%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO111^5 : 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 : n013.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 09:53:24 AM UTC 2026
% Result : Theorem 1.49s 1.27s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 37 ( 5 unt; 0 typ; 4 def)
% Number of atoms : 377 ( 99 equ; 0 cnn)
% Maximal formula atoms : 12 ( 10 avg)
% Number of connectives : 361 ( 104 ~; 84 |; 24 &; 134 @)
% ( 4 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 12 con; 0-2 aty)
% Number of variables : 115 ( 0 ^; 71 !; 44 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cG: $i > $o ).
thf(func_def_1,type,
cN: $i > $o ).
thf(func_def_2,type,
cM: $i > $o ).
thf(f63,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f32,f40,f57,f59,f62]) ).
thf(f62,plain,
~ spl6_1,
inference(avatar_contradiction_clause,[status(thm)],[f61]) ).
thf(f61,plain,
( $false
| ~ spl6_1 ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
( ( $true != $true )
| ~ spl6_1 ),
inference(superposition,[status(thm)],[f17,f27]) ).
thf(f27,plain,
( ! [X9: $i] :
( ( cM @ X9 )
= $true )
| ~ spl6_1 ),
inference(avatar_component_clause,[status(thm)],[f26]) ).
thf(f26,definition,
( spl6_1
<=> ! [X9: $i] :
( ( cM @ X9 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition]) ).
thf(f17,plain,
( ( cM @ sK5 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
( ! [X0: $i] :
( ( $true
!= ( cN @ X0 ) )
| ( $true
!= ( cG @ sK0 ) ) )
& ( ( ( $true
!= ( cM @ sK1 ) )
& ! [X3: $i] :
( ( cN @ X3 )
!= $true ) )
| ! [X4: $i] :
( ( cM @ X4 )
= $true )
| ( ! [X5: $i] :
( ( cG @ X5 )
= $true )
& ( ( cN @ sK2 )
= $true ) )
| ( $true
!= ( cG @ sK3 ) ) )
& ! [X8: $i] :
( ( cG @ X8 )
= $true )
& ! [X9: $i] :
( ( ( cN @ sK4 )
= $true )
| ( ( cM @ X9 )
= $true ) )
& ( ( cM @ sK5 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f15,f14,f13,f12,f11,f10]) ).
thf(f10,plain,
( ? [X1: $i] :
( ( cG @ X1 )
!= $true )
=> ( $true
!= ( cG @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X2: $i] :
( ( cM @ X2 )
!= $true )
=> ( $true
!= ( cM @ sK1 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X6: $i] :
( ( cN @ X6 )
= $true )
=> ( ( cN @ sK2 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X7: $i] :
( ( cG @ X7 )
!= $true )
=> ( $true
!= ( cG @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X10: $i] :
( $true
= ( cN @ X10 ) )
=> ( ( cN @ sK4 )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X11: $i] :
( $true
!= ( cM @ X11 ) )
=> ( ( cM @ sK5 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( $true
!= ( cN @ X0 ) )
| ? [X1: $i] :
( ( cG @ X1 )
!= $true ) )
& ( ( ? [X2: $i] :
( ( cM @ X2 )
!= $true )
& ! [X3: $i] :
( ( cN @ X3 )
!= $true ) )
| ! [X4: $i] :
( ( cM @ X4 )
= $true )
| ( ! [X5: $i] :
( ( cG @ X5 )
= $true )
& ? [X6: $i] :
( ( cN @ X6 )
= $true ) )
| ? [X7: $i] :
( ( cG @ X7 )
!= $true ) )
& ! [X8: $i] :
( ( cG @ X8 )
= $true )
& ! [X9: $i] :
( ? [X10: $i] :
( $true
= ( cN @ X10 ) )
| ( ( cM @ X9 )
= $true ) )
& ? [X11: $i] :
( $true
!= ( cM @ X11 ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X7: $i] :
( ( $true
!= ( cN @ X7 ) )
| ? [X8: $i] :
( ( cG @ X8 )
!= $true ) )
& ( ( ? [X2: $i] :
( ( cM @ X2 )
!= $true )
& ! [X3: $i] :
( ( cN @ X3 )
!= $true ) )
| ! [X5: $i] :
( $true
= ( cM @ X5 ) )
| ( ! [X1: $i] :
( ( cG @ X1 )
= $true )
& ? [X0: $i] :
( $true
= ( cN @ X0 ) ) )
| ? [X4: $i] :
( $true
!= ( cG @ X4 ) ) )
& ! [X6: $i] :
( $true
= ( cG @ X6 ) )
& ! [X10: $i] :
( ? [X11: $i] :
( $true
= ( cN @ X11 ) )
| ( $true
= ( cM @ X10 ) ) )
& ? [X9: $i] :
( ( cM @ X9 )
!= $true ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X9: $i] :
( ( cM @ X9 )
!= $true )
& ! [X7: $i] :
( ( $true
!= ( cN @ X7 ) )
| ? [X8: $i] :
( ( cG @ X8 )
!= $true ) )
& ! [X6: $i] :
( $true
= ( cG @ X6 ) )
& ! [X10: $i] :
( ? [X11: $i] :
( $true
= ( cN @ X11 ) )
| ( $true
= ( cM @ X10 ) ) )
& ( ( ? [X2: $i] :
( ( cM @ X2 )
!= $true )
& ! [X3: $i] :
( ( cN @ X3 )
!= $true ) )
| ! [X5: $i] :
( $true
= ( cM @ X5 ) )
| ( ! [X1: $i] :
( ( cG @ X1 )
= $true )
& ? [X0: $i] :
( $true
= ( cN @ X0 ) ) )
| ? [X4: $i] :
( $true
!= ( cG @ X4 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ? [X4: $i] :
( $true
!= ( cG @ X4 ) )
| ~ ( ! [X0: $i] :
( $true
!= ( cN @ X0 ) )
| ~ ! [X1: $i] :
( ( cG @ X1 )
= $true ) )
| ! [X5: $i] :
( $true
= ( cM @ X5 ) )
| ~ ( ! [X2: $i] :
( ( cM @ X2 )
= $true )
| ? [X3: $i] :
( ( cN @ X3 )
= $true ) ) )
=> ( ! [X9: $i] :
( ( cM @ X9 )
= $true )
| ~ ! [X7: $i] :
( ( $true
!= ( cN @ X7 ) )
| ~ ! [X8: $i] :
( ( cG @ X8 )
= $true ) )
| ? [X6: $i] :
( $true
!= ( cG @ X6 ) )
| ~ ! [X10: $i] :
( ? [X11: $i] :
( $true
= ( cN @ X11 ) )
| ( $true
= ( cM @ X10 ) ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ~ ( ! [X0: $i] :
( $true
!= ( cN @ X0 ) )
| ~ ! [X1: $i] :
( ( cG @ X1 )
= $true ) )
| ~ ( ! [X2: $i] :
( ( cM @ X2 )
= $true )
| ? [X3: $i] :
( ( cN @ X3 )
= $true ) )
| ? [X4: $i] :
( $true
!= ( cG @ X4 ) )
| ! [X5: $i] :
( $true
= ( cM @ X5 ) ) )
=> ( ? [X6: $i] :
( $true
!= ( cG @ X6 ) )
| ~ ! [X7: $i] :
( ~ ! [X8: $i] :
( ( cG @ X8 )
= $true )
| ( $true
!= ( cN @ X7 ) ) )
| ! [X9: $i] :
( ( cM @ X9 )
= $true )
| ~ ! [X10: $i] :
( ? [X11: $i] :
( $true
= ( cN @ X11 ) )
| ( $true
= ( cM @ X10 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ~ ( ! [X0: $i] :
~ ( cN @ X0 )
| ~ ! [X1: $i] : ( cG @ X1 ) )
| ~ ( ! [X2: $i] : ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) )
| ? [X4: $i] :
~ ( cG @ X4 )
| ! [X5: $i] : ( cM @ X5 ) )
=> ( ? [X6: $i] :
~ ( cG @ X6 )
| ~ ! [X7: $i] :
( ~ ! [X8: $i] : ( cG @ X8 )
| ~ ( cN @ X7 ) )
| ! [X9: $i] : ( cM @ X9 )
| ~ ! [X10: $i] :
( ( cM @ X10 )
| ? [X11: $i] : ( cN @ X11 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ~ ( ! [X4: $i] :
~ ( cN @ X4 )
| ~ ! [X5: $i] : ( cG @ X5 ) )
| ~ ( ! [X2: $i] : ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ! [X0: $i] : ( cM @ X0 ) )
=> ( ? [X1: $i] :
~ ( cG @ X1 )
| ~ ! [X4: $i] :
( ~ ! [X5: $i] : ( cG @ X5 )
| ~ ( cN @ X4 ) )
| ! [X0: $i] : ( cM @ X0 )
| ~ ! [X2: $i] :
( ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ~ ( ! [X4: $i] :
~ ( cN @ X4 )
| ~ ! [X5: $i] : ( cG @ X5 ) )
| ~ ( ! [X2: $i] : ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) )
| ? [X1: $i] :
~ ( cG @ X1 )
| ! [X0: $i] : ( cM @ X0 ) )
=> ( ? [X1: $i] :
~ ( cG @ X1 )
| ~ ! [X4: $i] :
( ~ ! [X5: $i] : ( cG @ X5 )
| ~ ( cN @ X4 ) )
| ! [X0: $i] : ( cM @ X0 )
| ~ ! [X2: $i] :
( ( cM @ X2 )
| ? [X3: $i] : ( cN @ X3 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2C6nSZ2Aqe/DTF2THF_23713.p',cTHM80) ).
thf(f59,plain,
spl6_3,
inference(avatar_contradiction_clause,[status(thm)],[f58]) ).
thf(f58,plain,
( $false
| spl6_3 ),
inference(subsumption_resolution,[status(thm)],[f36,f19]) ).
thf(f19,plain,
! [X8: $i] :
( ( cG @ X8 )
= $true ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f36,plain,
( ( $true
!= ( cG @ sK0 ) )
| spl6_3 ),
inference(avatar_component_clause,[status(thm)],[f34]) ).
thf(f34,definition,
( spl6_3
<=> ( $true
= ( cG @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition]) ).
thf(f57,plain,
( ~ spl6_2
| ~ spl6_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f56]) ).
thf(f56,plain,
( $false
| ~ spl6_2
| ~ spl6_4 ),
inference(subsumption_resolution,[status(thm)],[f31,f39]) ).
thf(f39,plain,
( ! [X0: $i] :
( $true
!= ( cN @ X0 ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[status(thm)],[f38]) ).
thf(f38,definition,
( spl6_4
<=> ! [X0: $i] :
( $true
!= ( cN @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition]) ).
thf(f31,plain,
( ( ( cN @ sK4 )
= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[status(thm)],[f29]) ).
thf(f29,definition,
( spl6_2
<=> ( ( cN @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition]) ).
thf(f40,plain,
( ~ spl6_3
| spl6_4 ),
inference(avatar_split_clause,[status(thm)],[f24,f38,f34]) ).
thf(f24,plain,
! [X0: $i] :
( ( $true
!= ( cG @ sK0 ) )
| ( $true
!= ( cN @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
thf(f32,plain,
( spl6_1
| spl6_2 ),
inference(avatar_split_clause,[status(thm)],[f18,f29,f26]) ).
thf(f18,plain,
! [X9: $i] :
( ( ( cM @ X9 )
= $true )
| ( ( cN @ sK4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO111^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n013.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 14:24:23 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SYO111^5 : TPTP v9.2.1. Released v4.0.0.
% 0.29/0.45 % Domain : Syntactic
% 0.29/0.45 % Problem : TPS problem THM80
% 0.29/0.45 % Version : Especial.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.29/0.45 % Source : [Bro09]
% 0.29/0.45 % Names : tps_0465 [Bro09]
% 0.29/0.45 % : tps_1015 [Bro09]
% 0.29/0.45 % : THM80 [TPS]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 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 v6.0.0, 0.00 v4.0.0
% 0.29/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.29/0.45 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 12 ( 12 avg)
% 0.29/0.45 % Number of connectives : 33 ( 10 ~; 10 |; 0 &; 12 @)
% 0.29/0.45 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 11 ( 11 avg)
% 0.29/0.45 % Number of types : 2 ( 0 usr)
% 0.29/0.45 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-1 aty)
% 0.29/0.45 % Number of variables : 12 ( 0 ^; 8 !; 4 ?; 12 :)
% 0.29/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.29/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.29/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.29/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(cG,type,
% 0.29/0.45 cG: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cN,type,
% 0.29/0.45 cN: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cM,type,
% 0.29/0.45 cM: $i > $o ).
% 0.29/0.45
% 0.29/0.45 thf(cTHM80,conjecture,
% 0.29/0.45 ( ( ! [R: $i] : ( cM @ R )
% 0.29/0.45 | ? [X: $i] :
% 0.29/0.45 ~ ( cG @ X )
% 0.29/0.45 | ~ ( ! [Y: $i] : ( cM @ Y )
% 0.29/0.45 | ? [S: $i] : ( cN @ S ) )
% 0.29/0.45 | ~ ( ! [Z: $i] :
% 0.29/0.45 ~ ( cN @ Z )
% 0.29/0.45 | ~ ! [T: $i] : ( cG @ T ) ) )
% 0.29/0.45 => ( ! [R: $i] : ( cM @ R )
% 0.29/0.45 | ? [X: $i] :
% 0.29/0.45 ~ ( cG @ X )
% 0.29/0.45 | ~ ! [Y: $i] :
% 0.29/0.45 ( ( cM @ Y )
% 0.29/0.45 | ? [S: $i] : ( cN @ S ) )
% 0.29/0.45 | ~ ! [Z: $i] :
% 0.29/0.45 ( ~ ( cN @ Z )
% 0.29/0.45 | ~ ! [T: $i] : ( cG @ T ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 1.49/1.24 ---- Embedded in THF ---
% 1.49/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.24 %%% Generated on Tue Feb 24 14:24:24 EST 2026
% 1.49/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.24 %%% Logic specification used:
% 1.49/1.24 %%% thf(spec, logic, $$dhol).
% 1.49/1.24
% 1.49/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2C6nSZ2Aqe/DTF2DTF23713.p
% See solution above
% 1.49/1.24 ------------------------
% 1.49/1.25 ---- Cleaned THF ---
% 1.49/1.25 thf(cG,type,
% 1.49/1.25 cG: $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(cN,type,
% 1.49/1.25 cN: $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(cM,type,
% 1.49/1.25 cM: $i > $o ).
% 1.49/1.25
% 1.49/1.25 thf(cTHM80,conjecture,
% 1.49/1.25 ( ( ! [R: $i] : ( cM @ R )
% 1.49/1.25 | ? [X: $i] :
% 1.49/1.25 ~ ( cG @ X )
% 1.49/1.25 | ~ ( ! [Y: $i] : ( cM @ Y )
% 1.49/1.25 | ? [S: $i] : ( cN @ S ) )
% 1.49/1.25 | ~ ( ! [Z: $i] :
% 1.49/1.25 ~ ( cN @ Z )
% 1.49/1.25 | ~ ! [T: $i] : ( cG @ T ) ) )
% 1.49/1.25 => ( ! [R: $i] : ( cM @ R )
% 1.49/1.25 | ? [X: $i] :
% 1.49/1.25 ~ ( cG @ X )
% 1.49/1.25 | ~ ! [Y: $i] :
% 1.49/1.25 ( ( cM @ Y )
% 1.49/1.25 | ? [S: $i] : ( cN @ S ) )
% 1.49/1.25 | ~ ! [Z: $i] :
% 1.49/1.25 ( ~ ( cN @ Z )
% 1.49/1.25 | ~ ! [T: $i] : ( cG @ T ) ) ) ) ).
% 1.49/1.25 ------------------------
% 1.49/1.26 % (23816)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23713 for (3000ds/18Mi)
% 1.49/1.26 % (23815)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_23713 for (3000ds/275Mi)
% 1.49/1.26 % (23816)First to succeed.
% 1.49/1.26 % (23815)Also succeeded, but the first one will report.
% 1.49/1.27 % (23816)Refutation found. Thanks to Tanya!
% 1.49/1.27 % SZS status Theorem for DTF2THF_23713
% 1.49/1.27 % SZS output start Proof for DTF2THF_23713
% 1.49/1.27 thf(func_def_0, type, cG: $i > $o).
% 1.49/1.27 thf(func_def_1, type, cN: $i > $o).
% 1.49/1.27 thf(func_def_2, type, cM: $i > $o).
% 1.49/1.27 thf(f63,plain,(
% 1.49/1.27 $false),
% 1.49/1.27 inference(avatar_sat_refutation,[status(thm)],[f32,f40,f57,f59,f62])).
% 1.49/1.27 thf(f62,plain,(
% 1.49/1.27 ~spl6_1),
% 1.49/1.27 inference(avatar_contradiction_clause,[status(thm)],[f61])).
% 1.49/1.27 thf(f61,plain,(
% 1.49/1.27 $false | ~spl6_1),
% 1.49/1.27 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.49/1.27 thf(f60,plain,(
% 1.49/1.27 ($true != $true) | ~spl6_1),
% 1.49/1.27 inference(superposition,[status(thm)],[f17,f27])).
% 1.49/1.27 thf(f27,plain,(
% 1.49/1.27 ( ! [X9 : $i] : (((cM @ X9) = $true)) ) | ~spl6_1),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f26])).
% 1.49/1.27 thf(f26,definition,(
% 1.49/1.27 spl6_1 <=> ! [X9 : $i] : ((cM @ X9) = $true)),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl6_1])],[avatar_definition])).
% 1.49/1.27 thf(f17,plain,(
% 1.49/1.27 ((cM @ sK5) != $true)),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f16])).
% 1.49/1.27 thf(f16,plain,(
% 1.49/1.27 ! [X0 : $i] : (($true != (cN @ X0)) | ($true != (cG @ sK0))) & ((($true != (cM @ sK1)) & ! [X3 : $i] : ((cN @ X3) != $true)) | ! [X4 : $i] : ((cM @ X4) = $true) | (! [X5 : $i] : ((cG @ X5) = $true) & ((cN @ sK2) = $true)) | ($true != (cG @ sK3))) & ! [X8 : $i] : ((cG @ X8) = $true) & ! [X9 : $i] : (((cN @ sK4) = $true) | ((cM @ X9) = $true)) & ((cM @ sK5) != $true)),
% 1.49/1.27 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f9,f15,f14,f13,f12,f11,f10])).
% 1.49/1.27 thf(f10,plain,(
% 1.49/1.27 ? [X1 : $i] : ((cG @ X1) != $true) => ($true != (cG @ sK0))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f11,plain,(
% 1.49/1.27 ? [X2 : $i] : ((cM @ X2) != $true) => ($true != (cM @ sK1))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f12,plain,(
% 1.49/1.27 ? [X6 : $i] : ((cN @ X6) = $true) => ((cN @ sK2) = $true)),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f13,plain,(
% 1.49/1.27 ? [X7 : $i] : ((cG @ X7) != $true) => ($true != (cG @ sK3))),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f14,plain,(
% 1.49/1.27 ? [X10 : $i] : ($true = (cN @ X10)) => ((cN @ sK4) = $true)),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f15,plain,(
% 1.49/1.27 ? [X11 : $i] : ($true != (cM @ X11)) => ((cM @ sK5) != $true)),
% 1.49/1.27 introduced(definition,[],[choice_axiom])).
% 1.49/1.27 thf(f9,plain,(
% 1.49/1.27 ! [X0 : $i] : (($true != (cN @ X0)) | ? [X1 : $i] : ((cG @ X1) != $true)) & ((? [X2 : $i] : ((cM @ X2) != $true) & ! [X3 : $i] : ((cN @ X3) != $true)) | ! [X4 : $i] : ((cM @ X4) = $true) | (! [X5 : $i] : ((cG @ X5) = $true) & ? [X6 : $i] : ((cN @ X6) = $true)) | ? [X7 : $i] : ((cG @ X7) != $true)) & ! [X8 : $i] : ((cG @ X8) = $true) & ! [X9 : $i] : (? [X10 : $i] : ($true = (cN @ X10)) | ((cM @ X9) = $true)) & ? [X11 : $i] : ($true != (cM @ X11))),
% 1.49/1.27 inference(rectify,[status(thm)],[f8])).
% 1.49/1.27 thf(f8,plain,(
% 1.49/1.27 ! [X7 : $i] : (($true != (cN @ X7)) | ? [X8 : $i] : ((cG @ X8) != $true)) & ((? [X2 : $i] : ((cM @ X2) != $true) & ! [X3 : $i] : ((cN @ X3) != $true)) | ! [X5 : $i] : ($true = (cM @ X5)) | (! [X1 : $i] : ((cG @ X1) = $true) & ? [X0 : $i] : ($true = (cN @ X0))) | ? [X4 : $i] : ($true != (cG @ X4))) & ! [X6 : $i] : ($true = (cG @ X6)) & ! [X10 : $i] : (? [X11 : $i] : ($true = (cN @ X11)) | ($true = (cM @ X10))) & ? [X9 : $i] : ((cM @ X9) != $true)),
% 1.49/1.27 inference(flattening,[status(thm)],[f7])).
% 1.49/1.27 thf(f7,plain,(
% 1.49/1.27 (? [X9 : $i] : ((cM @ X9) != $true) & ! [X7 : $i] : (($true != (cN @ X7)) | ? [X8 : $i] : ((cG @ X8) != $true)) & ! [X6 : $i] : ($true = (cG @ X6)) & ! [X10 : $i] : (? [X11 : $i] : ($true = (cN @ X11)) | ($true = (cM @ X10)))) & ((? [X2 : $i] : ((cM @ X2) != $true) & ! [X3 : $i] : ((cN @ X3) != $true)) | ! [X5 : $i] : ($true = (cM @ X5)) | (! [X1 : $i] : ((cG @ X1) = $true) & ? [X0 : $i] : ($true = (cN @ X0))) | ? [X4 : $i] : ($true != (cG @ X4)))),
% 1.49/1.27 inference(ennf_transformation,[status(thm)],[f6])).
% 1.49/1.27 thf(f6,plain,(
% 1.49/1.27 ~((? [X4 : $i] : ($true != (cG @ X4)) | ~(! [X0 : $i] : ($true != (cN @ X0)) | ~! [X1 : $i] : ((cG @ X1) = $true)) | ! [X5 : $i] : ($true = (cM @ X5)) | ~(! [X2 : $i] : ((cM @ X2) = $true) | ? [X3 : $i] : ((cN @ X3) = $true))) => (! [X9 : $i] : ((cM @ X9) = $true) | ~! [X7 : $i] : (($true != (cN @ X7)) | ~! [X8 : $i] : ((cG @ X8) = $true)) | ? [X6 : $i] : ($true != (cG @ X6)) | ~! [X10 : $i] : (? [X11 : $i] : ($true = (cN @ X11)) | ($true = (cM @ X10)))))),
% 1.49/1.27 inference(flattening,[status(thm)],[f5])).
% 1.49/1.27 thf(f5,plain,(
% 1.49/1.27 ~((~(! [X0 : $i] : ~($true = (cN @ X0)) | ~! [X1 : $i] : ((cG @ X1) = $true)) | ~(! [X2 : $i] : ((cM @ X2) = $true) | ? [X3 : $i] : ((cN @ X3) = $true)) | ? [X4 : $i] : ~($true = (cG @ X4)) | ! [X5 : $i] : ($true = (cM @ X5))) => (? [X6 : $i] : ~($true = (cG @ X6)) | ~! [X7 : $i] : (~! [X8 : $i] : ((cG @ X8) = $true) | ~($true = (cN @ X7))) | ! [X9 : $i] : ((cM @ X9) = $true) | ~! [X10 : $i] : (? [X11 : $i] : ($true = (cN @ X11)) | ($true = (cM @ X10)))))),
% 1.49/1.27 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.27 thf(f4,plain,(
% 1.49/1.27 ~((~(! [X0 : $i] : ~(cN @ X0) | ~! [X1 : $i] : (cG @ X1)) | ~(! [X2 : $i] : (cM @ X2) | ? [X3 : $i] : (cN @ X3)) | ? [X4 : $i] : ~(cG @ X4) | ! [X5 : $i] : (cM @ X5)) => (? [X6 : $i] : ~(cG @ X6) | ~! [X7 : $i] : (~! [X8 : $i] : (cG @ X8) | ~(cN @ X7)) | ! [X9 : $i] : (cM @ X9) | ~! [X10 : $i] : ((cM @ X10) | ? [X11 : $i] : (cN @ X11))))),
% 1.49/1.27 inference(rectify,[status(thm)],[f2])).
% 1.49/1.27 thf(f2,negated_conjecture,(
% 1.49/1.27 ~((~(! [X4 : $i] : ~(cN @ X4) | ~! [X5 : $i] : (cG @ X5)) | ~(! [X2 : $i] : (cM @ X2) | ? [X3 : $i] : (cN @ X3)) | ? [X1 : $i] : ~(cG @ X1) | ! [X0 : $i] : (cM @ X0)) => (? [X1 : $i] : ~(cG @ X1) | ~! [X4 : $i] : (~! [X5 : $i] : (cG @ X5) | ~(cN @ X4)) | ! [X0 : $i] : (cM @ X0) | ~! [X2 : $i] : ((cM @ X2) | ? [X3 : $i] : (cN @ X3))))),
% 1.49/1.27 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.27 thf(f1,conjecture,(
% 1.49/1.27 (~(! [X4 : $i] : ~(cN @ X4) | ~! [X5 : $i] : (cG @ X5)) | ~(! [X2 : $i] : (cM @ X2) | ? [X3 : $i] : (cN @ X3)) | ? [X1 : $i] : ~(cG @ X1) | ! [X0 : $i] : (cM @ X0)) => (? [X1 : $i] : ~(cG @ X1) | ~! [X4 : $i] : (~! [X5 : $i] : (cG @ X5) | ~(cN @ X4)) | ! [X0 : $i] : (cM @ X0) | ~! [X2 : $i] : ((cM @ X2) | ? [X3 : $i] : (cN @ X3)))),
% 1.49/1.27 file('/export/starexec/sandbox2/tmp/tmp.2C6nSZ2Aqe/DTF2THF_23713.p',cTHM80)).
% 1.49/1.27 thf(f59,plain,(
% 1.49/1.27 spl6_3),
% 1.49/1.27 inference(avatar_contradiction_clause,[status(thm)],[f58])).
% 1.49/1.27 thf(f58,plain,(
% 1.49/1.27 $false | spl6_3),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f36,f19])).
% 1.49/1.27 thf(f19,plain,(
% 1.49/1.27 ( ! [X8 : $i] : (((cG @ X8) = $true)) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f16])).
% 1.49/1.27 thf(f36,plain,(
% 1.49/1.27 ($true != (cG @ sK0)) | spl6_3),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f34])).
% 1.49/1.27 thf(f34,definition,(
% 1.49/1.27 spl6_3 <=> ($true = (cG @ sK0))),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl6_3])],[avatar_definition])).
% 1.49/1.27 thf(f57,plain,(
% 1.49/1.27 ~spl6_2 | ~spl6_4),
% 1.49/1.27 inference(avatar_contradiction_clause,[status(thm)],[f56])).
% 1.49/1.27 thf(f56,plain,(
% 1.49/1.27 $false | (~spl6_2 | ~spl6_4)),
% 1.49/1.27 inference(subsumption_resolution,[status(thm)],[f31,f39])).
% 1.49/1.27 thf(f39,plain,(
% 1.49/1.27 ( ! [X0 : $i] : (($true != (cN @ X0))) ) | ~spl6_4),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f38])).
% 1.49/1.27 thf(f38,definition,(
% 1.49/1.27 spl6_4 <=> ! [X0 : $i] : ($true != (cN @ X0))),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl6_4])],[avatar_definition])).
% 1.49/1.27 thf(f31,plain,(
% 1.49/1.27 ((cN @ sK4) = $true) | ~spl6_2),
% 1.49/1.27 inference(avatar_component_clause,[status(thm)],[f29])).
% 1.49/1.27 thf(f29,definition,(
% 1.49/1.27 spl6_2 <=> ((cN @ sK4) = $true)),
% 1.49/1.27 introduced(definition,[new_symbols(naming,[spl6_2])],[avatar_definition])).
% 1.49/1.27 thf(f40,plain,(
% 1.49/1.27 ~spl6_3 | spl6_4),
% 1.49/1.27 inference(avatar_split_clause,[status(thm)],[f24,f38,f34])).
% 1.49/1.27 thf(f24,plain,(
% 1.49/1.27 ( ! [X0 : $i] : (($true != (cG @ sK0)) | ($true != (cN @ X0))) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f16])).
% 1.49/1.27 thf(f32,plain,(
% 1.49/1.27 spl6_1 | spl6_2),
% 1.49/1.27 inference(avatar_split_clause,[status(thm)],[f18,f29,f26])).
% 1.49/1.27 thf(f18,plain,(
% 1.49/1.27 ( ! [X9 : $i] : (((cM @ X9) = $true) | ((cN @ sK4) = $true)) )),
% 1.49/1.27 inference(cnf_transformation,[status(thm)],[f16])).
% 1.49/1.27 % SZS output end Proof for DTF2THF_23713
% 1.49/1.27 % (23816)------------------------------
% 1.49/1.27 % (23816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.27 % (23816)Termination reason: Refutation
% 1.49/1.27
% 1.49/1.27 % (23816)Memory used [KB]: 5500
% 1.49/1.27 % (23816)Time elapsed: 0.003 s
% 1.49/1.27 % (23816)Instructions burned: 4 (million)
% 1.49/1.27 % (23816)------------------------------
% 1.49/1.27 % (23816)------------------------------
% 1.49/1.27 % (23809)Success in time 0.003 s
%------------------------------------------------------------------------------