%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO109^5 : 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 : n001.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 09:53:23 AM UTC 2026
% Result : Theorem 1.51s 1.29s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 3 unt; 0 typ; 2 def)
% Number of atoms : 462 ( 136 equ; 0 cnn)
% Maximal formula atoms : 12 ( 11 avg)
% Number of connectives : 507 ( 53 ~; 103 |; 28 &; 307 @)
% ( 2 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 0 ^; 91 !; 16 ?; 107 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $o ).
thf(func_def_1,type,
cN: $i > $i > $o ).
thf(func_def_2,type,
cM: $i > $i > $o ).
thf(func_def_7,type,
sK1: $i > $i ).
thf(f56,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f38,f52,f55]) ).
thf(f55,plain,
~ spl2_1,
inference(avatar_contradiction_clause,[status(thm)],[f54]) ).
thf(f54,plain,
( $false
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f53]) ).
thf(f53,plain,
( ( $true != $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f15,f34]) ).
thf(f34,plain,
( ! [X1: $i] :
( ( cP @ X1 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f33,definition,
( spl2_1
<=> ! [X1: $i] :
( ( cP @ X1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f15,plain,
( $true
!= ( cP @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( cM @ X0 @ X0 ) )
| ( ( cN @ X0 @ X1 )
= $true )
| ( ( cM @ X0 @ X1 )
= $true )
| ( ( cN @ X0 @ X0 )
= $true )
| ( ( $true
!= ( cN @ X1 @ X0 ) )
& ( $true
!= ( cM @ X1 @ X0 ) ) ) )
& ( $true
!= ( cP @ sK0 ) )
& ! [X3: $i] :
( ( ( cN @ ( sK1 @ X3 ) @ X3 )
= $true )
| ! [X5: $i] :
( $true
= ( cM @ ( sK1 @ X3 ) @ X5 ) ) )
& ! [X6: $i] :
( ! [X7: $i] :
( ( ( cM @ X6 @ X7 )
!= $true )
& ( ( cN @ X6 @ X7 )
!= $true ) )
| ( ( cP @ X6 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9]) ).
thf(f9,plain,
( ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
=> ( $true
!= ( cP @ sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( cN @ X4 @ X3 ) )
| ! [X5: $i] :
( $true
= ( cM @ X4 @ X5 ) ) )
=> ( ( ( cN @ ( sK1 @ X3 ) @ X3 )
= $true )
| ! [X5: $i] :
( $true
= ( cM @ ( sK1 @ X3 ) @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( cM @ X0 @ X0 ) )
| ( ( cN @ X0 @ X1 )
= $true )
| ( ( cM @ X0 @ X1 )
= $true )
| ( ( cN @ X0 @ X0 )
= $true )
| ( ( $true
!= ( cN @ X1 @ X0 ) )
& ( $true
!= ( cM @ X1 @ X0 ) ) ) )
& ? [X2: $i] :
( $true
!= ( cP @ X2 ) )
& ! [X3: $i] :
? [X4: $i] :
( ( $true
= ( cN @ X4 @ X3 ) )
| ! [X5: $i] :
( $true
= ( cM @ X4 @ X5 ) ) )
& ! [X6: $i] :
( ! [X7: $i] :
( ( ( cM @ X6 @ X7 )
!= $true )
& ( ( cN @ X6 @ X7 )
!= $true ) )
| ( ( cP @ X6 )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X5: $i,X6: $i] :
( ( ( cM @ X5 @ X5 )
= $true )
| ( ( cN @ X5 @ X6 )
= $true )
| ( $true
= ( cM @ X5 @ X6 ) )
| ( ( cN @ X5 @ X5 )
= $true )
| ( ( ( cN @ X6 @ X5 )
!= $true )
& ( $true
!= ( cM @ X6 @ X5 ) ) ) )
& ? [X7: $i] :
( $true
!= ( cP @ X7 ) )
& ! [X0: $i] :
? [X1: $i] :
( ( $true
= ( cN @ X1 @ X0 ) )
| ! [X2: $i] :
( ( cM @ X1 @ X2 )
= $true ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( cM @ X3 @ X4 )
!= $true )
& ( $true
!= ( cN @ X3 @ X4 ) ) )
| ( $true
= ( cP @ X3 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ? [X7: $i] :
( $true
!= ( cP @ X7 ) )
& ! [X0: $i] :
? [X1: $i] :
( ( $true
= ( cN @ X1 @ X0 ) )
| ! [X2: $i] :
( ( cM @ X1 @ X2 )
= $true ) )
& ! [X5: $i,X6: $i] :
( ( ( cM @ X5 @ X5 )
= $true )
| ( ( cN @ X5 @ X5 )
= $true )
| ( $true
= ( cM @ X5 @ X6 ) )
| ( ( cN @ X5 @ X6 )
= $true )
| ( ( ( cN @ X6 @ X5 )
!= $true )
& ( $true
!= ( cM @ X6 @ X5 ) ) ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( cM @ X3 @ X4 )
!= $true )
& ( $true
!= ( cN @ X3 @ X4 ) ) )
| ( $true
= ( cP @ X3 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
? [X1: $i] :
( ( $true
= ( cN @ X1 @ X0 ) )
| ! [X2: $i] :
( ( cM @ X1 @ X2 )
= $true ) )
& ! [X5: $i,X6: $i] :
( ( ( $true
= ( cM @ X6 @ X5 ) )
| ( ( cN @ X6 @ X5 )
= $true ) )
=> ( ( ( cM @ X5 @ X5 )
= $true )
| ( ( cN @ X5 @ X5 )
= $true )
| ( $true
= ( cM @ X5 @ X6 ) )
| ( ( cN @ X5 @ X6 )
= $true ) ) )
& ! [X3: $i] :
( ? [X4: $i] :
( ( ( cM @ X3 @ X4 )
= $true )
| ( $true
= ( cN @ X3 @ X4 ) ) )
=> ( $true
= ( cP @ X3 ) ) ) )
=> ! [X7: $i] :
( $true
= ( cP @ X7 ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
? [X1: $i] :
( ( cN @ X1 @ X0 )
| ! [X2: $i] : ( cM @ X1 @ X2 ) )
& ! [X3: $i] :
( ? [X4: $i] :
( ( cM @ X3 @ X4 )
| ( cN @ X3 @ X4 ) )
=> ( cP @ X3 ) )
& ! [X5: $i,X6: $i] :
( ( ( cN @ X6 @ X5 )
| ( cM @ X6 @ X5 ) )
=> ( ( cN @ X5 @ X6 )
| ( cM @ X5 @ X6 )
| ( cN @ X5 @ X5 )
| ( cM @ X5 @ X5 ) ) ) )
=> ! [X7: $i] : ( cP @ X7 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: $i] :
? [X3: $i] :
( ( cN @ X3 @ X2 )
| ! [X4: $i] : ( cM @ X3 @ X4 ) )
& ! [X0: $i] :
( ? [X1: $i] :
( ( cM @ X0 @ X1 )
| ( cN @ X0 @ X1 ) )
=> ( cP @ X0 ) )
& ! [X5: $i,X2: $i] :
( ( ( cN @ X2 @ X5 )
| ( cM @ X2 @ X5 ) )
=> ( ( cN @ X5 @ X2 )
| ( cM @ X5 @ X2 )
| ( cN @ X5 @ X5 )
| ( cM @ X5 @ X5 ) ) ) )
=> ! [X5: $i] : ( cP @ X5 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X2: $i] :
? [X3: $i] :
( ( cN @ X3 @ X2 )
| ! [X4: $i] : ( cM @ X3 @ X4 ) )
& ! [X0: $i] :
( ? [X1: $i] :
( ( cM @ X0 @ X1 )
| ( cN @ X0 @ X1 ) )
=> ( cP @ X0 ) )
& ! [X5: $i,X2: $i] :
( ( ( cN @ X2 @ X5 )
| ( cM @ X2 @ X5 ) )
=> ( ( cN @ X5 @ X2 )
| ( cM @ X5 @ X2 )
| ( cN @ X5 @ X5 )
| ( cM @ X5 @ X5 ) ) ) )
=> ! [X5: $i] : ( cP @ X5 ) ),
file('/export/starexec/sandbox/tmp/tmp.xOFi67xXag/DTF2THF_3725.p',cTHM271) ).
thf(f52,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f51,f36,f33]) ).
thf(f36,definition,
( spl2_2
<=> ! [X0: $i] :
( $true
= ( cN @ ( sK1 @ X0 ) @ X0 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f51,plain,
( ! [X0: $i] :
( ( cP @ X0 )
= $true )
| ~ spl2_2 ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ! [X0: $i] :
( ( ( cP @ X0 )
= $true )
| ( $true != $true ) )
| ~ spl2_2 ),
inference(superposition,[status(thm)],[f47,f37]) ).
thf(f37,plain,
( ! [X0: $i] :
( $true
= ( cN @ ( sK1 @ X0 ) @ X0 ) )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f47,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cN @ X1 @ X0 ) )
| ( ( cP @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f46,f13]) ).
thf(f13,plain,
! [X6: $i,X7: $i] :
( ( ( cM @ X6 @ X7 )
!= $true )
| ( ( cP @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f46,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cN @ X1 @ X0 ) )
| ( ( cP @ X0 )
= $true )
| ( ( cM @ X0 @ X1 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f45,f12]) ).
thf(f12,plain,
! [X6: $i,X7: $i] :
( ( ( cN @ X6 @ X7 )
!= $true )
| ( ( cP @ X6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f45,plain,
! [X0: $i,X1: $i] :
( ( ( cN @ X0 @ X0 )
= $true )
| ( ( cP @ X0 )
= $true )
| ( $true
!= ( cN @ X1 @ X0 ) )
| ( ( cM @ X0 @ X1 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f44,f12]) ).
thf(f44,plain,
! [X0: $i,X1: $i] :
( ( ( cN @ X0 @ X1 )
= $true )
| ( ( cM @ X0 @ X1 )
= $true )
| ( ( cN @ X0 @ X0 )
= $true )
| ( ( cP @ X0 )
= $true )
| ( $true
!= ( cN @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X0: $i,X1: $i] :
( ( ( cN @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( ( cN @ X0 @ X0 )
= $true )
| ( ( cM @ X0 @ X1 )
= $true )
| ( $true
!= ( cN @ X1 @ X0 ) )
| ( ( cP @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f13,f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cM @ X0 @ X0 ) )
| ( ( cM @ X0 @ X1 )
= $true )
| ( ( cN @ X0 @ X1 )
= $true )
| ( $true
!= ( cN @ X1 @ X0 ) )
| ( ( cN @ X0 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f38,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f31,f36,f33]) ).
thf(f31,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cN @ ( sK1 @ X0 ) @ X0 ) )
| ( ( cP @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: $i,X1: $i] :
( ( ( cP @ X1 )
= $true )
| ( $true != $true )
| ( $true
= ( cN @ ( sK1 @ X0 ) @ X0 ) ) ),
inference(superposition,[status(thm)],[f27,f14]) ).
thf(f14,plain,
! [X3: $i,X5: $i] :
( ( $true
= ( cM @ ( sK1 @ X3 ) @ X5 ) )
| ( ( cN @ ( sK1 @ X3 ) @ X3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f27,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cM @ X1 @ X0 ) )
| ( ( cP @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f26,f12]) ).
thf(f26,plain,
! [X0: $i,X1: $i] :
( ( ( cN @ X0 @ X1 )
= $true )
| ( $true
!= ( cM @ X1 @ X0 ) )
| ( ( cP @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f25,f12]) ).
thf(f25,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cM @ X1 @ X0 ) )
| ( ( cN @ X0 @ X0 )
= $true )
| ( ( cN @ X0 @ X1 )
= $true )
| ( ( cP @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f23,f13]) ).
thf(f23,plain,
! [X0: $i,X1: $i] :
( ( ( cP @ X0 )
= $true )
| ( ( cM @ X0 @ X1 )
= $true )
| ( ( cN @ X0 @ X1 )
= $true )
| ( ( cN @ X0 @ X0 )
= $true )
| ( $true
!= ( cM @ X1 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( cM @ X1 @ X0 ) )
| ( ( cP @ X0 )
= $true )
| ( ( cM @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( ( cN @ X0 @ X0 )
= $true )
| ( ( cN @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f13,f16]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( cM @ X0 @ X0 ) )
| ( ( cN @ X0 @ X1 )
= $true )
| ( $true
!= ( cM @ X1 @ X0 ) )
| ( ( cM @ X0 @ X1 )
= $true )
| ( ( cN @ X0 @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO109^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 14:25:05 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SYO109^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.45 % Domain : Syntactic
% 0.19/0.45 % Problem : TPS problem THM271
% 0.19/0.45 % Version : Especial.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.45 % Source : [Bro09]
% 0.19/0.45 % Names : tps_0425 [Bro09]
% 0.19/0.45 % : THM271 [TPS]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.17 v7.4.0, 0.22 v7.3.0, 0.20 v7.2.0, 0.25 v7.1.0, 0.29 v7.0.0, 0.25 v6.4.0, 0.29 v6.3.0, 0.33 v6.0.0, 0.17 v5.5.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.0.0
% 0.19/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.45 % Number of atoms : 12 ( 0 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 12 ( 12 avg)
% 0.19/0.45 % Number of connectives : 33 ( 0 ~; 6 |; 2 &; 22 @)
% 0.19/0.45 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 12 ( 12 avg)
% 0.19/0.45 % Number of types : 2 ( 0 usr)
% 0.19/0.45 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 3 ( 3 usr; 0 con; 1-2 aty)
% 0.19/0.45 % Number of variables : 8 ( 0 ^; 6 !; 2 ?; 8 :)
% 0.19/0.45 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(cP,type,
% 0.19/0.45 cP: $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cN,type,
% 0.19/0.45 cN: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cM,type,
% 0.19/0.45 cM: $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(cTHM271,conjecture,
% 0.19/0.45 ( ( ! [Xx: $i] :
% 0.19/0.45 ( ? [Xy: $i] :
% 0.19/0.45 ( ( cM @ Xx @ Xy )
% 0.19/0.45 | ( cN @ Xx @ Xy ) )
% 0.19/0.45 => ( cP @ Xx ) )
% 0.19/0.45 & ! [Xw: $i] :
% 0.19/0.45 ? [Xu: $i] :
% 0.19/0.45 ( ! [Xv: $i] : ( cM @ Xu @ Xv )
% 0.19/0.45 | ( cN @ Xu @ Xw ) )
% 0.19/0.45 & ! [Xw: $i,Xz: $i] :
% 0.19/0.45 ( ( ( cM @ Xw @ Xz )
% 0.19/0.45 | ( cN @ Xw @ Xz ) )
% 0.19/0.45 => ( ( cM @ Xz @ Xw )
% 0.19/0.45 | ( cN @ Xz @ Xw )
% 0.19/0.45 | ( cM @ Xz @ Xz )
% 0.19/0.45 | ( cN @ Xz @ Xz ) ) ) )
% 0.19/0.45 => ! [Xz: $i] : ( cP @ Xz ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.51/1.25 ---- Embedded in THF ---
% 1.51/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.25 %%% Generated on Tue Feb 24 14:25:06 EST 2026
% 1.51/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.25 %%% Logic specification used:
% 1.51/1.25 %%% thf(spec, logic, $$dhol).
% 1.51/1.25
% 1.51/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xOFi67xXag/DTF2DTF3725.p
% See solution above
% 1.51/1.25 ------------------------
% 1.51/1.26 ---- Cleaned THF ---
% 1.51/1.26 thf(cP,type,
% 1.51/1.26 cP: $i > $o ).
% 1.51/1.26
% 1.51/1.26 thf(cN,type,
% 1.51/1.26 cN: $i > $i > $o ).
% 1.51/1.26
% 1.51/1.26 thf(cM,type,
% 1.51/1.26 cM: $i > $i > $o ).
% 1.51/1.26
% 1.51/1.26 thf(cTHM271,conjecture,
% 1.51/1.26 ( ( ! [Xx: $i] :
% 1.51/1.26 ( ? [Xy: $i] :
% 1.51/1.26 ( ( cM @ Xx @ Xy )
% 1.51/1.26 | ( cN @ Xx @ Xy ) )
% 1.51/1.26 => ( cP @ Xx ) )
% 1.51/1.26 & ! [Xw: $i] :
% 1.51/1.26 ? [Xu: $i] :
% 1.51/1.26 ( ! [Xv: $i] : ( cM @ Xu @ Xv )
% 1.51/1.26 | ( cN @ Xu @ Xw ) )
% 1.51/1.26 & ! [Xw: $i,Xz: $i] :
% 1.51/1.26 ( ( ( cM @ Xw @ Xz )
% 1.51/1.26 | ( cN @ Xw @ Xz ) )
% 1.51/1.26 => ( ( cM @ Xz @ Xw )
% 1.51/1.26 | ( cN @ Xz @ Xw )
% 1.51/1.26 | ( cM @ Xz @ Xz )
% 1.51/1.26 | ( cN @ Xz @ Xz ) ) ) )
% 1.51/1.26 => ! [Xz: $i] : ( cP @ Xz ) ) ).
% 1.51/1.26 ------------------------
% 1.51/1.29 % (4021)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3725 for (3000ds/2Mi)
% 1.51/1.29 % (4019)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_3725 for (3000ds/4Mi)
% 1.51/1.29 % (4022)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_3725 for (3000ds/2Mi)
% 1.51/1.29 % (4020)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_3725 for (3000ds/27Mi)
% 1.51/1.29 % (4018)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3725 for (3000ds/183Mi)
% 1.51/1.29 % (4024)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3725 for (3000ds/18Mi)
% 1.51/1.29 % (4023)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_3725 for (3000ds/275Mi)
% 1.51/1.29 % (4021)Instruction limit reached!
% 1.51/1.29 % (4021)------------------------------
% 1.51/1.29 % (4021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (4021)Termination reason: Unknown
% 1.51/1.29 % (4021)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (4021)Memory used [KB]: 5500
% 1.51/1.29 % (4021)Time elapsed: 0.004 s
% 1.51/1.29 % (4021)Instructions burned: 2 (million)
% 1.51/1.29 % (4021)------------------------------
% 1.51/1.29 % (4021)------------------------------
% 1.51/1.29 % (4022)Instruction limit reached!
% 1.51/1.29 % (4022)------------------------------
% 1.51/1.29 % (4022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (4022)Termination reason: Unknown
% 1.51/1.29 % (4022)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (4022)Memory used [KB]: 5500
% 1.51/1.29 % (4022)Time elapsed: 0.004 s
% 1.51/1.29 % (4022)Instructions burned: 3 (million)
% 1.51/1.29 % (4022)------------------------------
% 1.51/1.29 % (4022)------------------------------
% 1.51/1.29 % (4019)Instruction limit reached!
% 1.51/1.29 % (4019)------------------------------
% 1.51/1.29 % (4019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (4019)Termination reason: Unknown
% 1.51/1.29 % (4019)Termination phase: Saturation
% 1.51/1.29
% 1.51/1.29 % (4019)Memory used [KB]: 5500
% 1.51/1.29 % (4019)Time elapsed: 0.005 s
% 1.51/1.29 % (4019)Instructions burned: 4 (million)
% 1.51/1.29 % (4019)------------------------------
% 1.51/1.29 % (4019)------------------------------
% 1.51/1.29 % (4023)First to succeed.
% 1.51/1.29 % (4018)Also succeeded, but the first one will report.
% 1.51/1.29 % (4023)Refutation found. Thanks to Tanya!
% 1.51/1.29 % SZS status Theorem for DTF2THF_3725
% 1.51/1.29 % SZS output start Proof for DTF2THF_3725
% 1.51/1.29 thf(func_def_0, type, cP: $i > $o).
% 1.51/1.29 thf(func_def_1, type, cN: $i > $i > $o).
% 1.51/1.29 thf(func_def_2, type, cM: $i > $i > $o).
% 1.51/1.29 thf(func_def_7, type, sK1: $i > $i).
% 1.51/1.29 thf(f56,plain,(
% 1.51/1.29 $false),
% 1.51/1.29 inference(avatar_sat_refutation,[status(thm)],[f38,f52,f55])).
% 1.51/1.29 thf(f55,plain,(
% 1.51/1.29 ~spl2_1),
% 1.51/1.29 inference(avatar_contradiction_clause,[status(thm)],[f54])).
% 1.51/1.29 thf(f54,plain,(
% 1.51/1.29 $false | ~spl2_1),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f53])).
% 1.51/1.29 thf(f53,plain,(
% 1.51/1.29 ($true != $true) | ~spl2_1),
% 1.51/1.29 inference(superposition,[status(thm)],[f15,f34])).
% 1.51/1.29 thf(f34,plain,(
% 1.51/1.29 ( ! [X1 : $i] : (((cP @ X1) = $true)) ) | ~spl2_1),
% 1.51/1.29 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.51/1.29 thf(f33,definition,(
% 1.51/1.29 spl2_1 <=> ! [X1 : $i] : ((cP @ X1) = $true)),
% 1.51/1.29 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.51/1.29 thf(f15,plain,(
% 1.51/1.29 ($true != (cP @ sK0))),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.29 thf(f11,plain,(
% 1.51/1.29 ! [X0 : $i,X1 : $i] : (($true = (cM @ X0 @ X0)) | ((cN @ X0 @ X1) = $true) | ((cM @ X0 @ X1) = $true) | ((cN @ X0 @ X0) = $true) | (($true != (cN @ X1 @ X0)) & ($true != (cM @ X1 @ X0)))) & ($true != (cP @ sK0)) & ! [X3 : $i] : (((cN @ (sK1 @ X3) @ X3) = $true) | ! [X5 : $i] : ($true = (cM @ (sK1 @ X3) @ X5))) & ! [X6 : $i] : (! [X7 : $i] : (((cM @ X6 @ X7) != $true) & ((cN @ X6 @ X7) != $true)) | ((cP @ X6) = $true))),
% 1.51/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f8,f10,f9])).
% 1.51/1.29 thf(f9,plain,(
% 1.51/1.29 ? [X2 : $i] : ($true != (cP @ X2)) => ($true != (cP @ sK0))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f10,plain,(
% 1.51/1.29 ! [X3 : $i] : (? [X4 : $i] : (($true = (cN @ X4 @ X3)) | ! [X5 : $i] : ($true = (cM @ X4 @ X5))) => (((cN @ (sK1 @ X3) @ X3) = $true) | ! [X5 : $i] : ($true = (cM @ (sK1 @ X3) @ X5))))),
% 1.51/1.29 introduced(definition,[],[choice_axiom])).
% 1.51/1.29 thf(f8,plain,(
% 1.51/1.29 ! [X0 : $i,X1 : $i] : (($true = (cM @ X0 @ X0)) | ((cN @ X0 @ X1) = $true) | ((cM @ X0 @ X1) = $true) | ((cN @ X0 @ X0) = $true) | (($true != (cN @ X1 @ X0)) & ($true != (cM @ X1 @ X0)))) & ? [X2 : $i] : ($true != (cP @ X2)) & ! [X3 : $i] : ? [X4 : $i] : (($true = (cN @ X4 @ X3)) | ! [X5 : $i] : ($true = (cM @ X4 @ X5))) & ! [X6 : $i] : (! [X7 : $i] : (((cM @ X6 @ X7) != $true) & ((cN @ X6 @ X7) != $true)) | ((cP @ X6) = $true))),
% 1.51/1.29 inference(rectify,[status(thm)],[f7])).
% 1.51/1.29 thf(f7,plain,(
% 1.51/1.29 ! [X5 : $i,X6 : $i] : (((cM @ X5 @ X5) = $true) | ((cN @ X5 @ X6) = $true) | ($true = (cM @ X5 @ X6)) | ((cN @ X5 @ X5) = $true) | (((cN @ X6 @ X5) != $true) & ($true != (cM @ X6 @ X5)))) & ? [X7 : $i] : ($true != (cP @ X7)) & ! [X0 : $i] : ? [X1 : $i] : (($true = (cN @ X1 @ X0)) | ! [X2 : $i] : ((cM @ X1 @ X2) = $true)) & ! [X3 : $i] : (! [X4 : $i] : (((cM @ X3 @ X4) != $true) & ($true != (cN @ X3 @ X4))) | ($true = (cP @ X3)))),
% 1.51/1.29 inference(flattening,[status(thm)],[f6])).
% 1.51/1.29 thf(f6,plain,(
% 1.51/1.29 ? [X7 : $i] : ($true != (cP @ X7)) & (! [X0 : $i] : ? [X1 : $i] : (($true = (cN @ X1 @ X0)) | ! [X2 : $i] : ((cM @ X1 @ X2) = $true)) & ! [X5 : $i,X6 : $i] : ((((cM @ X5 @ X5) = $true) | ((cN @ X5 @ X5) = $true) | ($true = (cM @ X5 @ X6)) | ((cN @ X5 @ X6) = $true)) | (((cN @ X6 @ X5) != $true) & ($true != (cM @ X6 @ X5)))) & ! [X3 : $i] : (! [X4 : $i] : (((cM @ X3 @ X4) != $true) & ($true != (cN @ X3 @ X4))) | ($true = (cP @ X3))))),
% 1.51/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.51/1.29 thf(f5,plain,(
% 1.51/1.29 ~((! [X0 : $i] : ? [X1 : $i] : (($true = (cN @ X1 @ X0)) | ! [X2 : $i] : ((cM @ X1 @ X2) = $true)) & ! [X5 : $i,X6 : $i] : ((($true = (cM @ X6 @ X5)) | ((cN @ X6 @ X5) = $true)) => (((cM @ X5 @ X5) = $true) | ((cN @ X5 @ X5) = $true) | ($true = (cM @ X5 @ X6)) | ((cN @ X5 @ X6) = $true))) & ! [X3 : $i] : (? [X4 : $i] : (((cM @ X3 @ X4) = $true) | ($true = (cN @ X3 @ X4))) => ($true = (cP @ X3)))) => ! [X7 : $i] : ($true = (cP @ X7)))),
% 1.51/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.51/1.29 thf(f4,plain,(
% 1.51/1.29 ~((! [X0 : $i] : ? [X1 : $i] : ((cN @ X1 @ X0) | ! [X2 : $i] : (cM @ X1 @ X2)) & ! [X3 : $i] : (? [X4 : $i] : ((cM @ X3 @ X4) | (cN @ X3 @ X4)) => (cP @ X3)) & ! [X5 : $i,X6 : $i] : (((cN @ X6 @ X5) | (cM @ X6 @ X5)) => ((cN @ X5 @ X6) | (cM @ X5 @ X6) | (cN @ X5 @ X5) | (cM @ X5 @ X5)))) => ! [X7 : $i] : (cP @ X7))),
% 1.51/1.29 inference(rectify,[status(thm)],[f2])).
% 1.51/1.29 thf(f2,negated_conjecture,(
% 1.51/1.29 ~((! [X2 : $i] : ? [X3 : $i] : ((cN @ X3 @ X2) | ! [X4 : $i] : (cM @ X3 @ X4)) & ! [X0 : $i] : (? [X1 : $i] : ((cM @ X0 @ X1) | (cN @ X0 @ X1)) => (cP @ X0)) & ! [X5 : $i,X2 : $i] : (((cN @ X2 @ X5) | (cM @ X2 @ X5)) => ((cN @ X5 @ X2) | (cM @ X5 @ X2) | (cN @ X5 @ X5) | (cM @ X5 @ X5)))) => ! [X5 : $i] : (cP @ X5))),
% 1.51/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.51/1.29 thf(f1,conjecture,(
% 1.51/1.29 (! [X2 : $i] : ? [X3 : $i] : ((cN @ X3 @ X2) | ! [X4 : $i] : (cM @ X3 @ X4)) & ! [X0 : $i] : (? [X1 : $i] : ((cM @ X0 @ X1) | (cN @ X0 @ X1)) => (cP @ X0)) & ! [X5 : $i,X2 : $i] : (((cN @ X2 @ X5) | (cM @ X2 @ X5)) => ((cN @ X5 @ X2) | (cM @ X5 @ X2) | (cN @ X5 @ X5) | (cM @ X5 @ X5)))) => ! [X5 : $i] : (cP @ X5)),
% 1.51/1.29 file('/export/starexec/sandbox/tmp/tmp.xOFi67xXag/DTF2THF_3725.p',cTHM271)).
% 1.51/1.29 thf(f52,plain,(
% 1.51/1.29 spl2_1 | ~spl2_2),
% 1.51/1.29 inference(avatar_split_clause,[status(thm)],[f51,f36,f33])).
% 1.51/1.29 thf(f36,definition,(
% 1.51/1.29 spl2_2 <=> ! [X0 : $i] : ($true = (cN @ (sK1 @ X0) @ X0))),
% 1.51/1.29 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.51/1.29 thf(f51,plain,(
% 1.51/1.29 ( ! [X0 : $i] : (((cP @ X0) = $true)) ) | ~spl2_2),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.51/1.29 thf(f50,plain,(
% 1.51/1.29 ( ! [X0 : $i] : (((cP @ X0) = $true) | ($true != $true)) ) | ~spl2_2),
% 1.51/1.29 inference(superposition,[status(thm)],[f47,f37])).
% 1.51/1.29 thf(f37,plain,(
% 1.51/1.29 ( ! [X0 : $i] : (($true = (cN @ (sK1 @ X0) @ X0))) ) | ~spl2_2),
% 1.51/1.29 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.51/1.29 thf(f47,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (($true != (cN @ X1 @ X0)) | ((cP @ X0) = $true)) )),
% 1.51/1.29 inference(subsumption_resolution,[status(thm)],[f46,f13])).
% 1.51/1.29 thf(f13,plain,(
% 1.51/1.29 ( ! [X6 : $i,X7 : $i] : (((cM @ X6 @ X7) != $true) | ((cP @ X6) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.29 thf(f46,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (($true != (cN @ X1 @ X0)) | ((cP @ X0) = $true) | ((cM @ X0 @ X1) = $true)) )),
% 1.51/1.29 inference(subsumption_resolution,[status(thm)],[f45,f12])).
% 1.51/1.29 thf(f12,plain,(
% 1.51/1.29 ( ! [X6 : $i,X7 : $i] : (((cN @ X6 @ X7) != $true) | ((cP @ X6) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.29 thf(f45,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((cN @ X0 @ X0) = $true) | ((cP @ X0) = $true) | ($true != (cN @ X1 @ X0)) | ((cM @ X0 @ X1) = $true)) )),
% 1.51/1.29 inference(subsumption_resolution,[status(thm)],[f44,f12])).
% 1.51/1.29 thf(f44,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((cN @ X0 @ X1) = $true) | ((cM @ X0 @ X1) = $true) | ((cN @ X0 @ X0) = $true) | ((cP @ X0) = $true) | ($true != (cN @ X1 @ X0))) )),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f40])).
% 1.51/1.29 thf(f40,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((cN @ X0 @ X1) = $true) | ($true != $true) | ((cN @ X0 @ X0) = $true) | ((cM @ X0 @ X1) = $true) | ($true != (cN @ X1 @ X0)) | ((cP @ X0) = $true)) )),
% 1.51/1.29 inference(superposition,[status(thm)],[f13,f17])).
% 1.51/1.29 thf(f17,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (($true = (cM @ X0 @ X0)) | ((cM @ X0 @ X1) = $true) | ((cN @ X0 @ X1) = $true) | ($true != (cN @ X1 @ X0)) | ((cN @ X0 @ X0) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.29 thf(f38,plain,(
% 1.51/1.29 spl2_1 | spl2_2),
% 1.51/1.29 inference(avatar_split_clause,[status(thm)],[f31,f36,f33])).
% 1.51/1.29 thf(f31,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (($true = (cN @ (sK1 @ X0) @ X0)) | ((cP @ X1) = $true)) )),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f28])).
% 1.51/1.29 thf(f28,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((cP @ X1) = $true) | ($true != $true) | ($true = (cN @ (sK1 @ X0) @ X0))) )),
% 1.51/1.29 inference(superposition,[status(thm)],[f27,f14])).
% 1.51/1.29 thf(f14,plain,(
% 1.51/1.29 ( ! [X3 : $i,X5 : $i] : (($true = (cM @ (sK1 @ X3) @ X5)) | ((cN @ (sK1 @ X3) @ X3) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.29 thf(f27,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (($true != (cM @ X1 @ X0)) | ((cP @ X0) = $true)) )),
% 1.51/1.29 inference(subsumption_resolution,[status(thm)],[f26,f12])).
% 1.51/1.29 thf(f26,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((cN @ X0 @ X1) = $true) | ($true != (cM @ X1 @ X0)) | ((cP @ X0) = $true)) )),
% 1.51/1.29 inference(subsumption_resolution,[status(thm)],[f25,f12])).
% 1.51/1.29 thf(f25,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (($true != (cM @ X1 @ X0)) | ((cN @ X0 @ X0) = $true) | ((cN @ X0 @ X1) = $true) | ((cP @ X0) = $true)) )),
% 1.51/1.29 inference(subsumption_resolution,[status(thm)],[f23,f13])).
% 1.51/1.29 thf(f23,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (((cP @ X0) = $true) | ((cM @ X0 @ X1) = $true) | ((cN @ X0 @ X1) = $true) | ((cN @ X0 @ X0) = $true) | ($true != (cM @ X1 @ X0))) )),
% 1.51/1.29 inference(trivial_inequality_removal,[status(thm)],[f21])).
% 1.51/1.29 thf(f21,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (($true != (cM @ X1 @ X0)) | ((cP @ X0) = $true) | ((cM @ X0 @ X1) = $true) | ($true != $true) | ((cN @ X0 @ X0) = $true) | ((cN @ X0 @ X1) = $true)) )),
% 1.51/1.29 inference(superposition,[status(thm)],[f13,f16])).
% 1.51/1.29 thf(f16,plain,(
% 1.51/1.29 ( ! [X0 : $i,X1 : $i] : (($true = (cM @ X0 @ X0)) | ((cN @ X0 @ X1) = $true) | ($true != (cM @ X1 @ X0)) | ((cM @ X0 @ X1) = $true) | ((cN @ X0 @ X0) = $true)) )),
% 1.51/1.29 inference(cnf_transformation,[status(thm)],[f11])).
% 1.51/1.29 % SZS output end Proof for DTF2THF_3725
% 1.51/1.29 % (4023)------------------------------
% 1.51/1.29 % (4023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.29 % (4023)Termination reason: Refutation
% 1.51/1.29
% 1.51/1.29 % (4023)Memory used [KB]: 5500
% 1.51/1.29 % (4023)Time elapsed: 0.009 s
% 1.51/1.29 % (4023)Instructions burned: 7 (million)
% 1.51/1.29 % (4023)------------------------------
% 1.51/1.29 % (4023)------------------------------
% 1.51/1.29 % (4017)Success in time 0.024 s
%------------------------------------------------------------------------------