TSTP Solution File: PUZ034-1.004 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : PUZ034-1.004 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 : Fri May 19 11:47:30 EDT 2023
% Result : Unsatisfiable 3.66s 1.89s
% Output : Refutation 3.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 31
% Syntax : Number of formulae : 50 ( 19 unt; 13 typ; 0 def)
% Number of atoms : 79 ( 0 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 354 ( 44 ~; 42 |; 0 &; 268 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 90 ( 0 ^; 90 !; 0 ?; 90 :)
% Comments :
%------------------------------------------------------------------------------
thf(queens_type,type,
queens: $i > $i > $o ).
thf(s_type,type,
s: $i > $i ).
thf(n0_type,type,
n0: $i ).
thf(select_type,type,
select: $i > $i > $i > $o ).
thf(cons_type,type,
cons: $i > $i > $i ).
thf(do_queens_type,type,
do_queens: $i > $i > $i > $o ).
thf(empty_list_type,type,
empty_list: $i ).
thf(diagonal_attack_type,type,
diagonal_attack: $i > $i > $i > $o ).
thf(attack_type,type,
attack: $i > $i > $o ).
thf(range_type,type,
range: $i > $i > $i > $o ).
thf(less_type,type,
less: $i > $i > $o ).
thf(sum_type,type,
sum: $i > $i > $i > $o ).
thf(same_type,type,
same: $i > $i > $o ).
thf(14,axiom,
! [A: $i] :
~ ( same @ n0 @ ( s @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',same_definition2) ).
thf(41,plain,
! [A: $i] :
~ ( same @ n0 @ ( s @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( queens @ A @ B )
| ~ ( sum @ A @ ( s @ n0 ) @ C )
| ~ ( sum @ A @ A @ D )
| ~ ( range @ C @ D @ E )
| ~ ( do_queens @ E @ empty_list @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set_up_queens) ).
thf(48,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( queens @ A @ B )
| ~ ( sum @ A @ ( s @ n0 ) @ C )
| ~ ( sum @ A @ A @ D )
| ~ ( range @ C @ D @ E )
| ~ ( do_queens @ E @ empty_list @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ A @ ( s @ B ) @ ( s @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( sum @ A @ B @ C )
| ( sum @ A @ ( s @ B ) @ ( s @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(13,axiom,
! [A: $i] : ( less @ n0 @ ( s @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less1) ).
thf(40,plain,
! [A: $i] : ( less @ n0 @ ( s @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: $i] : ( do_queens @ empty_list @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',place_a_queen2) ).
thf(24,plain,
! [A: $i] : ( do_queens @ empty_list @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [B: $i,A: $i] :
~ ( diagonal_attack @ A @ B @ empty_list ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',check_diagonals2) ).
thf(25,plain,
! [B: $i,A: $i] :
~ ( diagonal_attack @ A @ B @ empty_list ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( diagonal_attack @ A @ B @ ( cons @ C @ D ) )
| ~ ( sum @ E @ B @ C )
| ( same @ E @ A )
| ~ ( sum @ C @ B @ F )
| ( same @ F @ A )
| ~ ( sum @ B @ ( s @ n0 ) @ G )
| ( diagonal_attack @ A @ G @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',check_diagonals1) ).
thf(46,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( diagonal_attack @ A @ B @ ( cons @ C @ D ) )
| ~ ( sum @ E @ B @ C )
| ( same @ E @ A )
| ~ ( sum @ C @ B @ F )
| ( same @ F @ A )
| ~ ( sum @ B @ ( s @ n0 ) @ G )
| ( diagonal_attack @ A @ G @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i] : ( range @ A @ A @ ( cons @ A @ empty_list ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',make_list_of_numbers2) ).
thf(29,plain,
! [A: $i] : ( range @ A @ A @ ( cons @ A @ empty_list ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( diagonal_attack @ A @ ( s @ n0 ) @ B )
| ~ ( attack @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',attack) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( diagonal_attack @ A @ ( s @ n0 ) @ B )
| ~ ( attack @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(2,axiom,
! [B: $i,A: $i] : ( select @ A @ ( cons @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',select1) ).
thf(21,plain,
! [B: $i,A: $i] : ( select @ A @ ( cons @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,axiom,
! [A: $i] : ( sum @ A @ n0 @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',add_0) ).
thf(45,plain,
! [A: $i] : ( sum @ A @ n0 @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( same @ ( s @ A ) @ ( s @ B ) )
| ( same @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',same_definition3) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( same @ ( s @ A ) @ ( s @ B ) )
| ( same @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( less @ ( s @ A ) @ ( s @ B ) )
| ~ ( less @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',less2) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( less @ ( s @ A ) @ ( s @ B ) )
| ~ ( less @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( select @ A @ ( cons @ B @ C ) @ ( cons @ B @ D ) )
| ~ ( select @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',select2) ).
thf(22,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( select @ A @ ( cons @ B @ C ) @ ( cons @ B @ D ) )
| ~ ( select @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( do_queens @ A @ B @ C )
| ~ ( select @ D @ A @ E )
| ( attack @ D @ B )
| ~ ( do_queens @ E @ ( cons @ D @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',place_a_queen1) ).
thf(27,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( do_queens @ A @ B @ C )
| ~ ( select @ D @ A @ E )
| ( attack @ D @ B )
| ~ ( do_queens @ E @ ( cons @ D @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,axiom,
! [A: $i] :
~ ( same @ ( s @ A ) @ n0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',same_definition1) ).
thf(36,plain,
! [A: $i] :
~ ( same @ ( s @ A ) @ n0 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( range @ A @ B @ ( cons @ A @ C ) )
| ~ ( less @ A @ B )
| ~ ( sum @ A @ ( s @ n0 ) @ D )
| ~ ( range @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',make_list_of_numbers1) ).
thf(30,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( range @ A @ B @ ( cons @ A @ C ) )
| ~ ( less @ A @ B )
| ~ ( sum @ A @ ( s @ n0 ) @ D )
| ~ ( range @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1,negated_conjecture,
! [A: $i] :
~ ( queens @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',place_queens) ).
thf(19,plain,
! [A: $i] :
~ ( queens @ ( s @ ( s @ ( s @ ( s @ n0 ) ) ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(56,plain,
$false,
inference(e,[status(thm)],[41,48,43,40,24,25,46,29,38,21,45,32,34,22,27,36,30,19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : PUZ034-1.004 : TPTP v8.1.2. Released v1.0.0.
% 0.11/0.14 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 19:54:22 EDT 2023
% 0.15/0.35 % CPUTime :
% 0.99/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.34/1.01 % [INFO] Parsing done (138ms).
% 1.34/1.02 % [INFO] Running in sequential loop mode.
% 1.72/1.21 % [INFO] eprover registered as external prover.
% 1.72/1.22 % [INFO] cvc4 registered as external prover.
% 1.72/1.22 % [INFO] Scanning for conjecture ...
% 1.77/1.27 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 1.77/1.31 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.03/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 2.03/1.34 % [INFO] Type checking passed.
% 2.03/1.34 % [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 ...
% 3.66/1.89 % External prover 'e' found a proof!
% 3.66/1.89 % [INFO] Killing All external provers ...
% 3.66/1.89 % Time passed: 1384ms (effective reasoning time: 870ms)
% 3.66/1.89 % 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)>
% 3.66/1.89 % Axioms used in derivation (17): make_list_of_numbers2, check_diagonals1, place_a_queen2, select1, less1, check_diagonals2, same_definition3, add_0, attack, make_list_of_numbers1, same_definition2, select2, less2, same_definition1, set_up_queens, place_a_queen1, add
% 3.66/1.89 % No. of inferences in proof: 37
% 3.66/1.89 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1384 ms resp. 870 ms w/o parsing
% 3.87/1.93 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.87/1.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------