TSTP Solution File: SWV007-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV007-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 12:13:33 EDT 2023
% Result : Unsatisfiable 2.97s 1.71s
% Output : Refutation 2.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of formulae : 56 ( 27 unt; 9 typ; 0 def)
% Number of atoms : 83 ( 20 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 248 ( 46 ~; 36 |; 0 &; 166 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 50 ( 0 ^; 50 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
thf(less_than_type,type,
less_than: $i > $i > $o ).
thf(n_type,type,
n: $i ).
thf(k_type,type,
k: $i ).
thf(i_type,type,
i: $i ).
thf(m_type,type,
m: $i ).
thf(one_type,type,
one: $i ).
thf(a_type,type,
a: $i > $i ).
thf(predecessor_type,type,
predecessor: $i > $i ).
thf(successor_type,type,
successor: $i > $i ).
thf(16,axiom,
! [A: $i] : ( less_than @ ( predecessor @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',predecessor_less_than) ).
thf(56,plain,
! [A: $i] : ( less_than @ ( predecessor @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( successor @ A )
!= ( successor @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined_successor) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( successor @ A )
!= ( successor @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',all_related) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',anti_symmetry_of_less_than) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_than @ A @ B )
| ( C != B )
| ~ ( less_than @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_and_less_than_transitivity2) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( less_than @ A @ B )
| ( C != B )
| ~ ( less_than @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(1,negated_conjecture,
~ ( less_than @ n @ k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_1) ).
thf(26,plain,
~ ( less_than @ n @ k ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_than @ A @ B )
| ~ ( less_than @ A @ C )
| ~ ( less_than @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less_than) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( less_than @ A @ B )
| ~ ( less_than @ A @ C )
| ~ ( less_than @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(7,negated_conjecture,
k != m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_7) ).
thf(30,plain,
k != m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,negated_conjecture,
less_than @ i @ m,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_5) ).
thf(24,plain,
less_than @ i @ m,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(10,negated_conjecture,
! [A: $i] :
( ( less_than @ A @ i )
| ( less_than @ n @ A )
| ~ ( less_than @ one @ A )
| ~ ( less_than @ ( a @ A ) @ ( a @ ( predecessor @ i ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_10) ).
thf(25,plain,
! [A: $i] :
( ( less_than @ A @ i )
| ( less_than @ n @ A )
| ~ ( less_than @ one @ A )
| ~ ( less_than @ ( a @ A ) @ ( a @ ( predecessor @ i ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(13,axiom,
! [A: $i] :
( ( successor @ ( predecessor @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_predecessor) ).
thf(46,plain,
! [A: $i] :
( ( successor @ ( predecessor @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(17,axiom,
! [A: $i] : ( less_than @ A @ ( successor @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',less_than_successor) ).
thf(57,plain,
! [A: $i] : ( less_than @ A @ ( successor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(2,negated_conjecture,
~ ( less_than @ k @ i ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_2) ).
thf(29,plain,
~ ( less_than @ k @ i ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(9,negated_conjecture,
! [A: $i] :
( ~ ( less_than @ one @ A )
| ~ ( less_than @ A @ i )
| ~ ( less_than @ ( a @ A ) @ ( a @ ( predecessor @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_9) ).
thf(28,plain,
! [A: $i] :
( ~ ( less_than @ one @ A )
| ~ ( less_than @ A @ i )
| ~ ( less_than @ ( a @ A ) @ ( a @ ( predecessor @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,negated_conjecture,
less_than @ ( a @ m ) @ ( a @ k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_8) ).
thf(33,plain,
less_than @ ( a @ m ) @ ( a @ k ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,negated_conjecture,
! [A: $i] :
( ( less_than @ A @ i )
| ~ ( less_than @ A @ ( successor @ n ) )
| ~ ( less_than @ ( a @ A ) @ ( a @ k ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_11) ).
thf(32,plain,
! [A: $i] :
( ( less_than @ A @ i )
| ~ ( less_than @ A @ ( successor @ n ) )
| ~ ( less_than @ ( a @ A ) @ ( a @ k ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,negated_conjecture,
~ ( less_than @ n @ m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_4) ).
thf(34,plain,
~ ( less_than @ n @ m ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(12,axiom,
! [A: $i] :
( ( predecessor @ ( successor @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',predecessor_successor) ).
thf(44,plain,
! [A: $i] :
( ( predecessor @ ( successor @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(6,negated_conjecture,
~ ( less_than @ i @ one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_6) ).
thf(27,plain,
~ ( less_than @ i @ one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( predecessor @ A )
!= ( predecessor @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',well_defined_predecessor) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( predecessor @ A )
!= ( predecessor @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(20,axiom,
! [A: $i] :
~ ( less_than @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_not_less_than_x) ).
thf(63,plain,
! [A: $i] :
~ ( less_than @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( less_than @ A @ B )
| ( C != A )
| ~ ( less_than @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_and_less_than_transitivity1) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( less_than @ A @ B )
| ( C != A )
| ~ ( less_than @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,negated_conjecture,
less_than @ i @ n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clause_3) ).
thf(31,plain,
less_than @ i @ n,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(75,plain,
$false,
inference(e,[status(thm)],[56,52,60,65,71,26,58,30,24,25,46,57,29,28,33,32,34,44,27,48,63,67,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV007-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n025.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 02:42:04 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.86/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.17/0.99 % [INFO] Parsing done (141ms).
% 1.17/1.00 % [INFO] Running in sequential loop mode.
% 1.69/1.21 % [INFO] eprover registered as external prover.
% 1.69/1.21 % [INFO] cvc4 registered as external prover.
% 1.69/1.22 % [INFO] Scanning for conjecture ...
% 1.78/1.29 % [INFO] Found a conjecture and 12 axioms. Running axiom selection ...
% 1.78/1.32 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 1.78/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 2.02/1.33 % [INFO] Type checking passed.
% 2.02/1.33 % [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 ...
% 2.97/1.70 % External prover 'e' found a proof!
% 2.97/1.70 % [INFO] Killing All external provers ...
% 2.97/1.70 % Time passed: 1191ms (effective reasoning time: 701ms)
% 2.97/1.70 % 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)>
% 2.97/1.70 % Axioms used in derivation (12): well_defined_successor, all_related, predecessor_successor, predecessor_less_than, well_defined_predecessor, less_than_successor, x_not_less_than_x, successor_predecessor, anti_symmetry_of_less_than, equal_and_less_than_transitivity1, equal_and_less_than_transitivity2, transitivity_of_less_than
% 2.97/1.70 % No. of inferences in proof: 47
% 2.97/1.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1191 ms resp. 701 ms w/o parsing
% 2.97/1.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.97/1.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------