%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYN364^5 : 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 : n029.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 09:50:51 AM UTC 2026
% Result : Theorem 1.53s 1.35s
% Output : Refutation 1.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 41 ( 2 unt; 0 typ; 4 def)
% Number of atoms : 357 ( 93 equ; 0 cnn)
% Maximal formula atoms : 9 ( 8 avg)
% Number of connectives : 425 ( 71 ~; 56 |; 38 &; 239 @)
% ( 4 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 96 ( 0 ^; 73 !; 23 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cP: $i > $i > $o ).
thf(func_def_1,type,
g: $i > $i ).
thf(func_def_2,type,
cM: $i > $o ).
thf(func_def_3,type,
cQ: $i > $o ).
thf(func_def_4,type,
f: $i > $i > $i ).
thf(func_def_8,type,
sK0: $i > $i ).
thf(f47,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f25,f32,f35,f38,f46]) ).
thf(f46,plain,
~ spl2_4,
inference(avatar_contradiction_clause,[status(thm)],[f45]) ).
thf(f45,plain,
( $false
| ~ spl2_4 ),
inference(subsumption_resolution,[status(thm)],[f44,f31]) ).
thf(f31,plain,
( ! [X6: $i,X5: $i] :
( $true
!= ( cP @ X5 @ X6 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f30]) ).
thf(f30,definition,
( spl2_4
<=> ! [X6: $i,X5: $i] :
( $true
!= ( cP @ X5 @ X6 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f44,plain,
( ! [X0: $i] :
( ( cP @ X0 @ ( sK0 @ X0 ) )
= $true )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f43]) ).
thf(f43,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cP @ X0 @ ( sK0 @ X0 ) )
= $true ) )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f42,f15]) ).
thf(f15,plain,
! [X1: $i] :
( ( ( cQ @ ( f @ X1 @ ( sK0 @ X1 ) ) )
= $true )
| ( ( cP @ X1 @ ( sK0 @ X1 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
( ! [X0: $i] :
( ( ( cM @ ( g @ X0 ) )
!= $true )
| ( $true
!= ( cQ @ X0 ) ) )
& ! [X1: $i] :
( ( ( ( cM @ X1 )
= $true )
& ( ( cQ @ ( f @ X1 @ ( sK0 @ X1 ) ) )
= $true ) )
| ( ( cP @ X1 @ ( sK0 @ X1 ) )
= $true ) )
& ! [X4: $i] :
( ( $true
!= ( cP @ sK1 @ sK1 ) )
| ( $true
!= ( cP @ ( g @ sK1 ) @ X4 ) ) )
& ! [X5: $i] :
( ! [X6: $i] :
( $true
!= ( cP @ X5 @ X6 ) )
| ! [X7: $i] :
( ( cP @ X7 @ X7 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10]) ).
thf(f10,plain,
! [X1: $i] :
( ? [X2: $i] :
( ( ( ( cM @ X1 )
= $true )
& ( ( cQ @ ( f @ X1 @ X2 ) )
= $true ) )
| ( $true
= ( cP @ X1 @ X2 ) ) )
=> ( ( ( ( cM @ X1 )
= $true )
& ( ( cQ @ ( f @ X1 @ ( sK0 @ X1 ) ) )
= $true ) )
| ( ( cP @ X1 @ ( sK0 @ X1 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X3: $i] :
! [X4: $i] :
( ( ( cP @ X3 @ X3 )
!= $true )
| ( ( cP @ ( g @ X3 ) @ X4 )
!= $true ) )
=> ! [X4: $i] :
( ( $true
!= ( cP @ sK1 @ sK1 ) )
| ( $true
!= ( cP @ ( g @ sK1 ) @ X4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f9,plain,
( ! [X0: $i] :
( ( ( cM @ ( g @ X0 ) )
!= $true )
| ( $true
!= ( cQ @ X0 ) ) )
& ! [X1: $i] :
? [X2: $i] :
( ( ( ( cM @ X1 )
= $true )
& ( ( cQ @ ( f @ X1 @ X2 ) )
= $true ) )
| ( $true
= ( cP @ X1 @ X2 ) ) )
& ? [X3: $i] :
! [X4: $i] :
( ( ( cP @ X3 @ X3 )
!= $true )
| ( ( cP @ ( g @ X3 ) @ X4 )
!= $true ) )
& ! [X5: $i] :
( ! [X6: $i] :
( $true
!= ( cP @ X5 @ X6 ) )
| ! [X7: $i] :
( ( cP @ X7 @ X7 )
= $true ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ! [X0: $i] :
( ( ( cM @ ( g @ X0 ) )
!= $true )
| ( $true
!= ( cQ @ X0 ) ) )
& ! [X4: $i] :
? [X5: $i] :
( ( ( $true
= ( cM @ X4 ) )
& ( ( cQ @ ( f @ X4 @ X5 ) )
= $true ) )
| ( $true
= ( cP @ X4 @ X5 ) ) )
& ? [X6: $i] :
! [X7: $i] :
( ( ( cP @ X6 @ X6 )
!= $true )
| ( ( cP @ ( g @ X6 ) @ X7 )
!= $true ) )
& ! [X1: $i] :
( ! [X2: $i] :
( $true
!= ( cP @ X1 @ X2 ) )
| ! [X3: $i] :
( ( cP @ X3 @ X3 )
= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
( ? [X6: $i] :
! [X7: $i] :
( ( ( cP @ X6 @ X6 )
!= $true )
| ( ( cP @ ( g @ X6 ) @ X7 )
!= $true ) )
& ! [X0: $i] :
( ( ( cM @ ( g @ X0 ) )
!= $true )
| ( $true
!= ( cQ @ X0 ) ) )
& ! [X4: $i] :
? [X5: $i] :
( ( ( $true
= ( cM @ X4 ) )
& ( ( cQ @ ( f @ X4 @ X5 ) )
= $true ) )
| ( $true
= ( cP @ X4 @ X5 ) ) )
& ! [X1: $i] :
( ! [X2: $i] :
( $true
!= ( cP @ X1 @ X2 ) )
| ! [X3: $i] :
( ( cP @ X3 @ X3 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ( ! [X0: $i] :
( ( $true
= ( cQ @ X0 ) )
=> ( ( cM @ ( g @ X0 ) )
!= $true ) )
& ! [X4: $i] :
? [X5: $i] :
( ( ( $true
= ( cM @ X4 ) )
& ( ( cQ @ ( f @ X4 @ X5 ) )
= $true ) )
| ( $true
= ( cP @ X4 @ X5 ) ) )
& ! [X1: $i] :
( ? [X2: $i] :
( $true
= ( cP @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( cP @ X3 @ X3 )
= $true ) ) )
=> ! [X6: $i] :
? [X7: $i] :
( ( ( cP @ ( g @ X6 ) @ X7 )
= $true )
& ( ( cP @ X6 @ X6 )
= $true ) ) ),
inference(flattening,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: $i] :
( ( $true
= ( cQ @ X0 ) )
=> ( ( cM @ ( g @ X0 ) )
!= $true ) )
& ! [X1: $i] :
( ? [X2: $i] :
( $true
= ( cP @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( cP @ X3 @ X3 )
= $true ) )
& ! [X4: $i] :
? [X5: $i] :
( ( ( $true
= ( cM @ X4 ) )
& ( ( cQ @ ( f @ X4 @ X5 ) )
= $true ) )
| ( $true
= ( cP @ X4 @ X5 ) ) ) )
=> ! [X6: $i] :
? [X7: $i] :
( ( ( cP @ ( g @ X6 ) @ X7 )
= $true )
& ( ( cP @ X6 @ X6 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: $i] :
( ( cQ @ X0 )
=> ~ ( cM @ ( g @ X0 ) ) )
& ! [X1: $i] :
( ? [X2: $i] : ( cP @ X1 @ X2 )
=> ! [X3: $i] : ( cP @ X3 @ X3 ) )
& ! [X4: $i] :
? [X5: $i] :
( ( ( cQ @ ( f @ X4 @ X5 ) )
& ( cM @ X4 ) )
| ( cP @ X4 @ X5 ) ) )
=> ! [X6: $i] :
? [X7: $i] :
( ( cP @ X6 @ X6 )
& ( cP @ ( g @ X6 ) @ X7 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X5: $i] :
( ( cQ @ X5 )
=> ~ ( cM @ ( g @ X5 ) ) )
& ! [X0: $i] :
( ? [X1: $i] : ( cP @ X0 @ X1 )
=> ! [X2: $i] : ( cP @ X2 @ X2 ) )
& ! [X3: $i] :
? [X4: $i] :
( ( ( cQ @ ( f @ X3 @ X4 ) )
& ( cM @ X3 ) )
| ( cP @ X3 @ X4 ) ) )
=> ! [X3: $i] :
? [X4: $i] :
( ( cP @ X3 @ X3 )
& ( cP @ ( g @ X3 ) @ X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X5: $i] :
( ( cQ @ X5 )
=> ~ ( cM @ ( g @ X5 ) ) )
& ! [X0: $i] :
( ? [X1: $i] : ( cP @ X0 @ X1 )
=> ! [X2: $i] : ( cP @ X2 @ X2 ) )
& ! [X3: $i] :
? [X4: $i] :
( ( ( cQ @ ( f @ X3 @ X4 ) )
& ( cM @ X3 ) )
| ( cP @ X3 @ X4 ) ) )
=> ! [X3: $i] :
? [X4: $i] :
( ( cP @ X3 @ X3 )
& ( cP @ ( g @ X3 ) @ X4 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.KQc1Hb7sqG/DTF2THF_2240.p',cX2115) ).
thf(f42,plain,
( ! [X0: $i] :
( $true
!= ( cQ @ X0 ) )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cQ @ X0 ) ) )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f17,f40]) ).
thf(f40,plain,
( ! [X0: $i] :
( ( cM @ X0 )
= $true )
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cM @ X0 )
= $true ) )
| ~ spl2_4 ),
inference(superposition,[status(thm)],[f31,f16]) ).
thf(f16,plain,
! [X1: $i] :
( ( ( cP @ X1 @ ( sK0 @ X1 ) )
= $true )
| ( ( cM @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f17,plain,
! [X0: $i] :
( ( ( cM @ ( g @ X0 ) )
!= $true )
| ( $true
!= ( cQ @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f38,plain,
( ~ spl2_1
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f37]) ).
thf(f37,plain,
( $false
| ~ spl2_1
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
( ( $true != $true )
| ~ spl2_1
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f20,f28]) ).
thf(f28,plain,
( ! [X7: $i] :
( ( cP @ X7 @ X7 )
= $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl2_3
<=> ! [X7: $i] :
( ( cP @ X7 @ X7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f20,plain,
( ! [X4: $i] :
( $true
!= ( cP @ ( g @ sK1 ) @ X4 ) )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f19]) ).
thf(f19,definition,
( spl2_1
<=> ! [X4: $i] :
( $true
!= ( cP @ ( g @ sK1 ) @ X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f35,plain,
( spl2_2
| ~ spl2_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f34]) ).
thf(f34,plain,
( $false
| spl2_2
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
( ( $true != $true )
| spl2_2
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f24,f28]) ).
thf(f24,plain,
( ( $true
!= ( cP @ sK1 @ sK1 ) )
| spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f22]) ).
thf(f22,definition,
( spl2_2
<=> ( $true
= ( cP @ sK1 @ sK1 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f32,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f13,f30,f27]) ).
thf(f13,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( cP @ X5 @ X6 ) )
| ( ( cP @ X7 @ X7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
thf(f25,plain,
( spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f14,f22,f19]) ).
thf(f14,plain,
! [X4: $i] :
( ( $true
!= ( cP @ ( g @ sK1 ) @ X4 ) )
| ( $true
!= ( cP @ sK1 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYN364^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n029.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 13:56:29 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYN364^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem X2115
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0397 [Bro09]
% 0.16/0.39 % : THM69 [TPS]
% 0.16/0.39 % : X2115 [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.17 v9.1.0, 0.12 v9.0.0, 0.17 v8.2.0, 0.18 v8.1.0, 0.25 v7.5.0, 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 v5.3.0, 0.25 v5.2.0, 0.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 6 ( 0 unt; 5 typ; 0 def)
% 0.16/0.39 % Number of atoms : 9 ( 0 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 9 ( 9 avg)
% 0.16/0.39 % Number of connectives : 27 ( 1 ~; 1 |; 4 &; 18 @)
% 0.16/0.39 % ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 11 ( 11 avg)
% 0.16/0.39 % Number of types : 2 ( 0 usr)
% 0.16/0.39 % Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 5 ( 5 usr; 0 con; 1-2 aty)
% 0.16/0.39 % Number of variables : 8 ( 0 ^; 5 !; 3 ?; 8 :)
% 0.16/0.39 % SPC : TH0_THM_NEQ_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 % :
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(cP,type,
% 0.16/0.39 cP: $i > $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(g,type,
% 0.16/0.39 g: $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(cM,type,
% 0.16/0.39 cM: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(cQ,type,
% 0.16/0.39 cQ: $i > $o ).
% 0.16/0.39
% 0.16/0.39 thf(f,type,
% 0.16/0.39 f: $i > $i > $i ).
% 0.16/0.39
% 0.16/0.39 thf(cX2115,conjecture,
% 0.16/0.39 ( ( ! [Xx: $i] :
% 0.16/0.39 ( ? [Xy: $i] : ( cP @ Xx @ Xy )
% 0.16/0.39 => ! [Xz: $i] : ( cP @ Xz @ Xz ) )
% 0.16/0.39 & ! [Xu: $i] :
% 0.16/0.39 ? [Xv: $i] :
% 0.16/0.39 ( ( cP @ Xu @ Xv )
% 0.16/0.39 | ( ( cM @ Xu )
% 0.16/0.39 & ( cQ @ ( f @ Xu @ Xv ) ) ) )
% 0.16/0.39 & ! [Xw: $i] :
% 0.16/0.39 ( ( cQ @ Xw )
% 0.16/0.39 => ~ ( cM @ ( g @ Xw ) ) ) )
% 0.16/0.39 => ! [Xu: $i] :
% 0.16/0.39 ? [Xv: $i] :
% 0.16/0.39 ( ( cP @ ( g @ Xu ) @ Xv )
% 0.16/0.39 & ( cP @ Xu @ Xu ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.53/1.31 ---- Embedded in THF ---
% 1.53/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.31 %%% Generated on Tue Feb 24 13:56:30 EST 2026
% 1.53/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.31 %%% Logic specification used:
% 1.53/1.31 %%% thf(spec, logic, $$dhol).
% 1.53/1.31
% 1.53/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.KQc1Hb7sqG/DTF2DTF2240.p
% See solution above
% 1.53/1.31 ------------------------
% 1.53/1.32 ---- Cleaned THF ---
% 1.53/1.32 thf(cP,type,
% 1.53/1.32 cP: $i > $i > $o ).
% 1.53/1.32
% 1.53/1.32 thf(g,type,
% 1.53/1.32 g: $i > $i ).
% 1.53/1.32
% 1.53/1.32 thf(cM,type,
% 1.53/1.32 cM: $i > $o ).
% 1.53/1.32
% 1.53/1.32 thf(cQ,type,
% 1.53/1.32 cQ: $i > $o ).
% 1.53/1.32
% 1.53/1.32 thf(f,type,
% 1.53/1.32 f: $i > $i > $i ).
% 1.53/1.32
% 1.53/1.32 thf(cX2115,conjecture,
% 1.53/1.32 ( ( ! [Xx: $i] :
% 1.53/1.32 ( ? [Xy: $i] : ( cP @ Xx @ Xy )
% 1.53/1.32 => ! [Xz: $i] : ( cP @ Xz @ Xz ) )
% 1.53/1.32 & ! [Xu: $i] :
% 1.53/1.32 ? [Xv: $i] :
% 1.53/1.32 ( ( cP @ Xu @ Xv )
% 1.53/1.32 | ( ( cM @ Xu )
% 1.53/1.32 & ( cQ @ ( f @ Xu @ Xv ) ) ) )
% 1.53/1.32 & ! [Xw: $i] :
% 1.53/1.32 ( ( cQ @ Xw )
% 1.53/1.32 => ~ ( cM @ ( g @ Xw ) ) ) )
% 1.53/1.32 => ! [Xu: $i] :
% 1.53/1.32 ? [Xv: $i] :
% 1.53/1.32 ( ( cP @ ( g @ Xu ) @ Xv )
% 1.53/1.32 & ( cP @ Xu @ Xu ) ) ) ).
% 1.53/1.32 ------------------------
% 1.53/1.34 % (2343)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_2240 for (2999ds/275Mi)
% 1.53/1.34 % (2338)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_2240 for (2999ds/183Mi)
% 1.53/1.34 % (2342)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_2240 for (2999ds/2Mi)
% 1.53/1.34 % (2344)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_2240 for (2999ds/18Mi)
% 1.53/1.34 % (2339)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_2240 for (2999ds/4Mi)
% 1.53/1.34 % (2341)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_2240 for (2999ds/2Mi)
% 1.53/1.34 % (2340)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_2240 for (2999ds/27Mi)
% 1.53/1.35 % (2341)Instruction limit reached!
% 1.53/1.35 % (2341)------------------------------
% 1.53/1.35 % (2341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.35 % (2341)Termination reason: Unknown
% 1.53/1.35 % (2341)Termination phase: Saturation
% 1.53/1.35 % (2342)Instruction limit reached!
% 1.53/1.35 % (2342)------------------------------
% 1.53/1.35 % (2342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.35 % (2342)Termination reason: Unknown
% 1.53/1.35 % (2342)Termination phase: Saturation
% 1.53/1.35
% 1.53/1.35 % (2342)Memory used [KB]: 5500
% 1.53/1.35 % (2342)Time elapsed: 0.003 s
% 1.53/1.35 % (2342)Instructions burned: 2 (million)
% 1.53/1.35 % (2342)------------------------------
% 1.53/1.35 % (2342)------------------------------
% 1.53/1.35
% 1.53/1.35 % (2341)Memory used [KB]: 5373
% 1.53/1.35 % (2341)Time elapsed: 0.003 s
% 1.53/1.35 % (2341)Instructions burned: 2 (million)
% 1.53/1.35 % (2341)------------------------------
% 1.53/1.35 % (2341)------------------------------
% 1.53/1.35 % (2338)First to succeed.
% 1.53/1.35 % (2339)Instruction limit reached!
% 1.53/1.35 % (2339)------------------------------
% 1.53/1.35 % (2339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.35 % (2339)Termination reason: Unknown
% 1.53/1.35 % (2339)Termination phase: Saturation
% 1.53/1.35
% 1.53/1.35 % (2339)Memory used [KB]: 5500
% 1.53/1.35 % (2339)Time elapsed: 0.005 s
% 1.53/1.35 % (2339)Instructions burned: 4 (million)
% 1.53/1.35 % (2339)------------------------------
% 1.53/1.35 % (2339)------------------------------
% 1.53/1.35 % (2344)Also succeeded, but the first one will report.
% 1.53/1.35 % (2340)Also succeeded, but the first one will report.
% 1.53/1.35 % (2338)Refutation found. Thanks to Tanya!
% 1.53/1.35 % SZS status Theorem for DTF2THF_2240
% 1.53/1.35 % SZS output start Proof for DTF2THF_2240
% 1.53/1.35 thf(func_def_0, type, cP: $i > $i > $o).
% 1.53/1.35 thf(func_def_1, type, g: $i > $i).
% 1.53/1.35 thf(func_def_2, type, cM: $i > $o).
% 1.53/1.35 thf(func_def_3, type, cQ: $i > $o).
% 1.53/1.35 thf(func_def_4, type, f: $i > $i > $i).
% 1.53/1.35 thf(func_def_8, type, sK0: $i > $i).
% 1.53/1.35 thf(f47,plain,(
% 1.53/1.35 $false),
% 1.53/1.35 inference(avatar_sat_refutation,[status(thm)],[f25,f32,f35,f38,f46])).
% 1.53/1.35 thf(f46,plain,(
% 1.53/1.35 ~spl2_4),
% 1.53/1.35 inference(avatar_contradiction_clause,[status(thm)],[f45])).
% 1.53/1.35 thf(f45,plain,(
% 1.53/1.35 $false | ~spl2_4),
% 1.53/1.35 inference(subsumption_resolution,[status(thm)],[f44,f31])).
% 1.53/1.35 thf(f31,plain,(
% 1.53/1.35 ( ! [X6 : $i,X5 : $i] : (($true != (cP @ X5 @ X6))) ) | ~spl2_4),
% 1.53/1.35 inference(avatar_component_clause,[status(thm)],[f30])).
% 1.53/1.35 thf(f30,definition,(
% 1.53/1.35 spl2_4 <=> ! [X6 : $i,X5 : $i] : ($true != (cP @ X5 @ X6))),
% 1.53/1.35 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.53/1.35 thf(f44,plain,(
% 1.53/1.35 ( ! [X0 : $i] : (((cP @ X0 @ (sK0 @ X0)) = $true)) ) | ~spl2_4),
% 1.53/1.35 inference(trivial_inequality_removal,[status(thm)],[f43])).
% 1.53/1.35 thf(f43,plain,(
% 1.53/1.35 ( ! [X0 : $i] : (($true != $true) | ((cP @ X0 @ (sK0 @ X0)) = $true)) ) | ~spl2_4),
% 1.53/1.35 inference(superposition,[status(thm)],[f42,f15])).
% 1.53/1.35 thf(f15,plain,(
% 1.53/1.35 ( ! [X1 : $i] : (((cQ @ (f @ X1 @ (sK0 @ X1))) = $true) | ((cP @ X1 @ (sK0 @ X1)) = $true)) )),
% 1.53/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.35 thf(f12,plain,(
% 1.53/1.35 ! [X0 : $i] : (((cM @ (g @ X0)) != $true) | ($true != (cQ @ X0))) & ! [X1 : $i] : ((((cM @ X1) = $true) & ((cQ @ (f @ X1 @ (sK0 @ X1))) = $true)) | ((cP @ X1 @ (sK0 @ X1)) = $true)) & ! [X4 : $i] : (($true != (cP @ sK1 @ sK1)) | ($true != (cP @ (g @ sK1) @ X4))) & ! [X5 : $i] : (! [X6 : $i] : ($true != (cP @ X5 @ X6)) | ! [X7 : $i] : ((cP @ X7 @ X7) = $true))),
% 1.53/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f9,f11,f10])).
% 1.53/1.35 thf(f10,plain,(
% 1.53/1.35 ! [X1 : $i] : (? [X2 : $i] : ((((cM @ X1) = $true) & ((cQ @ (f @ X1 @ X2)) = $true)) | ($true = (cP @ X1 @ X2))) => ((((cM @ X1) = $true) & ((cQ @ (f @ X1 @ (sK0 @ X1))) = $true)) | ((cP @ X1 @ (sK0 @ X1)) = $true)))),
% 1.53/1.35 introduced(definition,[],[choice_axiom])).
% 1.53/1.35 thf(f11,plain,(
% 1.53/1.35 ? [X3 : $i] : ! [X4 : $i] : (((cP @ X3 @ X3) != $true) | ((cP @ (g @ X3) @ X4) != $true)) => ! [X4 : $i] : (($true != (cP @ sK1 @ sK1)) | ($true != (cP @ (g @ sK1) @ X4)))),
% 1.53/1.35 introduced(definition,[],[choice_axiom])).
% 1.53/1.35 thf(f9,plain,(
% 1.53/1.35 ! [X0 : $i] : (((cM @ (g @ X0)) != $true) | ($true != (cQ @ X0))) & ! [X1 : $i] : ? [X2 : $i] : ((((cM @ X1) = $true) & ((cQ @ (f @ X1 @ X2)) = $true)) | ($true = (cP @ X1 @ X2))) & ? [X3 : $i] : ! [X4 : $i] : (((cP @ X3 @ X3) != $true) | ((cP @ (g @ X3) @ X4) != $true)) & ! [X5 : $i] : (! [X6 : $i] : ($true != (cP @ X5 @ X6)) | ! [X7 : $i] : ((cP @ X7 @ X7) = $true))),
% 1.53/1.35 inference(rectify,[status(thm)],[f8])).
% 1.53/1.35 thf(f8,plain,(
% 1.53/1.35 ! [X0 : $i] : (((cM @ (g @ X0)) != $true) | ($true != (cQ @ X0))) & ! [X4 : $i] : ? [X5 : $i] : ((($true = (cM @ X4)) & ((cQ @ (f @ X4 @ X5)) = $true)) | ($true = (cP @ X4 @ X5))) & ? [X6 : $i] : ! [X7 : $i] : (((cP @ X6 @ X6) != $true) | ((cP @ (g @ X6) @ X7) != $true)) & ! [X1 : $i] : (! [X2 : $i] : ($true != (cP @ X1 @ X2)) | ! [X3 : $i] : ((cP @ X3 @ X3) = $true))),
% 1.53/1.35 inference(flattening,[status(thm)],[f7])).
% 1.53/1.35 thf(f7,plain,(
% 1.53/1.35 ? [X6 : $i] : ! [X7 : $i] : (((cP @ X6 @ X6) != $true) | ((cP @ (g @ X6) @ X7) != $true)) & (! [X0 : $i] : (((cM @ (g @ X0)) != $true) | ($true != (cQ @ X0))) & ! [X4 : $i] : ? [X5 : $i] : ((($true = (cM @ X4)) & ((cQ @ (f @ X4 @ X5)) = $true)) | ($true = (cP @ X4 @ X5))) & ! [X1 : $i] : (! [X2 : $i] : ($true != (cP @ X1 @ X2)) | ! [X3 : $i] : ((cP @ X3 @ X3) = $true)))),
% 1.53/1.35 inference(ennf_transformation,[status(thm)],[f6])).
% 1.53/1.35 thf(f6,plain,(
% 1.53/1.35 ~((! [X0 : $i] : (($true = (cQ @ X0)) => ((cM @ (g @ X0)) != $true)) & ! [X4 : $i] : ? [X5 : $i] : ((($true = (cM @ X4)) & ((cQ @ (f @ X4 @ X5)) = $true)) | ($true = (cP @ X4 @ X5))) & ! [X1 : $i] : (? [X2 : $i] : ($true = (cP @ X1 @ X2)) => ! [X3 : $i] : ((cP @ X3 @ X3) = $true))) => ! [X6 : $i] : ? [X7 : $i] : (((cP @ (g @ X6) @ X7) = $true) & ((cP @ X6 @ X6) = $true)))),
% 1.53/1.35 inference(flattening,[status(thm)],[f5])).
% 1.53/1.35 thf(f5,plain,(
% 1.53/1.35 ~((! [X0 : $i] : (($true = (cQ @ X0)) => ~((cM @ (g @ X0)) = $true)) & ! [X1 : $i] : (? [X2 : $i] : ($true = (cP @ X1 @ X2)) => ! [X3 : $i] : ((cP @ X3 @ X3) = $true)) & ! [X4 : $i] : ? [X5 : $i] : ((($true = (cM @ X4)) & ((cQ @ (f @ X4 @ X5)) = $true)) | ($true = (cP @ X4 @ X5)))) => ! [X6 : $i] : ? [X7 : $i] : (((cP @ (g @ X6) @ X7) = $true) & ((cP @ X6 @ X6) = $true)))),
% 1.53/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.53/1.35 thf(f4,plain,(
% 1.53/1.35 ~((! [X0 : $i] : ((cQ @ X0) => ~(cM @ (g @ X0))) & ! [X1 : $i] : (? [X2 : $i] : (cP @ X1 @ X2) => ! [X3 : $i] : (cP @ X3 @ X3)) & ! [X4 : $i] : ? [X5 : $i] : (((cQ @ (f @ X4 @ X5)) & (cM @ X4)) | (cP @ X4 @ X5))) => ! [X6 : $i] : ? [X7 : $i] : ((cP @ X6 @ X6) & (cP @ (g @ X6) @ X7)))),
% 1.53/1.35 inference(rectify,[status(thm)],[f2])).
% 1.53/1.35 thf(f2,negated_conjecture,(
% 1.53/1.35 ~((! [X5 : $i] : ((cQ @ X5) => ~(cM @ (g @ X5))) & ! [X0 : $i] : (? [X1 : $i] : (cP @ X0 @ X1) => ! [X2 : $i] : (cP @ X2 @ X2)) & ! [X3 : $i] : ? [X4 : $i] : (((cQ @ (f @ X3 @ X4)) & (cM @ X3)) | (cP @ X3 @ X4))) => ! [X3 : $i] : ? [X4 : $i] : ((cP @ X3 @ X3) & (cP @ (g @ X3) @ X4)))),
% 1.53/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.53/1.35 thf(f1,conjecture,(
% 1.53/1.35 (! [X5 : $i] : ((cQ @ X5) => ~(cM @ (g @ X5))) & ! [X0 : $i] : (? [X1 : $i] : (cP @ X0 @ X1) => ! [X2 : $i] : (cP @ X2 @ X2)) & ! [X3 : $i] : ? [X4 : $i] : (((cQ @ (f @ X3 @ X4)) & (cM @ X3)) | (cP @ X3 @ X4))) => ! [X3 : $i] : ? [X4 : $i] : ((cP @ X3 @ X3) & (cP @ (g @ X3) @ X4))),
% 1.53/1.35 file('/export/starexec/sandbox/tmp/tmp.KQc1Hb7sqG/DTF2THF_2240.p',cX2115)).
% 1.53/1.35 thf(f42,plain,(
% 1.53/1.35 ( ! [X0 : $i] : (($true != (cQ @ X0))) ) | ~spl2_4),
% 1.53/1.35 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.53/1.35 thf(f41,plain,(
% 1.53/1.35 ( ! [X0 : $i] : (($true != $true) | ($true != (cQ @ X0))) ) | ~spl2_4),
% 1.53/1.35 inference(superposition,[status(thm)],[f17,f40])).
% 1.53/1.35 thf(f40,plain,(
% 1.53/1.35 ( ! [X0 : $i] : (((cM @ X0) = $true)) ) | ~spl2_4),
% 1.53/1.35 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.53/1.35 thf(f39,plain,(
% 1.53/1.35 ( ! [X0 : $i] : (($true != $true) | ((cM @ X0) = $true)) ) | ~spl2_4),
% 1.53/1.35 inference(superposition,[status(thm)],[f31,f16])).
% 1.53/1.35 thf(f16,plain,(
% 1.53/1.35 ( ! [X1 : $i] : (((cP @ X1 @ (sK0 @ X1)) = $true) | ((cM @ X1) = $true)) )),
% 1.53/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.35 thf(f17,plain,(
% 1.53/1.35 ( ! [X0 : $i] : (((cM @ (g @ X0)) != $true) | ($true != (cQ @ X0))) )),
% 1.53/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.35 thf(f38,plain,(
% 1.53/1.35 ~spl2_1 | ~spl2_3),
% 1.53/1.35 inference(avatar_contradiction_clause,[status(thm)],[f37])).
% 1.53/1.35 thf(f37,plain,(
% 1.53/1.35 $false | (~spl2_1 | ~spl2_3)),
% 1.53/1.35 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.53/1.35 thf(f36,plain,(
% 1.53/1.35 ($true != $true) | (~spl2_1 | ~spl2_3)),
% 1.53/1.35 inference(superposition,[status(thm)],[f20,f28])).
% 1.53/1.35 thf(f28,plain,(
% 1.53/1.35 ( ! [X7 : $i] : (((cP @ X7 @ X7) = $true)) ) | ~spl2_3),
% 1.53/1.35 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.53/1.35 thf(f27,definition,(
% 1.53/1.35 spl2_3 <=> ! [X7 : $i] : ((cP @ X7 @ X7) = $true)),
% 1.53/1.35 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.53/1.35 thf(f20,plain,(
% 1.53/1.35 ( ! [X4 : $i] : (($true != (cP @ (g @ sK1) @ X4))) ) | ~spl2_1),
% 1.53/1.35 inference(avatar_component_clause,[status(thm)],[f19])).
% 1.53/1.35 thf(f19,definition,(
% 1.53/1.35 spl2_1 <=> ! [X4 : $i] : ($true != (cP @ (g @ sK1) @ X4))),
% 1.53/1.35 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.53/1.35 thf(f35,plain,(
% 1.53/1.35 spl2_2 | ~spl2_3),
% 1.53/1.35 inference(avatar_contradiction_clause,[status(thm)],[f34])).
% 1.53/1.35 thf(f34,plain,(
% 1.53/1.35 $false | (spl2_2 | ~spl2_3)),
% 1.53/1.35 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.53/1.35 thf(f33,plain,(
% 1.53/1.35 ($true != $true) | (spl2_2 | ~spl2_3)),
% 1.53/1.35 inference(superposition,[status(thm)],[f24,f28])).
% 1.53/1.35 thf(f24,plain,(
% 1.53/1.35 ($true != (cP @ sK1 @ sK1)) | spl2_2),
% 1.53/1.35 inference(avatar_component_clause,[status(thm)],[f22])).
% 1.53/1.35 thf(f22,definition,(
% 1.53/1.35 spl2_2 <=> ($true = (cP @ sK1 @ sK1))),
% 1.53/1.35 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.53/1.35 thf(f32,plain,(
% 1.53/1.35 spl2_3 | spl2_4),
% 1.53/1.35 inference(avatar_split_clause,[status(thm)],[f13,f30,f27])).
% 1.53/1.35 thf(f13,plain,(
% 1.53/1.35 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (cP @ X5 @ X6)) | ((cP @ X7 @ X7) = $true)) )),
% 1.53/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.35 thf(f25,plain,(
% 1.53/1.35 spl2_1 | ~spl2_2),
% 1.53/1.35 inference(avatar_split_clause,[status(thm)],[f14,f22,f19])).
% 1.53/1.35 thf(f14,plain,(
% 1.53/1.35 ( ! [X4 : $i] : (($true != (cP @ (g @ sK1) @ X4)) | ($true != (cP @ sK1 @ sK1))) )),
% 1.53/1.35 inference(cnf_transformation,[status(thm)],[f12])).
% 1.53/1.35 % SZS output end Proof for DTF2THF_2240
% 1.53/1.35 % (2338)------------------------------
% 1.53/1.35 % (2338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.35 % (2338)Termination reason: Refutation
% 1.53/1.35
% 1.53/1.35 % (2338)Memory used [KB]: 5500
% 1.53/1.35 % (2338)Time elapsed: 0.006 s
% 1.53/1.35 % (2338)Instructions burned: 3 (million)
% 1.53/1.35 % (2338)------------------------------
% 1.53/1.35 % (2338)------------------------------
% 1.53/1.35 % (2337)Success in time 0.02 s
%------------------------------------------------------------------------------