TSTP Solution File: KRS178+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KRS178+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 7 07:52:04 EDT 2024
% Result : Theorem 3.43s 1.86s
% Output : Refutation 3.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 22
% Syntax : Number of formulae : 38 ( 8 unt; 8 typ; 0 def)
% Number of atoms : 99 ( 0 equ; 0 cnn)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 336 ( 31 ~; 5 |; 33 &; 236 @)
% ( 6 <=>; 23 =>; 0 <=; 2 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 8 usr; 1 con; 0-3 aty)
% Number of variables : 103 ( 0 ^ 55 !; 48 ?; 103 :)
% Comments :
%------------------------------------------------------------------------------
thf(isa_type,type,
isa: $i > $i > $o ).
thf(status_type,type,
status: $i > $i > $i > $o ).
thf(mighta_type,type,
mighta: $i > $i > $o ).
thf(nota_type,type,
nota: $i > $i > $o ).
thf(nevera_type,type,
nevera: $i > $i > $o ).
thf(xora_type,type,
xora: $i > $i > $o ).
thf(model_type,type,
model: $i > $i > $o ).
thf(not_type,type,
not: $i > $i ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( model @ A @ B )
<~> ( model @ A @ ( not @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',completeness) ).
thf(56,plain,
! [A: $i,B: $i] :
~ ( ( ( model @ A @ B )
=> ( model @ A @ ( not @ B ) ) )
& ( ( model @ A @ B )
| ~ ( model @ A @ ( not @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( status @ C @ D @ A )
=> ( status @ C @ D @ B ) )
<=> ( isa @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa) ).
thf(25,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( status @ C @ D @ A )
=> ( status @ C @ D @ B ) )
=> ( isa @ A @ B ) )
& ( ( isa @ A @ B )
=> ! [C: $i,D: $i] :
( ( status @ C @ D @ A )
=> ( status @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( status @ C @ D @ A )
=> ~ ( status @ C @ D @ B ) )
<=> ( nevera @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nevera) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( status @ C @ D @ A )
=> ~ ( status @ C @ D @ B ) )
=> ( nevera @ A @ B ) )
& ( ( nevera @ A @ B )
=> ! [C: $i,D: $i] :
( ( status @ C @ D @ A )
=> ~ ( status @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
? [A: $i] :
! [B: $i] :
~ ( model @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',contradiction) ).
thf(73,plain,
? [A: $i] :
! [B: $i] :
~ ( model @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( status @ C @ D @ A )
<~> ( status @ C @ D @ B ) )
<=> ( xora @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xora) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
~ ( ( ( status @ C @ D @ A )
=> ( status @ C @ D @ B ) )
& ( ( status @ C @ D @ A )
| ~ ( status @ C @ D @ B ) ) )
=> ( xora @ A @ B ) )
& ( ( xora @ A @ B )
=> ! [C: $i,D: $i] :
~ ( ( ( status @ C @ D @ A )
=> ( status @ C @ D @ B ) )
& ( ( status @ C @ D @ A )
| ~ ( status @ C @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ? [C: $i,D: $i] :
( ( status @ C @ D @ A )
& ( status @ C @ D @ B ) )
<=> ( mighta @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mighta) ).
thf(18,plain,
! [A: $i,B: $i] :
( ( ? [C: $i,D: $i] :
( ( status @ C @ D @ A )
& ( status @ C @ D @ B ) )
=> ( mighta @ A @ B ) )
& ( ( mighta @ A @ B )
=> ? [C: $i,D: $i] :
( ( status @ C @ D @ A )
& ( status @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( model @ A @ B )
<=> ~ ( model @ A @ ( not @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( ( model @ A @ B )
=> ~ ( model @ A @ ( not @ B ) ) )
& ( ~ ( model @ A @ ( not @ B ) )
=> ( model @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(11,axiom,
? [A: $i] :
( ? [B: $i] : ( model @ B @ A )
& ? [B: $i] :
~ ( model @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',satisfiable) ).
thf(69,plain,
? [A: $i] :
( ? [B: $i] : ( model @ B @ A )
& ? [B: $i] :
~ ( model @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(15,axiom,
? [A: $i,B: $i,C: $i] :
( ( model @ A @ B )
& ~ ( model @ A @ C )
& ? [D: $i] : ( model @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',non_thm_spt) ).
thf(88,plain,
? [A: $i,B: $i,C: $i] :
( ( model @ A @ B )
& ~ ( model @ A @ C )
& ? [D: $i] : ( model @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(14,axiom,
? [A: $i,B: $i] :
( ? [C: $i] : ( model @ C @ A )
& ! [C: $i] :
( ( model @ C @ A )
=> ( model @ C @ B ) )
& ? [C: $i] :
( ~ ( model @ C @ A )
& ( model @ C @ B ) )
& ? [C: $i] :
~ ( model @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mixed_pair) ).
thf(81,plain,
? [A: $i,B: $i] :
( ? [C: $i] : ( model @ C @ A )
& ! [C: $i] :
( ( model @ C @ A )
=> ( model @ C @ B ) )
& ? [C: $i] :
( ~ ( model @ C @ A )
& ( model @ C @ B ) )
& ? [C: $i] :
~ ( model @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(13,axiom,
? [A: $i,B: $i] :
( ? [C: $i] :
( ( model @ C @ A )
& ( model @ C @ B ) )
& ? [C: $i] :
( ~ ( model @ C @ A )
| ~ ( model @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sat_non_taut_pair) ).
thf(76,plain,
? [A: $i,B: $i] :
( ? [C: $i] :
( ( model @ C @ A )
& ( model @ C @ B ) )
& ? [C: $i] :
( ~ ( model @ C @ A )
| ~ ( model @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,axiom,
? [A: $i] :
! [B: $i] : ( model @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tautology) ).
thf(67,plain,
? [A: $i] :
! [B: $i] : ( model @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i] : ( isa @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isa_reflexive) ).
thf(2,negated_conjecture,
~ ! [A: $i] : ( isa @ A @ A ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(16,plain,
~ ! [A: $i] : ( isa @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ? [C: $i,D: $i] :
( ( status @ C @ D @ A )
& ~ ( status @ C @ D @ B ) )
<=> ( nota @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nota) ).
thf(31,plain,
! [A: $i,B: $i] :
( ( ? [C: $i,D: $i] :
( ( status @ C @ D @ A )
& ~ ( status @ C @ D @ B ) )
=> ( nota @ A @ B ) )
& ( ( nota @ A @ B )
=> ? [C: $i,D: $i] :
( ( status @ C @ D @ A )
& ~ ( status @ C @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(93,plain,
$false,
inference(e,[status(thm)],[56,25,38,73,44,18,62,69,88,81,76,67,16,31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS178+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n008.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon May 6 15:19:54 EDT 2024
% 0.14/0.36 % CPUTime :
% 1.01/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/1.02 % [INFO] Parsing done (128ms).
% 1.36/1.02 % [INFO] Running in sequential loop mode.
% 1.79/1.23 % [INFO] eprover registered as external prover.
% 1.79/1.23 % [INFO] cvc4 registered as external prover.
% 1.79/1.23 % [INFO] Scanning for conjecture ...
% 1.79/1.28 % [INFO] Found a conjecture and 13 axioms. Running axiom selection ...
% 1.79/1.30 % [INFO] Axiom selection finished. Selected 13 axioms (removed 0 axioms).
% 2.10/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/1.34 % [INFO] Type checking passed.
% 2.10/1.34 % [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 ...
% 3.43/1.81 % External prover 'e' found a proof!
% 3.43/1.81 % [INFO] Killing All external provers ...
% 3.43/1.81 % Time passed: 1292ms (effective reasoning time: 784ms)
% 3.43/1.81 % 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)>
% 3.43/1.86 % Axioms used in derivation (13): completeness, nevera, contradiction, nota, mighta, isa, sat_non_taut_pair, satisfiable, mixed_pair, tautology, non_thm_spt, xora, not
% 3.43/1.86 % No. of inferences in proof: 30
% 3.43/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1292 ms resp. 784 ms w/o parsing
% 3.76/1.91 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.76/1.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------