%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO266^5 : 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 : n019.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 09:53:48 AM UTC 2026
% Result : Theorem 1.66s 1.45s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 52 ( 1 unt; 0 typ; 7 def)
% Number of atoms : 464 ( 136 equ; 0 cnn)
% Maximal formula atoms : 12 ( 8 avg)
% Number of connectives : 445 ( 105 ~; 118 |; 29 &; 177 @)
% ( 12 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 10 con; 0-2 aty)
% Number of variables : 61 ( 0 ^; 46 !; 15 ?; 61 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cQ: $i > $o ).
thf(func_def_1,type,
cP: $i > $o ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_6,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_8,type,
sK2: $i > $o ).
thf(func_def_10,type,
ph4:
!>[X0: $tType] : X0 ).
thf(f88,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f30,f34,f50,f54,f55,f56,f60,f73,f87]) ).
thf(f87,plain,
( spl3_2
| ~ spl3_1
| ~ spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f86,f32,f25,f28]) ).
thf(f28,definition,
( spl3_2
<=> ! [X5: $i] :
( ( $true
= ( cQ @ X5 ) )
| ( $true
= ( cP @ X5 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f25,definition,
( spl3_1
<=> ! [X4: $i] :
( ( ( cP @ X4 )
= $true )
| ( ( sK2 @ X4 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f32,definition,
( spl3_3
<=> ! [X4: $i] :
( ( $true
= ( cQ @ X4 ) )
| ( ( sK2 @ X4 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition]) ).
thf(f86,plain,
( ! [X0: $i] :
( ( $true
= ( cQ @ X0 ) )
| ( $true
= ( cP @ X0 ) ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(trivial_inequality_removal,[status(thm)],[f85]) ).
thf(f85,plain,
( ! [X0: $i] :
( ( $true
= ( cP @ X0 ) )
| ( $true != $true )
| ( $true
= ( cQ @ X0 ) ) )
| ~ spl3_1
| ~ spl3_3 ),
inference(superposition,[status(thm)],[f33,f26]) ).
thf(f26,plain,
( ! [X4: $i] :
( ( ( sK2 @ X4 )
= $true )
| ( ( cP @ X4 )
= $true ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f25]) ).
thf(f33,plain,
( ! [X4: $i] :
( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( cQ @ X4 ) ) )
| ~ spl3_3 ),
inference(avatar_component_clause,[status(thm)],[f32]) ).
thf(f73,plain,
( ~ spl3_2
| ~ spl3_6
| ~ spl3_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f72]) ).
thf(f72,plain,
( $false
| ~ spl3_2
| ~ spl3_6
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f71]) ).
thf(f71,plain,
( ( $true != $true )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_8 ),
inference(duplicate_literal_removal,[status(thm)],[f70]) ).
thf(f70,plain,
( ( $true != $true )
| ( $true != $true )
| ~ spl3_2
| ~ spl3_6
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f45,f69]) ).
thf(f69,plain,
( ( $true
= ( cQ @ ( sK0 @ cQ ) ) )
| ~ spl3_2
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f68]) ).
thf(f68,plain,
( ( $true
= ( cQ @ ( sK0 @ cQ ) ) )
| ( $true != $true )
| ~ spl3_2
| ~ spl3_8 ),
inference(equality_factoring,[status(thm)],[f64]) ).
thf(f64,plain,
( ! [X0: $i > $o] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( cQ @ ( sK0 @ X0 ) )
= $true ) )
| ~ spl3_2
| ~ spl3_8 ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
( ! [X0: $i > $o] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( $true != $true )
| ( ( cQ @ ( sK0 @ X0 ) )
= $true ) )
| ~ spl3_2
| ~ spl3_8 ),
inference(superposition,[status(thm)],[f53,f29]) ).
thf(f29,plain,
( ! [X5: $i] :
( ( $true
= ( cP @ X5 ) )
| ( $true
= ( cQ @ X5 ) ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f28]) ).
thf(f53,plain,
( ! [X0: $i > $o] :
( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) )
| ~ spl3_8 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl3_8
<=> ! [X0: $i > $o] :
( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition]) ).
thf(f45,plain,
( ! [X0: $i > $o] :
( ( $true
!= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( cQ @ ( sK0 @ X0 ) )
!= $true ) )
| ~ spl3_6 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl3_6
<=> ! [X0: $i > $o] :
( ( ( cQ @ ( sK0 @ X0 ) )
!= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition]) ).
thf(f60,plain,
( spl3_4
| ~ spl3_2
| spl3_7 ),
inference(avatar_split_clause,[status(thm)],[f59,f47,f28,f36]) ).
thf(f36,definition,
( spl3_4
<=> ( $true
= ( cQ @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition]) ).
thf(f47,definition,
( spl3_7
<=> ( $true
= ( cP @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition]) ).
thf(f59,plain,
( ( $true
= ( cQ @ sK1 ) )
| ~ spl3_2
| spl3_7 ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
( ( $true
= ( cQ @ sK1 ) )
| ( $true != $true )
| ~ spl3_2
| spl3_7 ),
inference(superposition,[status(thm)],[f49,f29]) ).
thf(f49,plain,
( ( $true
!= ( cP @ sK1 ) )
| spl3_7 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f56,plain,
( ~ spl3_4
| spl3_6 ),
inference(avatar_split_clause,[status(thm)],[f16,f44,f36]) ).
thf(f16,plain,
! [X0: $i > $o] :
( ( $true
!= ( cQ @ sK1 ) )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) ) )
| ( ( cQ @ ( sK0 @ X0 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
( ( ! [X0: $i > $o] :
( ( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) )
| ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ( ( cQ @ ( sK0 @ X0 ) )
!= $true ) ) )
| ( ( $true
!= ( cP @ sK1 ) )
& ( $true
!= ( cQ @ sK1 ) ) ) )
& ( ! [X4: $i] :
( ( ( ( cP @ X4 )
= $true )
| ( ( sK2 @ X4 )
= $true ) )
& ( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( cQ @ X4 ) ) ) )
| ! [X5: $i] :
( ( $true
= ( cP @ X5 ) )
| ( $true
= ( cQ @ X5 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10]) ).
thf(f10,plain,
! [X0: $i > $o] :
( ? [X1: $i] :
( ( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ X1 )
!= $true ) )
| ( ( ( X0 @ X1 )
= $true )
& ( ( cQ @ X1 )
!= $true ) ) )
=> ( ( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
& ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) )
| ( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
& ( ( cQ @ ( sK0 @ X0 ) )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X2: $i] :
( ( ( cP @ X2 )
!= $true )
& ( ( cQ @ X2 )
!= $true ) )
=> ( ( $true
!= ( cP @ sK1 ) )
& ( $true
!= ( cQ @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X3: $i > $o] :
! [X4: $i] :
( ( ( ( cP @ X4 )
= $true )
| ( $true
= ( X3 @ X4 ) ) )
& ( ( $true
!= ( X3 @ X4 ) )
| ( $true
= ( cQ @ X4 ) ) ) )
=> ! [X4: $i] :
( ( ( ( cP @ X4 )
= $true )
| ( ( sK2 @ X4 )
= $true ) )
& ( ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( cQ @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ( ! [X0: $i > $o] :
? [X1: $i] :
( ( ( ( cP @ X1 )
!= $true )
& ( ( X0 @ X1 )
!= $true ) )
| ( ( ( X0 @ X1 )
= $true )
& ( ( cQ @ X1 )
!= $true ) ) )
| ? [X2: $i] :
( ( ( cP @ X2 )
!= $true )
& ( ( cQ @ X2 )
!= $true ) ) )
& ( ? [X3: $i > $o] :
! [X4: $i] :
( ( ( ( cP @ X4 )
= $true )
| ( $true
= ( X3 @ X4 ) ) )
& ( ( $true
!= ( X3 @ X4 ) )
| ( $true
= ( cQ @ X4 ) ) ) )
| ! [X5: $i] :
( ( $true
= ( cP @ X5 ) )
| ( $true
= ( cQ @ X5 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ! [X1: $i > $o] :
? [X2: $i] :
( ( ( ( cP @ X2 )
!= $true )
& ( $true
!= ( X1 @ X2 ) ) )
| ( ( $true
= ( X1 @ X2 ) )
& ( ( cQ @ X2 )
!= $true ) ) )
| ? [X0: $i] :
( ( $true
!= ( cP @ X0 ) )
& ( $true
!= ( cQ @ X0 ) ) ) )
& ( ? [X1: $i > $o] :
! [X2: $i] :
( ( ( ( cP @ X2 )
= $true )
| ( $true
= ( X1 @ X2 ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( ( cQ @ X2 )
= $true ) ) )
| ! [X0: $i] :
( ( $true
= ( cP @ X0 ) )
| ( $true
= ( cQ @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X0: $i] :
( ( $true
= ( cP @ X0 ) )
| ( $true
= ( cQ @ X0 ) ) )
<~> ? [X1: $i > $o] :
! [X2: $i] :
( ( ( ( cP @ X2 )
= $true )
| ( $true
= ( X1 @ X2 ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( ( cQ @ X2 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: $i] :
( ( $true
= ( cP @ X0 ) )
| ( $true
= ( cQ @ X0 ) ) )
<=> ? [X1: $i > $o] :
! [X2: $i] :
( ( ( ( cP @ X2 )
= $true )
| ( $true
= ( X1 @ X2 ) ) )
& ( ( $true
!= ( X1 @ X2 ) )
| ( ( cQ @ X2 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ! [X0: $i] :
( ( $true
= ( cP @ X0 ) )
| ( $true
= ( cQ @ X0 ) ) )
<=> ? [X1: $i > $o] :
! [X2: $i] :
( ( ( ( cQ @ X2 )
= $true )
| ( $true
!= ( X1 @ X2 ) ) )
& ( ( ( cP @ X2 )
= $true )
| ( $true
= ( X1 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ! [X0: $i] :
( ( cP @ X0 )
| ( cQ @ X0 ) )
<=> ? [X1: $i > $o] :
! [X2: $i] :
( ( ( cQ @ X2 )
| ~ ( X1 @ X2 ) )
& ( ( cP @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ! [X2: $i] :
( ( cP @ X2 )
| ( cQ @ X2 ) )
<=> ? [X0: $i > $o] :
! [X1: $i] :
( ( ( cQ @ X1 )
| ~ ( X0 @ X1 ) )
& ( ( cP @ X1 )
| ( X0 @ X1 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ! [X2: $i] :
( ( cP @ X2 )
| ( cQ @ X2 ) )
<=> ? [X0: $i > $o] :
! [X1: $i] :
( ( ( cQ @ X1 )
| ~ ( X0 @ X1 ) )
& ( ( cP @ X1 )
| ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.VYXzj6BrmM/DTF2THF_23941.p',cTHM44) ).
thf(f55,plain,
( spl3_8
| ~ spl3_7 ),
inference(avatar_split_clause,[status(thm)],[f23,f47,f52]) ).
thf(f23,plain,
! [X0: $i > $o] :
( ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( $true
!= ( cP @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f54,plain,
( spl3_8
| ~ spl3_4 ),
inference(avatar_split_clause,[status(thm)],[f22,f36,f52]) ).
thf(f22,plain,
! [X0: $i > $o] :
( ( $true
!= ( cP @ ( sK0 @ X0 ) ) )
| ( $true
= ( X0 @ ( sK0 @ X0 ) ) )
| ( $true
!= ( cQ @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f50,plain,
( spl3_6
| ~ spl3_7 ),
inference(avatar_split_clause,[status(thm)],[f17,f47,f44]) ).
thf(f17,plain,
! [X0: $i > $o] :
( ( $true
!= ( cP @ sK1 ) )
| ( ( cQ @ ( sK0 @ X0 ) )
!= $true )
| ( $true
!= ( X0 @ ( sK0 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f34,plain,
( spl3_2
| spl3_3 ),
inference(avatar_split_clause,[status(thm)],[f14,f32,f28]) ).
thf(f14,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( cQ @ X4 ) )
| ( ( sK2 @ X4 )
!= $true )
| ( $true
= ( cQ @ X5 ) )
| ( $true
= ( cP @ X5 ) ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f30,plain,
( spl3_1
| spl3_2 ),
inference(avatar_split_clause,[status(thm)],[f15,f28,f25]) ).
thf(f15,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( cQ @ X5 ) )
| ( $true
= ( cP @ X5 ) )
| ( ( cP @ X4 )
= $true )
| ( ( sK2 @ X4 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO266^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:27:09 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.47 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SYO266^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.47 % Domain : Syntactic
% 0.20/0.47 % Problem : TPS problem THM44
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English :
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.47 % Source : [Bro09]
% 0.20/0.47 % Names : tps_0217 [Bro09]
% 0.20/0.47 % : THM44 [TPS]
% 0.20/0.47 % : THM44-SLOW [TPS]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.33 v6.1.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.20/0.47 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.47 % Number of atoms : 4 ( 0 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 4 ( 4 avg)
% 0.20/0.47 % Number of connectives : 12 ( 1 ~; 3 |; 1 &; 6 @)
% 0.20/0.47 % ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 8 ( 8 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 3 ( 3 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 2 ( 2 usr; 0 con; 1-1 aty)
% 0.20/0.47 % Number of variables : 3 ( 0 ^; 2 !; 1 ?; 3 :)
% 0.20/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.47 % : Useful in eliminating a quantifier on a second order variable.
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(cQ,type,
% 0.20/0.47 cQ: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cP,type,
% 0.20/0.47 cP: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(cTHM44,conjecture,
% 0.20/0.47 ( ? [S: $i > $o] :
% 0.20/0.47 ! [X: $i] :
% 0.20/0.47 ( ( ( S @ X )
% 0.20/0.47 | ( cP @ X ) )
% 0.20/0.47 & ( ~ ( S @ X )
% 0.20/0.47 | ( cQ @ X ) ) )
% 0.20/0.47 <=> ! [Y: $i] :
% 0.20/0.47 ( ( cP @ Y )
% 0.20/0.47 | ( cQ @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 1.66/1.41 ---- Embedded in THF ---
% 1.66/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.66/1.41 %%% Generated on Tue Feb 24 14:27:10 EST 2026
% 1.66/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.66/1.41 %%% Logic specification used:
% 1.66/1.41 %%% thf(spec, logic, $$dhol).
% 1.66/1.41
% 1.66/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.VYXzj6BrmM/DTF2DTF23941.p
% See solution above
% 1.66/1.42 ------------------------
% 1.66/1.42 ---- Cleaned THF ---
% 1.66/1.42 thf(cQ,type,
% 1.66/1.42 cQ: $i > $o ).
% 1.66/1.42
% 1.66/1.42 thf(cP,type,
% 1.66/1.42 cP: $i > $o ).
% 1.66/1.42
% 1.66/1.42 thf(cTHM44,conjecture,
% 1.66/1.42 ( ? [S: $i > $o] :
% 1.66/1.42 ! [X: $i] :
% 1.66/1.42 ( ( ( S @ X )
% 1.66/1.42 | ( cP @ X ) )
% 1.66/1.42 & ( ~ ( S @ X )
% 1.66/1.42 | ( cQ @ X ) ) )
% 1.66/1.42 <=> ! [Y: $i] :
% 1.66/1.42 ( ( cP @ Y )
% 1.66/1.42 | ( cQ @ Y ) ) ) ).
% 1.66/1.42 ------------------------
% 1.66/1.44 % (24039)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_23941 for (3000ds/4Mi)
% 1.66/1.44 % (24040)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_23941 for (3000ds/27Mi)
% 1.66/1.44 % (24042)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_23941 for (3000ds/2Mi)
% 1.66/1.44 % (24043)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_23941 for (3000ds/275Mi)
% 1.66/1.44 % (24038)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23941 for (3000ds/183Mi)
% 1.66/1.44 % (24044)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23941 for (3000ds/18Mi)
% 1.66/1.44 % (24041)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23941 for (3000ds/2Mi)
% 1.66/1.44 % (24041)Instruction limit reached!
% 1.66/1.44 % (24041)------------------------------
% 1.66/1.44 % (24041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (24041)Termination reason: Unknown
% 1.66/1.44 % (24041)Termination phase: Saturation
% 1.66/1.44
% 1.66/1.44 % (24042)Instruction limit reached!
% 1.66/1.44 % (24042)------------------------------
% 1.66/1.44 % (24042)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.44 % (24042)Termination reason: Unknown
% 1.66/1.44 % (24042)Termination phase: Saturation
% 1.66/1.44
% 1.66/1.44 % (24042)Memory used [KB]: 5500
% 1.66/1.44 % (24042)Time elapsed: 0.003 s
% 1.66/1.44 % (24042)Instructions burned: 2 (million)
% 1.66/1.44 % (24042)------------------------------
% 1.66/1.44 % (24042)------------------------------
% 1.66/1.44 % (24041)Memory used [KB]: 5500
% 1.66/1.44 % (24041)Time elapsed: 0.003 s
% 1.66/1.44 % (24041)Instructions burned: 2 (million)
% 1.66/1.44 % (24041)------------------------------
% 1.66/1.44 % (24041)------------------------------
% 1.66/1.45 % (24039)Instruction limit reached!
% 1.66/1.45 % (24039)------------------------------
% 1.66/1.45 % (24039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (24039)Termination reason: Unknown
% 1.66/1.45 % (24039)Termination phase: Saturation
% 1.66/1.45
% 1.66/1.45 % (24039)Memory used [KB]: 5500
% 1.66/1.45 % (24039)Time elapsed: 0.005 s
% 1.66/1.45 % (24039)Instructions burned: 5 (million)
% 1.66/1.45 % (24039)------------------------------
% 1.66/1.45 % (24039)------------------------------
% 1.66/1.45 % (24040)First to succeed.
% 1.66/1.45 % (24044)Also succeeded, but the first one will report.
% 1.66/1.45 % (24040)Refutation found. Thanks to Tanya!
% 1.66/1.45 % SZS status Theorem for DTF2THF_23941
% 1.66/1.45 % SZS output start Proof for DTF2THF_23941
% 1.66/1.45 thf(func_def_0, type, cQ: $i > $o).
% 1.66/1.45 thf(func_def_1, type, cP: $i > $o).
% 1.66/1.45 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.66/1.45 thf(func_def_6, type, sK0: ($i > $o) > $i).
% 1.66/1.45 thf(func_def_8, type, sK2: $i > $o).
% 1.66/1.45 thf(func_def_10, type, ph4: !>[X0: $tType]:(X0)).
% 1.66/1.45 thf(f88,plain,(
% 1.66/1.45 $false),
% 1.66/1.45 inference(avatar_sat_refutation,[status(thm)],[f30,f34,f50,f54,f55,f56,f60,f73,f87])).
% 1.66/1.45 thf(f87,plain,(
% 1.66/1.45 spl3_2 | ~spl3_1 | ~spl3_3),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f86,f32,f25,f28])).
% 1.66/1.45 thf(f28,definition,(
% 1.66/1.45 spl3_2 <=> ! [X5 : $i] : (($true = (cQ @ X5)) | ($true = (cP @ X5)))),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 1.66/1.45 thf(f25,definition,(
% 1.66/1.45 spl3_1 <=> ! [X4 : $i] : (((cP @ X4) = $true) | ((sK2 @ X4) = $true))),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 1.66/1.45 thf(f32,definition,(
% 1.66/1.45 spl3_3 <=> ! [X4 : $i] : (($true = (cQ @ X4)) | ((sK2 @ X4) != $true))),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl3_3])],[avatar_definition])).
% 1.66/1.45 thf(f86,plain,(
% 1.66/1.45 ( ! [X0 : $i] : (($true = (cQ @ X0)) | ($true = (cP @ X0))) ) | (~spl3_1 | ~spl3_3)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f85])).
% 1.66/1.45 thf(f85,plain,(
% 1.66/1.45 ( ! [X0 : $i] : (($true = (cP @ X0)) | ($true != $true) | ($true = (cQ @ X0))) ) | (~spl3_1 | ~spl3_3)),
% 1.66/1.45 inference(superposition,[status(thm)],[f33,f26])).
% 1.66/1.45 thf(f26,plain,(
% 1.66/1.45 ( ! [X4 : $i] : (((sK2 @ X4) = $true) | ((cP @ X4) = $true)) ) | ~spl3_1),
% 1.66/1.45 inference(avatar_component_clause,[status(thm)],[f25])).
% 1.66/1.45 thf(f33,plain,(
% 1.66/1.45 ( ! [X4 : $i] : (((sK2 @ X4) != $true) | ($true = (cQ @ X4))) ) | ~spl3_3),
% 1.66/1.45 inference(avatar_component_clause,[status(thm)],[f32])).
% 1.66/1.45 thf(f73,plain,(
% 1.66/1.45 ~spl3_2 | ~spl3_6 | ~spl3_8),
% 1.66/1.45 inference(avatar_contradiction_clause,[status(thm)],[f72])).
% 1.66/1.45 thf(f72,plain,(
% 1.66/1.45 $false | (~spl3_2 | ~spl3_6 | ~spl3_8)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f71])).
% 1.66/1.45 thf(f71,plain,(
% 1.66/1.45 ($true != $true) | (~spl3_2 | ~spl3_6 | ~spl3_8)),
% 1.66/1.45 inference(duplicate_literal_removal,[status(thm)],[f70])).
% 1.66/1.45 thf(f70,plain,(
% 1.66/1.45 ($true != $true) | ($true != $true) | (~spl3_2 | ~spl3_6 | ~spl3_8)),
% 1.66/1.45 inference(superposition,[status(thm)],[f45,f69])).
% 1.66/1.45 thf(f69,plain,(
% 1.66/1.45 ($true = (cQ @ (sK0 @ cQ))) | (~spl3_2 | ~spl3_8)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f68])).
% 1.66/1.45 thf(f68,plain,(
% 1.66/1.45 ($true = (cQ @ (sK0 @ cQ))) | ($true != $true) | (~spl3_2 | ~spl3_8)),
% 1.66/1.45 inference(equality_factoring,[status(thm)],[f64])).
% 1.66/1.45 thf(f64,plain,(
% 1.66/1.45 ( ! [X0 : $i > $o] : (($true = (X0 @ (sK0 @ X0))) | ((cQ @ (sK0 @ X0)) = $true)) ) | (~spl3_2 | ~spl3_8)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.66/1.45 thf(f63,plain,(
% 1.66/1.45 ( ! [X0 : $i > $o] : (($true = (X0 @ (sK0 @ X0))) | ($true != $true) | ((cQ @ (sK0 @ X0)) = $true)) ) | (~spl3_2 | ~spl3_8)),
% 1.66/1.45 inference(superposition,[status(thm)],[f53,f29])).
% 1.66/1.45 thf(f29,plain,(
% 1.66/1.45 ( ! [X5 : $i] : (($true = (cP @ X5)) | ($true = (cQ @ X5))) ) | ~spl3_2),
% 1.66/1.45 inference(avatar_component_clause,[status(thm)],[f28])).
% 1.66/1.45 thf(f53,plain,(
% 1.66/1.45 ( ! [X0 : $i > $o] : (($true != (cP @ (sK0 @ X0))) | ($true = (X0 @ (sK0 @ X0)))) ) | ~spl3_8),
% 1.66/1.45 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.66/1.45 thf(f52,definition,(
% 1.66/1.45 spl3_8 <=> ! [X0 : $i > $o] : (($true != (cP @ (sK0 @ X0))) | ($true = (X0 @ (sK0 @ X0))))),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl3_8])],[avatar_definition])).
% 1.66/1.45 thf(f45,plain,(
% 1.66/1.45 ( ! [X0 : $i > $o] : (($true != (X0 @ (sK0 @ X0))) | ((cQ @ (sK0 @ X0)) != $true)) ) | ~spl3_6),
% 1.66/1.45 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.66/1.45 thf(f44,definition,(
% 1.66/1.45 spl3_6 <=> ! [X0 : $i > $o] : (((cQ @ (sK0 @ X0)) != $true) | ($true != (X0 @ (sK0 @ X0))))),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl3_6])],[avatar_definition])).
% 1.66/1.45 thf(f60,plain,(
% 1.66/1.45 spl3_4 | ~spl3_2 | spl3_7),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f59,f47,f28,f36])).
% 1.66/1.45 thf(f36,definition,(
% 1.66/1.45 spl3_4 <=> ($true = (cQ @ sK1))),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl3_4])],[avatar_definition])).
% 1.66/1.45 thf(f47,definition,(
% 1.66/1.45 spl3_7 <=> ($true = (cP @ sK1))),
% 1.66/1.45 introduced(definition,[new_symbols(naming,[spl3_7])],[avatar_definition])).
% 1.66/1.45 thf(f59,plain,(
% 1.66/1.45 ($true = (cQ @ sK1)) | (~spl3_2 | spl3_7)),
% 1.66/1.45 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.66/1.45 thf(f58,plain,(
% 1.66/1.45 ($true = (cQ @ sK1)) | ($true != $true) | (~spl3_2 | spl3_7)),
% 1.66/1.45 inference(superposition,[status(thm)],[f49,f29])).
% 1.66/1.45 thf(f49,plain,(
% 1.66/1.45 ($true != (cP @ sK1)) | spl3_7),
% 1.66/1.45 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.66/1.45 thf(f56,plain,(
% 1.66/1.45 ~spl3_4 | spl3_6),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f16,f44,f36])).
% 1.66/1.45 thf(f16,plain,(
% 1.66/1.45 ( ! [X0 : $i > $o] : (($true != (cQ @ sK1)) | ($true != (X0 @ (sK0 @ X0))) | ((cQ @ (sK0 @ X0)) != $true)) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.45 thf(f13,plain,(
% 1.66/1.45 (! [X0 : $i > $o] : ((($true != (cP @ (sK0 @ X0))) & ($true != (X0 @ (sK0 @ X0)))) | (($true = (X0 @ (sK0 @ X0))) & ((cQ @ (sK0 @ X0)) != $true))) | (($true != (cP @ sK1)) & ($true != (cQ @ sK1)))) & (! [X4 : $i] : ((((cP @ X4) = $true) | ((sK2 @ X4) = $true)) & (((sK2 @ X4) != $true) | ($true = (cQ @ X4)))) | ! [X5 : $i] : (($true = (cP @ X5)) | ($true = (cQ @ X5))))),
% 1.66/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f9,f12,f11,f10])).
% 1.66/1.45 thf(f10,plain,(
% 1.66/1.45 ! [X0 : $i > $o] : (? [X1 : $i] : ((((cP @ X1) != $true) & ((X0 @ X1) != $true)) | (((X0 @ X1) = $true) & ((cQ @ X1) != $true))) => ((($true != (cP @ (sK0 @ X0))) & ($true != (X0 @ (sK0 @ X0)))) | (($true = (X0 @ (sK0 @ X0))) & ((cQ @ (sK0 @ X0)) != $true))))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f11,plain,(
% 1.66/1.45 ? [X2 : $i] : (((cP @ X2) != $true) & ((cQ @ X2) != $true)) => (($true != (cP @ sK1)) & ($true != (cQ @ sK1)))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f12,plain,(
% 1.66/1.45 ? [X3 : $i > $o] : ! [X4 : $i] : ((((cP @ X4) = $true) | ($true = (X3 @ X4))) & (($true != (X3 @ X4)) | ($true = (cQ @ X4)))) => ! [X4 : $i] : ((((cP @ X4) = $true) | ((sK2 @ X4) = $true)) & (((sK2 @ X4) != $true) | ($true = (cQ @ X4))))),
% 1.66/1.45 introduced(definition,[],[choice_axiom])).
% 1.66/1.45 thf(f9,plain,(
% 1.66/1.45 (! [X0 : $i > $o] : ? [X1 : $i] : ((((cP @ X1) != $true) & ((X0 @ X1) != $true)) | (((X0 @ X1) = $true) & ((cQ @ X1) != $true))) | ? [X2 : $i] : (((cP @ X2) != $true) & ((cQ @ X2) != $true))) & (? [X3 : $i > $o] : ! [X4 : $i] : ((((cP @ X4) = $true) | ($true = (X3 @ X4))) & (($true != (X3 @ X4)) | ($true = (cQ @ X4)))) | ! [X5 : $i] : (($true = (cP @ X5)) | ($true = (cQ @ X5))))),
% 1.66/1.45 inference(rectify,[status(thm)],[f8])).
% 1.66/1.45 thf(f8,plain,(
% 1.66/1.45 (! [X1 : $i > $o] : ? [X2 : $i] : ((((cP @ X2) != $true) & ($true != (X1 @ X2))) | (($true = (X1 @ X2)) & ((cQ @ X2) != $true))) | ? [X0 : $i] : (($true != (cP @ X0)) & ($true != (cQ @ X0)))) & (? [X1 : $i > $o] : ! [X2 : $i] : ((((cP @ X2) = $true) | ($true = (X1 @ X2))) & (($true != (X1 @ X2)) | ((cQ @ X2) = $true))) | ! [X0 : $i] : (($true = (cP @ X0)) | ($true = (cQ @ X0))))),
% 1.66/1.45 inference(nnf_transformation,[status(thm)],[f7])).
% 1.66/1.45 thf(f7,plain,(
% 1.66/1.45 ! [X0 : $i] : (($true = (cP @ X0)) | ($true = (cQ @ X0))) <~> ? [X1 : $i > $o] : ! [X2 : $i] : ((((cP @ X2) = $true) | ($true = (X1 @ X2))) & (($true != (X1 @ X2)) | ((cQ @ X2) = $true)))),
% 1.66/1.45 inference(ennf_transformation,[status(thm)],[f6])).
% 1.66/1.45 thf(f6,plain,(
% 1.66/1.45 ~(! [X0 : $i] : (($true = (cP @ X0)) | ($true = (cQ @ X0))) <=> ? [X1 : $i > $o] : ! [X2 : $i] : ((((cP @ X2) = $true) | ($true = (X1 @ X2))) & (($true != (X1 @ X2)) | ((cQ @ X2) = $true))))),
% 1.66/1.45 inference(flattening,[status(thm)],[f5])).
% 1.66/1.45 thf(f5,plain,(
% 1.66/1.45 ~(! [X0 : $i] : (($true = (cP @ X0)) | ($true = (cQ @ X0))) <=> ? [X1 : $i > $o] : ! [X2 : $i] : ((((cQ @ X2) = $true) | ~($true = (X1 @ X2))) & (((cP @ X2) = $true) | ($true = (X1 @ X2)))))),
% 1.66/1.45 inference(fool_elimination,[status(thm)],[f4])).
% 1.66/1.45 thf(f4,plain,(
% 1.66/1.45 ~(! [X0 : $i] : ((cP @ X0) | (cQ @ X0)) <=> ? [X1 : $i > $o] : ! [X2 : $i] : (((cQ @ X2) | ~(X1 @ X2)) & ((cP @ X2) | (X1 @ X2))))),
% 1.66/1.45 inference(rectify,[status(thm)],[f2])).
% 1.66/1.45 thf(f2,negated_conjecture,(
% 1.66/1.45 ~(! [X2 : $i] : ((cP @ X2) | (cQ @ X2)) <=> ? [X0 : $i > $o] : ! [X1 : $i] : (((cQ @ X1) | ~(X0 @ X1)) & ((cP @ X1) | (X0 @ X1))))),
% 1.66/1.45 inference(negated_conjecture,[status(cth)],[f1])).
% 1.66/1.45 thf(f1,conjecture,(
% 1.66/1.45 ! [X2 : $i] : ((cP @ X2) | (cQ @ X2)) <=> ? [X0 : $i > $o] : ! [X1 : $i] : (((cQ @ X1) | ~(X0 @ X1)) & ((cP @ X1) | (X0 @ X1)))),
% 1.66/1.45 file('/export/starexec/sandbox/tmp/tmp.VYXzj6BrmM/DTF2THF_23941.p',cTHM44)).
% 1.66/1.45 thf(f55,plain,(
% 1.66/1.45 spl3_8 | ~spl3_7),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f23,f47,f52])).
% 1.66/1.45 thf(f23,plain,(
% 1.66/1.45 ( ! [X0 : $i > $o] : (($true = (X0 @ (sK0 @ X0))) | ($true != (cP @ (sK0 @ X0))) | ($true != (cP @ sK1))) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.45 thf(f54,plain,(
% 1.66/1.45 spl3_8 | ~spl3_4),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f22,f36,f52])).
% 1.66/1.45 thf(f22,plain,(
% 1.66/1.45 ( ! [X0 : $i > $o] : (($true != (cP @ (sK0 @ X0))) | ($true = (X0 @ (sK0 @ X0))) | ($true != (cQ @ sK1))) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.45 thf(f50,plain,(
% 1.66/1.45 spl3_6 | ~spl3_7),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f17,f47,f44])).
% 1.66/1.45 thf(f17,plain,(
% 1.66/1.45 ( ! [X0 : $i > $o] : (($true != (cP @ sK1)) | ((cQ @ (sK0 @ X0)) != $true) | ($true != (X0 @ (sK0 @ X0)))) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.45 thf(f34,plain,(
% 1.66/1.45 spl3_2 | spl3_3),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f14,f32,f28])).
% 1.66/1.45 thf(f14,plain,(
% 1.66/1.45 ( ! [X4 : $i,X5 : $i] : (($true = (cQ @ X4)) | ((sK2 @ X4) != $true) | ($true = (cQ @ X5)) | ($true = (cP @ X5))) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.45 thf(f30,plain,(
% 1.66/1.45 spl3_1 | spl3_2),
% 1.66/1.45 inference(avatar_split_clause,[status(thm)],[f15,f28,f25])).
% 1.66/1.45 thf(f15,plain,(
% 1.66/1.45 ( ! [X4 : $i,X5 : $i] : (($true = (cQ @ X5)) | ($true = (cP @ X5)) | ((cP @ X4) = $true) | ((sK2 @ X4) = $true)) )),
% 1.66/1.45 inference(cnf_transformation,[status(thm)],[f13])).
% 1.66/1.45 % SZS output end Proof for DTF2THF_23941
% 1.66/1.45 % (24040)------------------------------
% 1.66/1.45 % (24040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.45 % (24040)Termination reason: Refutation
% 1.66/1.45
% 1.66/1.45 % (24040)Memory used [KB]: 5500
% 1.66/1.45 % (24040)Time elapsed: 0.006 s
% 1.66/1.45 % (24040)Instructions burned: 5 (million)
% 1.66/1.45 % (24040)------------------------------
% 1.66/1.45 % (24040)------------------------------
% 1.66/1.45 % (24037)Success in time 0.02 s
%------------------------------------------------------------------------------