%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV233^5 : 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 : n017.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 09:40:37 AM UTC 2026
% Result : Theorem 1.62s 1.33s
% Output : Refutation 1.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 37 ( 1 unt; 0 typ; 4 def)
% Number of atoms : 287 ( 76 equ; 0 cnn)
% Maximal formula atoms : 14 ( 7 avg)
% Number of connectives : 232 ( 46 ~; 36 |; 32 &; 95 @)
% ( 4 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 23 !; 13 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cE: $i > $o ).
thf(func_def_1,type,
cD: $i > $o ).
thf(func_def_5,type,
sK0: $i > $o ).
thf(f46,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f26,f31,f36,f37,f41,f45]) ).
thf(f45,plain,
( spl3_1
| ~ spl3_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f44]) ).
thf(f44,plain,
( $false
| spl3_1
| ~ spl3_4 ),
inference(subsumption_resolution,[status(thm)],[f43,f35]) ).
thf(f35,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl3_4
<=> ( $true
= ( sK0 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f43,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
( ( $true
!= ( sK0 @ sK1 ) )
| ( $true != $true )
| spl3_1 ),
inference(superposition,[status(thm)],[f21,f13]) ).
thf(f13,plain,
! [X3: $i] :
( ( ( cD @ X3 )
= $true )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( ( $true
= ( sK0 @ sK1 ) )
& ( $true
!= ( cD @ sK1 ) ) )
| ( ( ( sK0 @ sK2 )
= $true )
& ( $true
!= ( cE @ sK2 ) ) ) )
& ! [X3: $i] :
( ( ( ( cD @ X3 )
= $true )
& ( $true
= ( cE @ X3 ) ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8]) ).
thf(f8,plain,
( ? [X0: $i > $o] :
( ( ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( cD @ X1 )
!= $true ) )
| ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( cE @ X2 )
!= $true ) ) )
& ! [X3: $i] :
( ( ( ( cD @ X3 )
= $true )
& ( $true
= ( cE @ X3 ) ) )
| ( $true
!= ( X0 @ X3 ) ) ) )
=> ( ( ? [X1: $i] :
( ( ( sK0 @ X1 )
= $true )
& ( ( cD @ X1 )
!= $true ) )
| ? [X2: $i] :
( ( ( sK0 @ X2 )
= $true )
& ( ( cE @ X2 )
!= $true ) ) )
& ! [X3: $i] :
( ( ( ( cD @ X3 )
= $true )
& ( $true
= ( cE @ X3 ) ) )
| ( $true
!= ( sK0 @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ? [X1: $i] :
( ( ( sK0 @ X1 )
= $true )
& ( ( cD @ X1 )
!= $true ) )
=> ( ( $true
= ( sK0 @ sK1 ) )
& ( $true
!= ( cD @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X2: $i] :
( ( ( sK0 @ X2 )
= $true )
& ( ( cE @ X2 )
!= $true ) )
=> ( ( ( sK0 @ sK2 )
= $true )
& ( $true
!= ( cE @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f7,plain,
? [X0: $i > $o] :
( ( ? [X1: $i] :
( ( ( X0 @ X1 )
= $true )
& ( ( cD @ X1 )
!= $true ) )
| ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( cE @ X2 )
!= $true ) ) )
& ! [X3: $i] :
( ( ( ( cD @ X3 )
= $true )
& ( $true
= ( cE @ X3 ) ) )
| ( $true
!= ( X0 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: $i > $o] :
( ( ? [X3: $i] :
( ( $true
= ( X0 @ X3 ) )
& ( ( cD @ X3 )
!= $true ) )
| ? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
& ( ( cE @ X2 )
!= $true ) ) )
& ! [X1: $i] :
( ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) )
| ( ( X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: $i > $o] :
( ! [X1: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( ( cD @ X1 )
= $true )
& ( ( cE @ X1 )
= $true ) ) )
=> ( ! [X3: $i] :
( ( $true
= ( X0 @ X3 ) )
=> ( ( cD @ X3 )
= $true ) )
& ! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( cE @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cE @ X1 )
& ( cD @ X1 ) ) )
=> ( ! [X2: $i] :
( ( X0 @ X2 )
=> ( cE @ X2 ) )
& ! [X3: $i] :
( ( X0 @ X3 )
=> ( cD @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cE @ X1 )
& ( cD @ X1 ) ) )
=> ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cE @ X1 ) )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cD @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: $i > $o] :
( ! [X1: $i] :
( ( X0 @ X1 )
=> ( ( cE @ X1 )
& ( cD @ X1 ) ) )
=> ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( cE @ X1 ) )
& ! [X1: $i] :
( ( X0 @ X1 )
=> ( cD @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.fh44r2n8F7/DTF2THF_26583.p',cTHM46_pme) ).
thf(f21,plain,
( ( $true
!= ( cD @ sK1 ) )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl3_1
<=> ( $true
= ( cD @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f41,plain,
( ~ spl3_2
| spl3_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f40]) ).
thf(f40,plain,
( $false
| ~ spl3_2
| spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f39,f25]) ).
thf(f25,plain,
( ( ( sK0 @ sK2 )
= $true )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl3_2
<=> ( ( sK0 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f39,plain,
( ( ( sK0 @ sK2 )
!= $true )
| spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( ( sK0 @ sK2 )
!= $true )
| ( $true != $true )
| spl3_3 ),
inference(superposition,[status(thm)],[f30,f12]) ).
thf(f12,plain,
! [X3: $i] :
( ( $true
= ( cE @ X3 ) )
| ( $true
!= ( sK0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f30,plain,
( ( $true
!= ( cE @ sK2 ) )
| spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f28,definition,
( spl3_3
<=> ( $true
= ( cE @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f37,plain,
( spl3_4
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f16,f28,f33]) ).
thf(f16,plain,
( ( $true
= ( sK0 @ sK1 ) )
| ( $true
!= ( cE @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f36,plain,
( spl3_2
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f17,f33,f23]) ).
thf(f17,plain,
( ( ( sK0 @ sK2 )
= $true )
| ( $true
= ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f31,plain,
( ~ spl3_3
| ~ spl3_1 ),
inference(avatar_split_clause,[status(thm)],[f14,f19,f28]) ).
thf(f14,plain,
( ( $true
!= ( cD @ sK1 ) )
| ( $true
!= ( cE @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f26,plain,
( ~ spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f23,f19]) ).
thf(f15,plain,
( ( $true
!= ( cD @ sK1 ) )
| ( ( sK0 @ sK2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV233^5 : TPTP v9.2.1. Released v4.0.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n017.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:40:56 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEV233^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.45 % Domain : Set Theory (Sets of sets)
% 0.18/0.45 % Problem : TPS problem THM46
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English :
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.45 % Source : [Bro09]
% 0.18/0.45 % Names : tps_0383 [Bro09]
% 0.18/0.45 % : THM46 [TPS]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.08 v7.4.0, 0.11 v7.3.0, 0.10 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 v6.1.0, 0.00 v4.0.0
% 0.18/0.45 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.18/0.45 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 4 ( 4 avg)
% 0.18/0.45 % Number of connectives : 13 ( 0 ~; 0 |; 2 &; 7 @)
% 0.18/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 7 ( 7 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.18/0.45 % Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% 0.18/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.45 % : Polymorphic definitions expanded.
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(cE,type,
% 0.18/0.45 cE: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cD,type,
% 0.18/0.45 cD: $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(cTHM46_pme,conjecture,
% 0.18/0.45 ! [Xx: $i > $o] :
% 0.18/0.45 ( ! [Xx0: $i] :
% 0.18/0.45 ( ( Xx @ Xx0 )
% 0.18/0.45 => ( ( cD @ Xx0 )
% 0.18/0.45 & ( cE @ Xx0 ) ) )
% 0.18/0.45 => ( ! [Xx0: $i] :
% 0.18/0.45 ( ( Xx @ Xx0 )
% 0.18/0.45 => ( cD @ Xx0 ) )
% 0.18/0.45 & ! [Xx0: $i] :
% 0.18/0.45 ( ( Xx @ Xx0 )
% 0.18/0.45 => ( cE @ Xx0 ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 ------------------------
% 1.62/1.30 ---- Embedded in THF ---
% 1.62/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.62/1.30 %%% Generated on Tue Feb 24 12:40:57 EST 2026
% 1.62/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 1.62/1.30 %%% Logic specification used:
% 1.62/1.30 %%% thf(spec, logic, $$dhol).
% 1.62/1.30
% 1.62/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.fh44r2n8F7/DTF2DTF26583.p
% See solution above
% 1.62/1.30 ------------------------
% 1.62/1.31 ---- Cleaned THF ---
% 1.62/1.31 thf(cE,type,
% 1.62/1.31 cE: $i > $o ).
% 1.62/1.31
% 1.62/1.31 thf(cD,type,
% 1.62/1.31 cD: $i > $o ).
% 1.62/1.31
% 1.62/1.31 thf(cTHM46_pme,conjecture,
% 1.62/1.31 ! [Xx: $i > $o] :
% 1.62/1.31 ( ! [Xx0: $i] :
% 1.62/1.31 ( ( Xx @ Xx0 )
% 1.62/1.31 => ( ( cD @ Xx0 )
% 1.62/1.31 & ( cE @ Xx0 ) ) )
% 1.62/1.31 => ( ! [Xx0: $i] :
% 1.62/1.31 ( ( Xx @ Xx0 )
% 1.62/1.31 => ( cD @ Xx0 ) )
% 1.62/1.31 & ! [Xx0: $i] :
% 1.62/1.31 ( ( Xx @ Xx0 )
% 1.62/1.31 => ( cE @ Xx0 ) ) ) ) ).
% 1.62/1.31 ------------------------
% 1.62/1.33 % (26792)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26583 for (3000ds/183Mi)
% 1.62/1.33 % (26792)First to succeed.
% 1.62/1.33 % (26792)Refutation found. Thanks to Tanya!
% 1.62/1.33 % SZS status Theorem for DTF2THF_26583
% 1.62/1.33 % SZS output start Proof for DTF2THF_26583
% 1.62/1.33 thf(func_def_0, type, cE: $i > $o).
% 1.62/1.33 thf(func_def_1, type, cD: $i > $o).
% 1.62/1.33 thf(func_def_5, type, sK0: $i > $o).
% 1.62/1.33 thf(f46,plain,(
% 1.62/1.33 $false),
% 1.62/1.33 inference(avatar_sat_refutation,[status(thm)],[f26,f31,f36,f37,f41,f45])).
% 1.62/1.33 thf(f45,plain,(
% 1.62/1.33 spl3_1 | ~spl3_4),
% 1.62/1.33 inference(avatar_contradiction_clause,[status(thm)],[f44])).
% 1.62/1.33 thf(f44,plain,(
% 1.62/1.33 $false | (spl3_1 | ~spl3_4)),
% 1.62/1.33 inference(subsumption_resolution,[status(thm)],[f43,f35])).
% 1.62/1.33 thf(f35,plain,(
% 1.62/1.33 ($true = (sK0 @ sK1)) | ~spl3_4),
% 1.62/1.33 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.62/1.33 thf(f33,definition,(
% 1.62/1.33 spl3_4 <=> ($true = (sK0 @ sK1))),
% 1.62/1.33 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.62/1.33 thf(f43,plain,(
% 1.62/1.33 ($true != (sK0 @ sK1)) | spl3_1),
% 1.62/1.33 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.62/1.33 thf(f42,plain,(
% 1.62/1.33 ($true != (sK0 @ sK1)) | ($true != $true) | spl3_1),
% 1.62/1.33 inference(superposition,[status(thm)],[f21,f13])).
% 1.62/1.33 thf(f13,plain,(
% 1.62/1.33 ( ! [X3 : $i] : (((cD @ X3) = $true) | ($true != (sK0 @ X3))) )),
% 1.62/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.33 thf(f11,plain,(
% 1.62/1.33 ((($true = (sK0 @ sK1)) & ($true != (cD @ sK1))) | (((sK0 @ sK2) = $true) & ($true != (cE @ sK2)))) & ! [X3 : $i] : ((((cD @ X3) = $true) & ($true = (cE @ X3))) | ($true != (sK0 @ X3)))),
% 1.62/1.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f7,f10,f9,f8])).
% 1.62/1.33 thf(f8,plain,(
% 1.62/1.33 ? [X0 : $i > $o] : ((? [X1 : $i] : (((X0 @ X1) = $true) & ((cD @ X1) != $true)) | ? [X2 : $i] : (((X0 @ X2) = $true) & ((cE @ X2) != $true))) & ! [X3 : $i] : ((((cD @ X3) = $true) & ($true = (cE @ X3))) | ($true != (X0 @ X3)))) => ((? [X1 : $i] : (((sK0 @ X1) = $true) & ((cD @ X1) != $true)) | ? [X2 : $i] : (((sK0 @ X2) = $true) & ((cE @ X2) != $true))) & ! [X3 : $i] : ((((cD @ X3) = $true) & ($true = (cE @ X3))) | ($true != (sK0 @ X3))))),
% 1.62/1.33 introduced(definition,[],[choice_axiom])).
% 1.62/1.33 thf(f9,plain,(
% 1.62/1.33 ? [X1 : $i] : (((sK0 @ X1) = $true) & ((cD @ X1) != $true)) => (($true = (sK0 @ sK1)) & ($true != (cD @ sK1)))),
% 1.62/1.33 introduced(definition,[],[choice_axiom])).
% 1.62/1.33 thf(f10,plain,(
% 1.62/1.33 ? [X2 : $i] : (((sK0 @ X2) = $true) & ((cE @ X2) != $true)) => (((sK0 @ sK2) = $true) & ($true != (cE @ sK2)))),
% 1.62/1.33 introduced(definition,[],[choice_axiom])).
% 1.62/1.33 thf(f7,plain,(
% 1.62/1.33 ? [X0 : $i > $o] : ((? [X1 : $i] : (((X0 @ X1) = $true) & ((cD @ X1) != $true)) | ? [X2 : $i] : (((X0 @ X2) = $true) & ((cE @ X2) != $true))) & ! [X3 : $i] : ((((cD @ X3) = $true) & ($true = (cE @ X3))) | ($true != (X0 @ X3))))),
% 1.62/1.33 inference(rectify,[status(thm)],[f6])).
% 1.62/1.33 thf(f6,plain,(
% 1.62/1.33 ? [X0 : $i > $o] : ((? [X3 : $i] : (($true = (X0 @ X3)) & ((cD @ X3) != $true)) | ? [X2 : $i] : (((X0 @ X2) = $true) & ((cE @ X2) != $true))) & ! [X1 : $i] : ((((cD @ X1) = $true) & ((cE @ X1) = $true)) | ((X0 @ X1) != $true)))),
% 1.62/1.33 inference(ennf_transformation,[status(thm)],[f5])).
% 1.62/1.33 thf(f5,plain,(
% 1.62/1.33 ~! [X0 : $i > $o] : (! [X1 : $i] : (((X0 @ X1) = $true) => (((cD @ X1) = $true) & ((cE @ X1) = $true))) => (! [X3 : $i] : (($true = (X0 @ X3)) => ((cD @ X3) = $true)) & ! [X2 : $i] : (((X0 @ X2) = $true) => ((cE @ X2) = $true))))),
% 1.62/1.33 inference(fool_elimination,[status(thm)],[f4])).
% 1.62/1.33 thf(f4,plain,(
% 1.62/1.33 ~! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => ((cE @ X1) & (cD @ X1))) => (! [X2 : $i] : ((X0 @ X2) => (cE @ X2)) & ! [X3 : $i] : ((X0 @ X3) => (cD @ X3))))),
% 1.62/1.33 inference(rectify,[status(thm)],[f2])).
% 1.62/1.33 thf(f2,negated_conjecture,(
% 1.62/1.33 ~! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => ((cE @ X1) & (cD @ X1))) => (! [X1 : $i] : ((X0 @ X1) => (cE @ X1)) & ! [X1 : $i] : ((X0 @ X1) => (cD @ X1))))),
% 1.62/1.33 inference(negated_conjecture,[status(cth)],[f1])).
% 1.62/1.33 thf(f1,conjecture,(
% 1.62/1.33 ! [X0 : $i > $o] : (! [X1 : $i] : ((X0 @ X1) => ((cE @ X1) & (cD @ X1))) => (! [X1 : $i] : ((X0 @ X1) => (cE @ X1)) & ! [X1 : $i] : ((X0 @ X1) => (cD @ X1))))),
% 1.62/1.33 file('/export/starexec/sandbox/tmp/tmp.fh44r2n8F7/DTF2THF_26583.p',cTHM46_pme)).
% 1.62/1.33 thf(f21,plain,(
% 1.62/1.33 ($true != (cD @ sK1)) | spl3_1),
% 1.62/1.33 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.62/1.33 thf(f19,definition,(
% 1.62/1.33 spl3_1 <=> ($true = (cD @ sK1))),
% 1.62/1.33 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.62/1.33 thf(f41,plain,(
% 1.62/1.33 ~spl3_2 | spl3_3),
% 1.62/1.33 inference(avatar_contradiction_clause,[status(thm)],[f40])).
% 1.62/1.33 thf(f40,plain,(
% 1.62/1.33 $false | (~spl3_2 | spl3_3)),
% 1.62/1.33 inference(subsumption_resolution,[status(thm)],[f39,f25])).
% 1.62/1.33 thf(f25,plain,(
% 1.62/1.33 ((sK0 @ sK2) = $true) | ~spl3_2),
% 1.62/1.33 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.62/1.33 thf(f23,definition,(
% 1.62/1.33 spl3_2 <=> ((sK0 @ sK2) = $true)),
% 1.62/1.33 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.62/1.33 thf(f39,plain,(
% 1.62/1.33 ((sK0 @ sK2) != $true) | spl3_3),
% 1.62/1.33 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.62/1.33 thf(f38,plain,(
% 1.62/1.33 ((sK0 @ sK2) != $true) | ($true != $true) | spl3_3),
% 1.62/1.33 inference(superposition,[status(thm)],[f30,f12])).
% 1.62/1.33 thf(f12,plain,(
% 1.62/1.33 ( ! [X3 : $i] : (($true = (cE @ X3)) | ($true != (sK0 @ X3))) )),
% 1.62/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.33 thf(f30,plain,(
% 1.62/1.33 ($true != (cE @ sK2)) | spl3_3),
% 1.62/1.33 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.62/1.33 thf(f28,definition,(
% 1.62/1.33 spl3_3 <=> ($true = (cE @ sK2))),
% 1.62/1.33 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.62/1.33 thf(f37,plain,(
% 1.62/1.33 spl3_4 | ~spl3_3),
% 1.62/1.33 inference(avatar_split_clause,[status(thm)],[f16,f28,f33])).
% 1.62/1.33 thf(f16,plain,(
% 1.62/1.33 ($true = (sK0 @ sK1)) | ($true != (cE @ sK2))),
% 1.62/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.33 thf(f36,plain,(
% 1.62/1.33 spl3_2 | spl3_4),
% 1.62/1.33 inference(avatar_split_clause,[status(thm)],[f17,f33,f23])).
% 1.62/1.33 thf(f17,plain,(
% 1.62/1.33 ((sK0 @ sK2) = $true) | ($true = (sK0 @ sK1))),
% 1.62/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.33 thf(f31,plain,(
% 1.62/1.33 ~spl3_3 | ~spl3_1),
% 1.62/1.33 inference(avatar_split_clause,[status(thm)],[f14,f19,f28])).
% 1.62/1.33 thf(f14,plain,(
% 1.62/1.33 ($true != (cD @ sK1)) | ($true != (cE @ sK2))),
% 1.62/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.33 thf(f26,plain,(
% 1.62/1.33 ~spl3_1 | spl3_2),
% 1.62/1.33 inference(avatar_split_clause,[status(thm)],[f15,f23,f19])).
% 1.62/1.33 thf(f15,plain,(
% 1.62/1.33 ($true != (cD @ sK1)) | ((sK0 @ sK2) = $true)),
% 1.62/1.33 inference(cnf_transformation,[status(thm)],[f11])).
% 1.62/1.33 % SZS output end Proof for DTF2THF_26583
% 1.62/1.33 % (26792)------------------------------
% 1.62/1.33 % (26792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.62/1.33 % (26792)Termination reason: Refutation
% 1.62/1.33
% 1.62/1.33 % (26792)Memory used [KB]: 5500
% 1.62/1.33 % (26792)Time elapsed: 0.003 s
% 1.62/1.33 % (26792)Instructions burned: 3 (million)
% 1.62/1.33 % (26792)------------------------------
% 1.62/1.33 % (26792)------------------------------
% 1.62/1.33 % (26791)Success in time 0.013 s
%------------------------------------------------------------------------------