%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : PUZ141^1 : TPTP v9.2.1. Released v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 09:28:35 AM UTC 2026
% Result : Theorem 1.66s 1.34s
% Output : Refutation 1.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 113 ( 58 equ; 0 cnn)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 223 ( 23 ~; 13 |; 0 &; 177 @)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 37 ( 0 ^; 34 !; 3 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
direction: $tType ).
thf(type_def_6,type,
position: $tType ).
thf(type_def_8,type,
movelist: $tType ).
thf(func_def_0,type,
position: $tType ).
thf(func_def_1,type,
direction: $tType ).
thf(func_def_2,type,
left: direction ).
thf(func_def_3,type,
right: direction ).
thf(func_def_4,type,
top: direction ).
thf(func_def_5,type,
bottom: direction ).
thf(func_def_6,type,
next: position > direction > position ).
thf(func_def_8,type,
wall: position > $o ).
thf(func_def_9,type,
movelist: $tType ).
thf(func_def_10,type,
nomove: movelist ).
thf(func_def_11,type,
movedir: movelist > direction > movelist ).
thf(func_def_12,type,
playerpos: movelist > position ).
thf(func_def_13,type,
c00: position ).
thf(func_def_14,type,
c10: position ).
thf(func_def_15,type,
c20: position ).
thf(f72,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f71,f54]) ).
thf(f54,plain,
( $true
!= ( wall @ ( next @ ( playerpos @ nomove ) @ right ) ) ),
inference(definition_unfolding,[status(thm)],[f40,f52]) ).
thf(f52,plain,
( c10
= ( next @ ( playerpos @ nomove ) @ right ) ),
inference(definition_unfolding,[status(thm)],[f49,f45]) ).
thf(f45,plain,
( c00
= ( playerpos @ nomove ) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
thf(f11,axiom,
( c00
= ( playerpos @ nomove ) ),
file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',start_axiom) ).
thf(f49,plain,
( c10
= ( next @ c00 @ right ) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
thf(f6,axiom,
( c10
= ( next @ c00 @ right ) ),
file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',c10_defin) ).
thf(f40,plain,
( ( wall @ c10 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( wall @ c10 )
!= $true ),
inference(flattening,[status(thm)],[f30]) ).
thf(f30,plain,
( ( wall @ c10 )
!= $true ),
inference(true_and_false_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( $false
<=> ( ( wall @ c10 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,axiom,
( $false
= ( wall @ c10 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',c10_axiom) ).
thf(f71,plain,
( $true
= ( wall @ ( next @ ( playerpos @ nomove ) @ right ) ) ),
inference(subsumption_resolution,[status(thm)],[f70,f56]) ).
thf(f56,plain,
( $true
!= ( wall @ ( next @ ( next @ ( playerpos @ nomove ) @ right ) @ right ) ) ),
inference(definition_unfolding,[status(thm)],[f46,f53]) ).
thf(f53,plain,
( c20
= ( next @ ( next @ ( playerpos @ nomove ) @ right ) @ right ) ),
inference(definition_unfolding,[status(thm)],[f51,f52]) ).
thf(f51,plain,
( c20
= ( next @ c10 @ right ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,axiom,
( c20
= ( next @ c10 @ right ) ),
file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',c20_defin) ).
thf(f46,plain,
( ( wall @ c20 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ( wall @ c20 )
!= $true ),
inference(flattening,[status(thm)],[f22]) ).
thf(f22,plain,
( ( wall @ c20 )
!= $true ),
inference(true_and_false_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
( $false
<=> ( ( wall @ c20 )
= $true ) ),
inference(fool_elimination,[status(thm)],[f10]) ).
thf(f10,axiom,
( $false
= ( wall @ c20 ) ),
file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',c20_axiom) ).
thf(f70,plain,
( ( $true
= ( wall @ ( next @ ( next @ ( playerpos @ nomove ) @ right ) @ right ) ) )
| ( $true
= ( wall @ ( next @ ( playerpos @ nomove ) @ right ) ) ) ),
inference(equality_resolution,[status(thm)],[f63]) ).
thf(f63,plain,
! [X2: direction,X0: movelist,X1: direction] :
( ( ( next @ ( next @ ( playerpos @ X0 ) @ X1 ) @ X2 )
!= ( next @ ( next @ ( playerpos @ nomove ) @ right ) @ right ) )
| ( $true
= ( wall @ ( next @ ( playerpos @ X0 ) @ X1 ) ) )
| ( ( wall @ ( next @ ( next @ ( playerpos @ X0 ) @ X1 ) @ X2 ) )
= $true ) ),
inference(superposition,[status(thm)],[f61,f59]) ).
thf(f59,plain,
! [X2: movelist,X0: direction] :
( ( $true
= ( wall @ ( next @ ( playerpos @ X2 ) @ X0 ) ) )
| ( ( playerpos @ ( movedir @ X2 @ X0 ) )
= ( next @ ( playerpos @ X2 ) @ X0 ) ) ),
inference(equality_resolution,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: movelist,X0: direction,X1: position] :
( ( ( playerpos @ ( movedir @ X2 @ X0 ) )
= ( next @ X1 @ X0 ) )
| ( $true
= ( wall @ ( next @ X1 @ X0 ) ) )
| ( ( playerpos @ X2 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
thf(f39,plain,
! [X0: direction,X1: position,X2: movelist] :
( ( ( playerpos @ ( movedir @ X2 @ X0 ) )
= ( next @ X1 @ X0 ) )
| ( $true
= ( wall @ ( next @ X1 @ X0 ) ) )
| ( ( playerpos @ X2 )
!= X1 ) ),
inference(rectify,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: direction,X2: position,X1: movelist] :
( ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) )
| ( ( wall @ ( next @ X2 @ X0 ) )
= $true )
| ( ( playerpos @ X1 )
!= X2 ) ),
inference(flattening,[status(thm)],[f35]) ).
thf(f35,plain,
! [X1: movelist,X0: direction,X2: position] :
( ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) )
| ( ( wall @ ( next @ X2 @ X0 ) )
= $true )
| ( ( playerpos @ X1 )
!= X2 ) ),
inference(ennf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X1: movelist,X0: direction,X2: position] :
( ( ( playerpos @ X1 )
= X2 )
=> ( ( ( wall @ ( next @ X2 @ X0 ) )
!= $true )
=> ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: direction,X1: movelist,X2: position] :
( ( ( playerpos @ X1 )
= X2 )
=> ( ( ( wall @ ( next @ X2 @ X0 ) )
!= $true )
=> ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: direction,X1: movelist,X2: position] :
( ( ( playerpos @ X1 )
= X2 )
=> ( ~ ( wall @ ( next @ X2 @ X0 ) )
=> ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X5: direction,X4: movelist,X3: position] :
( ( ( playerpos @ X4 )
= X3 )
=> ( ~ ( wall @ ( next @ X3 @ X5 ) )
=> ( ( next @ X3 @ X5 )
= ( playerpos @ ( movedir @ X4 @ X5 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',player_move_legal) ).
thf(f61,plain,
! [X0: movelist,X1: direction] :
( ( ( next @ ( playerpos @ X0 ) @ X1 )
!= ( next @ ( next @ ( playerpos @ nomove ) @ right ) @ right ) )
| ( $true
= ( wall @ ( next @ ( playerpos @ X0 ) @ X1 ) ) ) ),
inference(superposition,[status(thm)],[f57,f59]) ).
thf(f57,plain,
! [X0: movelist] :
( ( playerpos @ X0 )
!= ( next @ ( next @ ( playerpos @ nomove ) @ right ) @ right ) ),
inference(definition_unfolding,[status(thm)],[f50,f53]) ).
thf(f50,plain,
! [X0: movelist] :
( c20
!= ( playerpos @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,plain,
! [X0: movelist] :
( c20
!= ( playerpos @ X0 ) ),
inference(ennf_transformation,[status(thm)],[f28]) ).
thf(f28,plain,
~ ? [X0: movelist] :
( c20
= ( playerpos @ X0 ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,negated_conjecture,
~ ? [X4: movelist] :
( ( playerpos @ X4 )
= c20 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f12,conjecture,
? [X4: movelist] :
( ( playerpos @ X4 )
= c20 ),
file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',exercise) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : PUZ141^1 : TPTP v9.2.1. Released v6.2.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n026.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 11:34:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.45 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : PUZ141^1 : TPTP v9.2.1. Released v6.2.0.
% 0.20/0.46 % Domain : Puzzles
% 0.20/0.46 % Problem : Labyrinth1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : Move 2 to the right.
% 0.20/0.46
% 0.20/0.46 % Refs : [Cam14] Camarero (2014), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Cam14]
% 0.20/0.46 % Names : labyrinth1 [Cam14]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.80 v6.2.0
% 0.20/0.46 % Syntax : Number of formulae : 27 ( 10 unt; 15 typ; 2 def)
% 0.20/0.46 % Number of atoms : 22 ( 14 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 3 ( 1 avg)
% 0.20/0.46 % Number of connectives : 46 ( 1 ~; 0 |; 0 &; 41 @)
% 0.20/0.46 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 10 ( 3 avg)
% 0.20/0.46 % Number of types : 4 ( 3 usr)
% 0.20/0.46 % Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 14 ( 12 usr; 9 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 12 ( 0 ^; 11 !; 1 ?; 12 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments :
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(position_type,type,
% 0.20/0.46 position: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(direction_type,type,
% 0.20/0.46 direction: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(left_type,type,
% 0.20/0.46 left: direction ).
% 0.20/0.46
% 0.20/0.46 thf(right_type,type,
% 0.20/0.46 right: direction ).
% 0.20/0.46
% 0.20/0.46 thf(top_type,type,
% 0.20/0.46 top: direction ).
% 0.20/0.46
% 0.20/0.46 thf(bottom_type,type,
% 0.20/0.46 bottom: direction ).
% 0.20/0.46
% 0.20/0.46 thf(next_type,type,
% 0.20/0.46 next: position > direction > position ).
% 0.20/0.46
% 0.20/0.46 thf(next_comm,axiom,
% 0.20/0.46 ! [D1: direction,D2: direction,P: position] :
% 0.20/0.46 ( ( next @ ( next @ P @ D1 ) @ D2 )
% 0.20/0.46 = ( next @ ( next @ P @ D2 ) @ D1 ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(left_right,axiom,
% 0.20/0.46 ! [P: position] :
% 0.20/0.46 ( ( next @ ( next @ P @ left ) @ right )
% 0.20/0.46 = P ) ).
% 0.20/0.46
% 0.20/0.46 thf(top_bottom,axiom,
% 0.20/0.46 ! [P: position] :
% 0.20/0.46 ( ( next @ ( next @ P @ top ) @ bottom )
% 0.20/0.46 = P ) ).
% 0.20/0.46
% 0.20/0.46 thf(wall_type,type,
% 0.20/0.46 wall: position > $o ).
% 0.20/0.46
% 0.20/0.46 %----Inductive MoveList. For the moment we do not include the inductive axioms.
% 0.20/0.46 thf(movelist_type,type,
% 0.20/0.46 movelist: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(nomove_type,type,
% 0.20/0.46 nomove: movelist ).
% 0.20/0.46
% 0.20/0.46 thf(movedir_type,type,
% 0.20/0.46 movedir: movelist > direction > movelist ).
% 0.20/0.46
% 0.20/0.46 %----The position of the player after a list of movements
% 0.20/0.46 thf(playerpos_type,type,
% 0.20/0.46 playerpos: movelist > position ).
% 0.20/0.46
% 0.20/0.46 thf(player_move_legal,axiom,
% 0.20/0.46 ! [PO: position,M: movelist,D: direction] :
% 0.20/0.46 ( ( ( playerpos @ M )
% 0.20/0.46 = PO )
% 0.20/0.46 => ( ~ ( wall @ ( next @ PO @ D ) )
% 0.20/0.46 => ( ( playerpos @ ( movedir @ M @ D ) )
% 0.20/0.46 = ( next @ PO @ D ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(player_move_illegal,axiom,
% 0.20/0.46 ! [PO: position,M: movelist,D: direction] :
% 0.20/0.46 ( ( ( playerpos @ M )
% 0.20/0.46 = PO )
% 0.20/0.46 => ( ( wall @ ( next @ PO @ D ) )
% 0.20/0.46 => ( ( playerpos @ ( movedir @ M @ D ) )
% 0.20/0.46 = PO ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(c00_type,type,
% 0.20/0.46 c00: position ).
% 0.20/0.46
% 0.20/0.46 thf(c10_type,type,
% 0.20/0.46 c10: position ).
% 0.20/0.46
% 0.20/0.46 thf(c20_type,type,
% 0.20/0.46 c20: position ).
% 0.20/0.46
% 0.20/0.46 thf(c10_defin,definition,
% 0.20/0.46 ( c10
% 0.20/0.46 = ( next @ c00 @ right ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(c20_defin,definition,
% 0.20/0.46 ( c20
% 0.20/0.46 = ( next @ c10 @ right ) ) ).
% 0.20/0.46
% 0.20/0.46 %----Exercise 1. Move 2 to the right
% 0.20/0.46 thf(c00_axiom,axiom,
% 0.20/0.46 ( ( wall @ c00 )
% 0.20/0.46 = $false ) ).
% 0.20/0.46
% 0.20/0.46 thf(c10_axiom,axiom,
% 0.20/0.46 ( ( wall @ c10 )
% 0.20/0.46 = $false ) ).
% 0.20/0.46
% 0.20/0.46 thf(c20_axiom,axiom,
% 0.20/0.46 ( ( wall @ c20 )
% 0.20/0.46 = $false ) ).
% 0.20/0.46
% 0.20/0.46 thf(start_axiom,axiom,
% 0.20/0.46 ( ( playerpos @ nomove )
% 0.20/0.46 = c00 ) ).
% 0.20/0.46
% 0.20/0.46 thf(exercise,conjecture,
% 0.20/0.46 ? [M: movelist] :
% 0.20/0.46 ( ( playerpos @ M )
% 0.20/0.46 = c20 ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.49/1.28 ---- Embedded in THF ---
% 1.49/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.49/1.28 %%% Generated on Tue Feb 24 11:34:41 EST 2026
% 1.49/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.49/1.28 %%% Logic specification used:
% 1.49/1.28 %%% thf(spec, logic, $$dhol).
% 1.49/1.28
% 1.49/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2DTF6218.p
% See solution above
% 1.49/1.28 ------------------------
% 1.49/1.29 ---- Cleaned THF ---
% 1.49/1.30 thf(position_type,type,
% 1.49/1.30 position: $tType ).
% 1.49/1.30
% 1.49/1.30 thf(direction_type,type,
% 1.49/1.30 direction: $tType ).
% 1.49/1.30
% 1.49/1.30 thf(left_type,type,
% 1.49/1.30 left: direction ).
% 1.49/1.30
% 1.49/1.30 thf(right_type,type,
% 1.49/1.30 right: direction ).
% 1.49/1.30
% 1.49/1.30 thf(top_type,type,
% 1.49/1.30 top: direction ).
% 1.49/1.30
% 1.49/1.30 thf(bottom_type,type,
% 1.49/1.30 bottom: direction ).
% 1.49/1.30
% 1.49/1.30 thf(next_type,type,
% 1.49/1.30 next: position > direction > position ).
% 1.49/1.30
% 1.49/1.30 thf(next_comm,axiom,
% 1.49/1.30 ! [D1: direction,D2: direction,P: position] :
% 1.49/1.30 ( ( next @ ( next @ P @ D1 ) @ D2 )
% 1.49/1.30 = ( next @ ( next @ P @ D2 ) @ D1 ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(left_right,axiom,
% 1.49/1.30 ! [P: position] :
% 1.49/1.30 ( ( next @ ( next @ P @ left ) @ right )
% 1.49/1.30 = P ) ).
% 1.49/1.30
% 1.49/1.30 thf(top_bottom,axiom,
% 1.49/1.30 ! [P: position] :
% 1.49/1.30 ( ( next @ ( next @ P @ top ) @ bottom )
% 1.49/1.30 = P ) ).
% 1.49/1.30
% 1.49/1.30 thf(wall_type,type,
% 1.49/1.30 wall: position > $o ).
% 1.49/1.30
% 1.49/1.30 thf(movelist_type,type,
% 1.49/1.30 movelist: $tType ).
% 1.49/1.30
% 1.49/1.30 thf(nomove_type,type,
% 1.49/1.30 nomove: movelist ).
% 1.49/1.30
% 1.49/1.30 thf(movedir_type,type,
% 1.49/1.30 movedir: movelist > direction > movelist ).
% 1.49/1.30
% 1.49/1.30 thf(playerpos_type,type,
% 1.49/1.30 playerpos: movelist > position ).
% 1.49/1.30
% 1.49/1.30 thf(player_move_legal,axiom,
% 1.49/1.30 ! [PO: position,M: movelist,D: direction] :
% 1.49/1.30 ( ( ( playerpos @ M )
% 1.49/1.30 = PO )
% 1.49/1.30 => ( ~ ( wall @ ( next @ PO @ D ) )
% 1.49/1.30 => ( ( playerpos @ ( movedir @ M @ D ) )
% 1.49/1.30 = ( next @ PO @ D ) ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(player_move_illegal,axiom,
% 1.49/1.30 ! [PO: position,M: movelist,D: direction] :
% 1.49/1.30 ( ( ( playerpos @ M )
% 1.49/1.30 = PO )
% 1.49/1.30 => ( ( wall @ ( next @ PO @ D ) )
% 1.49/1.30 => ( ( playerpos @ ( movedir @ M @ D ) )
% 1.49/1.30 = PO ) ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(c00_type,type,
% 1.49/1.30 c00: position ).
% 1.49/1.30
% 1.49/1.30 thf(c10_type,type,
% 1.49/1.30 c10: position ).
% 1.49/1.30
% 1.49/1.30 thf(c20_type,type,
% 1.49/1.30 c20: position ).
% 1.49/1.30
% 1.49/1.30 thf(c10_defin,definition,
% 1.49/1.30 ( c10
% 1.49/1.30 = ( next @ c00 @ right ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(c20_defin,definition,
% 1.49/1.30 ( c20
% 1.49/1.30 = ( next @ c10 @ right ) ) ).
% 1.49/1.30
% 1.49/1.30 thf(c00_axiom,axiom,
% 1.49/1.30 ( ( wall @ c00 )
% 1.49/1.30 = $false ) ).
% 1.49/1.30
% 1.49/1.30 thf(c10_axiom,axiom,
% 1.49/1.30 ( ( wall @ c10 )
% 1.49/1.30 = $false ) ).
% 1.49/1.30
% 1.49/1.30 thf(c20_axiom,axiom,
% 1.49/1.30 ( ( wall @ c20 )
% 1.49/1.30 = $false ) ).
% 1.49/1.30
% 1.49/1.30 thf(start_axiom,axiom,
% 1.49/1.30 ( ( playerpos @ nomove )
% 1.49/1.30 = c00 ) ).
% 1.49/1.30
% 1.49/1.30 thf(exercise,conjecture,
% 1.49/1.30 ? [M: movelist] :
% 1.49/1.30 ( ( playerpos @ M )
% 1.49/1.30 = c20 ) ).
% 1.49/1.30 ------------------------
% 1.66/1.31 % (6356)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/183Mi)
% 1.66/1.32 % (6358)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_6218 for (2999ds/27Mi)
% 1.66/1.32 % (6357)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_6218 for (2999ds/4Mi)
% 1.66/1.32 % (6360)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_6218 for (2999ds/2Mi)
% 1.66/1.32 % (6362)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/18Mi)
% 1.66/1.32 % (6361)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_6218 for (2999ds/275Mi)
% 1.66/1.32 % (6357)Instruction limit reached!
% 1.66/1.32 % (6357)------------------------------
% 1.66/1.32 % (6357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (6357)Termination reason: Unknown
% 1.66/1.32 % (6357)Termination phase: Saturation
% 1.66/1.32
% 1.66/1.32 % (6357)Memory used [KB]: 1023
% 1.66/1.32 % (6357)Time elapsed: 0.004 s
% 1.66/1.32 % (6357)Instructions burned: 4 (million)
% 1.66/1.32 % (6357)------------------------------
% 1.66/1.32 % (6357)------------------------------
% 1.66/1.32 % (6360)Instruction limit reached!
% 1.66/1.32 % (6360)------------------------------
% 1.66/1.32 % (6360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (6360)Termination reason: Unknown
% 1.66/1.32 % (6360)Termination phase: Property scanning
% 1.66/1.32
% 1.66/1.32 % (6360)Memory used [KB]: 1023
% 1.66/1.32 % (6360)Time elapsed: 0.004 s
% 1.66/1.32 % (6360)Instructions burned: 3 (million)
% 1.66/1.32 % (6360)------------------------------
% 1.66/1.32 % (6360)------------------------------
% 1.66/1.32 % (6361)Refutation not found, incomplete strategy
% 1.66/1.32 % (6361)------------------------------
% 1.66/1.32 % (6361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (6361)Termination reason: Refutation not found, incomplete strategy
% 1.66/1.32
% 1.66/1.32
% 1.66/1.32 % (6361)Memory used [KB]: 5500
% 1.66/1.32 % (6361)Time elapsed: 0.004 s
% 1.66/1.32 % (6361)Instructions burned: 2 (million)
% 1.66/1.32 % (6361)------------------------------
% 1.66/1.32 % (6361)------------------------------
% 1.66/1.32 % (6359)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/2Mi)
% 1.66/1.32 % (6359)Instruction limit reached!
% 1.66/1.32 % (6359)------------------------------
% 1.66/1.32 % (6359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.32 % (6359)Termination reason: Unknown
% 1.66/1.32 % (6359)Termination phase: Function definition elimination
% 1.66/1.32
% 1.66/1.32 % (6359)Memory used [KB]: 895
% 1.66/1.32 % (6359)Time elapsed: 0.004 s
% 1.66/1.32 % (6359)Instructions burned: 2 (million)
% 1.66/1.32 % (6359)------------------------------
% 1.66/1.32 % (6359)------------------------------
% 1.66/1.33 % (6362)Instruction limit reached!
% 1.66/1.33 % (6362)------------------------------
% 1.66/1.33 % (6362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (6362)Termination reason: Unknown
% 1.66/1.33 % (6362)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (6362)Memory used [KB]: 5500
% 1.66/1.33 % (6362)Time elapsed: 0.014 s
% 1.66/1.33 % (6362)Instructions burned: 19 (million)
% 1.66/1.33 % (6362)------------------------------
% 1.66/1.33 % (6362)------------------------------
% 1.66/1.33 % (6358)Instruction limit reached!
% 1.66/1.33 % (6358)------------------------------
% 1.66/1.33 % (6358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.33 % (6358)Termination reason: Unknown
% 1.66/1.33 % (6358)Termination phase: Saturation
% 1.66/1.33
% 1.66/1.33 % (6358)Memory used [KB]: 5500
% 1.66/1.33 % (6358)Time elapsed: 0.018 s
% 1.66/1.33 % (6358)Instructions burned: 27 (million)
% 1.66/1.33 % (6358)------------------------------
% 1.66/1.33 % (6358)------------------------------
% 1.66/1.34 % (6363)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/3Mi)
% 1.66/1.34 % (6364)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/37Mi)
% 1.66/1.34 % (6365)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/15Mi)
% 1.66/1.34 % (6363)Instruction limit reached!
% 1.66/1.34 % (6363)------------------------------
% 1.66/1.34 % (6363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (6363)Termination reason: Unknown
% 1.66/1.34 % (6363)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (6363)Memory used [KB]: 5500
% 1.66/1.34 % (6363)Time elapsed: 0.004 s
% 1.66/1.34 % (6363)Instructions burned: 3 (million)
% 1.66/1.34 % (6363)------------------------------
% 1.66/1.34 % (6363)------------------------------
% 1.66/1.34 % (6366)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6218 for (2999ds/3Mi)
% 1.66/1.34 % (6365)First to succeed.
% 1.66/1.34 % (6366)Instruction limit reached!
% 1.66/1.34 % (6366)------------------------------
% 1.66/1.34 % (6366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.34 % (6366)Termination reason: Unknown
% 1.66/1.34 % (6366)Termination phase: Saturation
% 1.66/1.34
% 1.66/1.34 % (6366)Memory used [KB]: 5500
% 1.66/1.34 % (6366)Time elapsed: 0.004 s
% 1.66/1.34 % (6366)Instructions burned: 3 (million)
% 1.66/1.34 % (6366)------------------------------
% 1.66/1.34 % (6366)------------------------------
% 1.66/1.34 % (6365)Refutation found. Thanks to Tanya!
% 1.66/1.34 % SZS status Theorem for DTF2THF_6218
% 1.66/1.34 % SZS output start Proof for DTF2THF_6218
% 1.66/1.34 thf(type_def_5, type, direction: $tType).
% 1.66/1.34 thf(type_def_6, type, position: $tType).
% 1.66/1.34 thf(type_def_8, type, movelist: $tType).
% 1.66/1.34 thf(func_def_0, type, position: $tType).
% 1.66/1.34 thf(func_def_1, type, direction: $tType).
% 1.66/1.34 thf(func_def_2, type, left: direction).
% 1.66/1.34 thf(func_def_3, type, right: direction).
% 1.66/1.34 thf(func_def_4, type, top: direction).
% 1.66/1.34 thf(func_def_5, type, bottom: direction).
% 1.66/1.34 thf(func_def_6, type, next: position > direction > position).
% 1.66/1.34 thf(func_def_8, type, wall: position > $o).
% 1.66/1.34 thf(func_def_9, type, movelist: $tType).
% 1.66/1.34 thf(func_def_10, type, nomove: movelist).
% 1.66/1.34 thf(func_def_11, type, movedir: movelist > direction > movelist).
% 1.66/1.34 thf(func_def_12, type, playerpos: movelist > position).
% 1.66/1.34 thf(func_def_13, type, c00: position).
% 1.66/1.34 thf(func_def_14, type, c10: position).
% 1.66/1.34 thf(func_def_15, type, c20: position).
% 1.66/1.34 thf(f72,plain,(
% 1.66/1.34 $false),
% 1.66/1.34 inference(subsumption_resolution,[status(thm)],[f71,f54])).
% 1.66/1.34 thf(f54,plain,(
% 1.66/1.34 ($true != (wall @ (next @ (playerpos @ nomove) @ right)))),
% 1.66/1.34 inference(definition_unfolding,[status(thm)],[f40,f52])).
% 1.66/1.34 thf(f52,plain,(
% 1.66/1.34 (c10 = (next @ (playerpos @ nomove) @ right))),
% 1.66/1.34 inference(definition_unfolding,[status(thm)],[f49,f45])).
% 1.66/1.34 thf(f45,plain,(
% 1.66/1.34 (c00 = (playerpos @ nomove))),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f11])).
% 1.66/1.34 thf(f11,axiom,(
% 1.66/1.34 (c00 = (playerpos @ nomove))),
% 1.66/1.34 file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',start_axiom)).
% 1.66/1.34 thf(f49,plain,(
% 1.66/1.34 (c10 = (next @ c00 @ right))),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f6])).
% 1.66/1.34 thf(f6,axiom,(
% 1.66/1.34 (c10 = (next @ c00 @ right))),
% 1.66/1.34 file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',c10_defin)).
% 1.66/1.34 thf(f40,plain,(
% 1.66/1.34 ((wall @ c10) != $true)),
% 1.66/1.34 inference(cnf_transformation,[status(thm)],[f31])).
% 1.66/1.34 thf(f31,plain,(
% 1.66/1.34 ((wall @ c10) != $true)),
% 1.66/1.34 inference(flattening,[status(thm)],[f30])).
% 1.66/1.34 thf(f30,plain,(
% 1.66/1.34 ~((wall @ c10) = $true)),
% 1.66/1.34 inference(true_and_false_elimination,[status(thm)],[f21])).
% 1.66/1.34 thf(f21,plain,(
% 1.66/1.35 $false <=> ((wall @ c10) = $true)),
% 1.66/1.35 inference(fool_elimination,[status(thm)],[f9])).
% 1.66/1.35 thf(f9,axiom,(
% 1.66/1.35 ($false = (wall @ c10))),
% 1.66/1.35 file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',c10_axiom)).
% 1.66/1.35 thf(f71,plain,(
% 1.66/1.35 ($true = (wall @ (next @ (playerpos @ nomove) @ right)))),
% 1.66/1.35 inference(subsumption_resolution,[status(thm)],[f70,f56])).
% 1.66/1.35 thf(f56,plain,(
% 1.66/1.35 ($true != (wall @ (next @ (next @ (playerpos @ nomove) @ right) @ right)))),
% 1.66/1.35 inference(definition_unfolding,[status(thm)],[f46,f53])).
% 1.66/1.35 thf(f53,plain,(
% 1.66/1.35 (c20 = (next @ (next @ (playerpos @ nomove) @ right) @ right))),
% 1.66/1.35 inference(definition_unfolding,[status(thm)],[f51,f52])).
% 1.66/1.35 thf(f51,plain,(
% 1.66/1.35 (c20 = (next @ c10 @ right))),
% 1.66/1.35 inference(cnf_transformation,[status(thm)],[f7])).
% 1.66/1.35 thf(f7,axiom,(
% 1.66/1.35 (c20 = (next @ c10 @ right))),
% 1.66/1.35 file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',c20_defin)).
% 1.66/1.35 thf(f46,plain,(
% 1.66/1.35 ((wall @ c20) != $true)),
% 1.66/1.35 inference(cnf_transformation,[status(thm)],[f23])).
% 1.66/1.35 thf(f23,plain,(
% 1.66/1.35 ((wall @ c20) != $true)),
% 1.66/1.35 inference(flattening,[status(thm)],[f22])).
% 1.66/1.35 thf(f22,plain,(
% 1.66/1.35 ~((wall @ c20) = $true)),
% 1.66/1.35 inference(true_and_false_elimination,[status(thm)],[f15])).
% 1.66/1.35 thf(f15,plain,(
% 1.66/1.35 $false <=> ((wall @ c20) = $true)),
% 1.66/1.35 inference(fool_elimination,[status(thm)],[f10])).
% 1.66/1.35 thf(f10,axiom,(
% 1.66/1.35 ($false = (wall @ c20))),
% 1.66/1.35 file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',c20_axiom)).
% 1.66/1.35 thf(f70,plain,(
% 1.66/1.35 ($true = (wall @ (next @ (next @ (playerpos @ nomove) @ right) @ right))) | ($true = (wall @ (next @ (playerpos @ nomove) @ right)))),
% 1.66/1.35 inference(equality_resolution,[status(thm)],[f63])).
% 1.66/1.35 thf(f63,plain,(
% 1.66/1.35 ( ! [X2 : direction,X0 : movelist,X1 : direction] : (((next @ (next @ (playerpos @ X0) @ X1) @ X2) != (next @ (next @ (playerpos @ nomove) @ right) @ right)) | ($true = (wall @ (next @ (playerpos @ X0) @ X1))) | ((wall @ (next @ (next @ (playerpos @ X0) @ X1) @ X2)) = $true)) )),
% 1.66/1.35 inference(superposition,[status(thm)],[f61,f59])).
% 1.66/1.35 thf(f59,plain,(
% 1.66/1.35 ( ! [X2 : movelist,X0 : direction] : (($true = (wall @ (next @ (playerpos @ X2) @ X0))) | ((playerpos @ (movedir @ X2 @ X0)) = (next @ (playerpos @ X2) @ X0))) )),
% 1.66/1.35 inference(equality_resolution,[status(thm)],[f47])).
% 1.66/1.35 thf(f47,plain,(
% 1.66/1.35 ( ! [X2 : movelist,X0 : direction,X1 : position] : (((playerpos @ (movedir @ X2 @ X0)) = (next @ X1 @ X0)) | ($true = (wall @ (next @ X1 @ X0))) | ((playerpos @ X2) != X1)) )),
% 1.66/1.35 inference(cnf_transformation,[status(thm)],[f39])).
% 1.66/1.35 thf(f39,plain,(
% 1.66/1.35 ! [X0 : direction,X1 : position,X2 : movelist] : (((playerpos @ (movedir @ X2 @ X0)) = (next @ X1 @ X0)) | ($true = (wall @ (next @ X1 @ X0))) | ((playerpos @ X2) != X1))),
% 1.66/1.35 inference(rectify,[status(thm)],[f36])).
% 1.66/1.35 thf(f36,plain,(
% 1.66/1.35 ! [X0 : direction,X2 : position,X1 : movelist] : (((next @ X2 @ X0) = (playerpos @ (movedir @ X1 @ X0))) | ((wall @ (next @ X2 @ X0)) = $true) | ((playerpos @ X1) != X2))),
% 1.66/1.35 inference(flattening,[status(thm)],[f35])).
% 1.66/1.35 thf(f35,plain,(
% 1.66/1.35 ! [X1 : movelist,X0 : direction,X2 : position] : ((((next @ X2 @ X0) = (playerpos @ (movedir @ X1 @ X0))) | ((wall @ (next @ X2 @ X0)) = $true)) | ((playerpos @ X1) != X2))),
% 1.66/1.35 inference(ennf_transformation,[status(thm)],[f29])).
% 1.66/1.35 thf(f29,plain,(
% 1.66/1.35 ! [X1 : movelist,X0 : direction,X2 : position] : (((playerpos @ X1) = X2) => (((wall @ (next @ X2 @ X0)) != $true) => ((next @ X2 @ X0) = (playerpos @ (movedir @ X1 @ X0)))))),
% 1.66/1.35 inference(flattening,[status(thm)],[f20])).
% 1.66/1.35 thf(f20,plain,(
% 1.66/1.35 ! [X0 : direction,X1 : movelist,X2 : position] : (((playerpos @ X1) = X2) => (~((wall @ (next @ X2 @ X0)) = $true) => ((next @ X2 @ X0) = (playerpos @ (movedir @ X1 @ X0)))))),
% 1.66/1.35 inference(fool_elimination,[status(thm)],[f19])).
% 1.66/1.35 thf(f19,plain,(
% 1.66/1.35 ! [X0 : direction,X1 : movelist,X2 : position] : (((playerpos @ X1) = X2) => (~(wall @ (next @ X2 @ X0)) => ((next @ X2 @ X0) = (playerpos @ (movedir @ X1 @ X0)))))),
% 1.66/1.35 inference(rectify,[status(thm)],[f4])).
% 1.66/1.35 thf(f4,axiom,(
% 1.66/1.35 ! [X5 : direction,X4 : movelist,X3 : position] : (((playerpos @ X4) = X3) => (~(wall @ (next @ X3 @ X5)) => ((next @ X3 @ X5) = (playerpos @ (movedir @ X4 @ X5)))))),
% 1.66/1.35 file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',player_move_legal)).
% 1.66/1.35 thf(f61,plain,(
% 1.66/1.35 ( ! [X0 : movelist,X1 : direction] : (((next @ (playerpos @ X0) @ X1) != (next @ (next @ (playerpos @ nomove) @ right) @ right)) | ($true = (wall @ (next @ (playerpos @ X0) @ X1)))) )),
% 1.66/1.35 inference(superposition,[status(thm)],[f57,f59])).
% 1.66/1.35 thf(f57,plain,(
% 1.66/1.35 ( ! [X0 : movelist] : (((playerpos @ X0) != (next @ (next @ (playerpos @ nomove) @ right) @ right))) )),
% 1.66/1.35 inference(definition_unfolding,[status(thm)],[f50,f53])).
% 1.66/1.35 thf(f50,plain,(
% 1.66/1.35 ( ! [X0 : movelist] : ((c20 != (playerpos @ X0))) )),
% 1.66/1.35 inference(cnf_transformation,[status(thm)],[f34])).
% 1.66/1.35 thf(f34,plain,(
% 1.66/1.35 ! [X0 : movelist] : (c20 != (playerpos @ X0))),
% 1.66/1.35 inference(ennf_transformation,[status(thm)],[f28])).
% 1.66/1.35 thf(f28,plain,(
% 1.66/1.35 ~? [X0 : movelist] : (c20 = (playerpos @ X0))),
% 1.66/1.35 inference(rectify,[status(thm)],[f13])).
% 1.66/1.35 thf(f13,negated_conjecture,(
% 1.66/1.35 ~? [X4 : movelist] : ((playerpos @ X4) = c20)),
% 1.66/1.35 inference(negated_conjecture,[status(cth)],[f12])).
% 1.66/1.35 thf(f12,conjecture,(
% 1.66/1.35 ? [X4 : movelist] : ((playerpos @ X4) = c20)),
% 1.66/1.35 file('/export/starexec/sandbox2/tmp/tmp.VDH2zSXDES/DTF2THF_6218.p',exercise)).
% 1.66/1.35 % SZS output end Proof for DTF2THF_6218
% 1.66/1.35 % (6365)------------------------------
% 1.66/1.35 % (6365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.66/1.35 % (6365)Termination reason: Refutation
% 1.66/1.35
% 1.66/1.35 % (6365)Memory used [KB]: 5500
% 1.66/1.35 % (6365)Time elapsed: 0.009 s
% 1.66/1.35 % (6365)Instructions burned: 8 (million)
% 1.66/1.35 % (6365)------------------------------
% 1.66/1.35 % (6365)------------------------------
% 1.66/1.35 % (6355)Success in time 0.043 s
%------------------------------------------------------------------------------