TSTP Solution File: SWV019-1 by Leo-III-SAT---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III-SAT---1.7.12
% Problem : SWV019-1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 05:50:19 EDT 2024
% Result : Unsatisfiable 15.69s 3.75s
% Output : Refutation 15.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 74 ( 22 unt; 10 typ; 0 def)
% Number of atoms : 175 ( 24 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 534 ( 79 ~; 93 |; 0 &; 362 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 43 ( 0 ^ 43 !; 0 ?; 43 :)
% Comments :
%------------------------------------------------------------------------------
thf(in_array_bounds_type,type,
in_array_bounds: $i > $i > $o ).
thf(array_type,type,
array: $i ).
thf(an_index_type,type,
an_index: $i ).
thf(less_than_type,type,
less_than: $i > $i > $o ).
thf(successor_type,type,
successor: $i > $i ).
thf(lower_bound_type,type,
lower_bound: $i ).
thf(upper_bound_type,type,
upper_bound: $i ).
thf(index_of_maximal_type,type,
index_of_maximal: $i ).
thf(maximal_value_type,type,
maximal_value: $i ).
thf(array_value_at_type,type,
array_value_at: $i > $i > $i ).
thf(1,negated_conjecture,
( ~ ( in_array_bounds @ array @ an_index )
| ( less_than @ ( successor @ an_index ) @ lower_bound )
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| ( less_than @ index_of_maximal @ lower_bound )
| ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
| ~ ( in_array_bounds @ array @ index_of_maximal )
| ( maximal_value
!= ( array_value_at @ array @ index_of_maximal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
( ~ ( in_array_bounds @ array @ an_index )
| ( less_than @ ( successor @ an_index ) @ lower_bound )
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| ( less_than @ index_of_maximal @ lower_bound )
| ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
| ~ ( in_array_bounds @ array @ index_of_maximal )
| ( maximal_value
!= ( array_value_at @ array @ index_of_maximal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ~ ( in_array_bounds @ array @ an_index )
| ( less_than @ ( successor @ an_index ) @ lower_bound )
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| ( less_than @ index_of_maximal @ lower_bound )
| ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
| ~ ( in_array_bounds @ array @ index_of_maximal )
| ( maximal_value
!= ( array_value_at @ array @ index_of_maximal ) ) ),
inference(cnf,[status(esa)],[11]) ).
thf(13,plain,
( ( ( array_value_at @ array @ index_of_maximal )
!= maximal_value )
| ~ ( in_array_bounds @ array @ an_index )
| ( less_than @ ( successor @ an_index ) @ lower_bound )
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| ( less_than @ index_of_maximal @ lower_bound )
| ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
| ~ ( in_array_bounds @ array @ index_of_maximal ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(10,axiom,
~ ( less_than @ index_of_maximal @ lower_bound ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_above_lower_bound) ).
thf(29,plain,
~ ( less_than @ index_of_maximal @ lower_bound ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(30,plain,
~ ( less_than @ index_of_maximal @ lower_bound ),
inference(polarity_switch,[status(thm)],[29]) ).
thf(48,plain,
( ( ( array_value_at @ array @ index_of_maximal )
!= maximal_value )
| ~ ( in_array_bounds @ array @ an_index )
| ( less_than @ ( successor @ an_index ) @ lower_bound )
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| $false
| ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
| ~ ( in_array_bounds @ array @ index_of_maximal ) ),
inference(rewrite,[status(thm)],[13,30]) ).
thf(49,plain,
( ( ( array_value_at @ array @ index_of_maximal )
!= maximal_value )
| ~ ( in_array_bounds @ array @ an_index )
| ( less_than @ ( successor @ an_index ) @ lower_bound )
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
| ~ ( in_array_bounds @ array @ index_of_maximal ) ),
inference(simp,[status(thm)],[48]) ).
thf(2,axiom,
! [A: $i] :
( ( less_than @ A @ lower_bound )
| ( less_than @ upper_bound @ A )
| ( in_array_bounds @ array @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',in_bounds) ).
thf(14,plain,
! [A: $i] :
( ( less_than @ A @ lower_bound )
| ( less_than @ upper_bound @ A )
| ( in_array_bounds @ array @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [A: $i] :
( ( less_than @ A @ lower_bound )
| ( less_than @ upper_bound @ A )
| ( in_array_bounds @ array @ A ) ),
inference(cnf,[status(esa)],[14]) ).
thf(9,axiom,
~ ( less_than @ upper_bound @ an_index ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_below_upper_bound) ).
thf(27,plain,
~ ( less_than @ upper_bound @ an_index ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(28,plain,
~ ( less_than @ upper_bound @ an_index ),
inference(polarity_switch,[status(thm)],[27]) ).
thf(62,plain,
! [A: $i] :
( ( less_than @ A @ lower_bound )
| ( in_array_bounds @ array @ A )
| ( ( less_than @ upper_bound @ A )
!= ( less_than @ upper_bound @ an_index ) ) ),
inference(paramod_ordered,[status(thm)],[15,28]) ).
thf(63,plain,
( ( less_than @ an_index @ lower_bound )
| ( in_array_bounds @ array @ an_index ) ),
inference(pattern_uni,[status(thm)],[62:[bind(A,$thf( an_index ))]]) ).
thf(8,axiom,
~ ( less_than @ an_index @ lower_bound ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',somewhere_above_lower_bound) ).
thf(25,plain,
~ ( less_than @ an_index @ lower_bound ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(26,plain,
~ ( less_than @ an_index @ lower_bound ),
inference(polarity_switch,[status(thm)],[25]) ).
thf(127,plain,
( $false
| ( in_array_bounds @ array @ an_index ) ),
inference(rewrite,[status(thm)],[63,26]) ).
thf(128,plain,
in_array_bounds @ array @ an_index,
inference(simp,[status(thm)],[127]) ).
thf(131,plain,
( ( ( array_value_at @ array @ index_of_maximal )
!= maximal_value )
| ~ $true
| ( less_than @ ( successor @ an_index ) @ lower_bound )
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
| ~ ( in_array_bounds @ array @ index_of_maximal ) ),
inference(rewrite,[status(thm)],[49,128]) ).
thf(132,plain,
( ( ( array_value_at @ array @ index_of_maximal )
!= maximal_value )
| ( less_than @ ( successor @ an_index ) @ lower_bound )
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| ~ ( less_than @ index_of_maximal @ ( successor @ an_index ) )
| ~ ( in_array_bounds @ array @ index_of_maximal ) ),
inference(simp,[status(thm)],[131]) ).
thf(5,axiom,
! [A: $i] : ( less_than @ A @ ( successor @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',successor_greater) ).
thf(20,plain,
! [A: $i] : ( less_than @ A @ ( successor @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(7,axiom,
less_than @ index_of_maximal @ an_index,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_before_somewhere) ).
thf(24,plain,
less_than @ index_of_maximal @ an_index,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ C )
| ( less_than @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_of_less) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ C )
| ( less_than @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ C )
| ( less_than @ A @ C ) ),
inference(cnf,[status(esa)],[18]) ).
thf(183,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ B @ C )
| ( less_than @ A @ C )
| ( ( less_than @ index_of_maximal @ an_index )
!= ( less_than @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[24,19]) ).
thf(184,plain,
! [A: $i] :
( ~ ( less_than @ an_index @ A )
| ( less_than @ index_of_maximal @ A ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( index_of_maximal )),bind(B,$thf( an_index ))]]) ).
thf(240,plain,
! [A: $i] :
( ~ ( less_than @ an_index @ A )
| ( less_than @ index_of_maximal @ A ) ),
inference(simp,[status(thm)],[184]) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( less_than @ index_of_maximal @ B )
| ( ( less_than @ A @ ( successor @ A ) )
!= ( less_than @ an_index @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20,240]) ).
thf(1026,plain,
less_than @ index_of_maximal @ ( successor @ an_index ),
inference(pattern_uni,[status(thm)],[1025:[bind(A,$thf( an_index )),bind(B,$thf( successor @ an_index ))]]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ~ ( less_than @ B @ C )
| ( ( less_than @ A @ C )
!= ( less_than @ an_index @ lower_bound ) ) ),
inference(paramod_ordered,[status(thm)],[19,26]) ).
thf(212,plain,
! [A: $i] :
( ~ ( less_than @ an_index @ A )
| ~ ( less_than @ A @ lower_bound ) ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( an_index )),bind(B,$thf( B )),bind(C,$thf( lower_bound ))]]) ).
thf(238,plain,
! [A: $i] :
( ~ ( less_than @ an_index @ A )
| ~ ( less_than @ A @ lower_bound ) ),
inference(simp,[status(thm)],[212]) ).
thf(553,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ B @ lower_bound )
| ( ( less_than @ A @ ( successor @ A ) )
!= ( less_than @ an_index @ B ) ) ),
inference(paramod_ordered,[status(thm)],[20,238]) ).
thf(554,plain,
~ ( less_than @ ( successor @ an_index ) @ lower_bound ),
inference(pattern_uni,[status(thm)],[553:[bind(A,$thf( an_index )),bind(B,$thf( successor @ an_index ))]]) ).
thf(58,plain,
! [A: $i] :
( ( less_than @ upper_bound @ A )
| ( in_array_bounds @ array @ A )
| ( ( less_than @ A @ lower_bound )
!= ( less_than @ index_of_maximal @ lower_bound ) ) ),
inference(paramod_ordered,[status(thm)],[15,30]) ).
thf(59,plain,
( ( less_than @ upper_bound @ index_of_maximal )
| ( in_array_bounds @ array @ index_of_maximal ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( index_of_maximal ))]]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( less_than @ A @ B )
| ( less_than @ A @ C )
| ( ( less_than @ index_of_maximal @ an_index )
!= ( less_than @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[24,19]) ).
thf(186,plain,
! [A: $i] :
( ~ ( less_than @ A @ index_of_maximal )
| ( less_than @ A @ an_index ) ),
inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( A )),bind(B,$thf( index_of_maximal )),bind(C,$thf( an_index ))]]) ).
thf(250,plain,
! [A: $i] :
( ( in_array_bounds @ array @ index_of_maximal )
| ( less_than @ A @ an_index )
| ( ( less_than @ upper_bound @ index_of_maximal )
!= ( less_than @ A @ index_of_maximal ) ) ),
inference(paramod_ordered,[status(thm)],[59,186]) ).
thf(251,plain,
( ( in_array_bounds @ array @ index_of_maximal )
| ( less_than @ upper_bound @ an_index ) ),
inference(pattern_uni,[status(thm)],[250:[bind(A,$thf( upper_bound ))]]) ).
thf(268,plain,
( ( in_array_bounds @ array @ index_of_maximal )
| $false ),
inference(rewrite,[status(thm)],[251,28]) ).
thf(269,plain,
in_array_bounds @ array @ index_of_maximal,
inference(simp,[status(thm)],[268]) ).
thf(6,axiom,
( ~ ( in_array_bounds @ array @ index_of_maximal )
| ( maximal_value
= ( array_value_at @ array @ index_of_maximal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',this_is_maximal) ).
thf(21,plain,
( ~ ( in_array_bounds @ array @ index_of_maximal )
| ( maximal_value
= ( array_value_at @ array @ index_of_maximal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(22,plain,
( ~ ( in_array_bounds @ array @ index_of_maximal )
| ( maximal_value
= ( array_value_at @ array @ index_of_maximal ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
( ( ( array_value_at @ array @ index_of_maximal )
= maximal_value )
| ~ ( in_array_bounds @ array @ index_of_maximal ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(270,plain,
( ( ( array_value_at @ array @ index_of_maximal )
= maximal_value )
| ~ $true ),
inference(rewrite,[status(thm)],[23,269]) ).
thf(271,plain,
( ( array_value_at @ array @ index_of_maximal )
= maximal_value ),
inference(simp,[status(thm)],[270]) ).
thf(1890,plain,
( ( maximal_value != maximal_value )
| $false
| ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[132,1026,554,269,271]) ).
thf(1891,plain,
less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ),
inference(simp,[status(thm)],[1890]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( less_than @ ( successor @ A ) @ ( successor @ B ) )
| ( less_than @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',predecessor_less) ).
thf(16,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ ( successor @ A ) @ ( successor @ B ) )
| ( less_than @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [B: $i,A: $i] :
( ~ ( less_than @ ( successor @ A ) @ ( successor @ B ) )
| ( less_than @ A @ B ) ),
inference(cnf,[status(esa)],[16]) ).
thf(1905,plain,
! [B: $i,A: $i] :
( ( less_than @ A @ B )
| ( ( less_than @ ( successor @ upper_bound ) @ ( successor @ an_index ) )
!= ( less_than @ ( successor @ A ) @ ( successor @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[1891,17]) ).
thf(1906,plain,
less_than @ upper_bound @ an_index,
inference(pattern_uni,[status(thm)],[1905:[bind(A,$thf( upper_bound )),bind(B,$thf( an_index ))]]) ).
thf(1957,plain,
$false,
inference(rewrite,[status(thm)],[1906,28]) ).
thf(1958,plain,
$false,
inference(simp,[status(thm)],[1957]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV019-1 : TPTP v8.2.0. Released v2.4.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n017.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 : Sun May 19 06:52:39 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.01/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.09/1.00 % [INFO] Parsing done (110ms).
% 1.09/1.00 % [INFO] Running in sequential loop mode.
% 1.66/1.22 % [INFO] nitpick registered as external prover.
% 1.66/1.23 % [INFO] Scanning for conjecture ...
% 1.77/1.29 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.77/1.31 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.77/1.31 % [INFO] Problem is propositional (TPTP CNF).
% 1.77/1.32 % [INFO] Type checking passed.
% 1.77/1.32 % [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 ...
% 15.69/3.73 % [INFO] Killing All external provers ...
% 15.69/3.74 % Time passed: 3193ms (effective reasoning time: 2729ms)
% 15.69/3.75 % Axioms used in derivation (9): maximal_before_somewhere, somewhere_below_upper_bound, successor_greater, this_is_maximal, somewhere_above_lower_bound, transitivity_of_less, in_bounds, maximal_above_lower_bound, predecessor_less
% 15.69/3.75 % No. of inferences in proof: 64
% 15.69/3.75 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3193 ms resp. 2729 ms w/o parsing
% 15.90/3.84 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 15.94/3.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------