%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO276^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 09:53:49 AM UTC 2026
% Result : Theorem 1.51s 1.27s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 36 ( 4 unt; 0 typ; 2 def)
% Number of atoms : 314 ( 126 equ; 0 cnn)
% Maximal formula atoms : 8 ( 8 avg)
% Number of connectives : 291 ( 39 ~; 37 |; 19 &; 181 @)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 96 ( 72 ^; 18 !; 6 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_3,type,
s: $i > $i ).
thf(func_def_8,type,
sK0: ( $i > $i > $o ) > $i ).
thf(func_def_9,type,
sK1: ( $i > $i > $o ) > $i ).
thf(func_def_12,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f92,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f47,f88,f91]) ).
thf(f91,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f90]) ).
thf(f90,plain,
( $false
| ~ spl2_1 ),
inference(subsumption_resolution,[status(thm)],[f89,f10]) ).
thf(f10,plain,
( ( cP @ m )
!= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
( ! [X0: $i > $i > $o] :
( ( ( ( X0 @ ( s @ ( sK1 @ X0 ) ) @ ( s @ ( sK0 @ X0 ) ) )
!= $true )
& ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
= $true ) )
| ( ( X0 @ cO @ cO )
!= $true )
| ( ( X0 @ n @ m )
= $true ) )
& ( ( cP @ n )
= $true )
& ( ( cP @ m )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8]) ).
thf(f8,plain,
! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] :
( ( $true
!= ( X0 @ ( s @ X2 ) @ ( s @ X1 ) ) )
& ( ( X0 @ X2 @ X1 )
= $true ) )
=> ( ( ( X0 @ ( s @ ( sK1 @ X0 ) ) @ ( s @ ( sK0 @ X0 ) ) )
!= $true )
& ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ! [X0: $i > $i > $o] :
( ? [X1: $i,X2: $i] :
( ( $true
!= ( X0 @ ( s @ X2 ) @ ( s @ X1 ) ) )
& ( ( X0 @ X2 @ X1 )
= $true ) )
| ( ( X0 @ cO @ cO )
!= $true )
| ( ( X0 @ n @ m )
= $true ) )
& ( ( cP @ n )
= $true )
& ( ( cP @ m )
!= $true ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ( cP @ m )
!= $true )
& ( ( cP @ n )
= $true )
& ! [X0: $i > $i > $o] :
( ( ( X0 @ n @ m )
= $true )
| ? [X1: $i,X2: $i] :
( ( $true
!= ( X0 @ ( s @ X2 ) @ ( s @ X1 ) ) )
& ( ( X0 @ X2 @ X1 )
= $true ) )
| ( ( X0 @ cO @ cO )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( cP @ n )
= $true )
& ! [X0: $i > $i > $o] :
( ( ! [X1: $i,X2: $i] :
( ( ( X0 @ X2 @ X1 )
= $true )
=> ( $true
= ( X0 @ ( s @ X2 ) @ ( s @ X1 ) ) ) )
& ( ( X0 @ cO @ cO )
= $true ) )
=> ( ( X0 @ n @ m )
= $true ) ) )
=> ( ( cP @ m )
= $true ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i > $i > $o] :
( ( ( X0 @ cO @ cO )
& ! [X1: $i,X2: $i] :
( ( X0 @ X2 @ X1 )
=> ( X0 @ ( s @ X2 ) @ ( s @ X1 ) ) ) )
=> ( X0 @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i > $i > $o] :
( ( ( X0 @ cO @ cO )
& ! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ ( s @ X1 ) @ ( s @ X2 ) ) ) )
=> ( X0 @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i > $i > $o] :
( ( ( X0 @ cO @ cO )
& ! [X2: $i,X1: $i] :
( ( X0 @ X1 @ X2 )
=> ( X0 @ ( s @ X1 ) @ ( s @ X2 ) ) ) )
=> ( X0 @ n @ m ) )
& ( cP @ n ) )
=> ( cP @ m ) ),
file('/export/starexec/sandbox2/tmp/tmp.nHA19iBzGZ/DTF2THF_3465.p',cBLEDSOE_FENG_SV_I2) ).
thf(f89,plain,
( ( ( cP @ m )
= $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f11,f42]) ).
thf(f42,plain,
( ( n = m )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl2_1
<=> ( n = m ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f11,plain,
( ( cP @ n )
= $true ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f88,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f87,f44,f40]) ).
thf(f44,definition,
( spl2_2
<=> ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f87,plain,
( ( n = m )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( ( s
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
!= ( s
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
| ( n = m )
| ~ spl2_2 ),
inference(forward_demodulation,[status(thm)],[f74,f46]) ).
thf(f46,plain,
( ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f74,plain,
( ( ( s
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
!= ( s
@ ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
| ( n = m ) ),
inference(equality_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( ( ( ( s
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
= ( s
@ ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
!= $true )
| ( n = m ) ),
inference(equality_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( ( ( m = n )
= $true )
| ( ( ( s
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
= ( s
@ ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( ( m = n )
= $true )
| ( ( ( s
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
= ( s
@ ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
!= $true )
| ( $true != $true ) ),
inference(boolean_simplification,[status(thm)],[f70]) ).
thf(f70,plain,
( ( ( ( s
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
= ( s
@ ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
!= $true )
| ( ( cO = cO )
!= $true )
| ( ( m = n )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ n
@ m )
= $true )
| ( $true
!= ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ ( s
@ ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
@ ( s
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ cO
@ cO )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: $i > $i > $o] :
( ( ( X0 @ ( s @ ( sK1 @ X0 ) ) @ ( s @ ( sK0 @ X0 ) ) )
!= $true )
| ( ( X0 @ n @ m )
= $true )
| ( ( X0 @ cO @ cO )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
thf(f47,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f38,f44,f40]) ).
thf(f38,plain,
( ( n = m )
| ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) ),
inference(equality_proxy_clausification,[status(thm)],[f37]) ).
thf(f37,plain,
( ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
| ( ( m = n )
= $true ) ),
inference(equality_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
= $true )
| ( ( m = n )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
= $true )
| ( ( m = n )
= $true )
| ( $true != $true ) ),
inference(boolean_simplification,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
= ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) )
= $true )
| ( ( m = n )
= $true )
| ( ( cO = cO )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f14]) ).
thf(f14,plain,
( ( $true
= ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ ( sK1
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) )
@ ( sK0
@ ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 ) ) ) )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ n
@ m )
= $true )
| ( ( ^ [Y0: $i,Y1: $i] : ( Y1 = Y0 )
@ cO
@ cO )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $i > $i > $o] :
( ( ( X0 @ ( sK1 @ X0 ) @ ( sK0 @ X0 ) )
= $true )
| ( ( X0 @ cO @ cO )
!= $true )
| ( ( X0 @ n @ m )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO276^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n020.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 14:27:27 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO276^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : TPS problem BLEDSOE-FENG-SV-I2
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [BF93] Bledsoe & Feng (1993), SET-VAR
% 0.19/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0505 [Bro09]
% 0.19/0.46 % : BLEDSOE-FENG-SV-I2 [TPS]
% 0.19/0.46 % : Example I2 [BF93]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.2.0, 0.33 v6.1.0, 0.17 v5.5.0, 0.20 v5.4.0, 0.25 v5.0.0, 0.50 v4.1.0, 0.67 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.19/0.46 % Number of atoms : 2 ( 0 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 2 ( 2 avg)
% 0.19/0.46 % Number of connectives : 17 ( 0 ~; 0 |; 2 &; 12 @)
% 0.19/0.46 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 12 ( 12 avg)
% 0.19/0.46 % Number of types : 2 ( 0 usr)
% 0.19/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 5 ( 5 usr; 3 con; 0-1 aty)
% 0.19/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.19/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(m,type,
% 0.19/0.46 m: $i ).
% 0.19/0.46
% 0.19/0.46 thf(cP,type,
% 0.19/0.46 cP: $i > $o ).
% 0.19/0.46
% 0.19/0.46 thf(n,type,
% 0.19/0.46 n: $i ).
% 0.19/0.46
% 0.19/0.46 thf(s,type,
% 0.19/0.46 s: $i > $i ).
% 0.19/0.46
% 0.19/0.46 thf(cO,type,
% 0.19/0.46 cO: $i ).
% 0.19/0.46
% 0.19/0.46 thf(cBLEDSOE_FENG_SV_I2,conjecture,
% 0.19/0.46 ( ( ! [A: $i > $i > $o] :
% 0.19/0.46 ( ( ( A @ cO @ cO )
% 0.19/0.46 & ! [Xx: $i,Xy: $i] :
% 0.19/0.46 ( ( A @ Xx @ Xy )
% 0.19/0.46 => ( A @ ( s @ Xx ) @ ( s @ Xy ) ) ) )
% 0.19/0.46 => ( A @ n @ m ) )
% 0.19/0.46 & ( cP @ n ) )
% 0.19/0.46 => ( cP @ m ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.51/1.23 ---- Embedded in THF ---
% 1.51/1.23 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.23 %%% Generated on Tue Feb 24 14:27:28 EST 2026
% 1.51/1.23 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.23 %%% Logic specification used:
% 1.51/1.23 %%% thf(spec, logic, $$dhol).
% 1.51/1.23
% 1.51/1.23 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nHA19iBzGZ/DTF2DTF3465.p
% See solution above
% 1.51/1.23 ------------------------
% 1.51/1.24 ---- Cleaned THF ---
% 1.51/1.24 thf(m,type,
% 1.51/1.24 m: $i ).
% 1.51/1.24
% 1.51/1.24 thf(cP,type,
% 1.51/1.24 cP: $i > $o ).
% 1.51/1.24
% 1.51/1.24 thf(n,type,
% 1.51/1.24 n: $i ).
% 1.51/1.24
% 1.51/1.24 thf(s,type,
% 1.51/1.24 s: $i > $i ).
% 1.51/1.24
% 1.51/1.24 thf(cO,type,
% 1.51/1.24 cO: $i ).
% 1.51/1.24
% 1.51/1.24 thf(cBLEDSOE_FENG_SV_I2,conjecture,
% 1.51/1.24 ( ( ! [A: $i > $i > $o] :
% 1.51/1.24 ( ( ( A @ cO @ cO )
% 1.51/1.24 & ! [Xx: $i,Xy: $i] :
% 1.51/1.24 ( ( A @ Xx @ Xy )
% 1.51/1.24 => ( A @ ( s @ Xx ) @ ( s @ Xy ) ) ) )
% 1.51/1.24 => ( A @ n @ m ) )
% 1.51/1.24 & ( cP @ n ) )
% 1.51/1.24 => ( cP @ m ) ) ).
% 1.51/1.24 ------------------------
% 1.51/1.25 % (3615)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_3465 for (2999ds/27Mi)
% 1.51/1.25 % (3617)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_3465 for (2999ds/2Mi)
% 1.51/1.25 % (3617)Instruction limit reached!
% 1.51/1.25 % (3617)------------------------------
% 1.51/1.25 % (3617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (3617)Termination reason: Unknown
% 1.51/1.25 % (3617)Termination phase: Saturation
% 1.51/1.25
% 1.51/1.25 % (3617)Memory used [KB]: 5500
% 1.51/1.25 % (3617)Time elapsed: 0.002 s
% 1.51/1.25 % (3617)Instructions burned: 2 (million)
% 1.51/1.25 % (3617)------------------------------
% 1.51/1.25 % (3617)------------------------------
% 1.51/1.25 % (3615)Refutation not found, incomplete strategy
% 1.51/1.25 % (3615)------------------------------
% 1.51/1.25 % (3615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.25 % (3615)Termination reason: Refutation not found, incomplete strategy
% 1.51/1.25
% 1.51/1.25
% 1.51/1.25 % (3615)Memory used [KB]: 5500
% 1.51/1.25 % (3615)Time elapsed: 0.002 s
% 1.51/1.25 % (3615)Instructions burned: 2 (million)
% 1.51/1.25 % (3615)------------------------------
% 1.51/1.25 % (3615)------------------------------
% 1.51/1.26 % (3616)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3465 for (2999ds/2Mi)
% 1.51/1.26 % (3613)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3465 for (2999ds/183Mi)
% 1.51/1.26 % (3614)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_3465 for (2999ds/4Mi)
% 1.51/1.26 % (3618)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_3465 for (2999ds/275Mi)
% 1.51/1.26 % (3619)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3465 for (2999ds/18Mi)
% 1.51/1.26 % (3616)Instruction limit reached!
% 1.51/1.26 % (3616)------------------------------
% 1.51/1.26 % (3616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (3616)Termination reason: Unknown
% 1.51/1.26 % (3616)Termination phase: Saturation
% 1.51/1.26
% 1.51/1.26 % (3616)Memory used [KB]: 5373
% 1.51/1.26 % (3616)Time elapsed: 0.003 s
% 1.51/1.26 % (3616)Instructions burned: 2 (million)
% 1.51/1.26 % (3616)------------------------------
% 1.51/1.26 % (3616)------------------------------
% 1.51/1.26 % (3620)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3465 for (2999ds/3Mi)
% 1.51/1.26 % (3614)Instruction limit reached!
% 1.51/1.26 % (3614)------------------------------
% 1.51/1.26 % (3614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (3614)Termination reason: Unknown
% 1.51/1.26 % (3614)Termination phase: Saturation
% 1.51/1.26
% 1.51/1.26 % (3614)Memory used [KB]: 5500
% 1.51/1.26 % (3614)Time elapsed: 0.005 s
% 1.51/1.26 % (3614)Instructions burned: 4 (million)
% 1.51/1.26 % (3614)------------------------------
% 1.51/1.26 % (3614)------------------------------
% 1.51/1.26 % (3621)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_3465 for (2999ds/37Mi)
% 1.51/1.26 % (3620)Instruction limit reached!
% 1.51/1.26 % (3620)------------------------------
% 1.51/1.26 % (3620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.26 % (3620)Termination reason: Unknown
% 1.51/1.26 % (3620)Termination phase: Saturation
% 1.51/1.26
% 1.51/1.26 % (3620)Memory used [KB]: 5500
% 1.51/1.26 % (3620)Time elapsed: 0.003 s
% 1.51/1.26 % (3620)Instructions burned: 5 (million)
% 1.51/1.26 % (3620)------------------------------
% 1.51/1.26 % (3620)------------------------------
% 1.51/1.26 % (3618)First to succeed.
% 1.51/1.27 % (3613)Also succeeded, but the first one will report.
% 1.51/1.27 % (3619)Also succeeded, but the first one will report.
% 1.51/1.27 % (3618)Refutation found. Thanks to Tanya!
% 1.51/1.27 % SZS status Theorem for DTF2THF_3465
% 1.51/1.27 % SZS output start Proof for DTF2THF_3465
% 1.51/1.27 thf(func_def_1, type, cP: $i > $o).
% 1.51/1.27 thf(func_def_3, type, s: $i > $i).
% 1.51/1.27 thf(func_def_8, type, sK0: ($i > $i > $o) > $i).
% 1.51/1.27 thf(func_def_9, type, sK1: ($i > $i > $o) > $i).
% 1.51/1.27 thf(func_def_12, type, ph3: !>[X0: $tType]:(X0)).
% 1.51/1.27 thf(f92,plain,(
% 1.51/1.27 $false),
% 1.51/1.27 inference(avatar_sat_refutation,[status(thm)],[f47,f88,f91])).
% 1.51/1.27 thf(f91,plain,(
% 1.51/1.27 ~spl2_1),
% 1.51/1.27 inference(avatar_contradiction_clause,[status(thm)],[f90])).
% 1.51/1.27 thf(f90,plain,(
% 1.51/1.27 $false | ~spl2_1),
% 1.51/1.27 inference(subsumption_resolution,[status(thm)],[f89,f10])).
% 1.51/1.27 thf(f10,plain,(
% 1.51/1.27 ((cP @ m) != $true)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.27 thf(f9,plain,(
% 1.51/1.27 ! [X0 : $i > $i > $o] : ((((X0 @ (s @ (sK1 @ X0)) @ (s @ (sK0 @ X0))) != $true) & ((X0 @ (sK1 @ X0) @ (sK0 @ X0)) = $true)) | ((X0 @ cO @ cO) != $true) | ((X0 @ n @ m) = $true)) & ((cP @ n) = $true) & ((cP @ m) != $true)),
% 1.51/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f8])).
% 1.51/1.27 thf(f8,plain,(
% 1.51/1.27 ! [X0 : $i > $i > $o] : (? [X1 : $i,X2 : $i] : (($true != (X0 @ (s @ X2) @ (s @ X1))) & ((X0 @ X2 @ X1) = $true)) => (((X0 @ (s @ (sK1 @ X0)) @ (s @ (sK0 @ X0))) != $true) & ((X0 @ (sK1 @ X0) @ (sK0 @ X0)) = $true)))),
% 1.51/1.27 introduced(definition,[],[choice_axiom])).
% 1.51/1.27 thf(f7,plain,(
% 1.51/1.27 ! [X0 : $i > $i > $o] : (? [X1 : $i,X2 : $i] : (($true != (X0 @ (s @ X2) @ (s @ X1))) & ((X0 @ X2 @ X1) = $true)) | ((X0 @ cO @ cO) != $true) | ((X0 @ n @ m) = $true)) & ((cP @ n) = $true) & ((cP @ m) != $true)),
% 1.51/1.27 inference(flattening,[status(thm)],[f6])).
% 1.51/1.27 thf(f6,plain,(
% 1.51/1.27 ((cP @ m) != $true) & (((cP @ n) = $true) & ! [X0 : $i > $i > $o] : (((X0 @ n @ m) = $true) | (? [X1 : $i,X2 : $i] : (($true != (X0 @ (s @ X2) @ (s @ X1))) & ((X0 @ X2 @ X1) = $true)) | ((X0 @ cO @ cO) != $true))))),
% 1.51/1.27 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.27 thf(f5,plain,(
% 1.51/1.27 ~((((cP @ n) = $true) & ! [X0 : $i > $i > $o] : ((! [X1 : $i,X2 : $i] : (((X0 @ X2 @ X1) = $true) => ($true = (X0 @ (s @ X2) @ (s @ X1)))) & ((X0 @ cO @ cO) = $true)) => ((X0 @ n @ m) = $true))) => ((cP @ m) = $true))),
% 1.51/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.27 thf(f4,plain,(
% 1.51/1.27 ~((! [X0 : $i > $i > $o] : (((X0 @ cO @ cO) & ! [X1 : $i,X2 : $i] : ((X0 @ X2 @ X1) => (X0 @ (s @ X2) @ (s @ X1)))) => (X0 @ n @ m)) & (cP @ n)) => (cP @ m))),
% 1.51/1.27 inference(rectify,[status(thm)],[f2])).
% 1.51/1.27 thf(f2,negated_conjecture,(
% 1.51/1.27 ~((! [X0 : $i > $i > $o] : (((X0 @ cO @ cO) & ! [X2 : $i,X1 : $i] : ((X0 @ X1 @ X2) => (X0 @ (s @ X1) @ (s @ X2)))) => (X0 @ n @ m)) & (cP @ n)) => (cP @ m))),
% 1.51/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.27 thf(f1,conjecture,(
% 1.51/1.27 (! [X0 : $i > $i > $o] : (((X0 @ cO @ cO) & ! [X2 : $i,X1 : $i] : ((X0 @ X1 @ X2) => (X0 @ (s @ X1) @ (s @ X2)))) => (X0 @ n @ m)) & (cP @ n)) => (cP @ m)),
% 1.51/1.27 file('/export/starexec/sandbox2/tmp/tmp.nHA19iBzGZ/DTF2THF_3465.p',cBLEDSOE_FENG_SV_I2)).
% 1.51/1.27 thf(f89,plain,(
% 1.51/1.27 ((cP @ m) = $true) | ~spl2_1),
% 1.51/1.27 inference(superposition,[status(thm)],[f11,f42])).
% 1.51/1.27 thf(f42,plain,(
% 1.51/1.27 (n = m) | ~spl2_1),
% 1.51/1.27 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.51/1.27 thf(f40,definition,(
% 1.51/1.27 spl2_1 <=> (n = m)),
% 1.51/1.27 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.51/1.27 thf(f11,plain,(
% 1.51/1.27 ((cP @ n) = $true)),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.27 thf(f88,plain,(
% 1.51/1.27 spl2_1 | ~spl2_2),
% 1.51/1.27 inference(avatar_split_clause,[status(thm)],[f87,f44,f40])).
% 1.51/1.27 thf(f44,definition,(
% 1.51/1.27 spl2_2 <=> ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))),
% 1.51/1.27 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.51/1.27 thf(f87,plain,(
% 1.51/1.27 (n = m) | ~spl2_2),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.51/1.27 thf(f86,plain,(
% 1.51/1.27 ((s @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) != (s @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) | (n = m) | ~spl2_2),
% 1.51/1.27 inference(forward_demodulation,[status(thm)],[f74,f46])).
% 1.51/1.27 thf(f46,plain,(
% 1.51/1.27 ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) | ~spl2_2),
% 1.51/1.27 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.51/1.27 thf(f74,plain,(
% 1.51/1.27 ((s @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) != (s @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) | (n = m)),
% 1.51/1.27 inference(equality_proxy_clausification,[status(thm)],[f73])).
% 1.51/1.27 thf(f73,plain,(
% 1.51/1.27 (((s @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) = (s @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) != $true) | (n = m)),
% 1.51/1.27 inference(equality_proxy_clausification,[status(thm)],[f72])).
% 1.51/1.27 thf(f72,plain,(
% 1.51/1.27 ((m = n) = $true) | (((s @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) = (s @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) != $true)),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.51/1.27 thf(f71,plain,(
% 1.51/1.27 ((m = n) = $true) | (((s @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) = (s @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) != $true) | ($true != $true)),
% 1.51/1.27 inference(boolean_simplification,[status(thm)],[f70])).
% 1.51/1.27 thf(f70,plain,(
% 1.51/1.27 (((s @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) = (s @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) != $true) | ((cO = cO) != $true) | ((m = n) = $true)),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.51/1.27 thf(f57,plain,(
% 1.51/1.27 (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ n @ m) = $true) | ($true != ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ (s @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) @ (s @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))))) | (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ cO @ cO) != $true)),
% 1.51/1.27 inference(primitive_instantiation,[status(thm)],[f13])).
% 1.51/1.27 thf(f13,plain,(
% 1.51/1.27 ( ! [X0 : $i > $i > $o] : (((X0 @ (s @ (sK1 @ X0)) @ (s @ (sK0 @ X0))) != $true) | ((X0 @ n @ m) = $true) | ((X0 @ cO @ cO) != $true)) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.27 thf(f47,plain,(
% 1.51/1.27 spl2_1 | spl2_2),
% 1.51/1.27 inference(avatar_split_clause,[status(thm)],[f38,f44,f40])).
% 1.51/1.27 thf(f38,plain,(
% 1.51/1.27 (n = m) | ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))),
% 1.51/1.27 inference(equality_proxy_clausification,[status(thm)],[f37])).
% 1.51/1.27 thf(f37,plain,(
% 1.51/1.27 ((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) | ((m = n) = $true)),
% 1.51/1.27 inference(equality_proxy_clausification,[status(thm)],[f36])).
% 1.51/1.27 thf(f36,plain,(
% 1.51/1.27 (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) = $true) | ((m = n) = $true)),
% 1.51/1.27 inference(trivial_inequality_removal,[status(thm)],[f35])).
% 1.51/1.27 thf(f35,plain,(
% 1.51/1.27 (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) = $true) | ((m = n) = $true) | ($true != $true)),
% 1.51/1.27 inference(boolean_simplification,[status(thm)],[f34])).
% 1.51/1.27 thf(f34,plain,(
% 1.51/1.27 (((sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) = (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))))) = $true) | ((m = n) = $true) | ((cO = cO) != $true)),
% 1.51/1.27 inference(beta_eta_normalization,[status(thm)],[f14])).
% 1.51/1.27 thf(f14,plain,(
% 1.51/1.27 ($true = ((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ (sK1 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))) @ (sK0 @ (^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0))))))) | (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ n @ m) = $true) | (((^[Y0 : $i]: ((^[Y1 : $i]: (Y1 = Y0)))) @ cO @ cO) != $true)),
% 1.51/1.27 inference(primitive_instantiation,[status(thm)],[f12])).
% 1.51/1.27 thf(f12,plain,(
% 1.51/1.27 ( ! [X0 : $i > $i > $o] : (((X0 @ (sK1 @ X0) @ (sK0 @ X0)) = $true) | ((X0 @ cO @ cO) != $true) | ((X0 @ n @ m) = $true)) )),
% 1.51/1.27 inference(cnf_transformation,[status(thm)],[f9])).
% 1.51/1.27 % SZS output end Proof for DTF2THF_3465
% 1.51/1.27 % (3618)------------------------------
% 1.51/1.27 % (3618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.27 % (3618)Termination reason: Refutation
% 1.51/1.27
% 1.51/1.27 % (3618)Memory used [KB]: 5500
% 1.51/1.27 % (3618)Time elapsed: 0.009 s
% 1.51/1.27 % (3618)Instructions burned: 7 (million)
% 1.51/1.27 % (3618)------------------------------
% 1.51/1.27 % (3618)------------------------------
% 1.51/1.27 % (3612)Success in time 0.019 s
%------------------------------------------------------------------------------