TSTP Solution File: PUZ142^1 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : PUZ142^1 : TPTP v8.2.0. Released v6.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 : Tue May 21 02:27:03 EDT 2024
% Result : Theorem 3.42s 2.05s
% Output : Refutation 3.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 75
% Syntax : Number of formulae : 104 ( 68 unt; 32 typ; 16 def)
% Number of atoms : 120 ( 55 equ; 0 cnn)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 274 ( 9 ~; 0 |; 0 &; 257 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 32 ( 29 usr; 27 con; 0-2 aty)
% Number of variables : 25 ( 0 ^ 22 !; 3 ?; 25 :)
% Comments :
%------------------------------------------------------------------------------
thf(position_type,type,
position: $tType ).
thf(direction_type,type,
direction: $tType ).
thf(left_type,type,
left: direction ).
thf(right_type,type,
right: direction ).
thf(top_type,type,
top: direction ).
thf(bottom_type,type,
bottom: direction ).
thf(next_type,type,
next: position > direction > position ).
thf(wall_type,type,
wall: position > $o ).
thf(movelist_type,type,
movelist: $tType ).
thf(nomove_type,type,
nomove: movelist ).
thf(movedir_type,type,
movedir: movelist > direction > movelist ).
thf(playerpos_type,type,
playerpos: movelist > position ).
thf(c00_type,type,
c00: position ).
thf(c10_type,type,
c10: position ).
thf(c10_def,definition,
( c10
= ( next @ c00 @ right ) ) ).
thf(c20_type,type,
c20: position ).
thf(c20_def,definition,
( c20
= ( next @ c10 @ right ) ) ).
thf(c30_type,type,
c30: position ).
thf(c30_def,definition,
( c30
= ( next @ c20 @ right ) ) ).
thf(c40_type,type,
c40: position ).
thf(c40_def,definition,
( c40
= ( next @ c30 @ right ) ) ).
thf(c01_type,type,
c01: position ).
thf(c01_def,definition,
( c01
= ( next @ c00 @ top ) ) ).
thf(c11_type,type,
c11: position ).
thf(c11_def,definition,
( c11
= ( next @ c10 @ top ) ) ).
thf(c21_type,type,
c21: position ).
thf(c21_def,definition,
( c21
= ( next @ c20 @ top ) ) ).
thf(c31_type,type,
c31: position ).
thf(c31_def,definition,
( c31
= ( next @ c30 @ top ) ) ).
thf(c41_type,type,
c41: position ).
thf(c02_type,type,
c02: position ).
thf(c02_def,definition,
( c02
= ( next @ c01 @ top ) ) ).
thf(c12_type,type,
c12: position ).
thf(c12_def,definition,
( c12
= ( next @ c11 @ top ) ) ).
thf(c22_type,type,
c22: position ).
thf(c22_def,definition,
( c22
= ( next @ c21 @ top ) ) ).
thf(c32_type,type,
c32: position ).
thf(c32_def,definition,
( c32
= ( next @ c31 @ top ) ) ).
thf(c42_type,type,
c42: position ).
thf(c03_type,type,
c03: position ).
thf(c03_def,definition,
( c03
= ( next @ c02 @ top ) ) ).
thf(c13_type,type,
c13: position ).
thf(c13_def,definition,
( c13
= ( next @ c12 @ top ) ) ).
thf(c23_type,type,
c23: position ).
thf(c23_def,definition,
( c23
= ( next @ c22 @ top ) ) ).
thf(c33_type,type,
c33: position ).
thf(c33_def,definition,
( c33
= ( next @ c32 @ top ) ) ).
thf(c43_type,type,
c43: position ).
thf(16,axiom,
( ( wall @ c10 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c10_axiom) ).
thf(56,plain,
wall @ ( next @ c00 @ right ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(19,axiom,
( ( wall @ c20 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c20_axiom) ).
thf(60,plain,
wall @ ( next @ ( next @ c00 @ right ) @ right ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(23,axiom,
( ( wall @ c30 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c30_axiom) ).
thf(65,plain,
wall @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(15,axiom,
! [A: direction,B: direction,C: position] :
( ( next @ ( next @ C @ A ) @ B )
= ( next @ ( next @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',next_comm) ).
thf(53,plain,
! [A: direction,B: direction,C: position] :
( ( next @ ( next @ C @ A ) @ B )
= ( next @ ( next @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(28,axiom,
( ( wall @ c13 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c13_axiom) ).
thf(77,plain,
wall @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ top ) @ top ) @ top ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(11,axiom,
( ( wall @ c02 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c02_axiom) ).
thf(44,plain,
wall @ ( next @ ( next @ c00 @ top ) @ top ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(24,axiom,
( ( wall @ c40 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c40_axiom) ).
thf(66,plain,
wall @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ right ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(6,axiom,
( ( wall @ c01 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c01_axiom) ).
thf(35,plain,
wall @ ( next @ c00 @ top ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(25,axiom,
! [A: position,B: movelist,C: direction] :
( ( ( playerpos @ B )
= A )
=> ( ( wall @ ( next @ A @ C ) )
=> ( ( playerpos @ ( movedir @ B @ C ) )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',player_move_illegal) ).
thf(67,plain,
! [A: position,B: movelist,C: direction] :
( ( ( playerpos @ B )
= A )
=> ( ( wall @ ( next @ A @ C ) )
=> ( ( playerpos @ ( movedir @ B @ C ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
! [A: position] :
( ( next @ ( next @ A @ top ) @ bottom )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',top_bottom) ).
thf(40,plain,
! [A: position] :
( ( next @ ( next @ A @ top ) @ bottom )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
( ( playerpos @ nomove )
= c11 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',start_axiom) ).
thf(58,plain,
( ( playerpos @ nomove )
= ( next @ ( next @ c00 @ right ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,axiom,
( ( wall @ c22 )
= $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c22_axiom) ).
thf(36,plain,
~ ( wall @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ top ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(21,axiom,
( ( wall @ c21 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c21_axiom) ).
thf(62,plain,
wall @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ top ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(13,axiom,
( ( wall @ c12 )
= $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c12_axiom) ).
thf(46,plain,
~ ( wall @ ( next @ ( next @ ( next @ c00 @ right ) @ top ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
( ( wall @ c00 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c00_axiom) ).
thf(57,plain,
wall @ c00,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1,conjecture,
? [A: movelist] :
( ( playerpos @ A )
= c31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exercise) ).
thf(2,negated_conjecture,
~ ? [A: movelist] :
( ( playerpos @ A )
= c31 ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(29,plain,
~ ? [A: movelist] :
( ( playerpos @ A )
= ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,axiom,
( ( wall @ c33 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c33_axiom) ).
thf(61,plain,
wall @ ( next @ ( next @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ top ) @ top ) @ top ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(27,axiom,
! [A: position] :
( ( next @ ( next @ A @ left ) @ right )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_right) ).
thf(74,plain,
! [A: position] :
( ( next @ ( next @ A @ left ) @ right )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
( ( wall @ c32 )
= $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c32_axiom) ).
thf(38,plain,
~ ( wall @ ( next @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ top ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
( ( wall @ c42 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c42_axiom) ).
thf(33,plain,
wall @ c42,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
( ( wall @ c03 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c03_axiom) ).
thf(45,plain,
wall @ ( next @ ( next @ ( next @ c00 @ top ) @ top ) @ top ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(3,axiom,
( ( wall @ c43 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c43_axiom) ).
thf(32,plain,
wall @ c43,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(5,axiom,
( ( wall @ c41 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c41_axiom) ).
thf(34,plain,
wall @ c41,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: position,B: movelist,C: direction] :
( ( ( playerpos @ B )
= A )
=> ( ~ ( wall @ ( next @ A @ C ) )
=> ( ( playerpos @ ( movedir @ B @ C ) )
= ( next @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',player_move_legal) ).
thf(48,plain,
! [A: position,B: movelist,C: direction] :
( ( ( playerpos @ B )
= A )
=> ( ~ ( wall @ ( next @ A @ C ) )
=> ( ( playerpos @ ( movedir @ B @ C ) )
= ( next @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(22,axiom,
( ( wall @ c31 )
= $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c31_axiom) ).
thf(63,plain,
~ ( wall @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ right ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(26,axiom,
( ( wall @ c11 )
= $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c11_axiom) ).
thf(72,plain,
~ ( wall @ ( next @ ( next @ c00 @ right ) @ top ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
( ( wall @ c23 )
= $true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c23_axiom) ).
thf(43,plain,
wall @ ( next @ ( next @ ( next @ ( next @ ( next @ c00 @ right ) @ right ) @ top ) @ top ) @ top ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(88,plain,
$false,
inference(cvc4,[status(thm)],[56,60,65,53,77,44,66,35,67,40,58,36,62,46,57,29,61,74,38,33,45,32,34,48,63,72,43]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : PUZ142^1 : TPTP v8.2.0. Released v6.2.0.
% 0.10/0.13 % Command : run_Leo-III %s %d
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat May 18 10:57:23 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.82/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.12/0.95 % [INFO] Parsing done (128ms).
% 1.12/0.96 % [INFO] Running in sequential loop mode.
% 1.69/1.21 % [INFO] eprover registered as external prover.
% 1.69/1.22 % [INFO] cvc4 registered as external prover.
% 1.69/1.22 % [INFO] Scanning for conjecture ...
% 1.73/1.30 % [INFO] Found a conjecture (or negated_conjecture) and 26 axioms. Running axiom selection ...
% 1.89/1.37 % [INFO] Axiom selection finished. Selected 26 axioms (removed 0 axioms).
% 2.07/1.40 % [INFO] Problem is higher-order (TPTP THF).
% 2.07/1.40 % [INFO] Type checking passed.
% 2.07/1.41 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 3.42/2.04 % External prover 'cvc4' found a proof!
% 3.42/2.04 % [INFO] Killing All external provers ...
% 3.42/2.04 % Time passed: 1574ms (effective reasoning time: 1083ms)
% 3.42/2.04 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 3.42/2.05 % Axioms used in derivation (26): c23_axiom, top_bottom, c11_axiom, c10_axiom, c31_axiom, c21_axiom, c43_axiom, c40_axiom, player_move_legal, c22_axiom, c41_axiom, c30_axiom, c03_axiom, player_move_illegal, c42_axiom, c32_axiom, c20_axiom, c13_axiom, c12_axiom, c00_axiom, c01_axiom, left_right, next_comm, c33_axiom, start_axiom, c02_axiom
% 3.42/2.05 % No. of inferences in proof: 56
% 3.42/2.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1574 ms resp. 1083 ms w/o parsing
% 3.81/2.11 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.81/2.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------