%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUM785^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n022.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 0.32s 1.34s
% Output : Refutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 164 ( 48 equ; 0 cnn)
% Maximal formula atoms : 6 ( 6 avg)
% Number of connectives : 229 ( 60 ~; 13 |; 4 &; 128 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 5 usr; 4 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,
less: rat > rat > $o ).
thf(func_def_4,type,
is: rat > rat > $o ).
thf(func_def_6,type,
more: rat > rat > $o ).
thf(f36,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f35,f33]) ).
thf(f33,plain,
( ( less @ x0 @ y0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f31]) ).
thf(f31,plain,
( ( $true != $true )
| ( ( less @ x0 @ y0 )
!= $true ) ),
inference(superposition,[status(thm)],[f27,f28]) ).
thf(f28,plain,
( ( more @ x0 @ y0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ( more @ x0 @ y0 )
= $true ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( ( ( more @ x0 @ y0 )
!= $true ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
~ ~ ( more @ x0 @ y0 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ~ ( more @ x0 @ y0 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
~ ( more @ x0 @ y0 ),
file('/export/starexec/sandbox2/tmp/tmp.0C1SnVzXa8/DTF2THF_12385.p',satz81d) ).
thf(f27,plain,
! [X0: rat,X1: rat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( less @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: rat,X1: rat] :
( ( ( ( less @ X1 @ X0 )
!= $true )
| ( $true
!= ( more @ X1 @ X0 ) ) )
& ( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( is @ X1 @ X0 )
!= $true ) )
& ( ( ( is @ X1 @ X0 )
!= $true )
| ( ( less @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: rat,X1: rat] :
( ( ( ( is @ X1 @ X0 )
!= $true )
| ( ( less @ X1 @ X0 )
!= $true ) )
& ( ( ( less @ X1 @ X0 )
!= $true )
| ( $true
!= ( more @ X1 @ X0 ) ) )
& ( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( is @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: rat,X1: rat] :
~ ( ( ( ( is @ X1 @ X0 )
= $true )
=> ( $true
!= ( more @ X1 @ X0 ) ) )
=> ( ( ( $true
= ( more @ X1 @ X0 ) )
=> ( ( less @ X1 @ X0 )
!= $true ) )
=> ~ ( ( ( less @ X1 @ X0 )
= $true )
=> ( ( is @ X1 @ X0 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: rat,X1: rat] :
~ ( ( ( ( is @ X1 @ X0 )
= $true )
=> ( $true
!= ( more @ X1 @ X0 ) ) )
=> ~ ~ ( ( ( $true
= ( more @ X1 @ X0 ) )
=> ( ( less @ X1 @ X0 )
!= $true ) )
=> ~ ( ( ( less @ X1 @ X0 )
= $true )
=> ( ( is @ X1 @ X0 )
!= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: rat,X1: rat] :
~ ( ( ( is @ X1 @ X0 )
=> ~ ( more @ X1 @ X0 ) )
=> ~ ~ ( ( ( more @ X1 @ X0 )
=> ~ ( less @ X1 @ X0 ) )
=> ~ ( ( less @ X1 @ X0 )
=> ~ ( is @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: rat,X1: rat] :
~ ( ( ( is @ X1 @ X2 )
=> ~ ( more @ X1 @ X2 ) )
=> ~ ~ ( ( ( more @ X1 @ X2 )
=> ~ ( less @ X1 @ X2 ) )
=> ~ ( ( less @ X1 @ X2 )
=> ~ ( is @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.0C1SnVzXa8/DTF2THF_12385.p',satz81b) ).
thf(f35,plain,
( ( less @ x0 @ y0 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f34]) ).
thf(f34,plain,
( ( ( less @ x0 @ y0 )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f32,f23]) ).
thf(f23,plain,
( ( ( is @ x0 @ y0 )
= $true )
| ( ( less @ x0 @ y0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ( is @ x0 @ y0 )
= $true )
| ( ( less @ x0 @ y0 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( less @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(flattening,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( less @ x0 @ y0 )
!= $true )
=> ( ( is @ x0 @ y0 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ~ ( less @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ~ ( less @ x0 @ y0 )
=> ( is @ x0 @ y0 ) ),
file('/export/starexec/sandbox2/tmp/tmp.0C1SnVzXa8/DTF2THF_12385.p',l) ).
thf(f32,plain,
( ( is @ x0 @ y0 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f30]) ).
thf(f30,plain,
( ( $true != $true )
| ( ( is @ x0 @ y0 )
!= $true ) ),
inference(superposition,[status(thm)],[f26,f28]) ).
thf(f26,plain,
! [X0: rat,X1: rat] :
( ( $true
!= ( more @ X1 @ X0 ) )
| ( ( is @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM785^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n022.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 11:14:06 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/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 : NUM785^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Number Theory
% 0.30/0.46 % Problem : Landau theorem 81d
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : ~(more x0 y0)
% 0.30/0.46
% 0.30/0.46 % Refs : [Lan30] Landau (1930), Grundlagen der Analysis
% 0.30/0.46 % : [vBJ79] van Benthem Jutting (1979), Checking Landau's "Grundla
% 0.30/0.46 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.46 % Source : [Bro09]
% 0.30/0.46 % Names : satz81d [Lan30]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % : Without extensionality : Theorem
% 0.30/0.46 % 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
% 0.30/0.46 % Syntax : Number of formulae : 10 ( 1 unt; 6 typ; 0 def)
% 0.30/0.46 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 6 ( 2 avg)
% 0.30/0.46 % Number of connectives : 36 ( 11 ~; 0 |; 0 &; 18 @)
% 0.30/0.46 % ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 13 ( 7 avg)
% 0.30/0.46 % Number of types : 2 ( 1 usr)
% 0.30/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 5 ( 5 usr; 2 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 3 ( 0 ^; 3 !; 0 ?; 3 :)
% 0.30/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.30/0.46
% 0.30/0.46 % Comments :
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(rat_type,type,
% 0.30/0.46 rat: $tType ).
% 0.30/0.46
% 0.30/0.46 thf(x0,type,
% 0.30/0.46 x0: rat ).
% 0.30/0.46
% 0.30/0.46 thf(y0,type,
% 0.30/0.46 y0: rat ).
% 0.30/0.46
% 0.30/0.46 thf(less,type,
% 0.30/0.46 less: rat > rat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(is,type,
% 0.30/0.46 is: rat > rat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(l,axiom,
% 0.30/0.46 ( ~ ( less @ x0 @ y0 )
% 0.30/0.46 => ( is @ x0 @ y0 ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(more,type,
% 0.30/0.46 more: rat > rat > $o ).
% 0.30/0.46
% 0.30/0.46 thf(et,axiom,
% 0.30/0.46 ! [Xa: $o] :
% 0.30/0.46 ( ~ ~ Xa
% 0.30/0.46 => Xa ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz81b,axiom,
% 0.30/0.46 ! [Xx0: rat,Xy0: rat] :
% 0.30/0.46 ~ ( ( ( is @ Xx0 @ Xy0 )
% 0.30/0.46 => ~ ( more @ Xx0 @ Xy0 ) )
% 0.30/0.46 => ~ ~ ( ( ( more @ Xx0 @ Xy0 )
% 0.30/0.46 => ~ ( less @ Xx0 @ Xy0 ) )
% 0.30/0.46 => ~ ( ( less @ Xx0 @ Xy0 )
% 0.30/0.46 => ~ ( is @ Xx0 @ Xy0 ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(satz81d,conjecture,
% 0.30/0.46 ~ ( more @ x0 @ y0 ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 0.32/1.30 ---- Embedded in THF ---
% 0.32/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.30 %%% Generated on Tue Feb 24 11:14:07 EST 2026
% 0.32/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.30 %%% Logic specification used:
% 0.32/1.30 %%% thf(spec, logic, $$dhol).
% 0.32/1.30
% 0.32/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.0C1SnVzXa8/DTF2DTF12385.p
% See solution above
% 0.32/1.30 ------------------------
% 0.32/1.31 ---- Cleaned THF ---
% 0.32/1.32 thf(rat_type,type,
% 0.32/1.32 rat: $tType ).
% 0.32/1.32
% 0.32/1.32 thf(x0,type,
% 0.32/1.32 x0: rat ).
% 0.32/1.32
% 0.32/1.32 thf(y0,type,
% 0.32/1.32 y0: rat ).
% 0.32/1.32
% 0.32/1.32 thf(less,type,
% 0.32/1.32 less: rat > rat > $o ).
% 0.32/1.32
% 0.32/1.32 thf(is,type,
% 0.32/1.32 is: rat > rat > $o ).
% 0.32/1.32
% 0.32/1.32 thf(l,axiom,
% 0.32/1.32 ( ~ ( less @ x0 @ y0 )
% 0.32/1.32 => ( is @ x0 @ y0 ) ) ).
% 0.32/1.32
% 0.32/1.32 thf(more,type,
% 0.32/1.32 more: rat > rat > $o ).
% 0.32/1.32
% 0.32/1.32 thf(et,axiom,
% 0.32/1.32 ! [Xa: $o] :
% 0.32/1.32 ( ~ ~ Xa
% 0.32/1.32 => Xa ) ).
% 0.32/1.32
% 0.32/1.32 thf(satz81b,axiom,
% 0.32/1.32 ! [Xx0: rat,Xy0: rat] :
% 0.32/1.32 ~ ( ( ( is @ Xx0 @ Xy0 )
% 0.32/1.32 => ~ ( more @ Xx0 @ Xy0 ) )
% 0.32/1.32 => ~ ~ ( ( ( more @ Xx0 @ Xy0 )
% 0.32/1.32 => ~ ( less @ Xx0 @ Xy0 ) )
% 0.32/1.32 => ~ ( ( less @ Xx0 @ Xy0 )
% 0.32/1.32 => ~ ( is @ Xx0 @ Xy0 ) ) ) ) ).
% 0.32/1.32
% 0.32/1.32 thf(satz81d,conjecture,
% 0.32/1.32 ~ ( more @ x0 @ y0 ) ).
% 0.32/1.32 ------------------------
% 0.32/1.33 % (12599)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_12385 for (2999ds/2Mi)
% 0.32/1.33 % (12599)Instruction limit reached!
% 0.32/1.33 % (12599)------------------------------
% 0.32/1.33 % (12599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.33 % (12599)Termination reason: Unknown
% 0.32/1.33 % (12599)Termination phase: Saturation
% 0.32/1.33
% 0.32/1.33 % (12599)Memory used [KB]: 1023
% 0.32/1.33 % (12599)Time elapsed: 0.002 s
% 0.32/1.33 % (12599)Instructions burned: 2 (million)
% 0.32/1.33 % (12599)------------------------------
% 0.32/1.33 % (12599)------------------------------
% 0.32/1.34 % (12596)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_12385 for (2999ds/4Mi)
% 0.32/1.34 % (12595)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12385 for (2999ds/183Mi)
% 0.32/1.34 % (12597)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_12385 for (2999ds/27Mi)
% 0.32/1.34 % (12598)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12385 for (2999ds/2Mi)
% 0.32/1.34 % (12600)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_12385 for (2999ds/275Mi)
% 0.32/1.34 % (12601)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12385 for (2999ds/18Mi)
% 0.32/1.34 % (12598)Instruction limit reached!
% 0.32/1.34 % (12598)------------------------------
% 0.32/1.34 % (12598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (12598)Termination reason: Unknown
% 0.32/1.34 % (12598)Termination phase: Saturation
% 0.32/1.34
% 0.32/1.34 % (12598)Memory used [KB]: 895
% 0.32/1.34 % (12598)Time elapsed: 0.003 s
% 0.32/1.34 % (12598)Instructions burned: 2 (million)
% 0.32/1.34 % (12598)------------------------------
% 0.32/1.34 % (12598)------------------------------
% 0.32/1.34 % (12600)First to succeed.
% 0.32/1.34 % (12596)Instruction limit reached!
% 0.32/1.34 % (12596)------------------------------
% 0.32/1.34 % (12596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (12596)Termination reason: Unknown
% 0.32/1.34 % (12596)Termination phase: Saturation
% 0.32/1.34
% 0.32/1.34 % (12596)Memory used [KB]: 5500
% 0.32/1.34 % (12596)Time elapsed: 0.005 s
% 0.32/1.34 % (12596)Instructions burned: 5 (million)
% 0.32/1.34 % (12596)------------------------------
% 0.32/1.34 % (12596)------------------------------
% 0.32/1.34 % (12601)Also succeeded, but the first one will report.
% 0.32/1.34 % (12597)Also succeeded, but the first one will report.
% 0.32/1.34 % (12600)Refutation found. Thanks to Tanya!
% 0.32/1.34 % SZS status Theorem for DTF2THF_12385
% 0.32/1.34 % SZS output start Proof for DTF2THF_12385
% 0.32/1.34 thf(type_def_5, type, rat: $tType).
% 0.32/1.34 thf(func_def_0, type, rat: $tType).
% 0.32/1.34 thf(func_def_1, type, x0: rat).
% 0.32/1.34 thf(func_def_2, type, y0: rat).
% 0.32/1.34 thf(func_def_3, type, less: rat > rat > $o).
% 0.32/1.34 thf(func_def_4, type, is: rat > rat > $o).
% 0.32/1.34 thf(func_def_6, type, more: rat > rat > $o).
% 0.32/1.34 thf(f36,plain,(
% 0.32/1.34 $false),
% 0.32/1.34 inference(subsumption_resolution,[status(thm)],[f35,f33])).
% 0.32/1.34 thf(f33,plain,(
% 0.32/1.34 ((less @ x0 @ y0) != $true)),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f31])).
% 0.32/1.34 thf(f31,plain,(
% 0.32/1.34 ($true != $true) | ((less @ x0 @ y0) != $true)),
% 0.32/1.34 inference(superposition,[status(thm)],[f27,f28])).
% 0.32/1.34 thf(f28,plain,(
% 0.32/1.34 ((more @ x0 @ y0) = $true)),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f15])).
% 0.32/1.34 thf(f15,plain,(
% 0.32/1.34 ((more @ x0 @ y0) = $true)),
% 0.32/1.34 inference(flattening,[status(thm)],[f14])).
% 0.32/1.34 thf(f14,plain,(
% 0.32/1.34 ~~((more @ x0 @ y0) = $true)),
% 0.32/1.34 inference(fool_elimination,[status(thm)],[f13])).
% 0.32/1.34 thf(f13,plain,(
% 0.32/1.34 ~~(more @ x0 @ y0)),
% 0.32/1.34 inference(rectify,[status(thm)],[f5])).
% 0.32/1.34 thf(f5,negated_conjecture,(
% 0.32/1.34 ~~(more @ x0 @ y0)),
% 0.32/1.34 inference(negated_conjecture,[status(cth)],[f4])).
% 0.32/1.34 thf(f4,conjecture,(
% 0.32/1.34 ~(more @ x0 @ y0)),
% 0.32/1.34 file('/export/starexec/sandbox2/tmp/tmp.0C1SnVzXa8/DTF2THF_12385.p',satz81d)).
% 0.32/1.34 thf(f27,plain,(
% 0.32/1.34 ( ! [X0 : rat,X1 : rat] : (($true != (more @ X1 @ X0)) | ((less @ X1 @ X0) != $true)) )),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 0.32/1.34 thf(f20,plain,(
% 0.32/1.34 ! [X0 : rat,X1 : rat] : ((((less @ X1 @ X0) != $true) | ($true != (more @ X1 @ X0))) & (($true != (more @ X1 @ X0)) | ((is @ X1 @ X0) != $true)) & (((is @ X1 @ X0) != $true) | ((less @ X1 @ X0) != $true)))),
% 0.32/1.34 inference(flattening,[status(thm)],[f19])).
% 0.32/1.34 thf(f19,plain,(
% 0.32/1.34 ! [X0 : rat,X1 : rat] : (((((is @ X1 @ X0) != $true) | ((less @ X1 @ X0) != $true)) & (((less @ X1 @ X0) != $true) | ($true != (more @ X1 @ X0)))) & (($true != (more @ X1 @ X0)) | ((is @ X1 @ X0) != $true)))),
% 0.32/1.34 inference(ennf_transformation,[status(thm)],[f18])).
% 0.32/1.34 thf(f18,plain,(
% 0.32/1.34 ! [X0 : rat,X1 : rat] : ~((((is @ X1 @ X0) = $true) => ($true != (more @ X1 @ X0))) => ((($true = (more @ X1 @ X0)) => ((less @ X1 @ X0) != $true)) => ~(((less @ X1 @ X0) = $true) => ((is @ X1 @ X0) != $true))))),
% 0.32/1.34 inference(flattening,[status(thm)],[f12])).
% 0.32/1.34 thf(f12,plain,(
% 0.32/1.34 ! [X0 : rat,X1 : rat] : ~((((is @ X1 @ X0) = $true) => ~($true = (more @ X1 @ X0))) => ~~((($true = (more @ X1 @ X0)) => ~((less @ X1 @ X0) = $true)) => ~(((less @ X1 @ X0) = $true) => ~((is @ X1 @ X0) = $true))))),
% 0.32/1.34 inference(fool_elimination,[status(thm)],[f11])).
% 0.32/1.34 thf(f11,plain,(
% 0.32/1.34 ! [X0 : rat,X1 : rat] : ~(((is @ X1 @ X0) => ~(more @ X1 @ X0)) => ~~(((more @ X1 @ X0) => ~(less @ X1 @ X0)) => ~((less @ X1 @ X0) => ~(is @ X1 @ X0))))),
% 0.32/1.34 inference(rectify,[status(thm)],[f3])).
% 0.32/1.34 thf(f3,axiom,(
% 0.32/1.34 ! [X2 : rat,X1 : rat] : ~(((is @ X1 @ X2) => ~(more @ X1 @ X2)) => ~~(((more @ X1 @ X2) => ~(less @ X1 @ X2)) => ~((less @ X1 @ X2) => ~(is @ X1 @ X2))))),
% 0.32/1.34 file('/export/starexec/sandbox2/tmp/tmp.0C1SnVzXa8/DTF2THF_12385.p',satz81b)).
% 0.32/1.34 thf(f35,plain,(
% 0.32/1.34 ((less @ x0 @ y0) = $true)),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f34])).
% 0.32/1.34 thf(f34,plain,(
% 0.32/1.34 ((less @ x0 @ y0) = $true) | ($true != $true)),
% 0.32/1.34 inference(superposition,[status(thm)],[f32,f23])).
% 0.32/1.34 thf(f23,plain,(
% 0.32/1.34 ((is @ x0 @ y0) = $true) | ((less @ x0 @ y0) = $true)),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f22])).
% 0.32/1.34 thf(f22,plain,(
% 0.32/1.34 ((is @ x0 @ y0) = $true) | ((less @ x0 @ y0) = $true)),
% 0.32/1.34 inference(ennf_transformation,[status(thm)],[f17])).
% 0.32/1.34 thf(f17,plain,(
% 0.32/1.34 ((less @ x0 @ y0) != $true) => ((is @ x0 @ y0) = $true)),
% 0.32/1.34 inference(flattening,[status(thm)],[f8])).
% 0.32/1.34 thf(f8,plain,(
% 0.32/1.34 ~((less @ x0 @ y0) = $true) => ((is @ x0 @ y0) = $true)),
% 0.32/1.34 inference(fool_elimination,[status(thm)],[f7])).
% 0.32/1.34 thf(f7,plain,(
% 0.32/1.34 ~(less @ x0 @ y0) => (is @ x0 @ y0)),
% 0.32/1.34 inference(rectify,[status(thm)],[f1])).
% 0.32/1.34 thf(f1,axiom,(
% 0.32/1.34 ~(less @ x0 @ y0) => (is @ x0 @ y0)),
% 0.32/1.34 file('/export/starexec/sandbox2/tmp/tmp.0C1SnVzXa8/DTF2THF_12385.p',l)).
% 0.32/1.34 thf(f32,plain,(
% 0.32/1.34 ((is @ x0 @ y0) != $true)),
% 0.32/1.34 inference(trivial_inequality_removal,[status(thm)],[f30])).
% 0.32/1.34 thf(f30,plain,(
% 0.32/1.34 ($true != $true) | ((is @ x0 @ y0) != $true)),
% 0.32/1.34 inference(superposition,[status(thm)],[f26,f28])).
% 0.32/1.34 thf(f26,plain,(
% 0.32/1.34 ( ! [X0 : rat,X1 : rat] : (($true != (more @ X1 @ X0)) | ((is @ X1 @ X0) != $true)) )),
% 0.32/1.34 inference(cnf_transformation,[status(thm)],[f20])).
% 0.32/1.34 % SZS output end Proof for DTF2THF_12385
% 0.32/1.34 % (12600)------------------------------
% 0.32/1.34 % (12600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.34 % (12600)Termination reason: Refutation
% 0.32/1.34
% 0.32/1.34 % (12600)Memory used [KB]: 5500
% 0.32/1.34 % (12600)Time elapsed: 0.004 s
% 0.32/1.34 % (12600)Instructions burned: 2 (million)
% 0.32/1.34 % (12600)------------------------------
% 0.32/1.34 % (12600)------------------------------
% 0.32/1.34 % (12594)Success in time 0.019 s
%------------------------------------------------------------------------------