%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM784^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 09:24:42 AM UTC 2026
% Result : Theorem 0.83s 0.89s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 173 ( 48 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 238 ( 63 ~; 15 |; 4 &; 130 @)
% ( 2 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 16 ( 0 ^; 16 !; 0 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
rat: $tType ).
thf(func_def_0,type,
rat: $tType ).
thf(func_def_1,type,
x0: rat ).
thf(func_def_2,type,
y0: rat ).
thf(func_def_3,type,
more: rat > rat > $o ).
thf(func_def_4,type,
is: rat > rat > $o ).
thf(func_def_6,type,
less: rat > rat > $o ).
thf(f46,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f41,f45]) ).
thf(f45,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
| ~ spl0_2 ),
inference(subsumption_resolution,[status(thm)],[f43,f37]) ).
thf(f37,plain,
( ( ( more @ x0 @ y0 )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl0_2
<=> ( ( more @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f43,plain,
( ( more @ x0 @ y0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( ( more @ x0 @ y0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f25,f28]) ).
thf(f28,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
~ ( ( ( less @ x0 @ y0 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
~ ~ ( less @ x0 @ y0 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ~ ( less @ x0 @ y0 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
~ ( less @ x0 @ y0 ),
file('/export/starexec/sandbox/tmp/tmp.eDtzwFMCXf/DTF2THF_30652.p',satz81c) ).
thf(f25,plain,
! [X0: rat,X1: rat] :
( ( $true
!= ( less @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: rat,X1: rat] :
( ( ( $true
!= ( is @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
!= $true ) )
& ( ( $true
!= ( less @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
!= $true ) )
& ( ( $true
!= ( is @ X0 @ X1 ) )
| ( $true
!= ( less @ X0 @ X1 ) ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: rat,X1: rat] :
( ( ( $true
!= ( is @ X0 @ X1 ) )
| ( $true
!= ( less @ X0 @ X1 ) ) )
& ( ( $true
!= ( less @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
!= $true ) )
& ( ( $true
!= ( is @ X0 @ X1 ) )
| ( ( more @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: rat,X1: rat] :
~ ( ( ( $true
= ( is @ X0 @ X1 ) )
=> ( ( more @ X0 @ X1 )
!= $true ) )
=> ( ( ( ( more @ X0 @ X1 )
= $true )
=> ( $true
!= ( less @ X0 @ X1 ) ) )
=> ~ ( ( $true
= ( less @ X0 @ X1 ) )
=> ( $true
!= ( is @ X0 @ X1 ) ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: rat,X1: rat] :
~ ( ( ( $true
= ( is @ X0 @ X1 ) )
=> ( ( more @ X0 @ X1 )
!= $true ) )
=> ~ ~ ( ( ( ( more @ X0 @ X1 )
= $true )
=> ( $true
!= ( less @ X0 @ X1 ) ) )
=> ~ ( ( $true
= ( less @ X0 @ X1 ) )
=> ( $true
!= ( is @ X0 @ X1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: rat,X1: rat] :
~ ( ( ( is @ X0 @ X1 )
=> ~ ( more @ X0 @ X1 ) )
=> ~ ~ ( ( ( more @ X0 @ X1 )
=> ~ ( less @ X0 @ X1 ) )
=> ~ ( ( less @ X0 @ X1 )
=> ~ ( is @ X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X1: rat,X2: rat] :
~ ( ( ( is @ X1 @ X2 )
=> ~ ( more @ X1 @ X2 ) )
=> ~ ~ ( ( ( more @ X1 @ X2 )
=> ~ ( less @ X1 @ X2 ) )
=> ~ ( ( less @ X1 @ X2 )
=> ~ ( is @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.eDtzwFMCXf/DTF2THF_30652.p',satz81b) ).
thf(f41,plain,
~ spl0_1,
inference(avatar_split_clause,[status(thm)],[f40,f31]) ).
thf(f31,definition,
( spl0_1
<=> ( ( is @ x0 @ y0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f40,plain,
( ( is @ x0 @ y0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true != $true )
| ( ( is @ x0 @ y0 )
!= $true ) ),
inference(superposition,[status(thm)],[f24,f28]) ).
thf(f24,plain,
! [X0: rat,X1: rat] :
( ( $true
!= ( less @ X0 @ X1 ) )
| ( $true
!= ( is @ X0 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f38,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f27,f35,f31]) ).
thf(f27,plain,
( ( ( is @ x0 @ y0 )
= $true )
| ( ( more @ x0 @ y0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ( more @ x0 @ y0 )
= $true )
| ( ( is @ x0 @ y0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ( ( more @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( more @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( more @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
file('/export/starexec/sandbox/tmp/tmp.eDtzwFMCXf/DTF2THF_30652.p',m) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : NUM784^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 11:14:45 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : NUM784^1 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.32 % Domain : Number Theory
% 0.07/0.32 % Problem : Landau theorem 81c
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English : ~(less x0 y0)
% 0.07/0.32
% 0.07/0.32 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.07/0.32 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.07/0.32 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : satz81c [Lan30]
% 0.07/0.32 % : satz41c [Lan30]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % : Without extensionality : Theorem
% 0.07/0.32 % Rating : 0.08 v9.1.0, 0.00 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.1, 0.33 v4.0.0, 0.00 v3.7.0
% 0.07/0.32 % Syntax : Number of formulae : 10 ( 1 unt; 6 typ; 0 def)
% 0.07/0.32 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 6 ( 2 avg)
% 0.07/0.32 % Number of connectives : 36 ( 11 ~; 0 |; 0 &; 18 @)
% 0.07/0.32 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 13 ( 7 avg)
% 0.07/0.32 % Number of types : 2 ( 1 usr)
% 0.07/0.32 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.07/0.32 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.07/0.32 % SPC : TH0_THM_NEQ_NAR
% 0.07/0.32
% 0.07/0.32 % Comments :
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(rat_type,type,
% 0.07/0.32 rat: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(x0,type,
% 0.07/0.32 x0: rat ).
% 0.07/0.32
% 0.07/0.32 thf(y0,type,
% 0.07/0.32 y0: rat ).
% 0.07/0.32
% 0.07/0.32 thf(more,type,
% 0.07/0.32 more: rat > rat > $o ).
% 0.07/0.32
% 0.07/0.32 thf(is,type,
% 0.07/0.32 is: rat > rat > $o ).
% 0.07/0.32
% 0.07/0.32 thf(m,axiom,
% 0.07/0.32 ( ~ ( more @ x0 @ y0 )
% 0.07/0.32 => ( is @ x0 @ y0 ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(less,type,
% 0.07/0.32 less: rat > rat > $o ).
% 0.07/0.32
% 0.07/0.32 thf(et,axiom,
% 0.07/0.32 ! [Xa: $o] :
% 0.07/0.32 ( ~ ~ Xa
% 0.07/0.32 => Xa ) ).
% 0.07/0.32
% 0.07/0.32 thf(satz81b,axiom,
% 0.07/0.32 ! [Xx0: rat,Xy0: rat] :
% 0.07/0.32 ~ ( ( ( is @ Xx0 @ Xy0 )
% 0.07/0.32 => ~ ( more @ Xx0 @ Xy0 ) )
% 0.07/0.32 => ~ ~ ( ( ( more @ Xx0 @ Xy0 )
% 0.07/0.32 => ~ ( less @ Xx0 @ Xy0 ) )
% 0.07/0.32 => ~ ( ( less @ Xx0 @ Xy0 )
% 0.07/0.32 => ~ ( is @ Xx0 @ Xy0 ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(satz81c,conjecture,
% 0.07/0.32 ~ ( less @ x0 @ y0 ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 0.83/0.87 ---- Embedded in THF ---
% 0.83/0.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.83/0.87 %%% Generated on Tue Feb 24 11:14:46 EST 2026
% 0.83/0.87 %%% using '$$dhol' embedding, version 1.3.0.
% 0.83/0.87 %%% Logic specification used:
% 0.83/0.87 %%% thf(spec, logic, $$dhol).
% 0.83/0.87
% 0.83/0.87 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.eDtzwFMCXf/DTF2DTF30652.p
% See solution above
% 0.83/0.87 ------------------------
% 0.83/0.87 ---- Cleaned THF ---
% 0.83/0.87 thf(rat_type,type,
% 0.83/0.87 rat: $tType ).
% 0.83/0.87
% 0.83/0.87 thf(x0,type,
% 0.83/0.87 x0: rat ).
% 0.83/0.87
% 0.83/0.87 thf(y0,type,
% 0.83/0.87 y0: rat ).
% 0.83/0.87
% 0.83/0.87 thf(more,type,
% 0.83/0.87 more: rat > rat > $o ).
% 0.83/0.87
% 0.83/0.87 thf(is,type,
% 0.83/0.87 is: rat > rat > $o ).
% 0.83/0.87
% 0.83/0.87 thf(m,axiom,
% 0.83/0.87 ( ~ ( more @ x0 @ y0 )
% 0.83/0.87 => ( is @ x0 @ y0 ) ) ).
% 0.83/0.87
% 0.83/0.87 thf(less,type,
% 0.83/0.87 less: rat > rat > $o ).
% 0.83/0.87
% 0.83/0.87 thf(et,axiom,
% 0.83/0.87 ! [Xa: $o] :
% 0.83/0.87 ( ~ ~ Xa
% 0.83/0.87 => Xa ) ).
% 0.83/0.87
% 0.83/0.87 thf(satz81b,axiom,
% 0.83/0.87 ! [Xx0: rat,Xy0: rat] :
% 0.83/0.87 ~ ( ( ( is @ Xx0 @ Xy0 )
% 0.83/0.87 => ~ ( more @ Xx0 @ Xy0 ) )
% 0.83/0.87 => ~ ~ ( ( ( more @ Xx0 @ Xy0 )
% 0.83/0.87 => ~ ( less @ Xx0 @ Xy0 ) )
% 0.83/0.87 => ~ ( ( less @ Xx0 @ Xy0 )
% 0.83/0.87 => ~ ( is @ Xx0 @ Xy0 ) ) ) ) ).
% 0.83/0.87
% 0.83/0.87 thf(satz81c,conjecture,
% 0.83/0.87 ~ ( less @ x0 @ y0 ) ).
% 0.83/0.87 ------------------------
% 0.83/0.89 % (30914)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30652 for (3000ds/183Mi)
% 0.83/0.89 % (30916)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_30652 for (3000ds/27Mi)
% 0.83/0.89 % (30915)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_30652 for (3000ds/4Mi)
% 0.83/0.89 % (30918)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_30652 for (3000ds/2Mi)
% 0.83/0.89 % (30917)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30652 for (3000ds/2Mi)
% 0.83/0.89 % (30919)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_30652 for (3000ds/275Mi)
% 0.83/0.89 % (30920)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_30652 for (3000ds/18Mi)
% 0.83/0.89 % (30919)Refutation not found, incomplete strategy
% 0.83/0.89 % (30919)------------------------------
% 0.83/0.89 % (30919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (30919)Termination reason: Refutation not found, incomplete strategy
% 0.83/0.89
% 0.83/0.89
% 0.83/0.89 % (30919)Memory used [KB]: 5500
% 0.83/0.89 % (30919)Time elapsed: 0.001 s
% 0.83/0.89 % (30919)Instructions burned: 1 (million)
% 0.83/0.89 % (30919)------------------------------
% 0.83/0.89 % (30919)------------------------------
% 0.83/0.89 % (30917)Instruction limit reached!
% 0.83/0.89 % (30917)------------------------------
% 0.83/0.89 % (30917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (30917)Termination reason: Unknown
% 0.83/0.89 % (30917)Termination phase: Saturation
% 0.83/0.89
% 0.83/0.89 % (30917)Memory used [KB]: 5500
% 0.83/0.89 % (30917)Time elapsed: 0.002 s
% 0.83/0.89 % (30917)Instructions burned: 2 (million)
% 0.83/0.89 % (30917)------------------------------
% 0.83/0.89 % (30917)------------------------------
% 0.83/0.89 % (30918)Instruction limit reached!
% 0.83/0.89 % (30918)------------------------------
% 0.83/0.89 % (30918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (30918)Termination reason: Unknown
% 0.83/0.89 % (30918)Termination phase: Saturation
% 0.83/0.89
% 0.83/0.89 % (30918)Memory used [KB]: 5500
% 0.83/0.89 % (30918)Time elapsed: 0.002 s
% 0.83/0.89 % (30918)Instructions burned: 3 (million)
% 0.83/0.89 % (30918)------------------------------
% 0.83/0.89 % (30918)------------------------------
% 0.83/0.89 % (30914)First to succeed.
% 0.83/0.89 % (30920)Also succeeded, but the first one will report.
% 0.83/0.89 % (30915)Instruction limit reached!
% 0.83/0.89 % (30915)------------------------------
% 0.83/0.89 % (30915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (30915)Termination reason: Unknown
% 0.83/0.89 % (30915)Termination phase: Saturation
% 0.83/0.89
% 0.83/0.89 % (30915)Memory used [KB]: 5500
% 0.83/0.89 % (30915)Time elapsed: 0.003 s
% 0.83/0.89 % (30915)Instructions burned: 5 (million)
% 0.83/0.89 % (30915)------------------------------
% 0.83/0.89 % (30915)------------------------------
% 0.83/0.89 % (30914)Refutation found. Thanks to Tanya!
% 0.83/0.89 % SZS status Theorem for DTF2THF_30652
% 0.83/0.89 % SZS output start Proof for DTF2THF_30652
% 0.83/0.89 thf(type_def_5, type, rat: $tType).
% 0.83/0.89 thf(func_def_0, type, rat: $tType).
% 0.83/0.89 thf(func_def_1, type, x0: rat).
% 0.83/0.89 thf(func_def_2, type, y0: rat).
% 0.83/0.89 thf(func_def_3, type, more: rat > rat > $o).
% 0.83/0.89 thf(func_def_4, type, is: rat > rat > $o).
% 0.83/0.89 thf(func_def_6, type, less: rat > rat > $o).
% 0.83/0.89 thf(f46,plain,(
% 0.83/0.89 $false),
% 0.83/0.89 inference(avatar_sat_refutation,[status(thm)],[f38,f41,f45])).
% 0.83/0.89 thf(f45,plain,(
% 0.83/0.89 ~spl0_2),
% 0.83/0.89 inference(avatar_contradiction_clause,[status(thm)],[f44])).
% 0.83/0.89 thf(f44,plain,(
% 0.83/0.89 $false | ~spl0_2),
% 0.83/0.89 inference(subsumption_resolution,[status(thm)],[f43,f37])).
% 0.83/0.89 thf(f37,plain,(
% 0.83/0.89 ((more @ x0 @ y0) = $true) | ~spl0_2),
% 0.83/0.89 inference(avatar_component_clause,[status(thm)],[f35])).
% 0.83/0.89 thf(f35,definition,(
% 0.83/0.89 spl0_2 <=> ((more @ x0 @ y0) = $true)),
% 0.83/0.89 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 0.83/0.89 thf(f43,plain,(
% 0.83/0.89 ((more @ x0 @ y0) != $true)),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 0.83/0.89 thf(f42,plain,(
% 0.83/0.89 ((more @ x0 @ y0) != $true) | ($true != $true)),
% 0.83/0.89 inference(superposition,[status(thm)],[f25,f28])).
% 0.83/0.89 thf(f28,plain,(
% 0.83/0.89 ((less @ x0 @ y0) = $true)),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f15])).
% 0.83/0.89 thf(f15,plain,(
% 0.83/0.89 ((less @ x0 @ y0) = $true)),
% 0.83/0.89 inference(flattening,[status(thm)],[f8])).
% 0.83/0.89 thf(f8,plain,(
% 0.83/0.89 ~~((less @ x0 @ y0) = $true)),
% 0.83/0.89 inference(fool_elimination,[status(thm)],[f7])).
% 0.83/0.89 thf(f7,plain,(
% 0.83/0.89 ~~(less @ x0 @ y0)),
% 0.83/0.89 inference(rectify,[status(thm)],[f5])).
% 0.83/0.89 thf(f5,negated_conjecture,(
% 0.83/0.89 ~~(less @ x0 @ y0)),
% 0.83/0.89 inference(negated_conjecture,[status(cth)],[f4])).
% 0.83/0.89 thf(f4,conjecture,(
% 0.83/0.89 ~(less @ x0 @ y0)),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.eDtzwFMCXf/DTF2THF_30652.p',satz81c)).
% 0.83/0.89 thf(f25,plain,(
% 0.83/0.89 ( ! [X0 : rat,X1 : rat] : (($true != (less @ X0 @ X1)) | ((more @ X0 @ X1) != $true)) )),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f22])).
% 0.83/0.89 thf(f22,plain,(
% 0.83/0.89 ! [X0 : rat,X1 : rat] : ((($true != (is @ X0 @ X1)) | ((more @ X0 @ X1) != $true)) & (($true != (less @ X0 @ X1)) | ((more @ X0 @ X1) != $true)) & (($true != (is @ X0 @ X1)) | ($true != (less @ X0 @ X1))))),
% 0.83/0.89 inference(flattening,[status(thm)],[f21])).
% 0.83/0.89 thf(f21,plain,(
% 0.83/0.89 ! [X0 : rat,X1 : rat] : (((($true != (is @ X0 @ X1)) | ($true != (less @ X0 @ X1))) & (($true != (less @ X0 @ X1)) | ((more @ X0 @ X1) != $true))) & (($true != (is @ X0 @ X1)) | ((more @ X0 @ X1) != $true)))),
% 0.83/0.89 inference(ennf_transformation,[status(thm)],[f17])).
% 0.83/0.89 thf(f17,plain,(
% 0.83/0.89 ! [X0 : rat,X1 : rat] : ~((($true = (is @ X0 @ X1)) => ((more @ X0 @ X1) != $true)) => ((((more @ X0 @ X1) = $true) => ($true != (less @ X0 @ X1))) => ~(($true = (less @ X0 @ X1)) => ($true != (is @ X0 @ X1)))))),
% 0.83/0.89 inference(flattening,[status(thm)],[f12])).
% 0.83/0.89 thf(f12,plain,(
% 0.83/0.89 ! [X0 : rat,X1 : rat] : ~((($true = (is @ X0 @ X1)) => ~((more @ X0 @ X1) = $true)) => ~~((((more @ X0 @ X1) = $true) => ~($true = (less @ X0 @ X1))) => ~(($true = (less @ X0 @ X1)) => ~($true = (is @ X0 @ X1)))))),
% 0.83/0.89 inference(fool_elimination,[status(thm)],[f11])).
% 0.83/0.89 thf(f11,plain,(
% 0.83/0.89 ! [X0 : rat,X1 : rat] : ~(((is @ X0 @ X1) => ~(more @ X0 @ X1)) => ~~(((more @ X0 @ X1) => ~(less @ X0 @ X1)) => ~((less @ X0 @ X1) => ~(is @ X0 @ X1))))),
% 0.83/0.89 inference(rectify,[status(thm)],[f3])).
% 0.83/0.89 thf(f3,axiom,(
% 0.83/0.89 ! [X1 : rat,X2 : rat] : ~(((is @ X1 @ X2) => ~(more @ X1 @ X2)) => ~~(((more @ X1 @ X2) => ~(less @ X1 @ X2)) => ~((less @ X1 @ X2) => ~(is @ X1 @ X2))))),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.eDtzwFMCXf/DTF2THF_30652.p',satz81b)).
% 0.83/0.89 thf(f41,plain,(
% 0.83/0.89 ~spl0_1),
% 0.83/0.89 inference(avatar_split_clause,[status(thm)],[f40,f31])).
% 0.83/0.89 thf(f31,definition,(
% 0.83/0.89 spl0_1 <=> ((is @ x0 @ y0) = $true)),
% 0.83/0.89 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 0.83/0.89 thf(f40,plain,(
% 0.83/0.89 ((is @ x0 @ y0) != $true)),
% 0.83/0.89 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 0.83/0.89 thf(f39,plain,(
% 0.83/0.89 ($true != $true) | ((is @ x0 @ y0) != $true)),
% 0.83/0.89 inference(superposition,[status(thm)],[f24,f28])).
% 0.83/0.89 thf(f24,plain,(
% 0.83/0.89 ( ! [X0 : rat,X1 : rat] : (($true != (less @ X0 @ X1)) | ($true != (is @ X0 @ X1))) )),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f22])).
% 0.83/0.89 thf(f38,plain,(
% 0.83/0.89 spl0_1 | spl0_2),
% 0.83/0.89 inference(avatar_split_clause,[status(thm)],[f27,f35,f31])).
% 0.83/0.89 thf(f27,plain,(
% 0.83/0.89 ((is @ x0 @ y0) = $true) | ((more @ x0 @ y0) = $true)),
% 0.83/0.89 inference(cnf_transformation,[status(thm)],[f19])).
% 0.83/0.89 thf(f19,plain,(
% 0.83/0.89 ((more @ x0 @ y0) = $true) | ((is @ x0 @ y0) = $true)),
% 0.83/0.89 inference(ennf_transformation,[status(thm)],[f16])).
% 0.83/0.89 thf(f16,plain,(
% 0.83/0.89 ((more @ x0 @ y0) != $true) => ((is @ x0 @ y0) = $true)),
% 0.83/0.89 inference(flattening,[status(thm)],[f10])).
% 0.83/0.89 thf(f10,plain,(
% 0.83/0.89 ~((more @ x0 @ y0) = $true) => ((is @ x0 @ y0) = $true)),
% 0.83/0.89 inference(fool_elimination,[status(thm)],[f9])).
% 0.83/0.89 thf(f9,plain,(
% 0.83/0.89 ~(more @ x0 @ y0) => (is @ x0 @ y0)),
% 0.83/0.89 inference(rectify,[status(thm)],[f1])).
% 0.83/0.89 thf(f1,axiom,(
% 0.83/0.89 ~(more @ x0 @ y0) => (is @ x0 @ y0)),
% 0.83/0.89 file('/export/starexec/sandbox/tmp/tmp.eDtzwFMCXf/DTF2THF_30652.p',m)).
% 0.83/0.89 % SZS output end Proof for DTF2THF_30652
% 0.83/0.89 % (30914)------------------------------
% 0.83/0.89 % (30914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.83/0.89 % (30914)Termination reason: Refutation
% 0.83/0.89
% 0.83/0.89 % (30914)Memory used [KB]: 5500
% 0.83/0.89 % (30914)Time elapsed: 0.002 s
% 0.83/0.89 % (30914)Instructions burned: 2 (million)
% 0.83/0.89 % (30914)------------------------------
% 0.83/0.89 % (30914)------------------------------
% 0.83/0.89 % (30913)Success in time 0.01 s
%------------------------------------------------------------------------------