TSTP Solution File: SET791+4 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SET791+4 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n015.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 11:54:19 EDT 2023
% Result : Theorem 4.07s 2.27s
% Output : Refutation 4.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 23
% Syntax : Number of formulae : 36 ( 1 unt; 12 typ; 0 def)
% Number of atoms : 178 ( 9 equ; 0 cnn)
% Maximal formula atoms : 28 ( 7 avg)
% Number of connectives : 588 ( 2 ~; 3 |; 76 &; 432 @)
% ( 10 <=>; 65 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 1 con; 0-4 aty)
% Number of variables : 117 ( 0 ^; 117 !; 0 ?; 117 :)
% Comments :
%------------------------------------------------------------------------------
thf(order_type,type,
order: $i > $i > $o ).
thf(greatest_type,type,
greatest: $i > $i > $i > $o ).
thf(max_type,type,
max: $i > $i > $i > $o ).
thf(member_type,type,
member: $i > $i > $o ).
thf(apply_type,type,
apply: $i > $i > $i > $o ).
thf(total_order_type,type,
total_order: $i > $i > $o ).
thf(upper_bound_type,type,
upper_bound: $i > $i > $i > $o ).
thf(lower_bound_type,type,
lower_bound: $i > $i > $i > $o ).
thf(least_type,type,
least: $i > $i > $i > $o ).
thf(min_type,type,
min: $i > $i > $i > $o ).
thf(least_upper_bound_type,type,
least_upper_bound: $i > $i > $i > $i > $o ).
thf(greatest_lower_bound_type,type,
greatest_lower_bound: $i > $i > $i > $i > $o ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( greatest @ C @ A @ B )
<=> ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest) ).
thf(121,plain,
! [A: $i,B: $i,C: $i] :
( ( ( greatest @ C @ A @ B )
=> ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ D @ C ) ) ) )
& ( ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ D @ C ) ) )
=> ( greatest @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ( max @ C @ A @ B )
<=> ( ( member @ C @ B )
& ! [D: $i] :
( ( ( member @ D @ B )
& ( apply @ A @ C @ D ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',max) ).
thf(137,plain,
! [A: $i,B: $i,C: $i] :
( ( ( max @ C @ A @ B )
=> ( ( member @ C @ B )
& ! [D: $i] :
( ( ( member @ D @ B )
& ( apply @ A @ C @ D ) )
=> ( C = D ) ) ) )
& ( ( ( member @ C @ B )
& ! [D: $i] :
( ( ( member @ D @ B )
& ( apply @ A @ C @ D ) )
=> ( C = D ) ) )
=> ( max @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( greatest_lower_bound @ A @ B @ C @ D )
<=> ( ( member @ A @ B )
& ( lower_bound @ A @ C @ B )
& ! [E: $i] :
( ( ( member @ E @ D )
& ( lower_bound @ E @ C @ B ) )
=> ( apply @ C @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',greatest_lower_bound) ).
thf(172,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( greatest_lower_bound @ A @ B @ C @ D )
=> ( ( member @ A @ B )
& ( lower_bound @ A @ C @ B )
& ! [E: $i] :
( ( ( member @ E @ D )
& ( lower_bound @ E @ C @ B ) )
=> ( apply @ C @ E @ A ) ) ) )
& ( ( ( member @ A @ B )
& ( lower_bound @ A @ C @ B )
& ! [E: $i] :
( ( ( member @ E @ D )
& ( lower_bound @ E @ C @ B ) )
=> ( apply @ C @ E @ A ) ) )
=> ( greatest_lower_bound @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ( total_order @ A @ B )
<=> ( ( order @ A @ B )
& ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ( ( apply @ A @ C @ D )
| ( apply @ A @ D @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_order) ).
thf(95,plain,
! [A: $i,B: $i] :
( ( ( total_order @ A @ B )
=> ( ( order @ A @ B )
& ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ( ( apply @ A @ C @ D )
| ( apply @ A @ D @ C ) ) ) ) )
& ( ( ( order @ A @ B )
& ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ( ( apply @ A @ C @ D )
| ( apply @ A @ D @ C ) ) ) )
=> ( total_order @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( lower_bound @ C @ A @ B )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_bound) ).
thf(114,plain,
! [A: $i,B: $i,C: $i] :
( ( ( lower_bound @ C @ A @ B )
=> ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ C @ D ) ) )
& ( ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ C @ D ) )
=> ( lower_bound @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( upper_bound @ C @ A @ B )
<=> ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_bound) ).
thf(107,plain,
! [A: $i,B: $i,C: $i] :
( ( ( upper_bound @ C @ A @ B )
=> ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ D @ C ) ) )
& ( ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ D @ C ) )
=> ( upper_bound @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( order @ A @ B )
& ( greatest @ C @ A @ B ) )
=> ( max @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV3) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( order @ A @ B )
& ( greatest @ C @ A @ B ) )
=> ( max @ C @ A @ B ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(13,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( order @ A @ B )
& ( greatest @ C @ A @ B ) )
=> ( max @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( least @ C @ A @ B )
<=> ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ( ( least @ C @ A @ B )
=> ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ C @ D ) ) ) )
& ( ( ( member @ C @ B )
& ! [D: $i] :
( ( member @ D @ B )
=> ( apply @ A @ C @ D ) ) )
=> ( least @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( least_upper_bound @ A @ B @ C @ D )
<=> ( ( member @ A @ B )
& ( upper_bound @ A @ C @ B )
& ! [E: $i] :
( ( ( member @ E @ D )
& ( upper_bound @ E @ C @ B ) )
=> ( apply @ C @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',least_upper_bound) ).
thf(161,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( least_upper_bound @ A @ B @ C @ D )
=> ( ( member @ A @ B )
& ( upper_bound @ A @ C @ B )
& ! [E: $i] :
( ( ( member @ E @ D )
& ( upper_bound @ E @ C @ B ) )
=> ( apply @ C @ A @ E ) ) ) )
& ( ( ( member @ A @ B )
& ( upper_bound @ A @ C @ B )
& ! [E: $i] :
( ( ( member @ E @ D )
& ( upper_bound @ E @ C @ B ) )
=> ( apply @ C @ A @ E ) ) )
=> ( least_upper_bound @ A @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( order @ A @ B )
<=> ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ C ) )
=> ( C = D ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(17,plain,
! [A: $i,B: $i] :
( ( ( order @ A @ B )
=> ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ C ) )
=> ( C = D ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) ) )
& ( ( ! [C: $i] :
( ( member @ C @ B )
=> ( apply @ A @ C @ C ) )
& ! [C: $i,D: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ C ) )
=> ( C = D ) ) )
& ! [C: $i,D: $i,E: $i] :
( ( ( member @ C @ B )
& ( member @ D @ B )
& ( member @ E @ B ) )
=> ( ( ( apply @ A @ C @ D )
& ( apply @ A @ D @ E ) )
=> ( apply @ A @ C @ E ) ) ) )
=> ( order @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( min @ C @ A @ B )
<=> ( ( member @ C @ B )
& ! [D: $i] :
( ( ( member @ D @ B )
& ( apply @ A @ D @ C ) )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',min) ).
thf(149,plain,
! [A: $i,B: $i,C: $i] :
( ( ( min @ C @ A @ B )
=> ( ( member @ C @ B )
& ! [D: $i] :
( ( ( member @ D @ B )
& ( apply @ A @ D @ C ) )
=> ( C = D ) ) ) )
& ( ( ( member @ C @ B )
& ! [D: $i] :
( ( ( member @ D @ B )
& ( apply @ A @ D @ C ) )
=> ( C = D ) ) )
=> ( min @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(183,plain,
$false,
inference(e,[status(thm)],[121,137,172,95,114,107,13,129,161,17,149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14 % Problem : SET791+4 : TPTP v8.1.2. Released v3.2.0.
% 0.15/0.17 % Command : run_Leo-III %s %d
% 0.17/0.39 % Computer : n015.cluster.edu
% 0.17/0.39 % Model : x86_64 x86_64
% 0.17/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.39 % Memory : 8042.1875MB
% 0.17/0.39 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.39 % CPULimit : 300
% 0.17/0.39 % WCLimit : 300
% 0.17/0.39 % DateTime : Thu May 18 19:18:53 EDT 2023
% 0.17/0.39 % CPUTime :
% 0.88/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.28/1.07 % [INFO] Parsing done (164ms).
% 1.28/1.07 % [INFO] Running in sequential loop mode.
% 1.81/1.33 % [INFO] eprover registered as external prover.
% 1.81/1.33 % [INFO] cvc4 registered as external prover.
% 1.81/1.34 % [INFO] Scanning for conjecture ...
% 1.91/1.40 % [INFO] Found a conjecture and 10 axioms. Running axiom selection ...
% 1.91/1.43 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 2.18/1.47 % [INFO] Problem is first-order (TPTP FOF).
% 2.18/1.47 % [INFO] Type checking passed.
% 2.18/1.48 % [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 ...
% 3.78/2.23 % External prover 'e' found a proof!
% 3.78/2.23 % [INFO] Killing All external provers ...
% 4.07/2.26 % Time passed: 1717ms (effective reasoning time: 1185ms)
% 4.07/2.26 % 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)>
% 4.07/2.27 % Axioms used in derivation (10): upper_bound, min, least, max, greatest, order, total_order, lower_bound, least_upper_bound, greatest_lower_bound
% 4.07/2.27 % No. of inferences in proof: 24
% 4.07/2.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1717 ms resp. 1185 ms w/o parsing
% 4.27/2.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.27/2.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------