%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ141^1 : TPTP v9.3.1. Released v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:20:58 AM UTC 2026
% Result : Theorem 0.07s 0.20s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 26 unt; 0 typ; 1 def)
% Number of atoms : 201 ( 102 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 382 ( 44 ~; 45 |; 0 &; 276 @)
% ( 3 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 61 !; 2 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
position: $tType ).
thf(type_def_6,type,
direction: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_8,type,
movelist: $tType ).
thf(func_def_0,type,
left: direction ).
thf(func_def_1,type,
right: direction ).
thf(func_def_2,type,
top: direction ).
thf(func_def_3,type,
bottom: direction ).
thf(func_def_4,type,
next: position > direction > position ).
thf(func_def_6,type,
wall: position > $o ).
thf(func_def_7,type,
nomove: movelist ).
thf(func_def_8,type,
movedir: movelist > direction > movelist ).
thf(func_def_9,type,
playerpos: movelist > position ).
thf(func_def_10,type,
c00: position ).
thf(func_def_11,type,
c10: position ).
thf(func_def_12,type,
c20: position ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(f4,axiom,
! [X2: direction,X1: movelist,X0: position] :
( ( ( playerpos @ X1 )
= X0 )
=> ( ~ ( wall @ ( next @ X0 @ X2 ) )
=> ( ( playerpos @ ( movedir @ X1 @ X2 ) )
= ( next @ X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',player_move_legal) ).
thf(f5,axiom,
! [X0: position,X2: direction,X1: movelist] :
( ( ( playerpos @ X1 )
= X0 )
=> ( ( wall @ ( next @ X0 @ X2 ) )
=> ( ( playerpos @ ( movedir @ X1 @ X2 ) )
= X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',player_move_illegal) ).
thf(f6,axiom,
( c10
= ( next @ c00 @ right ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10_defin) ).
thf(f7,axiom,
( c20
= ( next @ c10 @ right ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c20_defin) ).
thf(f9,axiom,
( ( wall @ c10 )
= $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10_axiom) ).
thf(f10,axiom,
( $false
= ( wall @ c20 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c20_axiom) ).
thf(f11,axiom,
( ( playerpos @ nomove )
= c00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_axiom) ).
thf(f12,conjecture,
? [X0: movelist] :
( ( playerpos @ X0 )
= c20 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exercise) ).
thf(f13,negated_conjecture,
~ ? [X0: movelist] :
( ( playerpos @ X0 )
= c20 ),
inference(negated_conjecture,[status(cth)],[f12]) ).
thf(f14,plain,
( ( ( wall @ c10 )
= $true )
<=> $false ),
inference(fool_elimination,[],[f9]) ).
thf(f15,plain,
( $false
<=> ( ( wall @ c20 )
= $true ) ),
inference(fool_elimination,[],[f10]) ).
thf(f16,plain,
! [X0: position,X1: direction,X2: movelist] :
( ( ( playerpos @ X2 )
= X0 )
=> ( ( wall @ ( next @ X0 @ X1 ) )
=> ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= X0 ) ) ),
inference(rectify,[],[f5]) ).
thf(f17,plain,
! [X1: direction,X2: movelist,X0: position] :
( ( ( playerpos @ X2 )
= X0 )
=> ( ( $true
= ( wall @ ( next @ X0 @ X1 ) ) )
=> ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= X0 ) ) ),
inference(fool_elimination,[],[f16]) ).
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,[],[f4]) ).
thf(f20,plain,
! [X0: direction,X1: movelist,X2: position] :
( ( ( playerpos @ X1 )
= X2 )
=> ( ( $true
!= ( wall @ ( next @ X2 @ X0 ) ) )
=> ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) ) ) ),
inference(fool_elimination,[],[f19]) ).
thf(f22,plain,
( ( wall @ c10 )
!= $true ),
inference(true_and_false_elimination,[],[f14]) ).
thf(f23,plain,
( ( wall @ c10 )
!= $true ),
inference(flattening,[],[f22]) ).
thf(f24,plain,
( ( wall @ c20 )
!= $true ),
inference(true_and_false_elimination,[],[f15]) ).
thf(f25,plain,
( ( wall @ c20 )
!= $true ),
inference(flattening,[],[f24]) ).
thf(f28,plain,
! [X1: movelist,X0: direction,X2: position] :
( ( ( playerpos @ X1 )
= X2 )
=> ( ( $true
!= ( wall @ ( next @ X2 @ X0 ) ) )
=> ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) ) ) ),
inference(flattening,[],[f20]) ).
thf(f29,plain,
! [X1: direction,X2: movelist,X0: position] :
( ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= X0 )
| ( $true
!= ( wall @ ( next @ X0 @ X1 ) ) )
| ( ( playerpos @ X2 )
!= X0 ) ),
inference(ennf_transformation,[],[f17]) ).
thf(f30,plain,
! [X0: position,X1: direction,X2: movelist] :
( ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= X0 )
| ( $true
!= ( wall @ ( next @ X0 @ X1 ) ) )
| ( ( playerpos @ X2 )
!= X0 ) ),
inference(flattening,[],[f29]) ).
thf(f31,plain,
! [X0: movelist] :
( c20
!= ( playerpos @ X0 ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f32,plain,
! [X1: movelist,X0: direction,X2: position] :
( ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) )
| ( $true
= ( wall @ ( next @ X2 @ X0 ) ) )
| ( ( playerpos @ X1 )
!= X2 ) ),
inference(ennf_transformation,[],[f28]) ).
thf(f33,plain,
! [X2: position,X0: direction,X1: movelist] :
( ( $true
= ( wall @ ( next @ X2 @ X0 ) ) )
| ( ( playerpos @ X1 )
!= X2 )
| ( ( next @ X2 @ X0 )
= ( playerpos @ ( movedir @ X1 @ X0 ) ) ) ),
inference(flattening,[],[f32]) ).
thf(f34,plain,
! [X0: position,X1: direction,X2: movelist] :
( ( $true
= ( wall @ ( next @ X0 @ X1 ) ) )
| ( ( playerpos @ X2 )
!= X0 )
| ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= ( next @ X0 @ X1 ) ) ),
inference(rectify,[],[f33]) ).
thf(f37,plain,
! [X2: movelist,X0: position,X1: direction] :
( ( $true
= ( wall @ ( next @ X0 @ X1 ) ) )
| ( ( playerpos @ X2 )
!= X0 )
| ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= ( next @ X0 @ X1 ) ) ),
inference(cnf_transformation,[],[f34]) ).
thf(f39,plain,
( c10
= ( next @ c00 @ right ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f40,plain,
! [X2: movelist,X0: position,X1: direction] :
( ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= X0 )
| ( $true
!= ( wall @ ( next @ X0 @ X1 ) ) )
| ( ( playerpos @ X2 )
!= X0 ) ),
inference(cnf_transformation,[],[f30]) ).
thf(f42,plain,
( ( wall @ c10 )
!= $true ),
inference(cnf_transformation,[],[f23]) ).
thf(f43,plain,
! [X0: movelist] :
( c20
!= ( playerpos @ X0 ) ),
inference(cnf_transformation,[],[f31]) ).
thf(f44,plain,
( c20
= ( next @ c10 @ right ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f45,plain,
( ( wall @ c20 )
!= $true ),
inference(cnf_transformation,[],[f25]) ).
thf(f47,plain,
( c00
= ( playerpos @ nomove ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f50,plain,
! [X2: movelist,X1: direction] :
( ( $true
= ( wall @ ( next @ ( playerpos @ X2 ) @ X1 ) ) )
| ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= ( next @ ( playerpos @ X2 ) @ X1 ) ) ),
inference(equality_resolution,[],[f37]) ).
thf(f51,plain,
! [X2: movelist,X1: direction] :
( ( $true
!= ( wall @ ( next @ ( playerpos @ X2 ) @ X1 ) ) )
| ( ( playerpos @ ( movedir @ X2 @ X1 ) )
= ( playerpos @ X2 ) ) ),
inference(equality_resolution,[],[f40]) ).
thf(f168,plain,
! [X0: direction] :
( ( ( next @ c00 @ X0 )
= ( playerpos @ ( movedir @ nomove @ X0 ) ) )
| ( $true
= ( wall @ ( next @ c00 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f50,f47]) ).
thf(f169,plain,
! [X0: movelist,X1: direction] :
( ( ( next @ ( playerpos @ X0 ) @ X1 )
= ( playerpos @ ( movedir @ X0 @ X1 ) ) )
| ( ( playerpos @ X0 )
= ( playerpos @ ( movedir @ X0 @ X1 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f51,f50]) ).
thf(f170,plain,
! [X0: movelist,X1: direction] :
( ( ( next @ ( playerpos @ X0 ) @ X1 )
= ( playerpos @ ( movedir @ X0 @ X1 ) ) )
| ( ( playerpos @ X0 )
= ( playerpos @ ( movedir @ X0 @ X1 ) ) ) ),
inference(trivial_inequality_removal,[],[f169]) ).
thf(f173,plain,
! [X0: direction] :
( ( c20
!= ( next @ c00 @ X0 ) )
| ( $true
= ( wall @ ( next @ c00 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f43,f168]) ).
thf(f174,plain,
( ( ( wall @ c10 )
= $true )
| ( c10 != c20 ) ),
inference(constrained_superposition,[],[f173,f39]) ).
thf(f175,plain,
c10 != c20,
inference(forward_subsumption_resolution,[],[f174,f42]) ).
thf(f179,plain,
! [X0: movelist,X1: direction] :
( ( c20
!= ( next @ ( playerpos @ X0 ) @ X1 ) )
| ( ( playerpos @ X0 )
= ( playerpos @ ( movedir @ X0 @ X1 ) ) ) ),
inference(constrained_superposition,[],[f43,f170]) ).
thf(f185,plain,
! [X0: direction,X1: direction] :
( ( c20
!= ( next @ ( next @ c00 @ X0 ) @ X1 ) )
| ( ( next @ c00 @ X0 )
= ( playerpos @ ( movedir @ ( movedir @ nomove @ X0 ) @ X1 ) ) )
| ( $true
= ( wall @ ( next @ c00 @ X0 ) ) ) ),
inference(constrained_superposition,[],[f179,f168]) ).
thf(f188,plain,
! [X0: direction] :
( ( c10
= ( playerpos @ ( movedir @ ( movedir @ nomove @ right ) @ X0 ) ) )
| ( c20
!= ( next @ c10 @ X0 ) )
| ( ( wall @ c10 )
= $true ) ),
inference(constrained_superposition,[],[f185,f39]) ).
thf(f195,plain,
! [X0: direction] :
( ( c20
!= ( next @ c10 @ X0 ) )
| ( c10
= ( playerpos @ ( movedir @ ( movedir @ nomove @ right ) @ X0 ) ) ) ),
inference(forward_subsumption_resolution,[],[f188,f42]) ).
thf(f197,plain,
( ( c20 != c20 )
| ( c10
= ( playerpos @ ( movedir @ ( movedir @ nomove @ right ) @ right ) ) ) ),
inference(constrained_superposition,[],[f195,f44]) ).
thf(f198,plain,
( c10
= ( playerpos @ ( movedir @ ( movedir @ nomove @ right ) @ right ) ) ),
inference(trivial_inequality_removal,[],[f197]) ).
thf(f210,definition,
( spl0_2
<=> ( c10
= ( playerpos @ ( movedir @ nomove @ right ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f211,plain,
( ( c10
!= ( playerpos @ ( movedir @ nomove @ right ) ) )
| spl0_2 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f212,plain,
( ( c10
= ( playerpos @ ( movedir @ nomove @ right ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f210]) ).
thf(f219,plain,
( ! [X0: direction] :
( ( ( next @ c10 @ X0 )
= ( playerpos @ ( movedir @ ( movedir @ nomove @ right ) @ X0 ) ) )
| ( $true
= ( wall @ ( next @ c10 @ X0 ) ) ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f50,f212]) ).
thf(f242,plain,
( ( c10
= ( next @ c10 @ right ) )
| ( $true
= ( wall @ ( next @ c10 @ right ) ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f219,f198]) ).
thf(f251,plain,
( ( $true
= ( wall @ ( next @ c10 @ right ) ) )
| ( c10 = c20 )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f242,f44]) ).
thf(f253,plain,
( ( $true
= ( wall @ ( next @ c10 @ right ) ) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f251,f175]) ).
thf(f255,plain,
( ( ( wall @ c20 )
= $true )
| ~ spl0_2 ),
inference(forward_demodulation,[],[f253,f44]) ).
thf(f258,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f255,f45]) ).
thf(f259,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f258]) ).
thf(f260,plain,
( ( c10
!= ( next @ c00 @ right ) )
| ( $true
= ( wall @ ( next @ c00 @ right ) ) )
| spl0_2 ),
inference(constrained_superposition,[],[f211,f168]) ).
thf(f263,plain,
( ( $true
= ( wall @ ( next @ c00 @ right ) ) )
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f260,f39]) ).
thf(f265,plain,
( ( ( wall @ c10 )
= $true )
| spl0_2 ),
inference(forward_demodulation,[],[f263,f39]) ).
thf(f267,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f265,f42]) ).
thf(f268,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f267]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f259]) ).
cnf(s5,plain,
spl0_2,
inference(sat_conversion,[],[f268]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s4,s5]) ).
thf(f269,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : PUZ141^1 : TPTP v9.3.1. Released v6.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.13 % Computer : n012.cluster.edu
% 0.07/0.13 % Model : x86_64 x86_64
% 0.07/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.13 % Memory : 8046.5625MB
% 0.07/0.13 % OS : Linux 6.8.0-71-generic
% 0.07/0.13 % CPULimit : 300
% 0.07/0.13 % WCLimit : 300
% 0.07/0.13 % DateTime : Tue Sep 29 13:26:34 UTC 2026
% 0.07/0.13 % CPUTime :
% 0.07/0.13 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.15 Running higher-order theorem proving
% 0.07/0.16 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.20 % (94056)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.07/0.20 % (94061)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2818323225:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.07/0.20 % (94063)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3493351368:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.07/0.20 % (94061) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-94056-94061"...
% 0.07/0.20 % (94061)...printing done.
% 0.07/0.20 % (94063)Instruction limit reached!
% 0.07/0.20 % (94063)------------------------------
% 0.07/0.20 % (94063)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.20 % (94063)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.20 % (94063)CaDiCaL version: 2.1.3
% 0.07/0.20 % (94063)Termination reason: Instruction limit
% 0.07/0.20 % (94063)Termination phase: Saturation
% 0.07/0.20 % (94063)Time elapsed: 0.002 s
% 0.07/0.20 % (94063)Peak memory usage: 12 MB
% 0.07/0.20 % (94063)Instructions burned: 5 (million)
% 0.07/0.20 % (94061)Refutation found. Thanks to Tanya!
% 0.07/0.20 % SZS status Theorem for theBenchmark
% 0.07/0.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.20 % (94061)------------------------------
% 0.07/0.20 % (94061)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.20 % (94061)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.20 % (94061)CaDiCaL version: 2.1.3
% 0.07/0.20 % (94061)Termination reason: Refutation
% 0.07/0.20 % (94061)Time elapsed: 0.008 s
% 0.07/0.20 % (94061)Peak memory usage: 13 MB
% 0.07/0.20 % (94061)Instructions burned: 25 (million)
% 0.07/0.20 % (94056)Success in time 0.035 s
% 0.07/0.20 % Vampire exiting
%------------------------------------------------------------------------------