TSTP Solution File: SWV411+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV411+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 12:15:40 EDT 2023
% Result : Theorem 3.58s 1.79s
% Output : Refutation 3.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 31
% Syntax : Number of formulae : 52 ( 19 unt; 12 typ; 0 def)
% Number of atoms : 91 ( 27 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 374 ( 15 ~; 8 |; 15 &; 308 @)
% ( 3 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 7 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 : 115 ( 0 ^; 109 !; 6 ?; 115 :)
% Comments :
%------------------------------------------------------------------------------
thf(contains_slb_type,type,
contains_slb: $i > $i > $o ).
thf(pair_in_list_type,type,
pair_in_list: $i > $i > $i > $o ).
thf(insert_slb_type,type,
insert_slb: $i > $i > $i ).
thf(pair_type,type,
pair: $i > $i > $i ).
thf(strictly_less_than_type,type,
strictly_less_than: $i > $i > $o ).
thf(less_than_type,type,
less_than: $i > $i > $o ).
thf(bottom_type,type,
bottom: $i ).
thf(isnonempty_slb_type,type,
isnonempty_slb: $i > $o ).
thf(create_slb_type,type,
create_slb: $i ).
thf(update_slb_type,type,
update_slb: $i > $i > $i ).
thf(remove_slb_type,type,
remove_slb: $i > $i > $i ).
thf(lookup_slb_type,type,
lookup_slb: $i > $i > $i ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( remove_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
thf(69,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)],[16]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',ax29) ).
thf(56,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)],[12]) ).
thf(9,axiom,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
thf(42,plain,
! [A: $i] :
( ( update_slb @ create_slb @ A )
= create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',ax27) ).
thf(89,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)],[20]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',ax25) ).
thf(59,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)],[13]) ).
thf(19,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/sandbox/benchmark/theBenchmark.p',ax30) ).
thf(86,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)],[19]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( lookup_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
thf(66,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)],[15]) ).
thf(14,axiom,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
thf(63,plain,
! [A: $i] :
~ ( contains_slb @ create_slb @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(17,axiom,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
thf(72,plain,
! [A: $i,B: $i] :
~ ( pair_in_list @ create_slb @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(18,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/sandbox/benchmark/theBenchmark.p',ax23) ).
thf(75,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)],[18]) ).
thf(6,axiom,
! [A: $i] : ( less_than @ bottom @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
thf(36,plain,
! [A: $i] : ( less_than @ bottom @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',ax21) ).
thf(47,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)],[11]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( less_than @ A @ B )
| ( less_than @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,conjecture,
! [A: $i] :
( ! [B: $i] :
( ( contains_slb @ A @ B )
=> ? [C: $i] : ( pair_in_list @ A @ B @ C ) )
=> ! [B: $i,C: $i,D: $i] :
( ( contains_slb @ ( insert_slb @ A @ ( pair @ C @ D ) ) @ B )
=> ? [E: $i] : ( pair_in_list @ ( insert_slb @ A @ ( pair @ C @ D ) ) @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l47_co) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ! [B: $i] :
( ( contains_slb @ A @ B )
=> ? [C: $i] : ( pair_in_list @ A @ B @ C ) )
=> ! [B: $i,C: $i,D: $i] :
( ( contains_slb @ ( insert_slb @ A @ ( pair @ C @ D ) ) @ B )
=> ? [E: $i] : ( pair_in_list @ ( insert_slb @ A @ ( pair @ C @ D ) ) @ B @ E ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ! [B: $i] :
( ( contains_slb @ A @ B )
=> ? [C: $i] : ( pair_in_list @ A @ B @ C ) )
=> ! [B: $i,C: $i,D: $i] :
( ( contains_slb @ ( insert_slb @ A @ ( pair @ C @ D ) ) @ B )
=> ? [E: $i] : ( pair_in_list @ ( insert_slb @ A @ ( pair @ C @ D ) ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
thf(45,plain,
! [A: $i,B: $i,C: $i] : ( isnonempty_slb @ ( insert_slb @ A @ ( pair @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i] : ( less_than @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
thf(32,plain,
! [A: $i] : ( less_than @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( less_than @ A @ B )
& ( less_than @ B @ C ) )
=> ( less_than @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
thf(34,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)],[5]) ).
thf(8,axiom,
~ ( isnonempty_slb @ create_slb ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
thf(40,plain,
~ ( isnonempty_slb @ create_slb ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( strictly_less_than @ A @ B )
<=> ( ( less_than @ A @ B )
& ~ ( less_than @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
thf(26,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)],[3]) ).
thf(93,plain,
$false,
inference(e,[status(thm)],[69,56,42,89,59,86,66,63,72,75,36,47,38,21,45,32,34,40,26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV411+1 : TPTP v8.1.2. Released v3.3.0.
% 0.15/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n004.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 02:39:40 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.32/0.98 % [INFO] Parsing done (117ms).
% 1.32/0.99 % [INFO] Running in sequential loop mode.
% 1.79/1.18 % [INFO] eprover registered as external prover.
% 1.79/1.18 % [INFO] cvc4 registered as external prover.
% 1.79/1.18 % [INFO] Scanning for conjecture ...
% 1.96/1.24 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 2.01/1.28 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.01/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 2.01/1.31 % [INFO] Type checking passed.
% 2.01/1.31 % [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 ...
% 3.58/1.78 % External prover 'e' found a proof!
% 3.58/1.78 % [INFO] Killing All external provers ...
% 3.58/1.79 % Time passed: 1250ms (effective reasoning time: 795ms)
% 3.58/1.79 % 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)>
% 3.58/1.79 % Axioms used in derivation (18): ax20, ax24, stricly_smaller_definition, ax28, ax27, ax21, reflexivity, ax22, ax19, totality, ax23, ax25, ax26, bottom_smallest, transitivity, ax30, ax18, ax29
% 3.58/1.79 % No. of inferences in proof: 40
% 3.58/1.79 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1250 ms resp. 795 ms w/o parsing
% 3.69/1.83 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.69/1.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------