%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN058^5 : 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 : n028.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 09:50:27 AM UTC 2026
% Result : Theorem 1.57s 1.34s
% Output : Refutation 1.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 6 unt; 0 typ; 6 def)
% Number of atoms : 415 ( 104 equ; 0 cnn)
% Maximal formula atoms : 12 ( 9 avg)
% Number of connectives : 345 ( 73 ~; 51 |; 52 &; 136 @)
% ( 6 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 68 ( 0 ^; 48 !; 20 ?; 68 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cG: $i > $o ).
thf(func_def_1,type,
cF: $i > $o ).
thf(func_def_2,type,
cP: $i > $o ).
thf(func_def_3,type,
cS: $i > $o ).
thf(func_def_4,type,
cQ: $i > $o ).
thf(func_def_5,type,
cR: $i > $o ).
thf(f69,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f37,f53,f54,f58,f61,f65,f68]) ).
thf(f68,plain,
( ~ spl3_4
| ~ spl3_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f67]) ).
thf(f67,plain,
( $false
| ~ spl3_4
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f66]) ).
thf(f66,plain,
( ( $true != $true )
| ~ spl3_4
| ~ spl3_5 ),
inference(superposition,[status(thm)],[f36,f41]) ).
thf(f41,plain,
( ( $true
= ( cS @ sK1 ) )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl3_5
<=> ( $true
= ( cS @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f36,plain,
( ! [X0: $i] :
( ( cS @ X0 )
!= $true )
| ~ spl3_4 ),
inference(avatar_component_clause,[status(thm)],[f35]) ).
thf(f35,definition,
( spl3_4
<=> ! [X0: $i] :
( ( cS @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f65,plain,
~ spl3_3,
inference(avatar_contradiction_clause,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
| ~ spl3_3 ),
inference(subsumption_resolution,[status(thm)],[f63,f13]) ).
thf(f13,plain,
( $true
= ( cF @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ! [X0: $i] :
( ( cS @ X0 )
!= $true )
| ! [X1: $i] :
( ( $true
!= ( cF @ X1 ) )
| ( $true
= ( cG @ X1 ) ) ) )
& ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ! [X3: $i] :
( $true
= ( cQ @ X3 ) ) )
& ( ( ( ( cR @ sK0 )
!= $true )
& ( $true
!= ( cQ @ sK0 ) ) )
| ( ( $true
= ( cS @ sK1 ) )
& ( $true
= ( cQ @ sK1 ) ) ) )
& ( $true
= ( cP @ sK2 ) )
& ( $true
!= ( cG @ sK2 ) )
& ( $true
= ( cF @ sK2 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9]) ).
thf(f9,plain,
( ? [X4: $i] :
( ( $true
!= ( cR @ X4 ) )
& ( $true
!= ( cQ @ X4 ) ) )
=> ( ( ( cR @ sK0 )
!= $true )
& ( $true
!= ( cQ @ sK0 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X5: $i] :
( ( $true
= ( cS @ X5 ) )
& ( $true
= ( cQ @ X5 ) ) )
=> ( ( $true
= ( cS @ sK1 ) )
& ( $true
= ( cQ @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: $i] :
( ( ( cP @ X6 )
= $true )
& ( $true
!= ( cG @ X6 ) )
& ( $true
= ( cF @ X6 ) ) )
=> ( ( $true
= ( cP @ sK2 ) )
& ( $true
!= ( cG @ sK2 ) )
& ( $true
= ( cF @ sK2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ( ! [X0: $i] :
( ( cS @ X0 )
!= $true )
| ! [X1: $i] :
( ( $true
!= ( cF @ X1 ) )
| ( $true
= ( cG @ X1 ) ) ) )
& ! [X2: $i] :
( ( $true
!= ( cP @ X2 ) )
| ! [X3: $i] :
( $true
= ( cQ @ X3 ) ) )
& ( ? [X4: $i] :
( ( $true
!= ( cR @ X4 ) )
& ( $true
!= ( cQ @ X4 ) ) )
| ? [X5: $i] :
( ( $true
= ( cS @ X5 ) )
& ( $true
= ( cQ @ X5 ) ) ) )
& ? [X6: $i] :
( ( ( cP @ X6 )
= $true )
& ( $true
!= ( cG @ X6 ) )
& ( $true
= ( cF @ X6 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ! [X2: $i] :
( $true
!= ( cS @ X2 ) )
| ! [X3: $i] :
( ( $true
!= ( cF @ X3 ) )
| ( $true
= ( cG @ X3 ) ) ) )
& ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ! [X1: $i] :
( ( cQ @ X1 )
= $true ) )
& ( ? [X4: $i] :
( ( $true
!= ( cR @ X4 ) )
& ( $true
!= ( cQ @ X4 ) ) )
| ? [X5: $i] :
( ( $true
= ( cS @ X5 ) )
& ( $true
= ( cQ @ X5 ) ) ) )
& ? [X6: $i] :
( ( ( cP @ X6 )
= $true )
& ( $true
!= ( cG @ X6 ) )
& ( $true
= ( cF @ X6 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X6: $i] :
( ( $true
!= ( cG @ X6 ) )
& ( $true
= ( cF @ X6 ) )
& ( ( cP @ X6 )
= $true ) )
& ! [X0: $i] :
( ( ( cP @ X0 )
!= $true )
| ! [X1: $i] :
( ( cQ @ X1 )
= $true ) )
& ( ? [X4: $i] :
( ( $true
!= ( cR @ X4 ) )
& ( $true
!= ( cQ @ X4 ) ) )
| ? [X5: $i] :
( ( $true
= ( cS @ X5 ) )
& ( $true
= ( cQ @ X5 ) ) ) )
& ( ! [X2: $i] :
( $true
!= ( cS @ X2 ) )
| ! [X3: $i] :
( ( $true
!= ( cF @ X3 ) )
| ( $true
= ( cG @ X3 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
=> ! [X1: $i] :
( ( cQ @ X1 )
= $true ) )
& ( ! [X4: $i] :
( ( $true
= ( cQ @ X4 ) )
| ( $true
= ( cR @ X4 ) ) )
=> ? [X5: $i] :
( ( $true
= ( cS @ X5 ) )
& ( $true
= ( cQ @ X5 ) ) ) )
& ( ? [X2: $i] :
( $true
= ( cS @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( cF @ X3 ) )
=> ( $true
= ( cG @ X3 ) ) ) ) )
=> ! [X6: $i] :
( ( ( $true
= ( cF @ X6 ) )
& ( ( cP @ X6 )
= $true ) )
=> ( $true
= ( cG @ X6 ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ! [X1: $i] : ( cQ @ X1 ) )
& ( ? [X2: $i] : ( cS @ X2 )
=> ! [X3: $i] :
( ( cF @ X3 )
=> ( cG @ X3 ) ) )
& ( ! [X4: $i] :
( ( cQ @ X4 )
| ( cR @ X4 ) )
=> ? [X5: $i] :
( ( cS @ X5 )
& ( cQ @ X5 ) ) ) )
=> ! [X6: $i] :
( ( ( cP @ X6 )
& ( cF @ X6 ) )
=> ( cG @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( cP @ X0 )
=> ! [X1: $i] : ( cQ @ X1 ) )
& ( ? [X0: $i] : ( cS @ X0 )
=> ! [X0: $i] :
( ( cF @ X0 )
=> ( cG @ X0 ) ) )
& ( ! [X0: $i] :
( ( cQ @ X0 )
| ( cR @ X0 ) )
=> ? [X0: $i] :
( ( cS @ X0 )
& ( cQ @ X0 ) ) ) )
=> ! [X0: $i] :
( ( ( cP @ X0 )
& ( cF @ X0 ) )
=> ( cG @ X0 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: $i] :
( ( cP @ X0 )
=> ! [X1: $i] : ( cQ @ X1 ) )
& ( ? [X0: $i] : ( cS @ X0 )
=> ! [X0: $i] :
( ( cF @ X0 )
=> ( cG @ X0 ) ) )
& ( ! [X0: $i] :
( ( cQ @ X0 )
| ( cR @ X0 ) )
=> ? [X0: $i] :
( ( cS @ X0 )
& ( cQ @ X0 ) ) ) )
=> ! [X0: $i] :
( ( ( cP @ X0 )
& ( cF @ X0 ) )
=> ( cG @ X0 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.2G69Ux8i4O/DTF2THF_9342.p',cPELL28) ).
thf(f63,plain,
( ( $true
!= ( cF @ sK2 ) )
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
( ( $true
!= ( cF @ sK2 ) )
| ( $true != $true )
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f14,f33]) ).
thf(f33,plain,
( ! [X1: $i] :
( ( $true
= ( cG @ X1 ) )
| ( $true
!= ( cF @ X1 ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f32,definition,
( spl3_3
<=> ! [X1: $i] :
( ( $true
!= ( cF @ X1 ) )
| ( $true
= ( cG @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f14,plain,
( $true
!= ( cG @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f61,plain,
( spl3_1
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f60]) ).
thf(f60,plain,
( $false
| spl3_1
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
( ( $true != $true )
| spl3_1
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f25,f52]) ).
thf(f52,plain,
( ! [X3: $i] :
( $true
= ( cQ @ X3 ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl3_8
<=> ! [X3: $i] :
( $true
= ( cQ @ X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f25,plain,
( ( $true
!= ( cQ @ sK0 ) )
| spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f23]) ).
thf(f23,definition,
( spl3_1
<=> ( $true
= ( cQ @ sK0 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f58,plain,
~ spl3_7,
inference(avatar_contradiction_clause,[status(thm)],[f57]) ).
thf(f57,plain,
( $false
| ~ spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f56]) ).
thf(f56,plain,
( ( $true != $true )
| ~ spl3_7 ),
inference(superposition,[status(thm)],[f49,f15]) ).
thf(f15,plain,
( $true
= ( cP @ sK2 ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f49,plain,
( ! [X2: $i] :
( $true
!= ( cP @ X2 ) )
| ~ spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl3_7
<=> ! [X2: $i] :
( $true
!= ( cP @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f54,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f17,f39,f23]) ).
thf(f17,plain,
( ( $true
!= ( cQ @ sK0 ) )
| ( $true
= ( cS @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f53,plain,
( spl3_7
| spl3_8 ),
inference(avatar_split_clause,[status(thm)],[f20,f51,f48]) ).
thf(f20,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( cQ @ X3 ) )
| ( $true
!= ( cP @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f37,plain,
( spl3_3
| spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f21,f35,f32]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cF @ X1 ) )
| ( $true
= ( cG @ X1 ) )
| ( ( cS @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN058^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n028.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 13:50:42 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.39 ---- Original DTF file ---
% 0.18/0.39 thf(spec,logic,$$dhol).
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 % File : SYN058^5 : TPTP v9.2.1. Released v4.0.0.
% 0.18/0.39 % Domain : Syntactic
% 0.18/0.39 % Problem : TPS problem PELL28
% 0.18/0.39 % Version : Especial.
% 0.18/0.39 % English :
% 0.18/0.39
% 0.18/0.39 % Refs : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au
% 0.18/0.39 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.18/0.39 % Source : [Bro09]
% 0.18/0.39 % Names : tps_0271 [Bro09]
% 0.18/0.39 % : PELL28 [TPS]
% 0.18/0.39 % : Pelletier 28 [Pel86]
% 0.18/0.39
% 0.18/0.39 % Status : Theorem
% 0.18/0.39 % Rating : 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.18/0.39 % Syntax : Number of formulae : 7 ( 0 unt; 6 typ; 0 def)
% 0.18/0.39 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.18/0.39 % Maximal formula atoms : 12 ( 12 avg)
% 0.18/0.39 % Number of connectives : 23 ( 0 ~; 1 |; 4 &; 12 @)
% 0.18/0.39 % ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% 0.18/0.39 % Maximal formula depth : 8 ( 8 avg)
% 0.18/0.39 % Number of types : 2 ( 0 usr)
% 0.18/0.39 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.18/0.39 % Number of symbols : 6 ( 6 usr; 0 con; 1-1 aty)
% 0.18/0.39 % Number of variables : 7 ( 0 ^; 5 !; 2 ?; 7 :)
% 0.18/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.18/0.39
% 0.18/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.18/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.18/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.18/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.18/0.39 % :
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 thf(cG,type,
% 0.18/0.39 cG: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cF,type,
% 0.18/0.39 cF: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cP,type,
% 0.18/0.39 cP: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cS,type,
% 0.18/0.39 cS: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cQ,type,
% 0.18/0.39 cQ: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cR,type,
% 0.18/0.39 cR: $i > $o ).
% 0.18/0.39
% 0.18/0.39 thf(cPELL28,conjecture,
% 0.18/0.39 ( ( ! [Xx: $i] :
% 0.18/0.39 ( ( cP @ Xx )
% 0.18/0.39 => ! [Xx0: $i] : ( cQ @ Xx0 ) )
% 0.18/0.39 & ( ! [Xx: $i] :
% 0.18/0.39 ( ( cQ @ Xx )
% 0.18/0.39 | ( cR @ Xx ) )
% 0.18/0.39 => ? [Xx: $i] :
% 0.18/0.39 ( ( cQ @ Xx )
% 0.18/0.39 & ( cS @ Xx ) ) )
% 0.18/0.39 & ( ? [Xx: $i] : ( cS @ Xx )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( cF @ Xx )
% 0.18/0.39 => ( cG @ Xx ) ) ) )
% 0.18/0.39 => ! [Xx: $i] :
% 0.18/0.39 ( ( ( cP @ Xx )
% 0.18/0.39 & ( cF @ Xx ) )
% 0.18/0.39 => ( cG @ Xx ) ) ) ).
% 0.18/0.39
% 0.18/0.39 %------------------------------------------------------------------------------
% 0.18/0.39 ------------------------
% 1.57/1.30 ---- Embedded in THF ---
% 1.57/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.57/1.31 %%% Generated on Tue Feb 24 13:50:43 EST 2026
% 1.57/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.57/1.31 %%% Logic specification used:
% 1.57/1.31 %%% thf(spec, logic, $$dhol).
% 1.57/1.31
% 1.57/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.2G69Ux8i4O/DTF2DTF9342.p
% See solution above
% 1.57/1.31 ------------------------
% 1.57/1.31 ---- Cleaned THF ---
% 1.57/1.32 thf(cG,type,
% 1.57/1.32 cG: $i > $o ).
% 1.57/1.32
% 1.57/1.32 thf(cF,type,
% 1.57/1.32 cF: $i > $o ).
% 1.57/1.32
% 1.57/1.32 thf(cP,type,
% 1.57/1.32 cP: $i > $o ).
% 1.57/1.32
% 1.57/1.32 thf(cS,type,
% 1.57/1.32 cS: $i > $o ).
% 1.57/1.32
% 1.57/1.32 thf(cQ,type,
% 1.57/1.32 cQ: $i > $o ).
% 1.57/1.32
% 1.57/1.32 thf(cR,type,
% 1.57/1.32 cR: $i > $o ).
% 1.57/1.32
% 1.57/1.32 thf(cPELL28,conjecture,
% 1.57/1.32 ( ( ! [Xx: $i] :
% 1.57/1.32 ( ( cP @ Xx )
% 1.57/1.32 => ! [Xx0: $i] : ( cQ @ Xx0 ) )
% 1.57/1.32 & ( ! [Xx: $i] :
% 1.57/1.32 ( ( cQ @ Xx )
% 1.57/1.32 | ( cR @ Xx ) )
% 1.57/1.32 => ? [Xx: $i] :
% 1.57/1.32 ( ( cQ @ Xx )
% 1.57/1.32 & ( cS @ Xx ) ) )
% 1.57/1.32 & ( ? [Xx: $i] : ( cS @ Xx )
% 1.57/1.32 => ! [Xx: $i] :
% 1.57/1.32 ( ( cF @ Xx )
% 1.57/1.32 => ( cG @ Xx ) ) ) )
% 1.57/1.32 => ! [Xx: $i] :
% 1.57/1.32 ( ( ( cP @ Xx )
% 1.57/1.32 & ( cF @ Xx ) )
% 1.57/1.32 => ( cG @ Xx ) ) ) ).
% 1.57/1.32 ------------------------
% 1.57/1.34 % (9444)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_9342 for (2999ds/275Mi)
% 1.57/1.34 % (9443)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_9342 for (2999ds/2Mi)
% 1.57/1.34 % (9445)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9342 for (2999ds/18Mi)
% 1.57/1.34 % (9442)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9342 for (2999ds/2Mi)
% 1.57/1.34 % (9440)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_9342 for (2999ds/4Mi)
% 1.57/1.34 % (9439)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9342 for (2999ds/183Mi)
% 1.57/1.34 % (9441)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_9342 for (2999ds/27Mi)
% 1.57/1.34 % (9442)Instruction limit reached!
% 1.57/1.34 % (9442)------------------------------
% 1.57/1.34 % (9442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (9442)Termination reason: Unknown
% 1.57/1.34 % (9442)Termination phase: Saturation
% 1.57/1.34 % (9443)Instruction limit reached!
% 1.57/1.34 % (9443)------------------------------
% 1.57/1.34 % (9443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (9443)Termination reason: Unknown
% 1.57/1.34 % (9443)Termination phase: Saturation
% 1.57/1.34
% 1.57/1.34 % (9443)Memory used [KB]: 5500
% 1.57/1.34 % (9443)Time elapsed: 0.003 s
% 1.57/1.34 % (9443)Instructions burned: 2 (million)
% 1.57/1.34 % (9443)------------------------------
% 1.57/1.34 % (9443)------------------------------
% 1.57/1.34
% 1.57/1.34 % (9442)Memory used [KB]: 5500
% 1.57/1.34 % (9442)Time elapsed: 0.003 s
% 1.57/1.34 % (9442)Instructions burned: 2 (million)
% 1.57/1.34 % (9442)------------------------------
% 1.57/1.34 % (9442)------------------------------
% 1.57/1.34 % (9444)First to succeed.
% 1.57/1.34 % (9440)Instruction limit reached!
% 1.57/1.34 % (9440)------------------------------
% 1.57/1.34 % (9440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (9440)Termination reason: Unknown
% 1.57/1.34 % (9440)Termination phase: Saturation
% 1.57/1.34
% 1.57/1.34 % (9440)Memory used [KB]: 5500
% 1.57/1.34 % (9440)Time elapsed: 0.005 s
% 1.57/1.34 % (9440)Instructions burned: 5 (million)
% 1.57/1.34 % (9440)------------------------------
% 1.57/1.34 % (9440)------------------------------
% 1.57/1.34 % (9441)Also succeeded, but the first one will report.
% 1.57/1.34 % (9439)Also succeeded, but the first one will report.
% 1.57/1.34 % (9444)Refutation found. Thanks to Tanya!
% 1.57/1.34 % SZS status Theorem for DTF2THF_9342
% 1.57/1.34 % SZS output start Proof for DTF2THF_9342
% 1.57/1.34 thf(func_def_0, type, cG: $i > $o).
% 1.57/1.34 thf(func_def_1, type, cF: $i > $o).
% 1.57/1.34 thf(func_def_2, type, cP: $i > $o).
% 1.57/1.34 thf(func_def_3, type, cS: $i > $o).
% 1.57/1.34 thf(func_def_4, type, cQ: $i > $o).
% 1.57/1.34 thf(func_def_5, type, cR: $i > $o).
% 1.57/1.34 thf(f69,plain,(
% 1.57/1.34 $false),
% 1.57/1.34 inference(avatar_sat_refutation,[status(thm)],[f37,f53,f54,f58,f61,f65,f68])).
% 1.57/1.34 thf(f68,plain,(
% 1.57/1.34 ~spl3_4 | ~spl3_5),
% 1.57/1.34 inference(avatar_contradiction_clause,[status(thm)],[f67])).
% 1.57/1.34 thf(f67,plain,(
% 1.57/1.34 $false | (~spl3_4 | ~spl3_5)),
% 1.57/1.34 inference(trivial_inequality_removal,[status(thm)],[f66])).
% 1.57/1.34 thf(f66,plain,(
% 1.57/1.34 ($true != $true) | (~spl3_4 | ~spl3_5)),
% 1.57/1.34 inference(superposition,[status(thm)],[f36,f41])).
% 1.57/1.34 thf(f41,plain,(
% 1.57/1.34 ($true = (cS @ sK1)) | ~spl3_5),
% 1.57/1.34 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.57/1.34 thf(f39,definition,(
% 1.57/1.34 spl3_5 <=> ($true = (cS @ sK1))),
% 1.57/1.34 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 1.57/1.34 thf(f36,plain,(
% 1.57/1.34 ( ! [X0 : $i] : (((cS @ X0) != $true)) ) | ~spl3_4),
% 1.57/1.34 inference(avatar_component_clause,[status(thm)],[f35])).
% 1.57/1.34 thf(f35,definition,(
% 1.57/1.34 spl3_4 <=> ! [X0 : $i] : ((cS @ X0) != $true)),
% 1.57/1.34 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.57/1.34 thf(f65,plain,(
% 1.57/1.34 ~spl3_3),
% 1.57/1.34 inference(avatar_contradiction_clause,[status(thm)],[f64])).
% 1.57/1.34 thf(f64,plain,(
% 1.57/1.34 $false | ~spl3_3),
% 1.57/1.34 inference(subsumption_resolution,[status(thm)],[f63,f13])).
% 1.57/1.34 thf(f13,plain,(
% 1.57/1.34 ($true = (cF @ sK2))),
% 1.57/1.34 inference(cnf_transformation,[status(thm)],[f12])).
% 1.57/1.34 thf(f12,plain,(
% 1.57/1.34 (! [X0 : $i] : ((cS @ X0) != $true) | ! [X1 : $i] : (($true != (cF @ X1)) | ($true = (cG @ X1)))) & ! [X2 : $i] : (($true != (cP @ X2)) | ! [X3 : $i] : ($true = (cQ @ X3))) & ((((cR @ sK0) != $true) & ($true != (cQ @ sK0))) | (($true = (cS @ sK1)) & ($true = (cQ @ sK1)))) & (($true = (cP @ sK2)) & ($true != (cG @ sK2)) & ($true = (cF @ sK2)))),
% 1.57/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f8,f11,f10,f9])).
% 1.57/1.34 thf(f9,plain,(
% 1.57/1.34 ? [X4 : $i] : (($true != (cR @ X4)) & ($true != (cQ @ X4))) => (((cR @ sK0) != $true) & ($true != (cQ @ sK0)))),
% 1.57/1.34 introduced(definition,[],[choice_axiom])).
% 1.57/1.34 thf(f10,plain,(
% 1.57/1.34 ? [X5 : $i] : (($true = (cS @ X5)) & ($true = (cQ @ X5))) => (($true = (cS @ sK1)) & ($true = (cQ @ sK1)))),
% 1.57/1.34 introduced(definition,[],[choice_axiom])).
% 1.57/1.34 thf(f11,plain,(
% 1.57/1.34 ? [X6 : $i] : (((cP @ X6) = $true) & ($true != (cG @ X6)) & ($true = (cF @ X6))) => (($true = (cP @ sK2)) & ($true != (cG @ sK2)) & ($true = (cF @ sK2)))),
% 1.57/1.34 introduced(definition,[],[choice_axiom])).
% 1.57/1.34 thf(f8,plain,(
% 1.57/1.34 (! [X0 : $i] : ((cS @ X0) != $true) | ! [X1 : $i] : (($true != (cF @ X1)) | ($true = (cG @ X1)))) & ! [X2 : $i] : (($true != (cP @ X2)) | ! [X3 : $i] : ($true = (cQ @ X3))) & (? [X4 : $i] : (($true != (cR @ X4)) & ($true != (cQ @ X4))) | ? [X5 : $i] : (($true = (cS @ X5)) & ($true = (cQ @ X5)))) & ? [X6 : $i] : (((cP @ X6) = $true) & ($true != (cG @ X6)) & ($true = (cF @ X6)))),
% 1.57/1.34 inference(rectify,[status(thm)],[f7])).
% 1.57/1.34 thf(f7,plain,(
% 1.57/1.34 (! [X2 : $i] : ($true != (cS @ X2)) | ! [X3 : $i] : (($true != (cF @ X3)) | ($true = (cG @ X3)))) & ! [X0 : $i] : (((cP @ X0) != $true) | ! [X1 : $i] : ((cQ @ X1) = $true)) & (? [X4 : $i] : (($true != (cR @ X4)) & ($true != (cQ @ X4))) | ? [X5 : $i] : (($true = (cS @ X5)) & ($true = (cQ @ X5)))) & ? [X6 : $i] : (((cP @ X6) = $true) & ($true != (cG @ X6)) & ($true = (cF @ X6)))),
% 1.57/1.34 inference(flattening,[status(thm)],[f6])).
% 1.57/1.34 thf(f6,plain,(
% 1.57/1.34 ? [X6 : $i] : (($true != (cG @ X6)) & (($true = (cF @ X6)) & ((cP @ X6) = $true))) & (! [X0 : $i] : (((cP @ X0) != $true) | ! [X1 : $i] : ((cQ @ X1) = $true)) & (? [X4 : $i] : (($true != (cR @ X4)) & ($true != (cQ @ X4))) | ? [X5 : $i] : (($true = (cS @ X5)) & ($true = (cQ @ X5)))) & (! [X2 : $i] : ($true != (cS @ X2)) | ! [X3 : $i] : (($true != (cF @ X3)) | ($true = (cG @ X3)))))),
% 1.57/1.34 inference(ennf_transformation,[status(thm)],[f5])).
% 1.57/1.34 thf(f5,plain,(
% 1.57/1.34 ~((! [X0 : $i] : (((cP @ X0) = $true) => ! [X1 : $i] : ((cQ @ X1) = $true)) & (! [X4 : $i] : (($true = (cQ @ X4)) | ($true = (cR @ X4))) => ? [X5 : $i] : (($true = (cS @ X5)) & ($true = (cQ @ X5)))) & (? [X2 : $i] : ($true = (cS @ X2)) => ! [X3 : $i] : (($true = (cF @ X3)) => ($true = (cG @ X3))))) => ! [X6 : $i] : ((($true = (cF @ X6)) & ((cP @ X6) = $true)) => ($true = (cG @ X6))))),
% 1.57/1.34 inference(fool_elimination,[status(thm)],[f4])).
% 1.57/1.34 thf(f4,plain,(
% 1.57/1.34 ~((! [X0 : $i] : ((cP @ X0) => ! [X1 : $i] : (cQ @ X1)) & (? [X2 : $i] : (cS @ X2) => ! [X3 : $i] : ((cF @ X3) => (cG @ X3))) & (! [X4 : $i] : ((cQ @ X4) | (cR @ X4)) => ? [X5 : $i] : ((cS @ X5) & (cQ @ X5)))) => ! [X6 : $i] : (((cP @ X6) & (cF @ X6)) => (cG @ X6)))),
% 1.57/1.34 inference(rectify,[status(thm)],[f2])).
% 1.57/1.34 thf(f2,negated_conjecture,(
% 1.57/1.34 ~((! [X0 : $i] : ((cP @ X0) => ! [X1 : $i] : (cQ @ X1)) & (? [X0 : $i] : (cS @ X0) => ! [X0 : $i] : ((cF @ X0) => (cG @ X0))) & (! [X0 : $i] : ((cQ @ X0) | (cR @ X0)) => ? [X0 : $i] : ((cS @ X0) & (cQ @ X0)))) => ! [X0 : $i] : (((cP @ X0) & (cF @ X0)) => (cG @ X0)))),
% 1.57/1.34 inference(negated_conjecture,[status(cth)],[f1])).
% 1.57/1.34 thf(f1,conjecture,(
% 1.57/1.34 (! [X0 : $i] : ((cP @ X0) => ! [X1 : $i] : (cQ @ X1)) & (? [X0 : $i] : (cS @ X0) => ! [X0 : $i] : ((cF @ X0) => (cG @ X0))) & (! [X0 : $i] : ((cQ @ X0) | (cR @ X0)) => ? [X0 : $i] : ((cS @ X0) & (cQ @ X0)))) => ! [X0 : $i] : (((cP @ X0) & (cF @ X0)) => (cG @ X0))),
% 1.57/1.34 file('/export/starexec/sandbox2/tmp/tmp.2G69Ux8i4O/DTF2THF_9342.p',cPELL28)).
% 1.57/1.34 thf(f63,plain,(
% 1.57/1.34 ($true != (cF @ sK2)) | ~spl3_3),
% 1.57/1.34 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.57/1.34 thf(f62,plain,(
% 1.57/1.34 ($true != (cF @ sK2)) | ($true != $true) | ~spl3_3),
% 1.57/1.34 inference(superposition,[status(thm)],[f14,f33])).
% 1.57/1.34 thf(f33,plain,(
% 1.57/1.34 ( ! [X1 : $i] : (($true = (cG @ X1)) | ($true != (cF @ X1))) ) | ~spl3_3),
% 1.57/1.34 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.57/1.34 thf(f32,definition,(
% 1.57/1.34 spl3_3 <=> ! [X1 : $i] : (($true != (cF @ X1)) | ($true = (cG @ X1)))),
% 1.57/1.34 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.57/1.34 thf(f14,plain,(
% 1.57/1.34 ($true != (cG @ sK2))),
% 1.57/1.34 inference(cnf_transformation,[status(thm)],[f12])).
% 1.57/1.34 thf(f61,plain,(
% 1.57/1.34 spl3_1 | ~spl3_8),
% 1.57/1.34 inference(avatar_contradiction_clause,[status(thm)],[f60])).
% 1.57/1.34 thf(f60,plain,(
% 1.57/1.34 $false | (spl3_1 | ~spl3_8)),
% 1.57/1.34 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.57/1.34 thf(f59,plain,(
% 1.57/1.34 ($true != $true) | (spl3_1 | ~spl3_8)),
% 1.57/1.34 inference(superposition,[status(thm)],[f25,f52])).
% 1.57/1.34 thf(f52,plain,(
% 1.57/1.34 ( ! [X3 : $i] : (($true = (cQ @ X3))) ) | ~spl3_8),
% 1.57/1.34 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.57/1.34 thf(f51,definition,(
% 1.57/1.34 spl3_8 <=> ! [X3 : $i] : ($true = (cQ @ X3))),
% 1.57/1.34 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.57/1.34 thf(f25,plain,(
% 1.57/1.34 ($true != (cQ @ sK0)) | spl3_1),
% 1.57/1.34 inference(avatar_component_clause,[status(thm)],[f23])).
% 1.57/1.34 thf(f23,definition,(
% 1.57/1.34 spl3_1 <=> ($true = (cQ @ sK0))),
% 1.57/1.34 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.57/1.34 thf(f58,plain,(
% 1.57/1.34 ~spl3_7),
% 1.57/1.34 inference(avatar_contradiction_clause,[status(thm)],[f57])).
% 1.57/1.34 thf(f57,plain,(
% 1.57/1.34 $false | ~spl3_7),
% 1.57/1.34 inference(trivial_inequality_removal,[status(thm)],[f56])).
% 1.57/1.34 thf(f56,plain,(
% 1.57/1.34 ($true != $true) | ~spl3_7),
% 1.57/1.34 inference(superposition,[status(thm)],[f49,f15])).
% 1.57/1.34 thf(f15,plain,(
% 1.57/1.34 ($true = (cP @ sK2))),
% 1.57/1.34 inference(cnf_transformation,[status(thm)],[f12])).
% 1.57/1.34 thf(f49,plain,(
% 1.57/1.34 ( ! [X2 : $i] : (($true != (cP @ X2))) ) | ~spl3_7),
% 1.57/1.34 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.57/1.34 thf(f48,definition,(
% 1.57/1.34 spl3_7 <=> ! [X2 : $i] : ($true != (cP @ X2))),
% 1.57/1.34 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.57/1.34 thf(f54,plain,(
% 1.57/1.34 ~spl3_1 | spl3_5),
% 1.57/1.34 inference(avatar_split_clause,[status(thm)],[f17,f39,f23])).
% 1.57/1.34 thf(f17,plain,(
% 1.57/1.34 ($true != (cQ @ sK0)) | ($true = (cS @ sK1))),
% 1.57/1.34 inference(cnf_transformation,[status(thm)],[f12])).
% 1.57/1.34 thf(f53,plain,(
% 1.57/1.34 spl3_7 | spl3_8),
% 1.57/1.34 inference(avatar_split_clause,[status(thm)],[f20,f51,f48])).
% 1.57/1.34 thf(f20,plain,(
% 1.57/1.34 ( ! [X2 : $i,X3 : $i] : (($true = (cQ @ X3)) | ($true != (cP @ X2))) )),
% 1.57/1.34 inference(cnf_transformation,[status(thm)],[f12])).
% 1.57/1.34 thf(f37,plain,(
% 1.57/1.34 spl3_3 | spl3_4),
% 1.57/1.34 inference(avatar_split_clause,[status(thm)],[f21,f35,f32])).
% 1.57/1.34 thf(f21,plain,(
% 1.57/1.34 ( ! [X0 : $i,X1 : $i] : (($true != (cF @ X1)) | ($true = (cG @ X1)) | ((cS @ X0) != $true)) )),
% 1.57/1.34 inference(cnf_transformation,[status(thm)],[f12])).
% 1.57/1.34 % SZS output end Proof for DTF2THF_9342
% 1.57/1.34 % (9444)------------------------------
% 1.57/1.34 % (9444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.57/1.34 % (9444)Termination reason: Refutation
% 1.57/1.34
% 1.57/1.34 % (9444)Memory used [KB]: 5500
% 1.57/1.34 % (9444)Time elapsed: 0.005 s
% 1.57/1.34 % (9444)Instructions burned: 3 (million)
% 1.57/1.34 % (9444)------------------------------
% 1.57/1.34 % (9444)------------------------------
% 1.57/1.34 % (9438)Success in time 0.02 s
%------------------------------------------------------------------------------