%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU844^5 : 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 : n031.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 09:37:34 AM UTC 2026
% Result : Theorem 1.50s 1.25s
% Output : Refutation 1.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 3 unt; 0 typ; 4 def)
% Number of atoms : 200 ( 59 equ; 0 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 164 ( 37 ~; 32 |; 17 &; 60 @)
% ( 4 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 24 ( 24 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 40 ( 0 ^; 34 !; 6 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cS: a > $o ).
thf(func_def_2,type,
cT: a > $o ).
thf(func_def_4,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK0: a ).
thf(func_def_8,type,
sK1: a ).
thf(func_def_10,type,
ph3:
!>[X0: $tType] : X0 ).
thf(f64,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f24,f29,f34,f35,f52,f61]) ).
thf(f61,plain,
( spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true != $true )
| spl2_1
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f19,f55]) ).
thf(f55,plain,
( ! [X0: a > $o] :
( ( X0 @ sK0 )
= $true )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ! [X0: a > $o] :
( ( ( X0 @ sK0 )
= $true )
| ( $false = $true ) )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f28,f37]) ).
thf(f37,plain,
! [X2: a > $o,X3: a > $o,X4: a] :
( ( $false
= ( X2 @ X4 ) )
| ( ( X3 @ X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f36]) ).
thf(f36,plain,
! [X2: a > $o,X3: a > $o,X4: a] :
( ( X3 @ X4 )
= ( X2 @ X4 ) ),
inference(argument_congruence,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: a > $o,X3: a > $o] : ( X2 = X3 ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( ( ( cS @ sK0 )
!= $true )
& ( ( cT @ sK0 )
= $true ) )
| ( ( ( cT @ sK1 )
!= $true )
& ( ( cS @ sK1 )
= $true ) ) )
& ! [X2: a > $o,X3: a > $o] : ( X2 = X3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8]) ).
thf(f8,plain,
( ? [X0: a] :
( ( ( cS @ X0 )
!= $true )
& ( $true
= ( cT @ X0 ) ) )
=> ( ( ( cS @ sK0 )
!= $true )
& ( ( cT @ sK0 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X1: a] :
( ( $true
!= ( cT @ X1 ) )
& ( ( cS @ X1 )
= $true ) )
=> ( ( ( cT @ sK1 )
!= $true )
& ( ( cS @ sK1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
( ( ? [X0: a] :
( ( ( cS @ X0 )
!= $true )
& ( $true
= ( cT @ X0 ) ) )
| ? [X1: a] :
( ( $true
!= ( cT @ X1 ) )
& ( ( cS @ X1 )
= $true ) ) )
& ! [X2: a > $o,X3: a > $o] : ( X2 = X3 ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ? [X3: a] :
( ( $true
!= ( cS @ X3 ) )
& ( ( cT @ X3 )
= $true ) )
| ? [X2: a] :
( ( ( cT @ X2 )
!= $true )
& ( ( cS @ X2 )
= $true ) ) )
& ! [X1: a > $o,X0: a > $o] : ( X0 = X1 ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
=> ( ! [X3: a] :
( ( ( cT @ X3 )
= $true )
=> ( $true
= ( cS @ X3 ) ) )
& ! [X2: a] :
( ( ( cS @ X2 )
= $true )
=> ( ( cT @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: a > $o,X1: a > $o] : ( X0 = X1 )
=> ( ! [X2: a] :
( ( cS @ X2 )
=> ( cT @ X2 ) )
& ! [X3: a] :
( ( cT @ X3 )
=> ( cS @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
=> ( ! [X2: a] :
( ( cS @ X2 )
=> ( cT @ X2 ) )
& ! [X2: a] :
( ( cT @ X2 )
=> ( cS @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X1: a > $o,X0: a > $o] : ( X0 = X1 )
=> ( ! [X2: a] :
( ( cS @ X2 )
=> ( cT @ X2 ) )
& ! [X2: a] :
( ( cT @ X2 )
=> ( cS @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.KAbvPESplC/DTF2THF_11846.p',cGAZING_THM8_pme) ).
thf(f28,plain,
( ( ( cT @ sK0 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl2_3
<=> ( ( cT @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f19,plain,
( ( ( cS @ sK0 )
!= $true )
| spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f17]) ).
thf(f17,definition,
( spl2_1
<=> ( ( cS @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f52,plain,
( ~ spl2_2
| spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f51]) ).
thf(f51,plain,
( $false
| ~ spl2_2
| spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f48]) ).
thf(f48,plain,
( ( $true != $true )
| ~ spl2_2
| spl2_4 ),
inference(superposition,[status(thm)],[f33,f44]) ).
thf(f44,plain,
( ! [X0: a > $o] :
( ( X0 @ sK1 )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X0: a > $o] :
( ( ( X0 @ sK1 )
= $true )
| ( $false = $true ) )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f23,f37]) ).
thf(f23,plain,
( ( ( cS @ sK1 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f21]) ).
thf(f21,definition,
( spl2_2
<=> ( ( cS @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f33,plain,
( ( ( cT @ sK1 )
!= $true )
| spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl2_4
<=> ( ( cT @ sK1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f35,plain,
( ~ spl2_4
| ~ spl2_1 ),
inference(avatar_split_clause,[status(thm)],[f15,f17,f31]) ).
thf(f15,plain,
( ( ( cT @ sK1 )
!= $true )
| ( ( cS @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f34,plain,
( spl2_3
| ~ spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f13,f31,f26]) ).
thf(f13,plain,
( ( ( cT @ sK0 )
= $true )
| ( ( cT @ sK1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f29,plain,
( spl2_3
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f12,f21,f26]) ).
thf(f12,plain,
( ( ( cT @ sK0 )
= $true )
| ( ( cS @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f24,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f21,f17]) ).
thf(f14,plain,
( ( ( cS @ sK0 )
!= $true )
| ( ( cS @ sK1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU844^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n031.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 12:36:33 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU844^5 : TPTP v9.2.1. Released v4.0.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : TPS problem GAZING-THM8
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English :
% 0.28/0.47
% 0.28/0.47 % Refs : [Bar92] Barker-Plummer D (1992), Gazing: An Approach to the Pr
% 0.28/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.28/0.47 % Source : [Bro09]
% 0.28/0.47 % Names : tps_0208 [Bro09]
% 0.28/0.47 % : 8 [Bar92]
% 0.28/0.47 % : GAZING-THM8 [TPS]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.28/0.47 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.28/0.47 % Number of atoms : 5 ( 1 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 5 ( 5 avg)
% 0.28/0.47 % Number of connectives : 8 ( 0 ~; 0 |; 1 &; 4 @)
% 0.28/0.47 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 6 ( 6 avg)
% 0.28/0.47 % Number of types : 2 ( 1 usr)
% 0.28/0.47 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 3 ( 2 usr; 0 con; 1-2 aty)
% 0.28/0.47 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.28/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.28/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.28/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.28/0.47 % : Polymorphic definitions expanded.
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(a_type,type,
% 0.28/0.47 a: $tType ).
% 0.28/0.47
% 0.28/0.47 thf(cS,type,
% 0.28/0.47 cS: a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cT,type,
% 0.28/0.47 cT: a > $o ).
% 0.28/0.47
% 0.28/0.47 thf(cGAZING_THM8_pme,conjecture,
% 0.28/0.47 ( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 )
% 0.28/0.47 => ( ! [Xx: a] :
% 0.28/0.47 ( ( cS @ Xx )
% 0.28/0.47 => ( cT @ Xx ) )
% 0.28/0.47 & ! [Xx: a] :
% 0.28/0.47 ( ( cT @ Xx )
% 0.28/0.47 => ( cS @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 1.50/1.22 ---- Embedded in THF ---
% 1.50/1.22 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.50/1.22 %%% Generated on Tue Feb 24 12:36:34 EST 2026
% 1.50/1.22 %%% using '$$dhol' embedding, version 1.3.0.
% 1.50/1.22 %%% Logic specification used:
% 1.50/1.22 %%% thf(spec, logic, $$dhol).
% 1.50/1.22
% 1.50/1.22 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.KAbvPESplC/DTF2DTF11846.p
% See solution above
% 1.50/1.22 ------------------------
% 1.50/1.23 ---- Cleaned THF ---
% 1.50/1.23 thf(a_type,type,
% 1.50/1.23 a: $tType ).
% 1.50/1.23
% 1.50/1.23 thf(cS,type,
% 1.50/1.23 cS: a > $o ).
% 1.50/1.23
% 1.50/1.23 thf(cT,type,
% 1.50/1.23 cT: a > $o ).
% 1.50/1.23
% 1.50/1.23 thf(cGAZING_THM8_pme,conjecture,
% 1.50/1.23 ( ! [S0: a > $o,T0: a > $o] : ( S0 = T0 )
% 1.50/1.23 => ( ! [Xx: a] :
% 1.50/1.23 ( ( cS @ Xx )
% 1.50/1.23 => ( cT @ Xx ) )
% 1.50/1.23 & ! [Xx: a] :
% 1.50/1.23 ( ( cT @ Xx )
% 1.50/1.23 => ( cS @ Xx ) ) ) ) ).
% 1.50/1.23 ------------------------
% 1.50/1.24 % (12114)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_11846 for (2999ds/2Mi)
% 1.50/1.24 % (12112)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_11846 for (2999ds/27Mi)
% 1.50/1.24 % (12114)Instruction limit reached!
% 1.50/1.24 % (12114)------------------------------
% 1.50/1.24 % (12114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.24 % (12114)Termination reason: Unknown
% 1.50/1.24 % (12114)Termination phase: Saturation
% 1.50/1.24
% 1.50/1.24 % (12114)Memory used [KB]: 5500
% 1.50/1.24 % (12114)Time elapsed: 0.003 s
% 1.50/1.24 % (12114)Instructions burned: 4 (million)
% 1.50/1.24 % (12114)------------------------------
% 1.50/1.24 % (12114)------------------------------
% 1.50/1.25 % (12112)First to succeed.
% 1.50/1.25 % (12112)Refutation found. Thanks to Tanya!
% 1.50/1.25 % SZS status Theorem for DTF2THF_11846
% 1.50/1.25 % SZS output start Proof for DTF2THF_11846
% 1.50/1.25 thf(type_def_5, type, a: $tType).
% 1.50/1.25 thf(func_def_0, type, a: $tType).
% 1.50/1.25 thf(func_def_1, type, cS: a > $o).
% 1.50/1.25 thf(func_def_2, type, cT: a > $o).
% 1.50/1.25 thf(func_def_4, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.50/1.25 thf(func_def_7, type, sK0: a).
% 1.50/1.25 thf(func_def_8, type, sK1: a).
% 1.50/1.25 thf(func_def_10, type, ph3: !>[X0: $tType]:(X0)).
% 1.50/1.25 thf(f64,plain,(
% 1.50/1.25 $false),
% 1.50/1.25 inference(avatar_sat_refutation,[status(thm)],[f24,f29,f34,f35,f52,f61])).
% 1.50/1.25 thf(f61,plain,(
% 1.50/1.25 spl2_1 | ~spl2_3),
% 1.50/1.25 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.50/1.25 thf(f60,plain,(
% 1.50/1.25 $false | (spl2_1 | ~spl2_3)),
% 1.50/1.25 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.50/1.25 thf(f59,plain,(
% 1.50/1.25 ($true != $true) | (spl2_1 | ~spl2_3)),
% 1.50/1.25 inference(superposition,[status(thm)],[f19,f55])).
% 1.50/1.25 thf(f55,plain,(
% 1.50/1.25 ( ! [X0 : a > $o] : (((X0 @ sK0) = $true)) ) | ~spl2_3),
% 1.50/1.25 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.50/1.25 thf(f53,plain,(
% 1.50/1.25 ( ! [X0 : a > $o] : (((X0 @ sK0) = $true) | ($false = $true)) ) | ~spl2_3),
% 1.50/1.25 inference(superposition,[status(thm)],[f28,f37])).
% 1.50/1.25 thf(f37,plain,(
% 1.50/1.25 ( ! [X2 : a > $o,X3 : a > $o,X4 : a] : (($false = (X2 @ X4)) | ((X3 @ X4) = $true)) )),
% 1.50/1.25 inference(binary_proxy_clausification,[status(thm)],[f36])).
% 1.50/1.25 thf(f36,plain,(
% 1.50/1.25 ( ! [X2 : a > $o,X3 : a > $o,X4 : a] : (((X3 @ X4) = (X2 @ X4))) )),
% 1.50/1.25 inference(argument_congruence,[status(thm)],[f11])).
% 1.50/1.25 thf(f11,plain,(
% 1.50/1.25 ( ! [X2 : a > $o,X3 : a > $o] : ((X2 = X3)) )),
% 1.50/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.25 thf(f10,plain,(
% 1.50/1.25 ((((cS @ sK0) != $true) & ((cT @ sK0) = $true)) | (((cT @ sK1) != $true) & ((cS @ sK1) = $true))) & ! [X2 : a > $o,X3 : a > $o] : (X2 = X3)),
% 1.50/1.25 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f7,f9,f8])).
% 1.50/1.25 thf(f8,plain,(
% 1.50/1.25 ? [X0 : a] : (((cS @ X0) != $true) & ($true = (cT @ X0))) => (((cS @ sK0) != $true) & ((cT @ sK0) = $true))),
% 1.50/1.25 introduced(definition,[],[choice_axiom])).
% 1.50/1.25 thf(f9,plain,(
% 1.50/1.25 ? [X1 : a] : (($true != (cT @ X1)) & ((cS @ X1) = $true)) => (((cT @ sK1) != $true) & ((cS @ sK1) = $true))),
% 1.50/1.25 introduced(definition,[],[choice_axiom])).
% 1.50/1.25 thf(f7,plain,(
% 1.50/1.25 (? [X0 : a] : (((cS @ X0) != $true) & ($true = (cT @ X0))) | ? [X1 : a] : (($true != (cT @ X1)) & ((cS @ X1) = $true))) & ! [X2 : a > $o,X3 : a > $o] : (X2 = X3)),
% 1.50/1.25 inference(rectify,[status(thm)],[f6])).
% 1.50/1.25 thf(f6,plain,(
% 1.50/1.25 (? [X3 : a] : (($true != (cS @ X3)) & ((cT @ X3) = $true)) | ? [X2 : a] : (((cT @ X2) != $true) & ((cS @ X2) = $true))) & ! [X1 : a > $o,X0 : a > $o] : (X0 = X1)),
% 1.50/1.25 inference(ennf_transformation,[status(thm)],[f5])).
% 1.50/1.25 thf(f5,plain,(
% 1.50/1.25 ~(! [X1 : a > $o,X0 : a > $o] : (X0 = X1) => (! [X3 : a] : (((cT @ X3) = $true) => ($true = (cS @ X3))) & ! [X2 : a] : (((cS @ X2) = $true) => ((cT @ X2) = $true))))),
% 1.50/1.25 inference(fool_elimination,[status(thm)],[f4])).
% 1.50/1.25 thf(f4,plain,(
% 1.50/1.25 ~(! [X0 : a > $o,X1 : a > $o] : (X0 = X1) => (! [X2 : a] : ((cS @ X2) => (cT @ X2)) & ! [X3 : a] : ((cT @ X3) => (cS @ X3))))),
% 1.50/1.25 inference(rectify,[status(thm)],[f2])).
% 1.50/1.25 thf(f2,negated_conjecture,(
% 1.50/1.25 ~(! [X1 : a > $o,X0 : a > $o] : (X0 = X1) => (! [X2 : a] : ((cS @ X2) => (cT @ X2)) & ! [X2 : a] : ((cT @ X2) => (cS @ X2))))),
% 1.50/1.25 inference(negated_conjecture,[status(cth)],[f1])).
% 1.50/1.25 thf(f1,conjecture,(
% 1.50/1.25 ! [X1 : a > $o,X0 : a > $o] : (X0 = X1) => (! [X2 : a] : ((cS @ X2) => (cT @ X2)) & ! [X2 : a] : ((cT @ X2) => (cS @ X2)))),
% 1.50/1.25 file('/export/starexec/sandbox2/tmp/tmp.KAbvPESplC/DTF2THF_11846.p',cGAZING_THM8_pme)).
% 1.50/1.25 thf(f28,plain,(
% 1.50/1.25 ((cT @ sK0) = $true) | ~spl2_3),
% 1.50/1.25 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.50/1.25 thf(f26,definition,(
% 1.50/1.25 spl2_3 <=> ((cT @ sK0) = $true)),
% 1.50/1.25 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.50/1.25 thf(f19,plain,(
% 1.50/1.25 ((cS @ sK0) != $true) | spl2_1),
% 1.50/1.25 inference(avatar_component_clause,[status(thm)],[f17])).
% 1.50/1.25 thf(f17,definition,(
% 1.50/1.25 spl2_1 <=> ((cS @ sK0) = $true)),
% 1.50/1.25 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.50/1.25 thf(f52,plain,(
% 1.50/1.25 ~spl2_2 | spl2_4),
% 1.50/1.25 inference(avatar_contradiction_clause,[status(thm)],[f51])).
% 1.50/1.25 thf(f51,plain,(
% 1.50/1.25 $false | (~spl2_2 | spl2_4)),
% 1.50/1.25 inference(trivial_inequality_removal,[status(thm)],[f48])).
% 1.50/1.25 thf(f48,plain,(
% 1.50/1.25 ($true != $true) | (~spl2_2 | spl2_4)),
% 1.50/1.25 inference(superposition,[status(thm)],[f33,f44])).
% 1.50/1.25 thf(f44,plain,(
% 1.50/1.25 ( ! [X0 : a > $o] : (((X0 @ sK1) = $true)) ) | ~spl2_2),
% 1.50/1.25 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.50/1.25 thf(f41,plain,(
% 1.50/1.25 ( ! [X0 : a > $o] : (((X0 @ sK1) = $true) | ($false = $true)) ) | ~spl2_2),
% 1.50/1.25 inference(superposition,[status(thm)],[f23,f37])).
% 1.50/1.25 thf(f23,plain,(
% 1.50/1.25 ((cS @ sK1) = $true) | ~spl2_2),
% 1.50/1.25 inference(avatar_component_clause,[status(thm)],[f21])).
% 1.50/1.25 thf(f21,definition,(
% 1.50/1.25 spl2_2 <=> ((cS @ sK1) = $true)),
% 1.50/1.25 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.50/1.25 thf(f33,plain,(
% 1.50/1.25 ((cT @ sK1) != $true) | spl2_4),
% 1.50/1.25 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.50/1.25 thf(f31,definition,(
% 1.50/1.25 spl2_4 <=> ((cT @ sK1) = $true)),
% 1.50/1.25 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.50/1.25 thf(f35,plain,(
% 1.50/1.25 ~spl2_4 | ~spl2_1),
% 1.50/1.25 inference(avatar_split_clause,[status(thm)],[f15,f17,f31])).
% 1.50/1.25 thf(f15,plain,(
% 1.50/1.25 ((cT @ sK1) != $true) | ((cS @ sK0) != $true)),
% 1.50/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.25 thf(f34,plain,(
% 1.50/1.25 spl2_3 | ~spl2_4),
% 1.50/1.25 inference(avatar_split_clause,[status(thm)],[f13,f31,f26])).
% 1.50/1.25 thf(f13,plain,(
% 1.50/1.25 ((cT @ sK0) = $true) | ((cT @ sK1) != $true)),
% 1.50/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.25 thf(f29,plain,(
% 1.50/1.25 spl2_3 | spl2_2),
% 1.50/1.25 inference(avatar_split_clause,[status(thm)],[f12,f21,f26])).
% 1.50/1.25 thf(f12,plain,(
% 1.50/1.25 ((cT @ sK0) = $true) | ((cS @ sK1) = $true)),
% 1.50/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.25 thf(f24,plain,(
% 1.50/1.25 ~spl2_1 | spl2_2),
% 1.50/1.25 inference(avatar_split_clause,[status(thm)],[f14,f21,f17])).
% 1.50/1.25 thf(f14,plain,(
% 1.50/1.25 ((cS @ sK0) != $true) | ((cS @ sK1) = $true)),
% 1.50/1.25 inference(cnf_transformation,[status(thm)],[f10])).
% 1.50/1.25 % SZS output end Proof for DTF2THF_11846
% 1.50/1.25 % (12112)------------------------------
% 1.50/1.25 % (12112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.50/1.25 % (12112)Termination reason: Refutation
% 1.50/1.25
% 1.50/1.25 % (12112)Memory used [KB]: 5500
% 1.50/1.25 % (12112)Time elapsed: 0.003 s
% 1.50/1.25 % (12112)Instructions burned: 2 (million)
% 1.50/1.25 % (12112)------------------------------
% 1.50/1.25 % (12112)------------------------------
% 1.50/1.25 % (12109)Success in time 0.013 s
%------------------------------------------------------------------------------