt; 0 typ; 0 def)
% 0.30/0.46 % Number of atoms : 4 ( 4 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 3 ( 4 avg)
% 0.30/0.46 % Number of connectives : 16 ( 3 ~; 0 |; 2 &; 9 @)
% 0.30/0.46 % ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 9 ( 9 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.46 % Number of variables : 6 ( 1 ^; 3 !; 2 ?; 6 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(cTHM143_EXPAND,conjecture,
% 0.30/0.46 ! [Xh: ( $i > $o ) > $i] :
% 0.30/0.46 ( ! [Xp: $i > $o,Xq: $i > $o] :
% 0.30/0.46 ( ( ( Xh @ Xp )
% 0.30/0.46 = ( Xh @ Xq ) )
% 0.30/0.46 => ( Xp = Xq ) )
% 0.30/0.46 => ~ ? [Xt: $i > $o] :
% 0.30/0.46 ( ~ ( Xt @ ( Xh @ Xt ) )
% 0.30/0.46 & ( ( Xh
% 0.30/0.46 @ ^ [Xz: $i] :
% 0.30/0.46 ? [Xt0: $i > $o] :
% 0.30/0.46 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 0.30/0.46 & ( Xz
% 0.30/0.46 = ( Xh @ Xt0 ) ) ) )
% 0.30/0.46 = ( Xh @ Xt ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.63/1.31 ---- Embedded in THF ---
% 1.63/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.63/1.32 %%% Generated on Tue Feb 24 14:27:22 EST 2026
% 1.63/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.63/1.32 %%% Logic specification used:
% 1.63/1.32 %%% thf(spec, logic, $$dhol).
% 1.63/1.32
% 1.63/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LTHERgGu6h/DTF2DTF9246.p
% See solution above
% 1.63/1.32 ------------------------
% 1.63/1.32 ---- Cleaned THF ---
% 1.63/1.33 thf(cTHM143_EXPAND,conjecture,
% 1.63/1.33 ! [Xh: ( $i > $o ) > $i] :
% 1.63/1.33 ( ! [Xp: $i > $o,Xq: $i > $o] :
% 1.63/1.33 ( ( ( Xh @ Xp )
% 1.63/1.33 = ( Xh @ Xq ) )
% 1.63/1.33 => ( Xp = Xq ) )
% 1.63/1.33 => ~ ? [Xt: $i > $o] :
% 1.63/1.33 ( ~ ( Xt @ ( Xh @ Xt ) )
% 1.63/1.33 & ( ( Xh
% 1.63/1.33 @ ^ [Xz: $i] :
% 1.63/1.33 ? [Xt0: $i > $o] :
% 1.63/1.33 ( ~ ( Xt0 @ ( Xh @ Xt0 ) )
% 1.63/1.33 & ( Xz
% 1.63/1.33 = ( Xh @ Xt0 ) ) ) )
% 1.63/1.33 = ( Xh @ Xt ) ) ) ) ).
% 1.63/1.33 ------------------------
% 1.63/1.34 % (9435)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9246 for (2999ds/183Mi)
% 1.63/1.34 % (9436)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_9246 for (2999ds/4Mi)
% 1.63/1.34 % (9439)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_9246 for (2999ds/2Mi)
% 1.63/1.34 % (9439)Instruction limit reached!
% 1.63/1.34 % (9439)------------------------------
% 1.63/1.34 % (9439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (9439)Termination reason: Unknown
% 1.63/1.34 % (9439)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (9439)Memory used [KB]: 5500
% 1.63/1.34 % (9439)Time elapsed: 0.002 s
% 1.63/1.34 % (9439)Instructions burned: 3 (million)
% 1.63/1.34 % (9439)------------------------------
% 1.63/1.34 % (9439)------------------------------
% 1.63/1.34 % (9436)Instruction limit reached!
% 1.63/1.34 % (9436)------------------------------
% 1.63/1.34 % (9436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.34 % (9436)Termination reason: Unknown
% 1.63/1.34 % (9436)Termination phase: Saturation
% 1.63/1.34
% 1.63/1.34 % (9436)Memory used [KB]: 5500
% 1.63/1.34 % (9436)Time elapsed: 0.003 s
% 1.63/1.34 % (9436)Instructions burned: 5 (million)
% 1.63/1.34 % (9436)------------------------------
% 1.63/1.34 % (9436)------------------------------
% 1.63/1.35 % (9438)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9246 for (2999ds/2Mi)
% 1.63/1.35 % (9437)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_9246 for (2999ds/27Mi)
% 1.63/1.35 % (9441)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9246 for (2999ds/18Mi)
% 1.63/1.35 % (9438)Instruction limit reached!
% 1.63/1.35 % (9438)------------------------------
% 1.63/1.35 % (9438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.35 % (9438)Termination reason: Unknown
% 1.63/1.35 % (9438)Termination phase: Saturation
% 1.63/1.35
% 1.63/1.35 % (9438)Memory used [KB]: 895
% 1.63/1.35 % (9438)Time elapsed: 0.003 s
% 1.63/1.35 % (9438)Instructions burned: 2 (million)
% 1.63/1.35 % (9438)------------------------------
% 1.63/1.35 % (9438)------------------------------
% 1.63/1.35 % (9443)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_9246 for (2999ds/37Mi)
% 1.63/1.35 % (9441)First to succeed.
% 1.63/1.35 % (9442)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9246 for (2999ds/3Mi)
% 1.63/1.35 % (9435)Also succeeded, but the first one will report.
% 1.63/1.36 % (9442)Instruction limit reached!
% 1.63/1.36 % (9442)------------------------------
% 1.63/1.36 % (9442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (9442)Termination reason: Unknown
% 1.63/1.36 % (9442)Termination phase: Saturation
% 1.63/1.36
% 1.63/1.36 % (9442)Memory used [KB]: 5500
% 1.63/1.36 % (9442)Time elapsed: 0.003 s
% 1.63/1.36 % (9442)Instructions burned: 4 (million)
% 1.63/1.36 % (9442)------------------------------
% 1.63/1.36 % (9442)------------------------------
% 1.63/1.36 % (9437)Also succeeded, but the first one will report.
% 1.63/1.36 % (9441)Refutation found. Thanks to Tanya!
% 1.63/1.36 % SZS status Theorem for DTF2THF_9246
% 1.63/1.36 % SZS output start Proof for DTF2THF_9246
% 1.63/1.36 thf(func_def_10, type, sK0: ($i > $o) > $i).
% 1.63/1.36 thf(func_def_11, type, sK1: $i > $o).
% 1.63/1.36 thf(func_def_13, type, ph3: !>[X0: $tType]:(X0)).
% 1.63/1.36 thf(func_def_14, type, sK4: $i > $i > $o).
% 1.63/1.36 thf(f48,plain,(
% 1.63/1.36 $false),
% 1.63/1.36 inference(subsumption_resolution,[status(thm)],[f44,f12])).
% 1.63/1.36 thf(f12,plain,(
% 1.63/1.36 ((sK1 @ (sK0 @ sK1)) != $true)),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.36 thf(f10,plain,(
% 1.63/1.36 ! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((sK0 @ X1) != (sK0 @ X2))) & (((sK1 @ (sK0 @ sK1)) != $true) & ((sK0 @ sK1) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))))))),
% 1.63/1.36 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.63/1.36 thf(f8,plain,(
% 1.63/1.36 ? [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((X0 @ X1) != (X0 @ X2))) & ? [X3 : $i > $o] : (((X3 @ (X0 @ X3)) != $true) & ((X0 @ X3) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1))))))))))) => (! [X2 : $i > $o,X1 : $i > $o] : ((X1 = X2) | ((sK0 @ X1) != (sK0 @ X2))) & ? [X3 : $i > $o] : (((X3 @ (sK0 @ X3)) != $true) & ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1)))))))) = (sK0 @ X3))))),
% 1.63/1.36 introduced(definition,[],[choice_axiom])).
% 1.63/1.36 thf(f9,plain,(
% 1.63/1.36 ? [X3 : $i > $o] : (((X3 @ (sK0 @ X3)) != $true) & ((sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1)))))))) = (sK0 @ X3))) => (((sK1 @ (sK0 @ sK1)) != $true) & ((sK0 @ sK1) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))))))),
% 1.63/1.36 introduced(definition,[],[choice_axiom])).
% 1.63/1.36 thf(f7,plain,(
% 1.63/1.36 ? [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : ((X1 = X2) | ((X0 @ X1) != (X0 @ X2))) & ? [X3 : $i > $o] : (((X3 @ (X0 @ X3)) != $true) & ((X0 @ X3) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1)))))))))))),
% 1.63/1.36 inference(ennf_transformation,[status(thm)],[f6])).
% 1.63/1.36 thf(f6,plain,(
% 1.63/1.36 ~! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) => ~? [X3 : $i > $o] : (((X3 @ (X0 @ X3)) != $true) & ((X0 @ X3) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1)))))))))))),
% 1.63/1.36 inference(flattening,[status(thm)],[f5])).
% 1.63/1.36 thf(f5,plain,(
% 1.63/1.36 ~! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) => ~? [X3 : $i > $o] : (((X0 @ X3) = (X0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((X0 @ Y1) = Y0) & (~ (Y1 @ (X0 @ Y1))))))))) & ~((X3 @ (X0 @ X3)) = $true)))),
% 1.63/1.36 inference(fool_elimination,[status(thm)],[f4])).
% 1.63/1.36 thf(f4,plain,(
% 1.63/1.36 ~! [X0 : ($i > $o) > $i] : (! [X1 : $i > $o,X2 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) => ~? [X3 : $i > $o] : (((X0 @ (^[X4 : $i] : (? [X5 : $i > $o] : (~(X5 @ (X0 @ X5)) & ((X0 @ X5) = X4))))) = (X0 @ X3)) & ~(X3 @ (X0 @ X3))))),
% 1.63/1.36 inference(rectify,[status(thm)],[f2])).
% 1.63/1.36 thf(f2,negated_conjecture,(
% 1.63/1.36 ~! [X0 : ($i > $o) > $i] : (! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) => ~? [X3 : $i > $o] : (((X0 @ (^[X4 : $i] : (? [X5 : $i > $o] : (~(X5 @ (X0 @ X5)) & ((X0 @ X5) = X4))))) = (X0 @ X3)) & ~(X3 @ (X0 @ X3))))),
% 1.63/1.36 inference(negated_conjecture,[status(cth)],[f1])).
% 1.63/1.36 thf(f1,conjecture,(
% 1.63/1.36 ! [X0 : ($i > $o) > $i] : (! [X2 : $i > $o,X1 : $i > $o] : (((X0 @ X1) = (X0 @ X2)) => (X1 = X2)) => ~? [X3 : $i > $o] : (((X0 @ (^[X4 : $i] : (? [X5 : $i > $o] : (~(X5 @ (X0 @ X5)) & ((X0 @ X5) = X4))))) = (X0 @ X3)) & ~(X3 @ (X0 @ X3))))),
% 1.63/1.36 file('/export/starexec/sandbox/tmp/tmp.LTHERgGu6h/DTF2THF_9246.p',cTHM143_EXPAND)).
% 1.63/1.36 thf(f44,plain,(
% 1.63/1.36 ((sK1 @ (sK0 @ sK1)) = $true)),
% 1.63/1.36 inference(trivial_inequality_removal,[status(thm)],[f37])).
% 1.63/1.36 thf(f37,plain,(
% 1.63/1.36 ($true != $true) | ((sK1 @ (sK0 @ sK1)) = $true)),
% 1.63/1.36 inference(superposition,[status(thm)],[f12,f35])).
% 1.63/1.36 thf(f35,plain,(
% 1.63/1.36 ( ! [X0 : $i > $o] : (($true = (sK1 @ (sK0 @ X0))) | ((X0 @ (sK0 @ X0)) = $true)) )),
% 1.63/1.36 inference(equality_resolution,[status(thm)],[f33])).
% 1.63/1.36 thf(f33,plain,(
% 1.63/1.36 ( ! [X2 : $i > $o,X1 : $i] : (((sK0 @ X2) != X1) | ((sK1 @ X1) = $true) | ((X2 @ (sK0 @ X2)) = $true)) )),
% 1.63/1.36 inference(equality_proxy_clausification,[status(thm)],[f32])).
% 1.63/1.36 thf(f32,plain,(
% 1.63/1.36 ( ! [X2 : $i > $o,X1 : $i] : (((X2 @ (sK0 @ X2)) = $true) | ((sK1 @ X1) = $true) | ($false = ((sK0 @ X2) = X1))) )),
% 1.63/1.36 inference(not_proxy_clausification,[status(thm)],[f31])).
% 1.63/1.36 thf(f31,plain,(
% 1.63/1.36 ( ! [X2 : $i > $o,X1 : $i] : (($false = (~ (X2 @ (sK0 @ X2)))) | ((sK1 @ X1) = $true) | ($false = ((sK0 @ X2) = X1))) )),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f30])).
% 1.63/1.36 thf(f30,plain,(
% 1.63/1.36 ( ! [X2 : $i > $o,X1 : $i] : (((sK1 @ X1) = $true) | ($false = (((sK0 @ X2) = X1) & (~ (X2 @ (sK0 @ X2)))))) )),
% 1.63/1.36 inference(beta_eta_normalization,[status(thm)],[f29])).
% 1.63/1.36 thf(f29,plain,(
% 1.63/1.36 ( ! [X2 : $i > $o,X1 : $i] : (((sK1 @ X1) = $true) | ($false = ((^[Y0 : $i > $o]: (((sK0 @ Y0) = X1) & (~ (Y0 @ (sK0 @ Y0))))) @ X2))) )),
% 1.63/1.36 inference(pi_clausification,[status(thm)],[f21])).
% 1.63/1.36 thf(f21,plain,(
% 1.63/1.36 ( ! [X1 : $i] : (((sK1 @ X1) = $true) | ($false = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: (((sK0 @ Y0) = X1) & (~ (Y0 @ (sK0 @ Y0)))))))) )),
% 1.63/1.36 inference(binary_proxy_clausification,[status(thm)],[f20])).
% 1.63/1.36 thf(f20,plain,(
% 1.63/1.36 ( ! [X1 : $i] : (((sK1 @ X1) = (?? @ ($i > $o) @ (^[Y0 : $i > $o]: (((sK0 @ Y0) = X1) & (~ (Y0 @ (sK0 @ Y0)))))))) )),
% 1.63/1.36 inference(beta_eta_normalization,[status(thm)],[f19])).
% 1.63/1.36 thf(f19,plain,(
% 1.63/1.36 ( ! [X1 : $i] : (((sK1 @ X1) = ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))) @ X1))) )),
% 1.63/1.36 inference(argument_congruence,[status(thm)],[f18])).
% 1.63/1.36 thf(f18,plain,(
% 1.63/1.36 (sK1 = (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))))),
% 1.63/1.36 inference(equality_resolution,[status(thm)],[f16])).
% 1.63/1.36 thf(f16,plain,(
% 1.63/1.36 ( ! [X0 : $i > $o] : (((sK0 @ X0) != (sK0 @ sK1)) | ((^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1))))))) = X0)) )),
% 1.63/1.36 inference(superposition,[status(thm)],[f13,f11])).
% 1.63/1.36 thf(f11,plain,(
% 1.63/1.36 ((sK0 @ sK1) = (sK0 @ (^[Y0 : $i]: (?? @ ($i > $o) @ (^[Y1 : $i > $o]: (((sK0 @ Y1) = Y0) & (~ (Y1 @ (sK0 @ Y1)))))))))),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.36 thf(f13,plain,(
% 1.63/1.36 ( ! [X2 : $i > $o,X1 : $i > $o] : (((sK0 @ X1) != (sK0 @ X2)) | (X1 = X2)) )),
% 1.63/1.36 inference(cnf_transformation,[status(thm)],[f10])).
% 1.63/1.36 % SZS output end Proof for DTF2THF_9246
% 1.63/1.36 % (9441)------------------------------
% 1.63/1.36 % (9441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.63/1.36 % (9441)Termination reason: Refutation
% 1.63/1.36
% 1.63/1.36 % (9441)Memory used [KB]: 5500
% 1.63/1.36 % (9441)Time elapsed: 0.008 s
% 1.63/1.36 % (9441)Instructions burned: 7 (million)
% 1.63/1.36 % (9441)------------------------------
% 1.63/1.36 % (9441)------------------------------
% 1.63/1.36 % (9434)Success in time 0.024 s
%------------------------------------------------------------------------------