TSTP Solution File: SWV409+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 12:15:39 EDT 2023
% Result : Theorem 3.41s 1.97s
% Output : Refutation 3.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 34
% Syntax : Number of formulae : 58 ( 19 unt; 12 typ; 0 def)
% Number of atoms : 116 ( 27 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 449 ( 15 ~; 11 |; 31 &; 364 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 130 ( 0 ^; 123 !; 7 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(contains_slb_type,type,
contains_slb: $i > $i > $o ).
thf(strictly_less_than_type,type,
strictly_less_than: $i > $i > $o ).
thf(pair_in_list_type,type,
pair_in_list: $i > $i > $i > $o ).
thf(update_slb_type,type,
update_slb: $i > $i > $i ).
thf(less_than_type,type,
less_than: $i > $i > $o ).
thf(isnonempty_slb_type,type,
isnonempty_slb: $i > $o ).
thf(insert_slb_type,type,
insert_slb: $i > $i > $i ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(lookup_slb_type,type,
lookup_slb: $i > $i > $i ).
thf(remove_slb_type,type,
remove_slb: $i > $i > $i ).
thf(create_slb_type,type,
create_slb: $i ).
thf(bottom_type,type,
bottom: $i ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
<=> ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
thf(85,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E )
=> ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) ) )
& ( ( ( pair_in_list @ A @ C @ E )
| ( ( B = C )
& ( D = E ) ) )
=> ( pair_in_list @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( strictly_less_than @ A @ B )
<=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(70,plain,
! [A: $i,B: $i] :
( ( ( strictly_less_than @ A @ B )
=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) )
& ( ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) )
=> ( strictly_less_than @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( contains_slb @ A @ B )
=> ? [C: $i] : ( pair_in_list @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( contains_slb @ A @ B )
=> ? [C: $i] : ( pair_in_list @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( less_than @ A @ B )
& ( less_than @ B @ C ) )
=> ( less_than @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
thf(53,plain,
! [A: $i,B: $i,C: $i] :
( ( ( less_than @ A @ B )
& ( less_than @ B @ C ) )
=> ( less_than @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( less_than @ C @ D )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
thf(96,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( less_than @ C @ D )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
thf(80,plain,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(8,axiom,
! [A: $i] : ( less_than @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
thf(48,plain,
! [A: $i] : ( less_than @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( lookup_slb @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).
thf(99,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( lookup_slb @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( strictly_less_than @ D @ C )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
thf(55,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( strictly_less_than @ D @ C )
=> ( ( update_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( update_slb @ A @ C ) @ ( pair @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
thf(58,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B != C )
& ( contains_slb @ A @ C ) )
=> ( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
= ( insert_slb @ ( remove_slb @ A @ C ) @ ( pair @ B @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( pair_in_list @ A @ B @ C )
& ( strictly_less_than @ B @ D )
& ( less_than @ D @ C ) )
=> ? [E: $i] :
( ( pair_in_list @ ( update_slb @ A @ D ) @ B @ E )
& ( less_than @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l49) ).
thf(62,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( pair_in_list @ A @ B @ C )
& ( strictly_less_than @ B @ D )
& ( less_than @ D @ C ) )
=> ? [E: $i] :
( ( pair_in_list @ ( update_slb @ A @ D ) @ B @ E )
& ( less_than @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( contains_slb @ A @ B )
& ( strictly_less_than @ B @ C ) )
=> ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ C )
| ? [D: $i] :
( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ D )
& ( less_than @ C @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_co) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( contains_slb @ A @ B )
& ( strictly_less_than @ B @ C ) )
=> ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ C )
| ? [D: $i] :
( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ D )
& ( less_than @ C @ D ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(24,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( contains_slb @ A @ B )
& ( strictly_less_than @ B @ C ) )
=> ( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ C )
| ? [D: $i] :
( ( pair_in_list @ ( update_slb @ A @ C ) @ B @ D )
& ( less_than @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(6,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
thf(37,plain,
~ ( isnonempty_slb @ create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(18,axiom,
! [A: $i] : ( less_than @ bottom @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
thf(78,plain,
! [A: $i] : ( less_than @ bottom @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
thf(29,plain,
! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( pair_in_list @ A @ B @ C )
& ( strictly_less_than @ B @ D )
& ( strictly_less_than @ C @ D ) )
=> ( pair_in_list @ ( update_slb @ A @ D ) @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_l48) ).
thf(76,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( pair_in_list @ A @ B @ C )
& ( strictly_less_than @ B @ D )
& ( strictly_less_than @ C @ D ) )
=> ( pair_in_list @ ( update_slb @ A @ D ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
<=> ( ( contains_slb @ A @ C )
| ( B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
thf(39,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C )
=> ( ( contains_slb @ A @ C )
| ( B = C ) ) )
& ( ( ( contains_slb @ A @ C )
| ( B = C ) )
=> ( contains_slb @ ( insert_slb @ A @ ( pair @ B @ D ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
thf(50,plain,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(15,axiom,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
thf(67,plain,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(103,plain,
$false,
inference(e,[status(thm)],[85,70,65,53,96,34,80,48,99,55,58,62,83,24,37,78,29,76,39,50,67,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SWV409+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.10 % Command : run_Leo-III %s %d
% 0.10/0.29 % Computer : n012.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Fri May 19 02:09:18 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.72/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.09/0.91 % [INFO] Parsing done (145ms).
% 1.16/0.93 % [INFO] Running in sequential loop mode.
% 1.47/1.18 % [INFO] eprover registered as external prover.
% 1.47/1.18 % [INFO] cvc4 registered as external prover.
% 1.64/1.19 % [INFO] Scanning for conjecture ...
% 1.71/1.26 % [INFO] Found a conjecture and 21 axioms. Running axiom selection ...
% 1.92/1.31 % [INFO] Axiom selection finished. Selected 21 axioms (removed 0 axioms).
% 1.92/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 1.92/1.36 % [INFO] Type checking passed.
% 1.92/1.37 % [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 ...
% 3.41/1.97 % External prover 'e' found a proof!
% 3.41/1.97 % [INFO] Killing All external provers ...
% 3.41/1.97 % Time passed: 1547ms (effective reasoning time: 1035ms)
% 3.41/1.97 % 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)>
% 3.41/1.97 % Axioms used in derivation (21): ax20, ax24, stricly_smaller_definition, ax28, ax27, ax21, l45_l49, l45_li4647, ax22, ax19, totality, ax23, ax25, reflexivity, l45_l48, ax26, bottom_smallest, transitivity, ax30, ax18, ax29
% 3.41/1.97 % No. of inferences in proof: 46
% 3.41/1.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1547 ms resp. 1035 ms w/o parsing
% 3.79/2.02 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.79/2.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------